{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_76989/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_76989","id":"gutenberg_76989","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/76989","summary":null,"tags":["Category: Essays, Letters & Speeches","Category: Philosophy & Ethics","Category: Science - Physics","English essays -- 20th century","Science"],"text":"ASPECTS OF SCIENCE\n\n\n\n\n                          ASPECTS OF SCIENCE\n\n\n                        _By_ J. W. N. SULLIVAN\n\n\n\n\n                                LONDON\n                       RICHARD COBDEN-SANDERSON\n                            17 THAVIES INN\n\n\n\n\n                            Copyright 1923\n\n\n\n\n                                PREFACE\n\n\nThe papers which make up this volume have been selected because,\nalthough they deal with different aspects of various scientific ideas,\nyet they do illustrate, more or less, one point of view. That point\nof view may be described, perhaps as \u00e6sthetic, but rather better as\nhumanistic. Scientific ideas have a history; they arose to satisfy\ncertain human needs; to see them in their context is to see them as\npart of the general intellectual and emotional life of man. What they\nexist to do they do better than does anything else, and the needs they\nsatisfy are not peculiar to scientific specialists. These papers try\nto show one or two of the many reasons why, for people who are not\nspecialists as well as for those who are, science may be interesting.\n\nJ. W. N. SULLIVAN.\n\n\n\n\n                               CONTENTS\n\n\n                                                            PAGE\n\n THE INTEREST OF SCIENCE                                        9\n\n A PHYSICIST ON PHYSICS                                        23\n\n SCIENCE AND CULTURE                                           36\n\n JAMES CLERK MAXWELL                                           41\n\n ASSUMPTIONS                                                   49\n\n ON LEARNING SCIENCE                                           72\n\n THE ENTENTE CORDIALE                                          77\n\n POPULAR SCIENCE                                               82\n\n PATIENT PLODDERS                                              89\n\n THE AMATEUR ASTRONOMER                                        95\n\n SCIENTIFIC CITIZENS                                          100\n\n THE SCEPTIC AND THE SPIRITS                                  105\n\n THE SCIENTIFIC MIND                                          112\n\n THE SCIENTIFIC CONTRIBUTION                                  116\n\n THEORIES AND PERSONALITIES                                   122\n\n THE IDEAL SCIENTIFIC MAN                                     128\n\n PARALLEL STRAIGHT LINES                                      133\n\n THE NEW SCIENTIFIC HORIZON                                   139\n\n THE HOPE OF SCIENCE                                          145\n\n THE RETURN OF MYSTERY                                        151\n\n MATHEMATICS AND MUSIC                                        159\n\n HUMAN TESTIMONY                                              177\n\n\n\n\n\n                        THE INTEREST OF SCIENCE\n\n                                   I\n\n\nThe conception of science as a body of thought embracing the whole\nof our rational convictions about reality has hardly yet been\ngenerally reached. Man is still so far from being a rational animal\nthat the application of rational methods of inquiry to all branches\nof his experience is still instinctively resisted--as if reason\nwere an alien and hostile intruder. Beliefs which are held with\npassion, being the expression of instinctive preferences, are felt\nnot to belong to the \u201csphere\u201d of science. On all questions where\nhis passions are strongly engaged, man prizes certitude and fears\nknowledge. Dispassionate inquiry is welcomed only when the result is\nindifferent. Nearly every great scientific generalisation has incurred\nthe _odium theologicum_--which is not the exclusive possession\nof theologians--from the Copernican hypothesis to the theory of herd\ninstinct. That science, although continually wounding men, should\nnevertheless have progressed, is evidence that it serves impulses\ndeeply rooted in man\u2019s nature. The great scientific innovator, like\nthe great altruist, is treated with ignominy by the society whose\ndeepest instincts he lives to serve.\n\nScience, the child of irrational impulse, has inherited something\nof the parental character. Its history reveals it as purblind and\nfumbling, with no clear vision of its aim, no premonition of its\nimperial state. Unlike philosophy, it did not aspire to universal\ndominion. It was content to investigate the particular instance,\nand did not reject a certain incoherence in explanation rather than\naccept a generalisation which did not spring from its own ground. It\nrefused foreign assistance, but kept its independence. That scientific\nmen did not always understand that science must, from its nature, be\nautonomous, is evident from the history of every particular science.\nEven as late as Descartes it was considered quite natural to deduce\nphenomena from metaphysical principles; and an admixture of mythical\nelements is not entirely absent from some branches of science, even at\nthe present day. Science has not yet reached full consciousness of its\nproper ground and aims.\n\nThe values served by science, in terms of which its claim to\nconsideration is to be judged, have become more numerous as science has\ndeveloped. The earliest scientific researches were concerned wholly\nwith the particular event, with, at most, the vaguest inkling of large\nperspectives. The savage who discovers that the branch lying partly\nin the stream is not really bent, is prompted by the same localised\nand detached curiosity which led to most of the early scientific\ndiscoveries. Interest in the oddity of an event is undoubtedly the\nroot of scientific observations. The more closely the events concern\nus, the more pregnant they may be with possible pleasure or pain,\nthe greater the degree of abstraction necessary to see them in their\nrelations. Human beings remain miracles to us long after we have\nlearned to predict the motion of a planet. Psychology is the latest\nof the sciences, not so much because of the intrinsic difficulty of\nits subject-matter as because our interest in the subject-matter is so\nvehement that it is almost impossible to be indifferent to the results.\nAn intelligent fish would probably have found most of the painfully won\nresults of human psychology fairly obvious.\n\nFrom the accumulation of facts and the attempt to see them in\nrelation springs the scientific theory. With the construction of\ntheories science enters on a new phase in its development, and\nserves a different set of human values. Its facts, the products\nof local curiosities, now take on an order, and serve the desire\nfor comprehension. The apparently dissimilar becomes related; law\nsupervenes on chaos. The desire for knowledge becomes transformed into\nthe desire for _significant_ knowledge--significant primarily\nfor contemplation, and secondarily for practice. It is the scientific\ntheory alone that gives to science its true being and makes it worthy\nof a deep concern. The desire for comprehension is deeply rooted in\nhuman nature. Religious myths and philosophical systems arose in\nobedience to this impulse. Science also exists to satisfy this craving,\nand the terms on which it does so are altogether to its advantage. The\nfact that it is an extension of common knowledge, and infers nothing\nthat cannot be verified, differentiates it from myth, and is the secret\nof the grave and serious satisfaction it affords. Those accustomed\nto this homely, invigorating atmosphere find the rarer air of much\ntraditional philosophy quite insupportable. A certain indifference to\nother methods of describing reality becomes more evident as the years\nadvance and the domain of science becomes more and more extended.\nPeaceful penetration takes the place of open warfare, and in face of\nrival systems men of science feel less inclined to disprove what they\nfeel more at liberty to ignore.\n\nScience still falls far short of affording complete comprehension or\nof providing so finished a picture of reality that we feel no need\nof other speculations. The different sciences do not yet conspire to\nform one single coherent body of truth. The interstices between them\nare still sufficiently large to admit foreign interpretations. But the\nimpulse to comprehension, which created science, will be justified by\nit: we may have so much faith. Even that moiety of mankind who care for\nlittle beyond pure immediacy will find that science alone can give\nthem much of what they desire. Scientific theories possess a value\neven to those who are strangers to the pleasures of contemplation, for\nscience has powerful reactions in the world of practice. To those who\nhave lost their birthright it can offer a mess of pottage.\n\nBesides serving curiosity, comprehension and practice, science offers\nrichly satisfying objects to the \u00e6sthetic impulse. The language of\n\u00e6sthetics is not far to seek in the writings of men of science, and\nwere it not that the word arouses such a proprietary fury, we should\nagree, reviewing their motives and the kind of their satisfactions,\nto call them artists. The matter of the highest art, like that of\ntrue science, is reality, and the measure in which science falls\nshort as art is the measure in which it is incomplete as science. All\ngood philosophy, art or science partakes of the nature of the other\ntwo. When these three are regarded as one, each will have reached its\napotheosis.\n\n\n                                  II\n\nIt is unfortunately true that as a science advances it grows more\ncomplex. Not only does its language depart more and more from ordinary\nspeech by the accumulation of technical terms, but the terms in current\nuse at any time are defined in terms of others which are defined in\nterms of others--something after the manner of the description of\nthe house that Jack built. The most obvious case of this Chinese box\nkind of language is, of course, that of mathematics. A mathematical\ntheorem occupying one line of type might very well occupy a volume if\nwritten out in ordinary prose in which no terms were used which were\nnot common property. For this reason modern mathematical discoveries,\nexcept in very special instances, cannot be made intelligible except\nto mathematicians. To learn the language of a highly developed science\nlike mathematics takes about as long as to learn Chinese, but the\ntask of translation into English is very much harder. For this reason\nmathematicians cannot hope for intelligent popular recognition; they\nmust be content to be regarded either as vaguely impressive figures\nor else as mild lunatics busied with incomprehensible and probably\ntrifling abstractions. Compared with writers, musicians or painters,\nthey are, for social purposes, mental outlaws. It is apparent, however,\nthat mathematics was not always so remote. It was possible for Voltaire\nto take an interest which was, at any rate, enthusiastic, in the work\nof Newton. This was doubtless due, in some degree, to the obviously\ndramatic quality of Newton\u2019s discoveries, but it was also due to the\nfact that his discoveries could be expressed in comparatively simple\nlanguage. Again, physics and chemistry at that time, and for some years\nlater, were not only intelligible to men without special training, but\nsuch men could actually make valuable discoveries in these sciences.\nAs these sciences progressed their language became more and more\nforbidding and their fundamental notions more and more abstract. Men\nwithout special training, but with scientific curiosity, turned their\nattention to the biological sciences. They collected birds\u2019 eggs and\nbutterflies; they bought microscopes and wrote little papers on the\nsea-shells they discovered in a morning\u2019s walk. But biology has now\ndeveloped a technical language, and the days of the untrained observer\nare almost over. The one science which is still, to some extent,\naccessible to these amiable people is psychology. It is growing more\ntechnical, it is true, but the majority of the books dealing with\npsychology may still be read almost as easily as a treatise on the\nhistory of the Balkans. And the \u201cpsychological\u201d novelist can still\nregard himself as being, from one point of view, a scientific man.\nPsycho-analysis is, as yet, a favourite subject of discussion in\nadvanced drawing-rooms where discussions of the principle of relativity\nare comparatively rare.\n\nThe divorce between science and the general intellectual world is\nunfortunate, but inevitable. It is unfortunate both for the scientific\nman and for the general _intelligentsia_. The scientific man,\nmentally companionless except for the little circle of his immediate\nco-workers, becomes less complete as a human being; he fails as a\nhumanist. He too often accepts his outlawed position and turns his\nspecial interests into his exclusive interests, as if, through some\ninverted generosity, he refused to take where he could not give. He\nmay grow to ignore the other intellectual activities of his time,\nas Darwin, to his distress, found he had grown to ignore poetry,\nor he may actually become intolerant of such activities and so add\ncontempt to the ignorance with which his preoccupations are regarded\nby the outside world. For the outside world, also, this divorce is\nunfortunate. For science, in its own way, satisfies just the same\nimpulses as do other intellectual interests, and some of them it\nsatisfies more completely and in a richer way. A great waste of mental\nenergy and much inconclusive discussion would be avoided were certain\nscientific results more generally known, and, more particularly, were\nthe advantages of the scientific method more widely recognised and the\nmethod itself more extensively practised. An air of superiority is\noften noticed in the references of scientific men to certain current\ndiscussions. It is a fault of manner, but one difficult to avoid.\n\u201cInside\u201d information usually has this effect on the possessor, and\nwhen it is information that cannot be shared the attitude is apt to\nbecome chronic. Both sides, then, are the poorer for their lack of\nintercourse. But this state of affairs seems to be inevitable. The\nclaims of the Latin and Greek literatures to attention, whether they\nare justified or not, have led to the study of these languages being\nimposed on perhaps the majority of the people in this country who are\npredominantly interested in intellectual affairs. It is a training\nwhich consumes several years: is a training in the sciences to be\nadded? This is manifestly impossible. Even if our whole educational\nsystem were radically altered, only those sciences, such as biology and\npsychology, which may be understood with comparatively little training,\ncould ever become objects of common knowledge. But sciences where, in\naddition to a severe and prolonged discipline, special aptitude is\nnecessary, must always be the property of the few. As, every year,\nall the sciences grow more complex, so the difficulty of obtaining an\nadequate knowledge of them increases. A dead language may be learnt\nonce for all, but the language of a science must be learnt afresh every\nfew years. The popular article of Huxley\u2019s day, the link between the\nman of science and the general public, is now the link between the more\nand less advanced students of the same science. A so-called \u201cpopular\u201d\naccount of Relativity Theory, for instance, is like an annotated\nedition of Pindar; a very fair knowledge of the language is assumed\nbeforehand. It might be thought that the process of reduction, as it\nwere, could be continued, until finally an account was prepared where\nno technical terms were used. But such an account would be, at best,\nlike a translation of Greek poetry; the essential quality would be\ngone. Such translations have, of course, their uses, but the attraction\nof science for the scientific man, like the attraction of a poem for\nthe poet, is not to be communicated in this way. In art the separation\nof matter and form is not really possible, and the same is true of the\nsciences.\n\n\n                                  III\n\nIn their apologias, which have now become so common, men of science\nnever weary of pointing out that it is the method of science which\nis really worthy of adoption by philosophers and that the results of\nscience are merely provisional. The philosopher who bases his system\nupon the results reached at any given time by any given science has\nensured the ultimate downfall of his system. He is sometimes told that\nthe adoption of scientific methods, on the other hand, will enable him\nto make sure progress. At first sight there seems to be a contradiction\nhere, for if the scientific method is infallible why are the results\nreached by it provisional? To judge from the history of science, the\nscientific method is excellent as a means of obtaining plausible\nconclusions which are always wrong, but hardly as a means of reaching\nthe truth. The contradiction is only apparent, however, for it will\nbe found that there is a part of every discarded hypothesis which is\nincorporated in the new theory. The discarded hypothesis proves to\nhave been too general; the scientific man made a mistake of the same\nkind as the philosopher who uses the hypothesis as the basis of a\ngeneral system. It is now known, for instance, that Newton\u2019s theory of\ngravitation is very probably not exactly true; in most cases, however,\nit remains very nearly true, and there are large regions of dynamical\nastronomy which are unaffected by the alteration. The Newtonian laws\nof motion, again, are not sufficient to describe the motion of bodies\nmoving with very large velocities, but they are very nearly true\nfor all ordinary velocities. That the theories which have taken the\nplace of those abandoned are exactly true is very improbable; they\nare, however, nearer the truth. We may say, therefore, that while the\nscientific method may, quite possibly, never enable us to reach the\nexact truth, successive applications of it enable us to approximate\nnearer and nearer to the exact truth. In this lies its chief difference\nfrom the methods usually adopted in philosophy, which aim at obtaining,\nat one blow, theories which shall never need revision. It is for this\nreason that philosophy does not progress.\n\nIn what, then, does the scientific method consist? It would be\ndifficult to give a precise definition; it has, however, two main\ncharacteristics, the choice of facts and the treatment of facts. It\ndoes not seem to be generally recognised that scientific men do choose\ntheir facts; there are many people who suppose that all facts are of\nequal interest to scientific men, and that information respecting the\nnumber of nightingales heard in Hertfordshire during a certain month,\nfor instance, is a contribution to scientific knowledge. It should\nbe obvious, however, that a mere random collection of facts is very\nunlikely to aid either practice or theory. The aim of science is not to\nform catalogues, but to form theories describing phenomena, and to this\nend some facts are pertinent and a very great number are not. All men,\nfaced with a problem of any kind, choose such facts for examination\nas they consider relevant. Sherlock Holmes often bewildered Watson by\npondering over facts that Watson considered irrelevant, but Watson\u2019s\nsurprise was a proof that even he had a standard of relevance. The\nhistory of any science shows that the facts first chosen were those\nmost likely to be repeated. Such facts obviously lead to statements\nwhich have a greater or less degree of generality. That an unsupported\nstone falls to the ground is a fact of this kind. The facts chosen\nby the man of science are those that permit generalisation. For this\nreason they usually differ entirely from the facts of interest to\nhistorians. After selecting, in accordance with this principle, the\nfacts which are to be examined, the next step consists in establishing\nrelations between sets of these facts. The precise expression of these\nrelations is called a law of nature, to use a somewhat old-fashioned\nterminology. If now all the relations between certain sets of facts\ncan be expressed in one general statement, that general statement is\ncalled a scientific theory. The ultimate aim of the scientific method\nis to create scientific theories. The scientific theory, however,\nusually introduces an element which has not been or cannot be directly\nobserved, and also, as we have seen, usually proves to have been too\nhasty a generalisation. Its function is to co-ordinate known phenomena\nand to predict hitherto unobserved phenomena. The extent to which it\ndoes this is the measure of its success as a scientific theory, and,\nsince the primary object of the scientific theory is to express the\nharmonies which are found to exist in nature, we see at once that these\ntheories must have an \u00e6sthetic value. The measure of the success of a\nscientific theory is, in fact, a measure of its \u00e6sthetic value, since\nit is a measure of the extent to which it has introduced harmony in\nwhat was before chaos.\n\nIt is in its \u00e6sthetic value that the justification of the scientific\ntheory is to be found, and with it the justification of the scientific\nmethod. Since facts without laws would be of no interest, and laws\nwithout theories would have, at most, a practical utility, we see that\nthe motives which guide the scientific man are, from the beginning,\nmanifestations of the \u00e6sthetic impulse. The reason why certain facts\nand not others interest the scientific man, the reason why he makes a\nchoice, is because truth without beauty is as uninteresting to him as\nto any other artist. In the words of Poincar\u00e9: \u201cLe savant n\u2019\u00e9tudie pas\nla nature parce que cela est utile; il l\u2019\u00e9tudie parce qu\u2019il y prend\nplaisir, et il y prend plaisir parce qu\u2019elle est belle. Si la nature\nn\u2019\u00e9tait pas belle, elle ne vaudrait pas la peine d\u2019\u00eatre connue, la vie\nne vaudrait pas la peine d\u2019\u00eatre v\u00e9cue.\u201d\n\n\n\n\n                        A PHYSICIST ON PHYSICS\n\n\n                                   I\n\nThe well-meant and industrious efforts of professional metaphysicians\nto explain to men of science in what sense science is true, in what\nsense it has meaning and in what its value really consists, practically\nall suffer from the defect that men of science do not recognise the\nsubject of investigation as being science at all. It is almost true to\nsay that the professional philosopher is only convincing when he is\ntalking about the Absolute, for that is a subject with which nobody\nelse is concerned; but when he devotes his attention to subjects with\nwhich other people are familiar, it often becomes possible to put\nthe book down before finishing it. Thus treatises on \u00e6sthetics are\nusually convincing to everybody but poets, painters and musicians,\nand philosophical writings on science are probably in great demand\namongst classical scholars. Nevertheless, since philosophising on these\nsubjects is an agreeable mental exercise, we find that some artists\nare now engaged in developing an \u00e6sthetic for themselves, and some\nmen of science are engaged in trying to find out what science is.\nIn each case the work consists chiefly in making explicit processes\nwhich are instinctive. This fact is of the greatest importance, for,\nif the instinctive equipment be lacking, the results will inevitably\nbe unsatisfactory. There are treatises on \u00e6sthetics, for instance,\nwhose chief effect on the poet is to make him doubt whether the author\ncould tell a good poem from a bad one; this is an absolutely fatal\nobjection. If poets cannot recognise what they call poetry as being\nthe subject of the discussion, then, as a discussion of poetry, that\ndiscussion is worthless. Practitioners, whether artists or men of\nscience, seldom have the inclination to uncover and dissect what is\nto them an instinctive and delightful process; but it is quite easy\nfor them to see (or, rather, to feel) that a suggested explanation\nis unsatisfactory, although they may find it wholly impossible to\ngive reasons for their dissatisfaction. Nevertheless, when this\ndissatisfaction is due to an inability to recognise the subject-matter,\nthe explanation must be condemned. It is perfectly possible, for\ninstance, that psycho-analysis, by introducing a mother-complex, an\ninferiority-complex, and two or three more, might \u201cexplain\u201d the Ode to\na Nightingale. But if this explanation left out everything which made\npoets regard that composition as a poem, it would not be a satisfactory\nexplanation.\n\nWe have treated this point at some length because Dr. Campbell, in\na recent valuable book on the Elements of Physics, insists that the\nphysics he is talking about is that of physicists. He has endeavoured\nto supply a criticism of the terms used in Physics, to find what is\nmeant by a Law, by a Theory, what a physicist means when he says a\nproposition is \u201ctrue,\u201d or that something \u201cexists,\u201d or that a theory has\n\u201cmeaning.\u201d Mr. Campbell is perfectly aware that all these subjects have\nalready been treated by the professional metaphysician, but he claims,\nand we have no doubt that his claim is just, that he is speaking not\nonly for himself but for the great majority of scientific men when\nhe says that in these discussions he not only does not recognise\nthe subject-matter, but he does not recognise any subject-matter.\nSuch words as \u201creality\u201d and \u201cexistence,\u201d as they are employed by\nmetaphysicians, he finds productive of nothing but great discomfort and\nintense mental confusion. As he unhesitatingly rejects the hypothesis\nthat metaphysicians are imbeciles, he thinks this confusion can be due\nonly to the fact that these words are used by metaphysicians in senses\nquite different from those they bear to men of science. He has not\nbeen able to explain precisely in what the difference consists, since\nhe has not been able to discover what meanings metaphysicians attach\nto these words. Accordingly he has confined himself to explaining the\nmeanings these words have in science. The result is a subtle, fairly\nclear, and frequently entertaining piece of analysis. He acknowledges\nthat his two masters have been Poincar\u00e9 and Bertrand Russell, and he\nshows complete familiarity with other writers of the kind. But part\nof his reason for publishing the book, he tells us, is that even the\nmathematical philosophers occasionally misrepresent science as the\nexperimental physicist knows it. That they are mathematicians and\nnot physicists is a little too evident in some of their conclusions.\nThus Mach\u2019s idea that the object of science is to economise thought\nis only plausible, he thinks, to a mathematician; and a fundamental\nproposition that Russell and Whitehead find quite necessary to thought\nMr. Campbell does not find necessary at all. He thinks it quite likely,\nalso, that scientific thinking is illogical, but not therefore invalid.\nThe point of view, in fact, is that there are different kinds of minds\nwith different needs and different satisfactions, and Mr. Campbell\nclaims that physicists, for example, belong to a certain species and\nthat the science of physics is something which exists in the minds of\nphysicists. Therefore this book, as he insists, is not only written\nby a physicist, but it is written for physicists. He is confident\nthat what he has to say will be found an explicit statement of their\ninstinctive processes, and he thinks the highest compliment that could\nbe paid to his book would be for physicists to say they knew it all\nbefore.\n\nNow it is true that nobody but a physicist could have written this\nbook and that nobody ignorant of physics could understand it. It may\nalso be true that none but a practising physicist could understand it\nwith the intimacy that Mr. Campbell desires. But any reader who is\nnot, in Mr. Campbell\u2019s sense, half-educated (the other half consists\nof science--preferably physics) will find the book not only valuable,\nbut delightful. The slight touch of _brusquerie_ that the\nmetaphysician or the equally unfortunate \u201chalf-educated\u201d person might\nattribute to Mr. Campbell from the above exposition is not in the\nleast that of the horny-handed son of toil, but is the half-humorous\nimpatience of a subtle and vigorous thinker who is by no means na\u00efve.\nThere is no reason why the audience that reads Poincar\u00e9\u2019s popular four\nvolumes should not also read this book, and there are many reasons why\nit should. Many of the questions raised there are here developed more\nfully; most of the questions, in fact, raised by the speculations of\nsuch men as Poincar\u00e9, Russell, Mach, etc., in so far as they affect\nscience, are here given systematic treatment. We hope to devote a\nfuture article to the exposition of some of Mr. Campbell\u2019s more\ninteresting results; we are concerned here to indicate the nature and\nscope of the book.\n\nThe present volume is in two pretty distinct parts, the first part\nbeing concerned with the propositions of science, and the second part\nwith measurement. These are to be followed by Part III. on Space and\nTime, Part IV. on Force, and Part V. on Energy, although, regarding\nthese parts, Mr. Campbell says: \u201cI have not the remotest idea when,\nif ever, they will be published.\u201d Without anticipating a future\ndiscussion of the more technical parts of Mr. Campbell\u2019s work, we may\nrefer here, because of the general interest taken in the subject, to\nthe explanation he gives of the fact that while the outside world\nresolutely marks off Science from Art, yet this distinction is not at\nall clear to scientific men. It is difficult, for example, in studying\nthe life of a great man of science, to resist the conclusion that his\nincentives and satisfactions are indistinguishable from those of a\ngreat artist. Yet it seems to be undoubtedly true that a work of Art\nis something personal, whereas Science is obviously impersonal. Mr.\nCampbell asks us to distinguish between truth and meaning. The truth\nof science is something impersonal, but its meaning is personal. The\nachievement of Newton and Maxwell is as personal as that of Giotto,\nShakespeare and Bach. Their dreams were not less personal, nor less\ndelightful, and it is nothing to their discredit that their dreams also\ncame true. And the fact that the meaning of a scientific theory is\nsomething that exists, perhaps, only for men of science, has an obvious\nparallel in Art. The following passage from Mr. Campbell\u2019s book is one\nto which every man of science would give instant assent:\n\n Nobody who has any portion of the scientific spirit can fail to\n remember times when he has thrilled to a new discovery as if it were\n his own. He has greeted a new theory with the passionate exclamation,\n \u201cIt must be true!\u201d He has felt that its eternal value is beyond\n all reasoning, that it is to be defended, if need be, not by the\n cold-blooded methods of the laboratory or the soulless processes of\n formal logic, but, like the honour of a friend, by simple affirmation\n and eloquent appeal. The mood will and should pass; the impersonal\n enquiry must be made before the new ideas can be admitted to our\n complete confidence. But in that one moment we have known the real\n meaning of science, we have experienced its highest value; unless such\n knowledge and such experience were possible, science would be without\n meaning and therefore without truth.\n\n\n                                  II\n\nWhat kind of Physics would be developed by a man alone on an island?\nWe are assuming, of course, that this favourite figure of speculative\nwriters enjoys the properties usually attributed to him; he is\nremarkably intelligent, and can create by a word any scientific\napparatus he requires. The point is that he has no need to take into\naccount the judgments of other people. Let us choose an experiment\ndesigned to make clear the consequences of his isolated state.\nSuppose our islander, after looking at a red patch, glances at a\nwhite ceiling. He sees a green patch. Now suppose that he heats a\ncopper wire in the flame of a Bunsen burner. The flame turns green.\nWill our islander proceed to construct a physics which shall embrace\nboth these observations? Before we can answer this question we must\nconsider why our own physics distinguishes so sharply between them.\nIn the first place, it may be said that all observers, except the man\nwho contemplated a patch of red, agree that the colour of the ceiling\nis unchanged, whereas, in the case of the copper wire, all observers\nagree that the flame has turned green. In the first case, therefore,\nwe say that there has occurred a change in the observer, and in the\nsecond case a change in the flame. We invoke the criterion of universal\nassent. But it can readily be shown that we have not, in fact, invoked\nthis criterion, for in saying that the flame has turned green, we have\nleft out the testimony of colour-blind persons. Not everybody would\nagree that the flame has turned green, and on what principle are we to\ndecide between the conflicting opinions of different observers? Mr.\nCampbell\u2019s examination of this question appears to take us to the root\nof the matter. Universal assent is involved, but also something more,\nand it is the something more which will probably enable our islander\nto form a physics like our own. Let us first consider the way in which\nuniversal assent is involved in science.\n\nWe must obviously leave out judgments of colour; similarly, science\ndoes not now measure electrical quantities in the manner of Cavendish,\nby comparing the intensities of electric shocks experienced by the\nobserver. Science makes a choice of the judgments it shall consider;\nit does not even embrace all judgments for which universal assent may\nbe obtained. The judgments on which science is based, and for which\nuniversal agreement may be obtained, are divided by Mr. Campbell into\nthree groups: (1) Judgments of simultaneity, consecutiveness and\n\u201cbetweenness\u201d in time;[1] (2) Judgments of coincidence and betweenness\nin space; (3) Judgments of number, such as, The number of the group\nA is equal to, greater than or less than, the number of the group\nB. Now it is judgments of this kind that are involved in physical\nobservations: the deflection of a spot of light on a scale, the reading\nof a stop-watch, and so on. These judgments are fundamental to science\nand are such that universal assent may be obtained for them. Let us\nnow consider the case of the copper wire in the Bunsen flame. We have\nsaid that not all people will agree that the flame has turned green.\nBut the light from the Bunsen has other properties than its colour;\nit has a measurable refrangibility and a measurable wave-length. The\nimportant point for physics is that all observers, both \u201cnormal\u201d\nand colour-blind, would agree on these measurements, since they are\nconnected with the fundamental judgments mentioned above. The fact that\ndifferent observers associate these same measurements with different\ncolours is a fact of no importance for physics; \u201ccolour\u201d is not a\nnotion essential to physics at all; when phrases containing such words\nas \u201cred\u201d or \u201cyellow\u201d occur in physics they may always be replaced by\nwords depending for their meaning solely on fundamental time, space and\nnumber judgments. It is for this reason, then, that science builds on\nperfectly sure foundations; its foundations can only be denied by an\nimposter, that is, by one whose actions show that he actually believes\nwhat he says he denies. Now, how does this apply to our islander?\nWe may assume that he can measure refrangibility and wave-length.\nHe finds that, in these particulars, the light from the ceiling is\nunaltered, while the light from the Bunsen flame is altered. But these\nobservations have no greater support than his colour judgments. On both\noccasions the only testimony is his own. But he would notice a great\ndifference directly he began to establish the laws connecting these\nphenomena. The laws derived from the second set of observations would\nbe much more satisfactory than those derived from the first set. He\nwould undoubtedly prefer them and would unhesitatingly adopt them. When\nit is put in this way, there certainly seems something arbitrary about\nthe process by which science selects its fundamental judgments. They\nare selected because they fall neatly and satisfactorily into laws. Mr.\nCampbell further suggests that the laws used in science are selected\nfrom amongst other possible laws because the selected laws fit into\ntheories, \u201cthe form of which is dictated chiefly by preconceived ideas\nof what a theory should be.\u201d It may be stated at once that Mr. Campbell\nadmits the presence of an arbitrary element in science, but it is\nprecisely his case that this arbitrary element gives to science its\nvalue.\n\nWe cannot here summarise his exposition, because it would be\nunintelligible except to readers with a scientific training, since Mr.\nCampbell has adopted the very sound method of analysing the actual\nlaws and theories current in physics. We may indicate, however, the\ngeneral lines of his investigation. He attempts to analyse the kind of\nrelation involved in a scientific \u201claw.\u201d It has been generally assumed\nby philosophers that this relation is the \u201ccausal\u201d relation, but, in\nfact, it is very doubtful whether this relation is ever used in the\nstatement of laws. It is a very special kind of relation, and its\nsupposed importance to science seems to rest on a confusion between the\npsychological process in an observer performing an experiment and the\nrelation stated to exist between his observations. Thus, in Ohm\u2019s Law,\ndoes the potential difference enter as cause or effect of the current?\nThe question is sufficient to show that the causal relation is not\nconcerned. Mr. Campbell admits that he has not succeeded in making a\nfinal analysis of the propositions called laws, but we think that he\nhas certainly established several points of great value. It is more to\nour present purpose, however, that this analysis shows more clearly\nhow an arbitrary element enters into scientific laws. A law does\nnot simply relate concepts in a manner consistent with observation;\nit would be perfectly possible, for instance, to replace Ohm\u2019s Law,\nexpressing simple proportionality between current and potential\ndifference, by a much more complicated expression which should agree\nequally well with observation. There are always several laws which will\nsatisfy the observations; the one that is chosen is chosen for its\nsimplicity, i.e., because of the mental satisfaction it affords. The\nfact that it does fit the observations gives it what Mr. Campbell calls\nits \u201ctruth,\u201d and the fact that it affords intellectual satisfaction\ngives it what he calls its \u201cmeaning.\u201d\n\nWhen we pass from laws to theories we find that the element of\n\u201cmeaning\u201d becomes much more prominent. Now the truth of a law is\nsomething that rests on universal assent; this is not the case,\nhowever, for the meaning of a law. It may be that the contemplation\nof Ohm\u2019s Law gives you no satisfaction whatever; if it satisfies me,\nhowever, then to me it has meaning. It is only necessary, therefore,\nthat scientific laws should have meaning for scientific men; their\ntruth, however, is the same for all. When we come to consider theories\nwe find that, concerning their meaning, there is much more difference\nof opinion. This difference, in fact, almost follows national lines,\nso that of the two great classes of theories, the \u201cmechanical\u201d and the\n\u201cmathematical,\u201d the former is largely a product of British physicists,\nwhile continental physicists prefer the second type. Mr. Campbell\nanalyses very acutely the differences between the two classes as\nwell as the elements they have in common. As he says, there may be a\n\u201ctaste\u201d for certain kinds of theories, as there is a taste for oysters.\nThe result of this analysis is to show very clearly in what respects\nscience is impersonal and in what respects personal; it also helps to\nmake clear what science is. It is true that the impersonal element in\nscience is the most important, in this sense, that if any law or theory\ncan be shown not to be true, then, however much meaning it may have,\nit must be at once rejected. It is also true that it is the meaning\nof laws and theories, particularly theories, which gives them their\nvalue to scientific men. We therefore reach once more the conclusion,\nsufficiently familiar, but seldom so satisfactorily prepared, that the\nvalue of science is in the \u00e6sthetic satisfactions it affords. In Mr.\nCampbell\u2019s words, \u201cScience is the noblest of the arts.\u201d\n\n\nFOOTNOTES:\n\n[Footnote 1: Assuming, in accordance with the principle of Relativity,\nthat all observers have the same motion.]\n\n\n\n\n                          SCIENCE AND CULTURE\n\n\nThe influence of scientific discoveries on that vaguely defined\ncomplex of beliefs and intellectual interests called culture seems, at\nfirst sight, to have something paradoxical about it. There can be no\nquestion that this influence is very widespread, and there can be as\nlittle question that ignorance of scientific discoveries is equally\nwidespread. If our admittedly cultured classes were submitted to such a\n_questionnaire_ as the workers in Sheffield were recently called\nupon to answer, we should doubtless find that such questions as Who\nwas Dante? Who was Plato? would act like holes in a dam; but it is to\nbe feared that the questions under the heading _Science_ would\nevoke the merest trickle of information. And yet many of the questions\nin other parts of the _questionnaire_ would be answered very\ndifferently were it not for those scientific discoveries of which the\nexaminee can give no satisfactory description. The apparent paradox is\nresolved by remembering that it is only the broadest generalisations\nof science, and only certain aspects of those, which exert a marked\ninfluence on the rest of a man\u2019s beliefs. The varied and highly\ncomplicated studies which make up modern astronomy, for instance,\ncan be known, in any real sense, to but a few specialists; the one\nsignificant thing, for purposes of general culture, that emerges from\nthese studies, is that the earth is materially insignificant in the\nuniverse. We need not mind if so much knowledge and no more percolates\nthrough the barriers of a literary education; the damage is done;\nthe rest of the man\u2019s beliefs begin to be profoundly affected. In\nthe papers on geology and biology the majority of cultured people\nwould fail; they would all be amused, however, at the idea that the\nearth was formed in 4004 B.C. and that man was a special and\nseparate creation. Psychological studies have not yet reached, perhaps,\na great and easily understood generalisation, but there is a growing\ncharity vis-\u00e0-vis the \u201ccriminal classes\u201d and other moral outcasts. Our\nVictorian parents\u2019 hearty condemnation of everybody they disliked is\nnow just a little more difficult. Such generalisations as we have been\nmentioning are important to general culture because of what we may\ncall their perspective effect. Their bearing on the rest of a man\u2019s\nmental furniture is not direct; they put the furniture in a different\nsetting. A change of residence, if the difference between the two\nhouses be sufficiently marked, may well lead to a change of habits,\nand the furniture which looked quite well in four rooms may seem a\nlittle inadequate in forty. Those writers who declare that there is\nno \u201creal\u201d conflict between science and religion, for instance, may be\nperfectly good logicians; the point is whether a particular religion\nlooks adequate in the modern universe of science. It is not a question\nof destroying the furniture; it is whether the contents of a bijou\nvilla adequately furnish Salisbury Plain. The influence of science\non philosophy is similarly indirect. Perhaps there is no philosophy\nwhich does not still find defenders; our objection to many of these\nphilosophies is not that they are illogical, but that they look so\nfunny.\n\nWhen we come to study the influence of science on the arts we see that\nthere is yet another way in which science modifies culture. Many of the\npleasurable emotions associated with the arts are not unknown to the\nstudent of science. The study of such sciences as astronomy, physics\nor biology awakens emotions not readily distinguishable from those\nevoked by even the greatest works of art. It is as if the universe with\nwhich science deals was itself a work of art; it is, to an increasing\nnumber of people, the greatest of all works of art. Such students often\nacquire a new standard of \u00e6sthetic excellence. Darwin\u2019s indifference to\npoetry in his later years was probably the result, not of the atrophy\nof a faculty, but of its fuller exercise elsewhere. The young William\nThomson, reading at night in the library, and drawing great breaths of\nrapture over Lagrange\u2019s _M\u00e9canique Analytique_, was experiencing\nemotions probably not very different from those of Swinburne when\nreading Shakespeare. Before such satisfactions become accessible to the\nordinary cultured classes more is required than that vague acquaintance\nwith outstanding generalities to which we have referred. In such a\nscience as astronomy the mere results are often sufficiently attractive\nto rouse pleasurable emotions in the reader, although the actual march\nof the investigation by which the results were obtained is often of\nequal interest. At the present day both results and the broad lines\nof the investigations are in many cases accessible to the ordinary\ncultured person, with the result that his intellectual interests are\nadded to, or at least find a new field for deployment. A greater number\nof \u00e6sthetic objects people his world, and it may even happen that the\nnew arrivals affect the estimate in which he held the old. He may\ndiscover an unsuspected futility in some of his earlier occupations; he\nmay, in fact, change his ideals of culture.\n\nBut it is, in truth, impossible to trace precisely the effect on an\nindividual of a new belief or of a new interest. Psychologists have\nmade us aware of the fact that the mind is not only immensely complex,\nbut that the connections between its elements are often of the most\nunsuspected character. Destruction of an old belief or the grafting\nof a new interest may issue in results as unlike their cause as the\nbutterfly is unlike the chrysalis. The effect of the impact of science\non the old culture cannot be foreseen; it has, however, already\nproduced such changes that the culture of the comparatively near future\nwill probably differ from ours by more than ours differs from that of\nBabylon.\n\n\n\n\n                          JAMES CLERK MAXWELL\n\n\nThe place that will be held by James Clerk Maxwell in the history of\nphysics is not easy to determine. That it will be a very high place is\nobvious, that he will emerge as the greatest of the physicists of the\nnineteenth century is probable, but the student of Maxwell must feel\nthat this kind of ranking is somehow irrelevant, or likely to become\nirrelevant, to his peculiar effect. The unique impression produced by\nMaxwell\u2019s achievement is not adequately described by being referred to\nhis \u201coriginality.\u201d There are different ways of being original; it is\nnot a sufficiently penetrating term. A number of Maxwell\u2019s scientific\ncontemporaries were original men, but one is conscious that they\nhad more in common with one another than Maxwell had with them. An\nexception from this statement is found in W. K. Clifford, who, as has\noften been remarked, had a genius curiously akin to Maxwell\u2019s. Both men\nwere exceptionally _independent_ thinkers, both men resisted the\nattraction of the high road; both men, if the term may be permitted,\nhad a personal and unique angle of approach to the problems of their\ntime. But this, though true, is not a sufficient description. It is\nimportant that in neither case do we feel their individual quality\nto be an eccentricity; their work has a power, and, still more, a\ncomprehensive serenity, which is never the product of mere oddity--the\noddity, for instance, of a Samuel Butler. If we try to get closer to\nthis elusive and important characteristic we do not meet with much\nsuccess; but we may suggest that the ideas of these men have the\neffect of springing from an unusually rich, subtle and comprehensive\n_context_. The fundamental ideas of the science of their time were\nsubtly modified by reception into these minds; they were connected in a\npersonal and unusual web of implications.\n\nIt is doubtless worth noting in this connection that Maxwell, unlike\nmost of the scientific men of his time, was genuinely interested in\nmetaphysical speculation. This was not merely another interest of\nhis; it was, at most, another field of attention; he brought the same\nattitude of mind to all the objects with which he was concerned. We\ncannot make an exception even in the case of his religious views; to\nthis man the problems of metaphysics, of physics, of morality, are\nalmost arbitrary divisions of the one object of his thought. He was\nexpressing a real difference from himself when he said that some men\nseem to have water-tight compartments in their minds. When we study the\nkind of homogeneity characteristic of Maxwell\u2019s mental life it is easy\nto understand those who call him a mystic. Even as a purely scientific\nman, his rational faculty, as evidenced by his mathematical reasoning,\nwas a distinctly more fallible thing than his intuition. This is not to\nsay that he was not a fine mathematician, but it is his intuitive grasp\nof a physical problem which gives him his high position, and not his\npurely mathematical verifications. His mathematics, in fact, was not\nalways impeccable, as Sir Joseph Larmor points out in the new edition\nof _Matter and Motion_. But it is characteristic of Maxwell, that,\neven when his proofs were faulty, his results were usually sound. His\nown way of confirming a difficult intuition was not to provide a formal\nmathematical verification, but to make appeal to easier intuitions--in\nfact, to construct mechanical models. He always liked to _see_ the\nway things worked. It is important to remember that this desire for a\nparticular kind of verification was not due to any lack of power to\nform abstractions; it was due to something quite different, to a lack\nof ease when faced by a purely logical chain of deduction. On Maxwell\u2019s\nfamous _Treatise on Electricity and Magnetism_, Poincar\u00e9 comments\nthat its difficulty resides precisely in its great abstraction. It is\nthis presentation of his theory to which one has to turn; nevertheless\nMaxwell, as if for his private satisfaction, developed some extremely\ncomplicated models which seemed to him to make his theory clearer. It\nwas doubtless this combination, a great power of abstraction on the one\nhand, and a desire for very definite, even unnecessarily definite,\nconfirmation on the other, which enabled him to be at once extremely\noriginal and remarkably sound.\n\nIn his boyhood he was constantly making all kinds of experiments with\ncommon substances, drawing complicated diagrams, constructing solid\ngeometrical figures, even knitting elaborate pieces of wool-work;\npractically all these pursuits were dictated by the same desire, the\ndesire to see an abstract principle embodied in a concrete instance.\nNo man was less at the mercy of words. But it was, nevertheless,\nthe abstract principle with which Maxwell was concerned; he merely\nwished to be quite sure that he understood it. His occasional trick of\nsupplying an unexpectedly simple proof of a difficult theorem is due to\nthis habit of realisation. Platitudes acquired a wealth of implication\nin Maxwell\u2019s hands. During his student life at Cambridge, when he seems\nto have been chiefly occupied in making a survey of things in general,\nwe find the same desire to reduce everything to a few principles; but\nthe principles must first stand a rigorous examination. Merely vague\nunifications provoked his irony, and where no principle could be made\nto work, then, in spite of his love for coherent and inclusive systems,\nhe would admit ignorance. And, in spite of his need for principles,\nand the tenacity with which he clung to those that met his need, he\nclaimed no \u201cabsolute\u201d quality for his beliefs. In his own words,\n\u201cNothing is to be _holy ground_ consecrated to Stationary Faith,\nwhether positive or negative.\u201d And, later, \u201cAgain, I assert the Right\nof Trespass on any plot of Holy Ground which any man has set apart....\u201d\nSuch questioning as Maxwell applied to himself was to be applied to\nall other men. He was conservative, but not on exterior authority. His\nscepticism was, in truth, very profound, and it was always present.\nIt informs his criticism, which is often extremely penetrating. The\nletters he wrote on the death of his friend Pomeroy, shortly after\nMaxwell had become a Fellow of Trinity, are very instructive from this\npoint of view. His distrust of the \u201crationalisations\u201d that men give of\ntheir beliefs extends to the beliefs themselves. As he says, men \u201care\nignorant even of their own true faith till something brings it into\naction.\u201d This was a deep-rooted conviction with him, and is responsible\nfor the flavour of irony which is never long absent from his comments\non philosophic matters, indefatigable student as he was. He can direct\nthis scepticism against himself, as in the entry in his programme of\nfuture study: \u201c4. Metaphysics--Kant\u2019s _Kritik of Pure Reason_\nin German, read with a determination to make it agree with Sir W.\nHamilton.\u201d On another occasion he writes to a friend pointing out that,\nin reading an author, he had to find out first of all, not what the\nauthor meant, but that it was not what he was convinced must be meant.\nA little experience of criticism persuades us that this is, indeed, a\nvery necessary procedure.\n\nThis aspect of Maxwell, as a critic at large, as it were, would\nwell repay study, and it is unfortunate that our material for it is\ncontained in a scarcely ideal biography. He differed from the run of\nscientific men, whose absorption in one pursuit makes their mental life\nunrepresentative; his chief problems are not found in his scientific\nwritings, and they are the problems of us all. There was nothing\nsuperficial in Maxwell, and he had no easily won conclusions. It is\nthe path he followed that gives interest to his goal. We should like\nto know, for instance, what experiences, what reflections, enabled him\nto write: \u201cLong ago I felt like a peasant in a country overrun with\nsoldiers, and saw nothing but carnage and danger. Since then I have\nlearned at least that some soldiers in the field die nobly, and that\nall are summoned there for a cause.\u201d That Maxwell, either suddenly\nor gradually, developed a mystic consciousness of life, is borne\nout by many passages of his correspondence. We can attach no other\nsignificance to his description of his \u201cnostrum\u201d: \u201can abandonment of\nwilfulness without extinction of will, but rather by means of a great\ndevelopment of will, whereby, instead of being consciously free and\nreally in subjection to unknown laws, it becomes consciously acting by\nlaw, and really free from the interference of unrecognised laws\u201d; and\nhis letters to his wife, dealing with passages from the Bible, abound\nin interpretations which are indubitably mystical. Yet we have no\nevidence that he was acquainted with the literature and terminology\nof mysticism; he is speaking of personal experiences, not of acquired\ndoctrines.\n\nThe maintenance of a mystical outlook on life, together with a\nperfect realisation of the implications of physical science, was\naccomplished, in Maxwell\u2019s case, by denying the ordinary conception of\nthe _direction_ of scientific progress. It is the idea which would\ninevitably occur to him, for it is the peculiar merit of his own work\nthat it was not the result of straightforward progress. He made a new\nway of thinking necessary just as, in our own time, Quantum Theory and\nRelativity Theory have fundamentally disturbed our most unquestionable\nassumptions. The way Maxwell actually approached the problem we have\nmentioned was by insisting on what he called, by a mathematical\nanalogy, the \u201csingular points\u201d of existences, that is, the points where\nthe equations break down, and he postulated that the more there were\nof these singular points the higher the rank of the existence. At a\n\u201csingular point\u201d influences which are usually negligible may assume a\ndominating importance, and Maxwell saw the science of the future as\nbeing largely concerned with these lapses in continuity--as, in fact,\nscience since his time has been. In this way he escaped determinism. In\nhis own words:\n\n If, therefore, those cultivators of physical science from whom the\n intelligent public deduce their conception of the physicist, and\n whose style is recognized as marking with a scientific stamp the\n doctrines they promulgate, are led in the pursuit of the arcana of\n science to the study of the singularities and instabilities, rather\n than the continuities and stabilities of things, the promotion of\n natural knowledge may tend to remove that prejudice in favour of\n determinism which seems to arise from assuming that the physical\n science of the future is a mere magnified image of that of the past.\n\nThis speculation, the problem of evil, and in what sense the individual\nmay be said to persist in Time, are the kind of questions which\nconcerned him during the last years of his life. It would be merely\nfanciful to mention these things as evidence of that \u201ccontext\u201d of which\nwe spoke, but we think it is possible to understand more intimately the\norigin of the Electromagnetic Theory of Light if we remember that it\noriginated in a mind which also constantly entertained these other, and\napparently disconnected, speculations.\n\n\n\n\n                              ASSUMPTIONS\n\n\n                                   I\n\nIt has been remarked that man\u2019s senses were given him, not to\nphilosophise with, but to help him in the struggle for existence;\nBoltzmann, the great German physicist, was frankly distrustful of\nmany of the natural motions of the mind. He could admit that Science,\nalthough often very abstract, had a certain validity, since it issues\nin the prediction of events which are accessible to sense perception.\nBut philosophy, he insisted, was in an altogether different case, and\nhe thought the chances considerable that its impalpable conclusions\nwere the merest moonshine. It is a speculation that must have exercised\neveryone who has whole-heartedly accepted the evolutionary account of\nthe rise of intelligence. Why should this instrument be adapted to\nother than its original uses? Doubts of this kind, however, are both\ntoo vague and too comprehensive to serve any useful purpose. They\ndo not tell us in what way and to what extent our intelligence is\nuntrustworthy; they do not enable us to make one step towards drawing\nup an Index of Forbidden Subjects. At the most they enable a man with\na constitutional dislike of philosophic speculations to indulge his\ncontempt for that occupation with an easy conscience. Nevertheless,\na tincture of this doubt is very wholesome, and more particularly if\nit be the result of an acquaintance with the history of human thought\nrather than the product of a kind of lazy _a priori_ scepticism.\nA student of the history of science, for instance, is inevitably led\nto reflect on the curious nature of the barriers to further advance\nwhich the mind itself has set up. It is as if the mind could only take\nexercise within some imaginary prisoner\u2019s yard, and that the great\nadvances were really the result of liberations. These liberations are\nonly partial; the mythical boundaries are set a little further off, but\nit is agreed that the high walls exist.\n\nIt is interesting to review the progress of Science from this point of\nview, to see it as a gradual secession from unwarrantable assumptions.\nThe exceedingly cautious, the almost groping character, of the\nadvance of knowledge, becomes very apparent. And, although such a\nsurvey may lead us to become very conscious of this particular mental\nlimitation, we are not one whit nearer being enfranchised. It is still\nthe prerogative of genius to be innocent, to turn surprised eyes on\none of our most arbitrary assumptions, and to say: But that is not\nnecessary. The history of Astronomy, of course, provides some of the\nbest examples of mental prison yards. That the planets must move in\ncircles because the circle is the perfect figure is an assumption now\nsufficiently remote from our acquired sense of probability to seem\nexceedingly strange. That it was an assumption possessing a high degree\nof obviousness is apparent from the fact that even Copernicus did not\nquestion it. The attempt to enter into this assumption, to see it as\nobviously reasonable, would be a useful exercise for the historian,\nsince it involves, very largely, a reconstitution of the mental life\nof that age. It acquired its obvious character from the fact that it\n_fitted in_; it was the natural companion of a great number of\nother equally obvious assumptions; it was not an isolated eccentricity\nof the mind. It is for that reason that Copernicus never freed himself\nfrom it, and that Kepler only succeeded after a difficult struggle.\nKepler was required to question not merely an isolated doctrine, but to\nescape from a veritable _Zeitgeist_. The Inquisitorial examination\nof Galileo, also, was not directed merely to correcting the erroneous\nstatement of an isolated fact; it was, in truth, a whole system of\nthought that stood on trial. It is this double aspect of any given\nabandoned assumption that accounts for our unimaginative surprise on\nlearning that very intelligent men once mistook it for an obvious\ntruth. We are judging the assumption, not on its own merits, as it\nwere, but from the standpoint of an alien system of thought.\n\nWe can form a juster estimate of the degree of credulity manifested by\nthe contemporaries of Copernicus by considering assumptions that have\nbeen but recently questioned, or rather, which have only recently been\ngenerally questioned. The assumptions regarding animal psychology form\na vivid example. Such men as Darwin and Romanes found it quite natural\nto assume that the emotions and many of the intellectual processes of\nwhich they were conscious in themselves furnished an adequate key to\nanimal behaviour. It is an assumption which the average educated man\nof to-day makes quite readily, although he may not share Aristotle\u2019s\nviews on the perfection of circles. We now know that there is no reason\nwhatever to suppose, for example, that the psychology of snails has\nthe slightest resemblance to the psychology of human beings. We may be\nconfident that, in a very few years, the assumptions of Darwin and most\nother people will appear almost inexplicably gratuitous. It will take\nlonger, we think, for the Freudian ideas about man himself to become\nacclimatised; man will take a long time to learn that in trusting his\nimmediate awareness of himself he is making a number of unwarrantable\nassumptions. The system of thought into which his present assumptions\nfit is so profound and extensive that it is impossible, even now, to\npicture the thoroughly enfranchised man.\n\nA general acceptance of the Einsteinian ideas of space and time is\neasier to predict. The current conceptions of space and time, although\nEuclidean when reduced to a logical scheme, are not, in fact, present\nas a logical scheme in the mind of the ordinary man. He is sufficiently\nvague about his fundamental assumptions to offer no strenuous\nresistance to their subtle modification. We think that part of his\ngeneral bewilderment about Einstein\u2019s space and time is due to his\nbewilderment on thinking about space and time at all. His assumptions\non these questions, whatever those assumptions may be, are not really\npart of a general scheme of beliefs. Nothing that greatly concerns him\nis incompatible with non-Euclidean geometry, and we confidently expect\nthat the grandchildren of the ordinary man will as blandly believe they\nhave swallowed Einstein as the contemporary ordinary man believes he\nhas swallowed Euclid. For an assumption which is not an integral part\nof a general scheme of thought is readily abandoned. It is the lopping\nof connections which the mind resists. It is no paradox to say that the\nmathematician and philosopher finds it harder to accept Einstein than\ndoes the ordinary man. That is because the mathematician\u2019s acceptance\ninvolves both believing more and disbelieving more.\n\n\n                                  II\n\nProbability is, of course, the guide of life. If all our assumptions\nwere expressed, we should find the phrase \u201cit is reasonable to suppose\u201d\noccurred more frequently than any other, whether we were engaged\nin crossing a street or in writing a philosophical essay. Yet our\nperception of the reasonableness of anything rests on a sentiment\nwhich is often very delicate and extremely difficult to define. The\nmathematicians have succeeded in giving exact expression to some of the\nsimplest manifestations of this sentiment, but most of the cases we\nare called upon to solve in ordinary daily life cannot be dealt with\nby their analysis. It is the great strength of science that it builds\nwholly upon this sentiment. We are not called upon to \u201ctranscend\u201d\nreason by faith; we are asked to believe nothing that sins against\nour sense of probability. It is admitted, of course, that there are\nscientific theories that do not sound reasonable on a first hearing;\nindeed, they sometimes outrage common sense, and every scientific\nengineer knows the difficulty of persuading the \u201cpractical\u201d man that\nthe obvious thing is not always the right thing. Nevertheless, it is\nclaimed for science that, on the evidence, its conclusions are the\nmost reasonable ones even when they are wrong. The sense of what is\nreasonable depends upon the evidence, but the word \u201cevidence\u201d must\noften be taken to include a great deal of which the mind is not fully\nconscious. It was at one time thought quite reasonable that the\nheavenly bodies should move in circles round the earth. The belief was\nnot wholly a matter of astronomical evidence. It was considered that\nthere was something peculiarly and inherently reasonable in circular\nmotion for heavenly bodies. We can see that this expectation was\nconnected with the \u00e6sthetic properties of the circle, and we now think\nthat expectations based on such considerations are, in astronomical\nmatters, illegitimate. Something akin to such considerations still\nplays a part in science, however, although in a less obvious form.\nOther things being equal, a simple explanation of natural phenomena is\npreferred to a more complicated one, although, as Fresnel remarked,\nthere is no _a priori_ reason to suppose that Nature takes any\naccount of analytical difficulties. The history of the Copernican\ntheory of the solar system is instructive from this point of view. The\nnotion that the Earth and other planets went round the sun immediately\nmade a number of puzzling things clear. It seemed, on the whole, a very\nreasonable notion. It was attended, however, by one great difficulty.\nIf, at the end of six months, the earth were really at opposite ends\nof a long line, it should follow that the stars, viewed from these\ntwo points, should seem to shift their relative positions in the sky,\njust as the trees in a wood seem to change their relative positions as\nwe pass them in a train. Tycho Brahe, one of the greatest astronomers\nwho ever lived, was so impressed by the fact that this expected change\ndoes not occur, that he could not accept the Copernican theory as it\nstood. He invented a curious hybrid theory of his own, according to\nwhich, while the other planets went round the sun, they, together with\nthe sun, revolved round the earth. He does not seem to have made many\nconverts to this view; it somehow offends one\u2019s sense of probability.\nThe Copernican hypothesis persisted, in spite of the difficulty we have\nmentioned, but not without causing considerable mental discomfort. When\nHorrebow at last thought that he had obtained evidence of the apparent\nannual motion of the stars he published his discovery under the title\n_Copernicus Triumphans_. It was found, however, that the supposed\ndifferences were caused by temperature changes affecting the observer\u2019s\nclock, and the old difficulty persisted. It might be thought that the\ncorrect solution was obvious; one had only to assume that the stars\nare so far away that, with such instruments as were then used, their\napparent motion is imperceptible. We now know that this solution is\nthe right solution, but in the eighteenth century it did not appear\na reasonable solution. It was felt that if the stars were really at\nsuch immense distances as this hypothesis required, then Nature showed\na grave lack of economy in space. Such enormous stellar distances\npointed, so far as these astronomers could see, to a most unreasonable\nwaste of space. No farmer would behave in such a fashion, and although\nthe eighteenth-century astronomers would have denied that they viewed\nthe universe as a gigantic farm, yet this delicate and elusive notion\nof what is reasonable was, in this case, greatly influenced by farming\nconsiderations. It is not possible to form reasonable expectations\nexcept on the basis of experience, and sometimes the most irrelevant\nconsiderations play a part in our estimate.\n\nAs instruments improved, however, the expected motion was observed,\nand the distances of some stars calculated. They proved to be\nenormous; the great waste of space does occur. God is not a farmer.\nThis being established, one could approach the general problem of\nstellar distribution free from certain prepossessions. One\u2019s sense\nof the reasonable acquired a different orientation, as it were. But\nit still remains reasonable to suppose that the brighter stars are,\non the whole, nearer to us than the fainter stars. This assumption\nmust, however, be employed with caution. If a list be formed of\nthe nearest stars from amongst those whose distances have actually\nbeen determined, we reach some rather unexpected results. Knowing\nthe apparent magnitudes of these stars, and their distances, we can\ncalculate their actual luminosity compared with the sun as a standard.\nThe apparent magnitudes range from Sirius, which is considerably\nbrighter than a first-magnitude star, to stars of more than the ninth\nmagnitude, that is, to stars quite invisible to the naked eye. Some\nof the nearest stars may be fainter yet, for determinations of the\ndistances of stars fainter than magnitude 9.5 are lacking. The actual\nluminosities of these stars range from forty-eight times that of the\nsun to four-thousandths that of the sun. The actual distribution of\nthe nearer stars is not at all that which would appear reasonable\nif we were guided by considerations of apparent brightness. Some of\nthe very brightest stars, such as Canopus, must be at inconceivable\ndistances, and their actual brightness must be thousands of times,\nperhaps very many thousands of times, that of the sun. Here again our\nunsophisticated notion of what is reasonable is apt to be more of a\nhindrance than a help. Excellent as a guide through not too unfamiliar\ncountry, it is apt to lead us sadly astray when we advance into\ncompletely unknown territory. Nevertheless, it is the only guide we\nhave.\n\n\n                                  III\n\nIf we contrast ancient with modern scientific theories we find\nthat the chief distinguishing characteristic of the former is that\nthey employ principles drawn from other branches of knowledge or\nspeculation. It would be, perhaps, rash to say that modern science,\nin all its branches, is yet completely autonomous; sometimes, for\ninstance, it seems to make assumptions which are the result of an\nuncritical philosophy, but even the grossest of these examples,\ncompared with many celebrated early scientific theories, shows how\ngreat is the purification that has been effected. The chief error of\nthe old speculators consisted in imagining that the world is a more\nobvious unity than we have now any reason to suppose. Hence they were\nalways willing to argue by \u201canalogy,\u201d comparing terms between which\nwe cannot now find the slightest resemblance. The method was not only\nillegitimate, but sometimes led to quite unnecessary complexities of\nexplanation. The Ptolemaic system of astronomy, for instance, conceived\nas the theory that the heavenly bodies revolve round the earth, was\na perfectly reasonable and satisfactory theory. It was capable of\nexplaining all the observed planetary motions, except a few minute\nirregularities requiring precise measurements for their detection. Its\nproper development required, of course, complete docility in face of\nthe facts. But in its actual development it was forced to accommodate\nitself to quite other considerations. It had to take into account the\nvenerable principle that, the celestial bodies being obviously sublime,\nincorrupt and perfect, their orbits must be perfect and described with\nuniform velocities. The only possible perfect orbit was as obviously\na circle. Hence the Ptolemaic theory was loaded with the task of\nexplaining the observed heavenly motions on two grounds: first, that\nthe earth was stationary and at the centre of the system, and second,\nthat the planetary orbits were circular and described with unvarying\nvelocities. Alternative hypotheses were not only stupid but impious.\nThe task thus set to the early astronomers was one of considerable\ndifficulty.\n\nThe observed path of a planet, say Mars, or Jupiter, or Saturn, is\nby no means simple. If its motion amongst the stars be watched from\nnight to night it is seen to be moving sometimes from east to west\nand sometimes from west to east. Further, in changing its direction\nof motion it does not retrace its path amongst the stars. Its actual\nobserved path exhibits irregular loops, and, more rarely, a twisted\nline. It was at once obvious that a circular orbit, traversed with\nuniform velocity, would not suffice to explain these appearances.\nNevertheless, the principle must be preserved. The astronomers\novercame this difficulty by a device that strikes one as being almost\ndisingenuous. They imagined a small circle whose centre traversed the\ncircumference of the big circle with a constant velocity and round\nwhose own circumference the planet moved with a constant velocity. By\nassigning suitable velocities to these two motions the crude features\nof the planet\u2019s actual observed motion could be represented--it would\nsometimes be retrograde and sometimes direct. This is ingenious, but it\nis questionable whether it preserves the principle. The planet\u2019s motion\nis obtained by circular motions, it is true, but it is not itself a\ncircular motion with reference to the earth as centre. The astronomers\nhave entered on a slippery path. We view them with the same suspicion\nwith which we watch a Broad Churchman expounding the Thirty-Nine\nArticles. But they had to go further. The theoretical and the observed\nmotions did not fit well enough. On the little circle it was necessary\nto imagine a still smaller circle, and to place the planet on its\ncircumference. After all, this interpretation of \u201ccircular motion\u201d once\nadmitted, there was no reason why it should not be followed up. But\nprogress in this direction soon came to a halt. It became evident that\nthis method would not, by itself, reconcile observation and theory.\nThe principle had to be strained again, and this time in an almost\nindefensible manner. It was declared that the big circle was eccentric\nwith respect to the earth and that the little circles were eccentric\nwith respect to their supposed former centres. This assertion must have\nbeen a great strain on the faith of the orthodox believer. He may well\nhave wondered whether, by this time, the pure doctrine of his fathers\nhad not been subtly undermined. Circular motion was still preserved, in\na way, it is true, but with so many circles, and their centres all over\nthe place--this must have appeared something very different from what\nhe supposed the principle to mean.\n\nThe same difficulty was felt by simple minds in modern times, when the\ncorrect explanations of statements in Genesis were worked out by the\ntheologians. And just as the simple story of the Creation in Genesis\nbecame transformed into an extremely obscure and ambiguous anticipation\nof the discoveries of Geology, so the interpretation of circular motion\nadvanced from complexity to complexity. Immutable principles must\nexist, of course--it is part of the glory of man that he should have\nbeen able to discover so many of them--but they sometimes seem more\ntrouble than they are worth. The old astronomers found that yet again a\nmore liberal interpretation must be given to the principle of circular\nmotion. This time it was found that the circles do not all lie in one\nplane. Each circle has its own plane, which may be inclined at any\nangle to the others. By this time the theorists, whom we might call the\n\u201ccommentators,\u201d had forged a very powerful method. Circles could be\nmultiplied; their centres could be placed anywhere; their planes could\nbe inclined at any angle. The rich content of the principle of circular\nmotion was now fully revealed. With all these variables to play with a\nvery close correspondence between theory and observation was effected.\n\nThe rise of the \u201chigher criticism\u201d of this system leads to the history\nof modern astronomy. It is to be noted, however, that the first higher\ncritic, like the first higher critics in other departments, was not\nwholly emancipated from his early teaching. Copernicus effected the\nimmense revolution of placing the sun in the centre of the system, but\nhe did not abandon circular motion. So he had to retain parts of the\nepicyclic apparatus. The revolution was first completely effected by\nKepler, but even he conducted his early researches as a semi-believer,\na kind of very Broad Churchman. He made nineteen successive attempts\nto explain the motions of Mars by the arrangements of eccentric\nand epicyclic motions, and only then did he frankly throw the great\nprinciple of circular motion overboard, and state that the actual paths\nof the planets were ellipses. And so, in a few years, a great immutable\nprinciple, a whole system of beliefs, the industry and thought of\ngenerations went for nothing, and now exist merely as an occasional\ncold reference in a treatise on Astronomy to the Ptolemaic system as a\n\u201cmonument of misplaced ingenuity.\u201d\n\n\n                                  IV\n\nWe may divide scientific theories into two classes, which have recently\nbeen distinguished by Einstein as theories of construction and theories\nof principle. His own theory of relativity is a theory of principle,\nand its attraction resides in its logical perfection. Such theories,\nwhatever charm they may have for the logician, are not, man being\nconstituted as he is, felt to be sufficient. A principle which natural\nphenomena obey, and which enables equations to be deduced expressing\nthe relations between phenomena, is, to a few austere souls, all with\nwhich science need concern itself, but the majority of men require, in\naddition, something they call an \u201cexplanation\u201d of the relations deduced\nfrom the principle. They desire to see events described in terms with\nwhich they are familiar. Thus, a description of the behaviour of the\nmaterial universe in terms of the mutual impacts of little billiard\nballs would afford genuine satisfaction to the mind, and important\nadvances have been made in science by the attempt to describe phenomena\nin these terms. The assumptions which underlie some such attempts\nmay seem, to the logician, preposterous, but there is no doubt that\nthe mind is impelled to make such assumptions. Our familiarity with\nthe motions of matter in bulk makes it quite natural that we should\nendeavour to give, as far as possible, dynamical explanations of\nevents, although, if we stop to ask ourselves why nature should be\nflexible enough to admit of descriptions in such terms, we are at a\nloss for an answer.\n\nThe history of theories of the \u00e6ther is particularly instructive from\nthis point of view, because the irrational nature of the impulse is\nhere most clearly apparent. The attempt to explain phenomena in terms\nof an \u00e6ther has led to some very remarkable theories of the nature of\nmatter itself. It has been supposed, for instance, that the ultimate\nparticles of matter are vortical whirls in the \u00e6ther, or, again, points\nof a very special kind of strain in the \u00e6ther. Nevertheless, a theory\nof the \u00e6ther is regarded as unsatisfactory which is not couched in\nterms of the observed behaviour of ordinary matter as we know it. A\ndynamical explanation is always sought after, and a great part of the\nscientific effort of the nineteenth century was devoted to describing\nthe \u00e6ther as an elastic solid. But men of science were not content\nwith showing that the laws of dynamics could be applied to the \u00e6ther;\nmany of them endeavoured to devise models which should represent, on a\nlarge scale, the actual construction of the \u00e6ther. It is difficult to\nknow to what extent their authors supposed these models to correspond\nto the reality; it is probably not sufficient, however, to say that\nthey regarded them merely as furnishing useful tools for subsequent\ninvestigations. The models were usually extremely complicated, for,\nfrom the very beginning, the \u00e6ther proved somewhat recalcitrant to this\nattempt to represent it as an elastic solid. The most obvious objection\nto this representation was provided by the observed motions of the\nplanets. It could be proved that, if there were any resistance to their\nmotions round the sun, it must be excessively minute, and how was this\nto be combined with the hypothesis that they were moving with great\nspeed through an elastic solid? The answer was found in cobbler\u2019s wax.\nSir George Stokes noticed that cobbler\u2019s wax, although rigid enough to\nbe capable of elastic vibration, is yet sufficiently plastic to permit\nother bodies to pass slowly through it. We have only to imagine that\nin the \u00e6ther these qualities are much exaggerated, and the motion of\nthe planets presents no difficulty. If no substance like cobbler\u2019s\nwax happened to be known it is difficult to know what satisfactory\nanswer could be returned to the objection. Here we have the first\nglimpse of the remarkable combination of qualities with which it was\nfound necessary to dower the \u00e6ther. The mathematical examination of\nthe properties of the \u00e6ther, undertaken by such men as Navier, Cauchy,\nPoisson, Green, was continually leading to queer and unsatisfactory\nresults, unsatisfactory, that is, in the light of our experience of\nthe properties of matter. Cauchy, in particular, deduced a number of\nremarkable physical properties which were irreconcilable with one\nanother, although one of his theories, that of the \u00e6ther considered as\na kind of foam, attracted the attention of Lord Kelvin.\n\nWith the rise of Maxwell\u2019s electromagnetic theory, the elastic solid\n\u00e6ther received less attention. Maxwell himself, in his great treatise,\ngives no mechanical explanation of his theory; he merely shows that\nan infinite number of mechanical explanations are possible. With the\npublication of Einstein\u2019s first principle of relativity in 1905,\nhowever, the \u00e6ther began to disappear; and now, with the generalised\ntheory of relativity, it has become a mere ghost. There are still\nsturdy champions of the \u00e6ther, and, indeed, it seems a pity to have\nto abandon the mechanical explanations it promised. But possibly\nthe attempt to find dynamical explanations of this kind is doomed\nto failure; perhaps, after all, nature is not flexible enough. The\norientation of modern science is in another direction. It is towards\na more abstract class of theories altogether--theories which tell us\nnothing about the mechanism of a process, but tell us the principles\nthe process must obey. Such theories effect a vast unification of\nknowledge. They are magnificently comprehensive, and it is possible\nthat they contain all that we can really know, although men will long\nbe reluctant to abandon all hope of ever approaching reality with the\nintimacy that the theory of the \u00e6ther seemed to promise.\n\n\n                                   V\n\nWhether or not it be true that the proper study of mankind is man, it\nis certain that he finds great difficulty in studying anything else.\nHis first impulse, when he thinks about the universe at large, is to\nconsider it in reference to himself, and to explain it in terms of his\nown actions and desires. In Astronomy, for example, it long seemed\nquite reasonable that in the peculiarities of men\u2019s bodies should be\nfound the system on which the universe is constructed. The arguments\nof Galileo\u2019s contemporaries amuse us now, for we have learned modesty,\nbut the tendency to explain all things in purely human terms, as it\nwere, is by no means yet extinct, and is still a hindrance to science.\nIt is even hinted that man\u2019s explanation of himself is not free from\nbias; psychologists inform us that a man\u2019s account of his own actions\nis not always to be trusted, that the true springs of his conduct\nare usually those he would blush to own. But if we are to say that\nman\u2019s speculations about the universe show an overwhelming sense of\nhis own importance we must allow him also a certain generosity. Until\nquite recent times he was willing to dower almost anything, animate or\ninanimate, with his own attributes. He credited stones with life and\ntrees with desire, while the whole animal world were his brothers. He\ncould admire the loving sentiments of the dove and weep for the sorrows\nof the crab. A pathetic confidence in man as the type and exemplar\nof the universe informed nearly all the early writings on animal\npsychology, and Descartes\u2019 theory that animals were automatic roused\na sentimental indignation which has not yet subsided. Nevertheless,\ncomparatively recent investigations tend to overthrow the natural\nassumption that worms and insects are little men inhabiting strange\nbodies. The modern biologist refuses to be conscience-stricken when\nreferred to the industry of the bee or the conjugal perfections of the\ndove. It is only recently that he has become so heartless. Darwin,\nin a celebrated passage, describes with simple reverence the mutual\naffection existing between snails. The intelligence of these little\ncreatures was also estimated highly by Romanes. Loeb, the great\nAmerican biologist, did much to upset this na\u00efve anthropomorphism.\nHe took some worms who are \u201calways attracted by light,\u201d and showed\nthat this movement did not testify to a \u201cmore light\u201d cry in these\nlittle souls, but was a purely automatic proceeding. The worm places\nitself so that both sides of its body are equally illuminated. It is a\nmechanical action due to the influence of light on the living matter of\nits body. If there are two lights the worm passes between them, thus\nsecuring equal illumination of its two sides.\n\nThe crab which, being held by a claw, sheds that claw and hurries to\nthe nearest rock for shelter, is found to do the same thing after its\neyes or brain have been destroyed. Dr. Georges Bohn, who has made many\nexperiments to determine how far the actions of the lower animals are\npurely mechanical, gives an interesting account of a certain parasitic\nworm which attaches itself to the fish called the torpedo. He finds\n(1) that if the amount of salt in the water be varied the reactions\nof the worm alter; (2) that if light be allowed to play first on one\npart and then on another part of the worm, its reactions alter; (3) if\nthe animal has already taken up its position, attached to the glass,\nfor instance, and a shadow be passed over the top of the vessel, the\nwhole body of the worm turns itself into the vertical in such a way\nthat if the shadow were caused by a passing torpedo, the worm could\nattach itself to the fish. If, however, it be already attached to a\ntorpedo, it does not raise itself at a passing shadow. Here, then, is\nan _association_ between the region of the body excited by light\nand the part fixed to the fish. It was found, also, that the crab which\nabandons its claw only does so when held by a certain part. The action\nappears to be purely automatic. If it were dependent in any way on the\ncrab\u2019s simultaneous visual perceptions, for instance, an associative\nphenomon would be established. But experimental tests find no such\ncorrespondence. As the result of numerous experiments of this kind\nbiologists have become very wary of offering psychical explanations of\nthe actions of the lower animals. Even when genuine associations are\nestablished one must be careful not to interpret them in terms of human\npsychology. In the very description of experiments an unwarrantable\nturn may be given to the phenomena by the fact that words of ordinary\nlanguage inevitably call up associations which may be out of place in\nthe discussion. To say that an am\u0153ba _learns_ to reject certain\nforeign particles in a solution, for instance, is a statement that\nrequires careful interpretation. How are we to picture an am\u0153ba\n_learning_ something?\n\nBut, indeed, the danger of anthropomorphic interpretations becomes\nvery obvious when we reflect on the purely physical phenomena which\naccompany man\u2019s own emotions. If the James-Lange theory be correct,\nit is in terms of these physical phenomena that we must understand\nman\u2019s emotions. Now consider the example given in Washburn\u2019s book,\n_The Animal Mind_. An angry man has a quickened heartbeat, altered\nbreathing, a change in muscular tension, and a change in the blood.\nConsider a wasp. It has no lungs, but breathes through its trache\u00e6;\nthe circulation of its blood is fundamentally different from that in\nman; all its muscles are attached internally because its skeleton is\neverywhere external. What, then, is an \u201cangry\u201d wasp? It seems clear\nthat if a man is to study anything but man he must forget himself as\nfar as possible.\n\n\n\n\n                          ON LEARNING SCIENCE\n\n\nIt is a well-known fact that a really intelligent child finds great\ndifficulty in believing that the earth is round. Stupid children,\non the other hand, believe anything they are told. The difficulty\nexperienced by the first child is due to the fact that, in however\nelementary a way, it is conscious of the implications of the statement.\nThe stupid child seems to be unaware that the statement has any\nimplications; it seems able to accept almost any statement in some\ncuriously bare, unrelated fashion. Hermann Bahr has an interesting and\namusing story of how profoundly his faith in his father was shaken when\nthe latter, _\u00e0 propos_ of a sunset, told the young boy that in\nreality it was the earth that turned round and not the sun. Completely\noverwhelming objections to this statement rose instantly in young\nHermann\u2019s mind, and, outraged by this insult to his intelligence, he\npreserved a hurt and dignified silence that lasted for days.\n\nWe notice the same essential difference in schoolboys and university\nstudents, and, in fact, in men of any age. Perhaps the majority\nof men, and less certainly of children, have but little sense of\nthe implications of a statement. The sense of implications does not\nnecessarily involve the ability to discover the implications--that is\na comparatively rare gift. It acts rather in a negative manner, making\nthe student restless under a subtly illogical presentation of a case,\nor leaving the schoolboy frankly mutinous at the end of a sermon. It\nis not a gift which makes a rapid learner, although its absence will\nprevent a man from ever knowing a subject properly. It is unfortunate\nthat education, as practised in this country, does not sufficiently\ntake into account this very desirable inhibition. The text-book plays\na very large part in contemporary education, and most text-books are\ndesigned for those who can swallow statements at great speed. That\ndelicate web of doubt, of half-seen alternative explanations, which\ncomes into the mind of the intelligent student when confronted with\nthe highly dogmatic statements and somewhat perfunctory \u201cproofs\u201d of\nmany modern text-books, counts as sheer loss in the examination race.\nThis is especially true of scientific text-books, which are usually\nconceived on an entirely wrong plan, judged from the standpoint of\nrational education. Statements which are the final expression of\nvery difficult and slowly acquired abstractions are presented in all\ntheir nakedness, and followed by a collection of \u201cexamples.\u201d The glib\nstudent learns these statements as if he were learning a foreign\nlanguage, and soon masters the tricks necessary to apply them. I\nhave known such students able to solve very difficult problems and\nyet entirely unable to meet, in any way, a sceptical attack upon\nthe fundamental theorem they employ. The fact is that this method\nof teaching science is psychologically unnatural, and the knowledge\nacquired on this method is largely sham knowledge. While it may not\nbe true that the child passes through \u201ccultural epochs\u201d in its mental\ngrowth, it is true that it will feel many of the hesitations and\ndifficulties experienced by the men who first formulated the concepts\nnow presented to it for its instant acceptance. It is for this reason\nthat the best method of teaching a science is probably the historic\nmethod. In this way not only are many doubts fairly met instead of\nbeing merely repressed, but the exact _port\u00e9e_ of a statement and\npossible lines of extension are much more clearly seen. The effect of\nthe modern text-book is to make the intelligent student feel that he is\nremarkably unintelligent; the text-book writer is so terribly cocksure.\n\nBut if the historic method must be rejected as too lengthy one may\nplead for its partial application. Let the text-book give the broad\noutlines, and let the student supplement these by reading, wherever\npossible, the standard memoirs written by the original discoverers.\nIn this way he will gain something much more valuable than a more\nthorough acquaintance with his subject; he will learn something of the\nmental gesture of the true man of science, something very different\nfrom the glittering efficiency of the text-book writer. Consider, for\ninstance, the following passage from Newton, writing on the theory of\nlight: He discusses a corpuscular theory, and continues:\n\n But they, that like not this, may suppose light any other corporeal\n emanation, or any impulse or motion of any other medium or \u00e6thereal\n spirit diffused through the main body of \u00e6ther, or what else they\n can imagine proper for this purpose. To avoid dispute, and make this\n hypothesis general, let every man here take his fancy; only whatever\n light be, I suppose it consists of rays differing from one another in\n contingent circumstances, as bigness, form, or vigour.\n\nThe subject here becomes alive in a way it never does in the text-book.\nIt is of the greatest importance that the student should see, not\nmerely the results, but the avenues of approach. He will gain more\nconfidence in his own powers and more interest in the subject.\n\nFor those people also who, without being students, take an interest in\nscience, the reading of original memoirs may be recommended. Much of\nthe science they learn in this way will be wrong, but they will see it\nas something thoroughly human and, it may be, as something thoroughly\nsympathetic. The text-book has an air of infallibility which is very\nrepellent, and it is difficult to avoid associating this with the\nscientific man. But it is merely a manifestation of the same tendency\nthat produces stereotyped restaurants. A reading of the old memoirs\nshows science as tentative, imaginative, courageous. They show that the\nman of science is a humanist.\n\n\n\n\n                         THE ENTENTE CORDIALE\n\n\nThose who are interested in current \u201cserious\u201d literature, and more\nparticularly that branch of it which deals in a speculative way\nwith those vague but impressive problems which have always haunted\nmen, the existence of God, the \u201cmeaning\u201d of the Universe and so on,\ncannot have failed to notice the unaccustomed prestige now enjoyed by\nscience. The supposed contributions of science to these discussions\nare now listened to with a gravity and politeness, with a kind of\nserious hush, which was formerly reserved for quotations from Plato\nand Aristotle. Compared with the crude materialists of Huxley\u2019s day,\nit is evident that the modern man of science has greatly improved his\nsocial standing; he now frequently talks to the best people, on equal\nterms, on such subjects as the Good and the Beautiful. The underbred,\npushing, clamorous self-assertion of the Victorian scientist is a rare\nnote in these improving conversations between philosophers and men\nof science. A man like Haeckel is dismissed as a mere vulgarian; no\none would trouble to refute him; his loud voice and hob-nailed boots\nare sufficient condemnation. Even Huxley is felt to be a rather noisy\nperson; the modern expositor of the relations of Science and Religion\nor Science and Philosophy no longer borrows his technique from the Hyde\nPark orator; he has adopted rather the insinuating charm of the curate.\nThere are, of course, survivals on both sides; sweetness and light\nare not yet universal; the general atmosphere of mutual forbearance\nand respect is still occasionally marred by the harsh note of some\nexceptionally fanatic or insensitive partisan. One or two grave lapses\nof this kind may be detected amongst the mass of recent books devoted\nto cosmical questions. There are still one or two literary men and\nphilosophers who hint at those dreadful early days of science, before\nit went to Oxford, and there are still one or two provincial men of\nscience, _farouche_, suspicious, who attend a modern cultured\nsalon carrying their obsolete life-preserver in their pocket. But on\nthe whole good manners prevail everywhere. It is realised that there is\nno reason why anybody should feel awkward at meeting anybody else in a\nworld which is so indulgent of the difference between a man\u2019s private\nand public capacities.\n\nTo be on amiable terms with everybody is worth a sacrifice, and in\nour relief at escaping from the ferocious savagery of the Victorian\ncontroversialists we may well endure the minor discomforts of a\nreconciliation between science, philosophy and religion so effective\nas to render indistinguishable the separate persons of this trinity.\nThe particular advantage of this amalgamation that concerns us here\nis the fact that it has brought a new branch of literature into\nexistence. As is usual in an amalgamation, each member profits by the\ncustom brought by the others, until finally a composite article is\nevolved which is, as it were, simultaneously buff and blue. That is\nhow we get these very curious and interesting modern works on cosmical\nquestions--works which seem to result from a close collaboration\nbetween, say, a professor of physics, an archdeacon and a Bond Street\ncrystal-gazer. A very comprehensive _Weltanschauung_ is thereby\nafforded, and doubtless a truly \u201cbalanced\u201d mind must result from the\nperusal of such works, but we may doubt whether each component, as\nit were, is presented in its purity. The advantages of association\nare only obtained by a certain loss of individuality. We cannot speak\nfor the philosophy and religion of these works, but we are impelled\nto these reflections by detecting a certain quality which pervades\nthe scientific part of the expositions. It is, as we have admitted,\na good thing for science that it has been taken up in this way. It\nmoves in an atmosphere of culture; it finds itself being described in\nchapters headed with Greek quotations; it is complimented on its strong\nvein of poetry; its peculiarities are explained, inaccurately but\nsympathetically, in columns of literary causerie, and the unexpected\nbut gratifying discovery is made that it by no means lacks the bump of\nreverence and proper respect for constituted authority.\n\nYet, kindly as are the surrounding faces, and pleasant as is the\nconsciousness that one\u2019s clothes and accent excite no comment, there\nis, on the part of many scientific men, a persistent uneasy feeling\nthat one has gained this position on false pretences. It is these\nremarkable modern books to which we have referred which render the\nfeeling acute. At the same time, it is very difficult to state\nprecisely the elements of this feeling. We understand, however, that\nthere are young poets and novelists who experience very much the same\nemotion when one of the great \u201cofficial\u201d men of letters talks about\nliterature. It appears that such people often get everything subtly\nwrong, that their criticism never pierces to the real heart of the\nmatter, that they make literature at once more pompous and more tame\nthan it really is. These new cultured expositors of science affect\none very much like that. Their indisputable intelligence and their\nwide knowledge do not save them; they lack something--it may be a\nmere familiar way of talking--which marks the practitioner; we feel\nthey touch their subject with padded fingers. We attribute no occult\ninfluence to laboratories, but we think the expositor of science who\nis not also a creator is something like that curiously unconvincing\ncreature--the theoretical sailor who has never been to sea. For\nthat reason we are uneasy in the presence of these numerous modern\nexpositions. Such work of the kind as was done in the old days was done\nby real men of science in their spare time. They had the competence,\nif also something of the crudity, of the workman in the factory who\nexplains to you how his machine works. The modern writers are so much\nmore like those frock-coated \u201cattendants\u201d at Exhibitions. One is\noppressed with the same suavity, the same incredible readiness, the\nsame secret doubt whether he has ever handled a tool in his life....\n\nSuch being our estimate of our modern teachers, we may be permitted to\nbe sceptical concerning the complete satisfactoriness of their account\nof the present disposition and relations of science. When they vouch\nfor the complete respectability and harmlessness of science we wonder\nif they are not a little too kind. We have an absurd nervousness, as\nin the presence of a reformed burglar. He looks well-dressed enough\nand his hands are not impossibly horny; moreover, we are told that\nthe two very respectable gentlemen with him find him a most charming\ncompanion. We are prejudiced, we suppose; but to our thinking there\nis a coarseness about the jaw, an occasional hard glint in the eye,\nwhich would make us reluctant to accept him as, at any rate, a sleeping\ncompanion. We wonder if those two gentlemen, the one reverend and the\nother nearly so, ever feel a little apprehensive during the night?\n\n\n\n\n                            POPULAR SCIENCE\n\n\nThe Victorian Age was unquestionably the great age of physical science.\nIt was not only the number and quality of the scientific men whose\nworking lives were covered by this period that were responsible for\nthis--although no period in history makes a braver show--but it was\ndue also to the fact that the scientific discoveries of that age were\noften of the kind that rouses a vast amount of public attention. The\nattention of a cultured minority was no new thing in the history\nof science. Newton\u2019s discoveries, largely through the influence of\nhis indefatigable populariser Voltaire, speedily became, in a more\nor less adequate form, the common property of the cultured part of\nEurope. But from the time of Newton to that of Davy there was no such\ngeneral attention paid to science; England and the Continent largely\nlost touch, even technical students working in comparative isolation,\nso that the great French advances in Newtonian philosophy were not\nappreciated for several years in England, and the cultured public in\nEngland itself no longer considered the intelligent observation of\nscientific progress to be one of its chief duties. It never did regain\nthis outlook; science, becoming increasingly technical, became more and\nmore completely the affair of a small and specialised class, until, by\nthe middle of the nineteenth century, it was the most dissociated of\nintellectual activities. The great recrudescence of general interest\nin science was brought about by the discovery that this dissociation\nwas merely a consequence of lack of attention, and that, in fact,\nscientific discovery was not unconnected with the major interests of\nmankind.\n\nThe publication in 1859 of Darwin\u2019s _Origin of Species_ persuaded\nthe men of that time, rightly or wrongly, that science and religion\nwere very intimately connected, and science, at one blow, obtained\na degree of public attention without precedent in its history. The\ninterest thus evoked was not always very intelligent, but it was\nintense and widely diffused; it extended to other branches of science,\ninfluenced the educational system of the country and gave rise to an\nenormous extension of \u201cpopular\u201d science lectures and articles. This\npopular interest was of a different kind from the leisurely interest\npreviously shown by the cultured classes. The latter was, indeed, much\nmore genuinely an interest in science for its own sake; the former\nhad a different emotional basis and was merely the diversion of an\ninterest in religious or social questions. There is a controversial\nair about nearly all the popular scientific writings of that time; the\nscientific man, like his audience, was fully aware that he was talking\nabout a good deal more than the ostensible subject of discussion.\nScience, the creature of the least popular of man\u2019s activities,\npatient and unprejudiced ratiocination, became associated with violent\nemotions. With Biology and Geology this association was inevitable and\nimmediate; their subject-matter happened to be that of the first few\nchapters of Genesis. But the more exact sciences, when public attention\nturned their way, could offer no such excitements. They seem to have\ncompromised by specialising on \u201cmarvels.\u201d The \u201cMarvels of Science\u201d\nbecame a familiar heading, and the unsophisticated public were stunned\nby figures: the distances of the stars, the number of molecules in\na cubic centimetre of water, the weight, in tons, of the earth, the\nincredible minuteness of light-waves, and so on, the whole object of\nsuch discourses being, as Maxwell unkindly put it, to prevent the\naudience realising that intellectual exhaustion had set in until the\nhour had elapsed.\n\nWe readily admit that popular science of a very different kind was\nalso provided. Faraday, Kelvin, Huxley, Tyndall, Maxwell himself, did\ntheir best to make the lay public acquainted with scientific methods\nas well as results, to present their results as part of a coherent\ntheory instead of as items in catalogue of marvels. But it is the\nmarvel-mongers who have proved most tenacious of life, so that\n\u201cpopular\u201d science has now become a term of contempt, and any statement\nwhatever, provided it has the right marvellous flavour, may be printed\nin our newspapers as scientific information. In America such marvellous\nstatements, not only inaccurate but meaningless, occupy pages of the\nSunday supplements, so that that meritorious organ, _The Scientific\nAmerican_, has to announce, in self-defence, that it publishes, not\n\u201cpopular\u201d science, but merely non-technical science. In our own country\nthat sober periodical _Nature_ used to print extracts from the\nmore marvellous scientific items provided by the daily press, thus\nfurnishing a little light relief from its own austere pages. The fact\nthat this quackery exists is not unimportant. If it does no more, it\noften leads to a waste of time, for there has been more than one worthy\ngentleman who has imagined himself to be attacking the pernicious\ndoctrines of science, when, as his argument makes clear, it is this\nkind of quackery he has in mind. The cure for this kind of thing would\nseem to be the development of a conscience in newspaper editors, unless\nwe prefer to wait patiently until a tincture of science forms part of\nthe education of an English adult.\n\nBut, turning to the popular but accurate scientific article, we may ask\nwhat purpose it serves. Should its object be to supply the deficiencies\nof a defective general education, to provide an easy introduction\nto science? Doubtless such articles or lectures have served such a\npurpose; Faraday himself, as we know, was won over to science by the\nblandishments of Mrs. Somerville, and there is more than one case where\nthe current of a man\u2019s life has been definitely changed by a lantern\nlecture. It is, nevertheless, a mistake to suppose that the attentive\nperusal of a number of popular science articles is equivalent to a\nscientific education, a mistake which is unfortunately very common. The\nfact is that the scientific treatise and the popular science article,\nso far from being rivals, serve entirely different ends, and may be\nread with profit by the same man. Broadly speaking, the function of\nthe popular science article is to present science in its humanistic\naspect. It should, while dealing with as definite a scientific problem\nas the author chooses, hint at the relations between this problem and\nthe other interests of mankind. Very often these relations are implicit\nin the subject; such subjects are, in fact, usually chosen, and for\nthat reason. But there is another type of article which has for its\nobject the exposition of relations which are not obvious, and this\nexposition may be the result of a genuine and valuable intellectual\neffort on the part of the writer. Such articles are really essays in\ncriticism and are not essentially different from the best type of\nliterary criticism. Some of the best articles of this kind--some of\nthose by W. K. Clifford, for example--are as truly \u201cresearch\u201d work as\nis the technical paper. A third type of article may, either by way\nof history or by way of logic, show the position occupied by a given\ntheory or fact in a scheme of knowledge. This type is usually of more\ninterest to the scientific student than to the general reader, since a\ngeneral acquaintance with the whole subject is presupposed, and in this\nconnection it is interesting to note that a powerful plea has recently\nbeen made for the more effective endowment of the teaching of the\nhistory of science.\n\nIf a popular science article serves none of these three purposes,\nit must inevitably be nothing but the description of a \u201cmarvel.\u201d In\ncompetent hands this may be agreeable enough; the appetite for marvels\nis vigorous and universal, and its indulgence cannot be condemned as a\nvice. To look at a marvel for the pleasure of gaping is not, however,\na very intelligent occupation, and, to judge from the number and kind\nof phenomena unhesitatingly ascribed to \u201cthe electricity in the air,\u201d\nmerely increases credulity. Regarded as a marvel, wireless telegraphy\nis, of course, merely a miracle, a fact extensively exploited by\nspiritualists. The human tendency to seize on the merely marvellous\nshould, in fact, be carefully allowed for by the writer of popular\nscience articles; he should, if anything, be even more reserved and\npedantically precise than when addressing a scientific audience; an\nincautiously flamboyant remark is very likely to be seized upon to\nsupport some preposterous philosophy or religion. Usually, however,\nthe popular science writer yields to the temptation, to _\u00e9pater_\nhis audience, to make himself more readable, as readability is now\nunderstood, and so he may, while speaking the truth, have all the\neffect of telling a lie.\n\nThus the division between the genuine and the quack science article is\nnot, in practice, clearly defined. The difference between the writers\nis definite enough; but it is writer and public together which make the\npopular science article. Lack of education is just as great a hindrance\nto perception as is lack of sensitiveness. The poet may be subtly and\ncompletely misunderstood because his audience lacks sensitiveness,\nand, to compare small things with great, the conscientious retailer of\nscientific information may be in a like case for a different reason.\nSo that if it is true that the best type of poetry is that written\nby the poet \u201cfor himself,\u201d it is perhaps true that the best type of\npopular science article is written for a similar reason--because the\nwriter is genuinely interested in working out certain speculations or\ntreating certain facts in a certain way. Some of the very best popular\narticles--those by Helmholtz, for example--are of this kind, and have\nachieved a relative immortality, although, like the poetry which is\nread chiefly by poets, they are probably read chiefly by scientific\nmen.\n\n\n\n\n                           PATIENT PLODDERS\n\n\nIt is a melancholy fact that the estimable qualities of patience\nand industry do not, by themselves, enable their possessor to\nattain eminence in the arts. There is very good reason to suppose\nthat character, particularly a certain simple type of integrity and\nsincerity, is necessary to great artistic achievement, but it is\ncertain that such gifts are not sufficient; they must be allied with\nvery unusual mental qualities. In the sciences, however, we often find\nwork of very great importance being performed by men of quite average\nintelligence, but of exceptional tenacity. A pure heart seems to be all\nthat is necessary. This is not true, of course, of the mathematical\nsciences--mathematicians, like musicians, are \u201cborn\u201d--but it is very\nobviously true of what are called the \u201cobservational\u201d sciences. A\nhistory of Astronomy, in particular, is interesting from this point\nof view. The fact that the whole of our knowledge of the heavens\ncomes through the sense of sight, and that we cannot experiment, in\nthe ordinary way, upon the heavenly bodies, means that the patient\nobserver, by merely accumulating observations, is performing an\nabsolutely essential function. There is no other subject which yields\nsuch rich rewards to mere patience. There is no other subject which\nhas so long a record of valuable discoveries achieved by purely\naverage ability. It is interesting to notice how often a telescope\nand a capacity for sitting still have made their owners immortal. In\nthe region of stellar astronomy the minuteness of the phenomena which\nmay be observed has narrowed possible competitors to those possessing\nlarge instruments, and that usually means public institutions and\nprofessional astronomers. But the history of our knowledge of the\nnearer heavenly bodies, the sun, the planets and the moon, owes much to\nthe industrious amateur. No history of planetary and lunar discoveries\nwould be complete without mention of Schr\u00f6ter, the \u201cOberamtmann\u201d\nof Lilienthal, who watched the moon and planets incessantly for\nthirty-four years with a patience only equalled by his enthusiasm. He\ndied of a \u201cbroken heart,\u201d the result of a French atrocity, for after\nfiring, on the night of April 20, 1813, the Vale of Lilies and thereby\ndestroying, amongst other things, the whole of Schr\u00f6ter\u2019s books and\nwritings, the French army under Vandamme broke into and pillaged his\nobservatory. The old man, then sixty-eight years of age, had not\nthe means to repair the catastrophe, and, deprived of his one great\ninterest, he died three years later, leaving, amongst his published\nworks, some of the most long-winded and entertaining observations in\nthe history of astronomy.\n\nBut although Schr\u00f6ter is undoubtedly the most amusing of all amateur\nobservers, he has had his prototypes in all countries. Francis Baily,\nthe \u201cphilosopher of Newbury,\u201d is a good example of our more sober\nEnglish product. We may have doubts as to what sort of chief magistrate\nold Schr\u00f6ter was, but we know that Baily took his profession of\nstockbroking with the utmost seriousness. He did not allow astronomy\nto interfere with business. Beginning in 1799, he remained on the\nStock Exchange in London for twenty-four years, devoting his leisure\nlargely to solar observations, particularly those connected with\neclipses. It is with two of these phenomena, the first annular, a\nring of the sun being visible round the moon, and the second total,\nthat Baily\u2019s name is particularly associated, in each case for the\nvivid and accurate account he gave of what he witnessed. The first\nphenomenon, a ring of bright points extending round that part of the\nmoon\u2019s circumference which has just entered on the solar disc, is\nmerely a consequence of the lunar edge being serrated with mountains.\nThese \u201cBaily\u2019s beads,\u201d as they were called, were successful, however,\nin stimulating interest in the physical aspect of eclipses, with the\nresult that the next total eclipse, that of 1842, was looked for with\nan unprecedented degree of enthusiasm. Astronomers like Airy, Otto\nStruve and Arago travelled to Central or Southern Europe to observe\nthe eclipse, and the indefatigable Mr. Baily accompanied them. He\nfitted up his telescope in an upper room of the University of Pavia.\nThe result was magnificent. At the instant of totality the sun appeared\ndecorated with a glorious _aur\u00e9ole_, the famous corona. It was\nnot, of course, an unknown phenomenon, but it had never before excited\nso much attention. Mr. Baily, in particular, was moved to write a most\neloquent description of this flaming object. He calls it splendid and\nastonishing, but continues: \u201cYet I must confess that there was at the\nsame time something in its singular and wonderful appearance that was\nappalling; and I can readily imagine that uncivilised nations may\noccasionally have become alarmed and terrified at such an object....\u201d\nBesides being a specialist on eclipses, Baily was an untiring editor\nof star-catalogues, and he also made no fewer than 2,153 laborious\nexperiments, on Cavendish\u2019s method, to determine the density of the\nearth. He was indeed a zealous worker in what Sir John Herschel called\nthe \u201carch\u00e6ology of astronomy.\u201d He was noted for his unvarying health,\nundisturbed equanimity and methodical habits.\n\nAnother testimonial to the importance of such qualities in astronomical\ndiscovery is furnished by the career of Heinrich Schwabe, of Dessau.\nIn the hope of escaping his fate as an apothecary he bought a small\ntelescope in 1826, and began to observe the sun, being advised to do\nso by a friend. He continued to observe the sun daily (weather and\nhealth permitting) for forty-three years. Every day he counted the\nnumber of spots visible on the surface of the sun. It was a simple\noccupation, but it led to important consequences. His immense record of\nsun-spot statistics showed that the increase and decrease in the number\nof sun-spots did not occur in a random manner, but fell into periods,\nmaxima alternating with minima, a complete period occupying about ten\nyears. This figure has been modified since, but the fact of sun-spot\nperiodicity is established and is at the present time one of the most\nsuggestive and probably far-reaching of solar phenomena. Schwabe\ndisplayed no striking quality of mind or character beyond an almost\nincomprehensible patience. He was buoyed up in his spot-counting,\nhowever, by the hope of discovering a planet between Mercury and the\nsun, and in order to distinguish between the tiny disc of the planet\ncrossing the face of the sun and a sun-spot, he found it necessary, in\nvirtue of his instrumental equipment, to count the spots. When he found\nthat, as a consequence of this pastime, he was world-famous, he likened\nhimself to Saul who, going forth to seek his father\u2019s asses, discovered\na kingdom. His magnificent serenity of body and mind enabled him to\nattain the age of eighty-six.\n\nPart of his mantle fell on Richard Carrington (born 1826), who built\nan observatory at Redhill with the intention of devoting himself to\na study of sun-spots throughout a complete cycle. He failed to finish\nthe cycle completely, as the death of his father made it necessary\nfor him to divert his energies to controlling a brewery. He achieved\nresults of great importance, however. His observations were concerned\nwith the positions and movements of the spots, and from a series of\n5,290 such observations he was enabled, amongst other things, to clear\nup the uncertainties attending the period of rotation of the sun.\nGalileo, apparently not appreciating the importance of the matter, had\nsaid that the sun rotated in \u201cabout a lunar month,\u201d and a number of\nother observers gave figures varying from 27 to 25 days. Carrington\nilluminated this darkness by remarking that there is no single period\nof rotation for the sun. The polar regions rotate more slowly than\nthose in the neighbourhood of the equator; the equator rotates in a\nlittle less than twenty-five days, while in latitude 50\u00b0 the period is\ntwenty-seven and a-half days. Thus the mystery was cleared up and a\nfresh direction given to solar investigation.\n\nIt is difficult to say whether Astronomy still offers such rewards\nto industry. It is probable, however, that it still yields more to\ncharacter, as distinguished from ability, than any other science, and\nincomparably more, alas! than the arts.\n\n\n\n\n                        THE AMATEUR ASTRONOMER\n\n\nThe indifference of the Englishman is, considered pragmatically,\nthe same thing as tolerance. It bestows freedom and leaves every\nman, within fairly wide limits, at ease to pursue his bent. There is\ndoubtless a relation between this English characteristic and the fact\nthat England, above any other country, is the home of the amateur.\nIn England, compared with the Continent, there are comparatively few\nmen whose dominant activity is their exclusive activity. There are\nmany fair specialists, but there are few specialised men. There are\ncountries such as France, where the _Gemeinplatz_ of intelligent\nmen is probably larger and more richly furnished than it is in England,\nbut it is comparatively difficult to meet the type of man who is an\neminent lawyer, an authority on Eastern poisons, and a really good\njudge of horseflesh. Such manifestations of a national quality may\nsometimes appear almost grotesque, but we believe that the quality\nof which they are partial manifestations is the most splendid and\nindividual characteristic of the English intellect. It is not a\nquality which produces many thrice-armed specialists, but it is a\nquality which produces a great number of amateurs. The English amateur\nin the arts belongs to a family well worth consideration, but our more\nimmediate concern is with the amateur in science.\n\nThere was a time when the scientific amateur abounded in England.\nIn the time of Huxley and his contemporaries, as we see from their\nletters, amateur zoologists, botanists, and, more rarely, amateur\nmathematicians and physicists, were scattered all over England and\noccasionally had something of interest, or even of value, to report. In\nthe days when R. A. Proctor edited _Knowledge_ the country seemed\nto be full of reverend gentlemen who owned small observatories and\nhome-made telescopes. This large and interesting family seems now to\nbe making towards extinction. The increasing complexity of the various\nsciences, to say nothing of the variety and cost of modern apparatus,\nhas made anything but trifling discoveries difficult to the verge of\nimpossibility for an amateur equipment. Perhaps the amateur who has\nsuffered least from these changes is the amateur astronomer. There is\ngood reason for supposing that his numbers have increased. In this\nbranch of science the English amateur has always been particularly\nstrong, and this cannot be attributed to the official encouragement\naccorded astronomy in this country. There are many more amateur\nastronomers in England than in France, although astronomy counts for\nmore in France than in England, and although, since Newton, France has\nplayed the leading r\u00f4le in the history of astronomy.\n\nThe popularity of amateur astronomy in England certainly needs\nexplanation, for it is a pursuit attended by many disappointments in\nso capricious a climate, and Englishmen have few opportunities of\nseeing a really impressive display of stars. Perhaps the Englishman\nis sufficient of a Northerner to be profoundly attracted by the\nsheer vastness and the mystery of stellar phenomena. Then the actual\ntelescope and its accessories probably appeal to the English love of\nmechanism. There are few instruments more delightful in themselves\nthan a properly mounted telescope of moderate aperture. Its adjustment\naffords a pleasure as refined as that given by operating a small hand\nprinting-press, and superior to that of mending a bicycle. Every\ntelescope has its distinctive \u201cperformance,\u201d and one can grow as\nenthusiastically partisan about makes of telescopes as one can about\nmakes of motor-cars or pianos. Whether or not these be the reasons\nit is certain that astronomy is the science which most attracts the\nEnglish amateur. The existence of the British Astronomical Association,\nan amateur society with some hundreds of members, is sufficient proof\nof this. It would perhaps be difficult to justify by the results the\namount of time and money spent in amateur stargazing, if one estimated\nresults from the severe standpoint of the professional astronomer. But\nif one adopts a broader outlook and estimates the results in rather\nmore human terms, then there is probably no pursuit which affords more\ninnocent pleasure and provides, in itself, a more liberal education.\nIt is said that the vast photographic telescopes of the present day\nhave rendered the small instrument valueless. Even Mr. Hinks, in his\nexcellent volume _Astronomy_ in the Home University Library, says\nthat the would-be amateur would do well to hesitate before buying a\nsmall telescope, and that a measuring machine, to measure photographs\ntaken by big instruments, would be a far better investment. This is the\nseverely professional point of view; it is to mistake the psychology\nof the amateur observer. The amateur likes to think that he might some\nday make a discovery, but that is only by the way. His real joy is in\ndoing precisely what the professional cannot do, and that is to enjoy\nthe _spectacle_ of the heavens. The ordinary run of work in a\nbig observatory is not much more exciting than work in an ordinary\nbusiness office. To sit up half the night measuring photographs would\nconceivably add to scientific knowledge, and there are doubtless stern\nmen who are willing to do it. These, like computers, are the martyrs\nof science. The average amateur will continue to prefer his present\npleasant, if ineffectual, method of adding to scientific knowledge. It\nis to be feared that, as one result of the war, this amiable occupation\nwill decline. A little before the war the amateur could purchase a\nmodest but thoroughly good, instrument at a reasonable price. The same\ninstrument to-day would cost at least twice as much, and there would\nprobably be an interval of several months between the order and the\ndelivery. One large firm of optical instrument makers announces that it\nis not now making astronomical telescopes at all. At the present time,\nwhen astronomy is entering on perhaps the most pregnant phase in its\nhistory, and when men are more than ever attracted by anything which\npromises escape from the fret of daily life, this lessening of the\nopportunities for acquaintance with the most serene of the sciences is\na minor calamity. The decline in amateur astronomy will probably have\nno appreciable reaction on the progress of science, but it will lead to\na real, if small decrease in the intellectual pleasures and spiritual\nwealth of the nation.\n\n\n\n\n                          SCIENTIFIC CITIZENS\n\n\nIt would be an entertaining pursuit to compile the characteristics of\nthe man of science--usually a Professor--as he is depicted in popular\nfiction, on the stage, and in the writings of exasperated conservatives\nin religious and social matters. It would be found that these\ncharacteristics combine to give one dominant and entirely untruthful\nimpression: the man of science is represented as being scientific on\nall occasions. We may ignore the inferior school that portrays him as\nbeing constantly obsessed by his work--like Dickens\u2019 learned gentleman\nwho mistook the nature of a dark lantern--and confine our attention\nto the Professor who is represented, not as imbecile, but merely as\nhomogeneous. This imaginary individual is never to be diverted from his\npassion for precise statement and strictly logical inference. Whether\nthe subject be politics or the state of the weather, he brings the same\npreliminary scepticism, the same demands for verification, that he\ncarries into his scientific researches. As we have said, this picture\nis untruthful; we think, however, that this is an unfortunate fact,\nand that it is highly desirable that men of science should begin to\nlive up to the story-teller\u2019s conception of them.\n\nWe think that, at the present stage of man\u2019s evolution, science is the\none activity in which he displays himself as a truly rational creature.\nThe reason is, of course, that success is granted on no other terms; in\neverything else, philosophy, theology, politics, reason is usually the\nhandmaid to prejudice. The penalties that visit error in these fields\nare not so swift nor so unambiguous. The ideal of truthfulness is\nprobably more rigorous with the scientist, _qua_ scientist, than\nwith any other kind of man. But it would appear that this dispassionate\nrationality is hardly won and precariously maintained. Outside his\nlaboratory the scientist may, and usually does, show himself as\nsimple, as kindly, as credulous, as irrational as any other man. On\nBolshevism, Disestablishment, the Morality of the Public Parks, his\nopinions will be indistinguishable from those of any other comfortable\nmember of the lower middle class; that is to say that opinions on all\nsuch matters are \u201cdistributed\u201d amongst scientific men according to\nthe same statistical rules as they are distributed amongst ordinary\ncitizens. Outside their views on purely scientific matters there is\nnothing _characteristic_ of men of science. The Royal Society may\nconceivably issue a unanimous report on some scientific matter; it\nwould issue a unanimous report on nothing else whatever. Now on the\nassumption that men of science are truly rational beings this is a very\nstrange state of affairs. Dispassionate attempts to sift evidence,\nto argue correctly and to base judgments solely on the outcome of\nthese processes could hardly result in so remarkable a multiplicity\nof opinions. We must assume that, for scientific men as a body, their\n\u201cscientific\u201d methods of thought function only within very narrow\nlimits. As a distinct community they are far less coherent than, for\ninstance, the community of artists--musicians, poets, painters. The\ncommunity of artists, with the exception of a few prosperous members,\nexhibits a really remarkable homogeneity in matters outside art.\nDoubtless this homogeneity is based on feeling--unless we are prepared\nto admit that artists, as a whole, are more rational than are men of\nscience--and it is probable that the scientist\u2019s difference from his\nfellow-citizens is more an intellectual than an emotional difference.\nBut it is surprising that greater emotional sensitiveness should prove\nso much more pervasive and dominating a peculiarity than greater\nintellectual subtlety.\n\nIt is time that men of science assumed a greater position in the\ngeneral community. If a scientific training has a tithe of the\n_general_ educational value that is claimed for it, it is time\nwe had some evidence of that fact. Men of science must adopt a higher\nideal of personal honour. At present the man who will conduct a\nlaboratory experiment with meticulous precision and describe his\nresults in an agony of honesty will be content to be a prejudiced\nobserver and a slovenly and inaccurate thinker in all other matters.\nThis is the chief reason, we are convinced, why men of science count\nfor so little in public affairs. If the Royal Society elected its own\nmember of Parliament, who would bother about the political opinion so\nexpressed? What greater weight would it have than the political opinion\nof an equal number of moderately prosperous ordinary citizens? Does not\nthe scientific man waggle his head just as solemnly over his morning\nnewspaper as does any unsophisticated voter?\n\nWe plead for the development of a class consciousness on the part\nof the man of science. We want scientific men to regard their ideal\nof evidence, their conception of proof, their really admirable\nscientific detachment, not merely as rules making for success in their\nparticular game, but as principles applicable to every subject that\nconcerns a citizen. Why should a man of science be merely a Liberal\nor a Conservative in politics? The alternative belongs to the stage\nof mental development that explained the material universe by saying\nthat its moving principle was fire, or, alternatively, water. We\nexpect a more sober contribution to political questions from, say, a\ndistinguished physicist, than the panacea \u201cShoot the miners.\u201d All the\nquestions on which scientific men now adopt \u201csides\u201d as uncritically\nas any simple dupe of the daily press are amenable to scientific\ninvestigation. They can reach a solution only by the application of\nscientific methods, and the modern world badly needs deliverance from\nthe method of charms and incantations by which these questions are at\npresent treated. How long are these vital matters to remain in the\nhands of the witch-doctors? With scientific men content to sit in the\ncircle and help beat the tom-toms what hope is there of real advance\nfounded on real knowledge? The artists cannot help us; they are useful\nindicators of the value of the product, as it were; they look pleased\nor they look disgusted, and that is very helpful in showing us where\nwe are. It is the scientific man who must show us how to go somewhere\nelse. So we plead for the conscious formation of a community of men\nof science, for scientific men who are at least as pervasively and\nconstantly scientific as a good Jesuit is Roman Catholic.\n\n\n\n\n                      THE SCEPTIC AND THE SPIRITS\n\n\nIt is only youth that has the energy to be bothered with everything.\nThere comes a time when one\u2019s mind is \u201cmade up\u201d on all sorts of things\nthat were once matters of inquiry; we have profited by experience; we\nknow that some things are not worth investigating. It is one of the\nmarvellous laws of growth that this increase in wisdom should accompany\nphysical decay. As our teeth and hair start to fall out our judgment\ngrows riper. The law of growth is not really as simple as this, for\nthere are many silly old men and there are one or two wise youths. The\nrich, mellow, balanced period is never reached by some people: Solomon,\non the other hand, was noted for his wisdom while still a young man.\nThere is, it must be admitted, something mechanical about old men\u2019s\nwisdom. Truth is one, of course, so that we should expect a certain\nunanimity. The answers of the old can usually be predicted. Wisdom can\nbe simulated; all that one lacks is the conviction, the spirit that\nanimates the letter.\n\nDeep conviction is a very impressive quality, especially to youth,\nwhich secretly doubts everything. The man of strong convictions is a\ncause of optimism in others, for life would appear a sad cheat if the\npayment for sixty years of it did not include one certainty. Youth\u2019s\ncertainties make as much noise, but everybody detects the bluff. A\nfearful man shouts to hearten himself, as all the world knows. Between\nthe certainties of youth and age there is scepticism, a _fine\nfleur_ of brief life, an exquisite tempering of the soul, neither\ntoo soft nor too hard, an infinite flexibility. It is a state of\nintense activity; life lived at this pace cannot long endure; the tired\nspirit relaxes and one finds rest either in credulity or in dogmatism,\naccident determining which attitude affords the soundest slumber. It is\nnot always easy to detect the true sceptic; that honourable title has\noften been wrongly bestowed--Voltaire, for instance, was a dogmatist.\nSceptics exist in all ages, but they are more clearly revealed at those\nperiods that see the birth of some new inquiry. It is essential to\ntheir indubitable manifestation that the inquiry should be attended by\nthe passionate interest of a large number of people. At the present\nday a very good test inquiry is spiritualism. It is a very much better\ntest than Free Trade and Tariff Reform, for, owing to its comparative\nremoteness, the true sceptic of that alternative might live and die in\nobscurity. But spiritualism is a subject on which no one is genuinely\nindifferent and towards which hardly anyone is genuinely sceptical.\nDispassionate inquiry on this, as on all matters where human interests\nare strongly engaged, is usually a pretence. We need not suppose that\nthe great ones of the Psychical Research Society are less credulous\nthan the majority of believers or less intolerant than their louder\nopponents; it is merely that, their traditions being scientific, they\nhave better manners.\n\nPsychical literature, as a whole, is as wearisome as theological\nliterature, as incredible but less amusing than the lives of the\nsaints. We lack the quality, be it faith, hope or charity, which would\nenable us to share these strange excitements. The \u201cexposers,\u201d on the\nother hand, are too sturdy in their common sense. We hear the mallet\nfall, but we are not always sure that the eggshell is broken. It is a\nsituation for the sceptic. In the late Lord Rayleigh\u2019s presidential\naddress to the Psychical Research Society we find that the sceptic has\nat last appeared. It is merely a record of his own experiences, very\nplain, very simple, and, like the experiences themselves, singularly\nelusive. Many years ago, in a friend\u2019s rooms at Cambridge, he witnessed\nan exhibition of the powers of Madame Card, the hypnotist. When she had\ncompleted her passes over the closed eyes of those present she asked\nthem to open their eyes. \u201cI and some others experienced no difficulty;\nand naturally she discarded us and developed her powers over\nthose--about half the sitters--who had failed or found difficulty.\u201d\nFrom hypnotism he passed to spiritualism, his interest aroused by Sir\nWilliam Crookes\u2019 experiences. He induced the medium, Mrs. Jencken, and\nher husband, to visit his country house as guests. He describes the\nresults as disappointing:\n\n I do not mean that very little happened, or that what did happen was\n always easy to explain. But most of the happenings were trifling,\n and not such as to preclude the idea of trickery. One\u2019s coat-tails\n would be pulled, paper cutters, etc., would fly about, knocks would\n shake our chairs, and so on. I do not count messages, usually of no\n interest, which were spelt out alphabetically by raps that seemed to\n come from the neighbourhood of the medium\u2019s feet. Perhaps what struck\n us most were lights which on one or two occasions floated about. They\n were real enough, but rather difficult to locate, though I do not\n think they were ever more than six or eight feet away from us.\n\nAnother incident was the gradual tipping over of a rather heavy table\nat which they had been sitting. \u201cMrs. Jencken, as well as ourselves\n[i.e. Lady Rayleigh and himself. The husband was not admitted to\nthese s\u00e9ances] was apparently standing quite clear of it.\u201d He found\nit very difficult to reproduce the phenomenon himself, using both\nhands. He endeavoured to \u201cimprove\u201d the conditions for some experiments.\nAfter being shown some writing, \u201csupposed to be spirit writing,\u201d he\narranged paper and pencils inside a large glass retort, which he then\nhermetically sealed. Nothing then appeared on the paper at these\ns\u00e9ances. \u201cPossibly this was too much to expect. I may add that on\nrecently inspecting the retort I find that the opportunity has remained\nneglected for forty-five years.\u201d\n\nAnd so he has left the matter. The experiences were certainly strange,\nyes, but in his judgment, not strange enough. On the other hand,\nhe is reluctant to believe they were due to fraud, and he is quite\nconvinced that he was not a victim of hallucinations. If Mrs. Jencken\nwere a clever fraud \u201cher acting was as wonderful as her conjuring.\u201d\nShe practically never made an intelligent remark on any occasion.\n\u201cHer interests seemed to be limited to the spirits and her baby.\u201d In\ninvestigating this subject he finds that the attitude of convinced\nbelievers makes a difficulty. They \u201ctake no pains over the details\nof evidence on which everything depends.\u201d Others attribute all these\nphenomena to the devil and will have nothing to do with them. \u201cI have\nsometimes pointed out that if during the long hours of s\u00e9ances we\ncould keep the devil occupied in so comparatively harmless a manner we\ndeserved well of our neighbours.\u201d\n\nThe general disbelief in scientific circles that meteorites really\ncame from outer space occurs to him. This disbelief was due, he points\nout, to the impossibility of producing the phenomena at pleasure in\nour laboratories. Nevertheless, the disbelief was unjustified. Spirit\nmanifestations may be, he thinks, just such sporadic phenomena. The\nsituation is made worse by the fact that there has undoubtedly been a\ngreat deal of fraud in connection with spiritualist phenomena. Eusapia\nPalladino, for instance, undoubtedly practised deception, \u201cbut that is\nnot the last word.\u201d Telepathy puzzles him. If there is such a means of\ncommunication, why should Nature have adopted the laborious method of\nbuilding up our very complicated senses? An antelope in danger from\na lion, for instance, depends on his senses and speed. \u201cBut would it\nnot be simpler if he could know something telepathically of the lion\u2019s\nintention, even if it were no more than vague apprehension warning\nhim to be on the move?\u201d He advises the society to continue their\ninvestigations, and mentions that it is quality, not quantity, that\nis so desirable in evidence. He concludes by saying that he fears his\nattitude, or want of attitude, will be disappointing to some members of\nthe society. He suggests that after forty-five years of hesitation \u201cit\nmay require some personal experience of a compelling kind to break the\ncrust.\u201d He apologises for this. \u201cSome of those who know me best think\nthat I ought to be more convinced than I am. Perhaps they are right.\u201d\n\nThere he leaves us. We do not believe more or disbelieve less, yet we\nare completely satisfied. His massive sincerity, his obvious competence\nand, above all, that impression of exquisite balance, have charmed us.\nSo far as present evidence is concerned we feel that while he has said\nnothing he has also said the last word. That is the function of the\nsceptic.\n\n\n\n\n                          THE SCIENTIFIC MIND\n\n\nIt is quite common, in reading and in conversation, to find references\nto the \u201cscientific mind,\u201d but it is difficult to ascertain precisely\nhow this mental structure is supposed to differ from other sorts\nof mind. The difficulty of defining an object does not, perhaps,\naffect the probability of the existence of the object; although it is\ndifficult for some people to refrain from concluding that because a man\ncannot define what he means he does not mean anything. We must suppose\nthat there is some particular kind of mind called the scientific mind,\nin spite of the fact that the numerous references to it tell us little\nabout it except that it is somewhat extensively disliked. So far as can\nbe judged from a superficial comparison of different references, the\n\u201cscientific mind\u201d is characterised by an inordinate appetite for facts\nand an absence of generosity in drawing conclusions from facts. In\nordinary times this absence of generosity is dismissed by most people\nas quibbling, while in time of war it becomes unpatriotic. During the\nwar every Englishman was supposed to believe a great number of things\non very slender evidence or even on no evidence. It was considered that\na right patriotic feeling not only could, but should, supply the place\nof evidence, and lead to correct conclusions. The majority of people\nin every class of the community found themselves able to adopt this\nmethod of thought without discomfort, and it became evident that the\nscientific mind is as rare amongst scientific men as amongst any other\nmen, while those who could not give this supreme proof of patriotism\nwere found pretty evenly distributed amongst the different classes. As\na type of mind, therefore, it is not peculiar to scientific men nor do\nthey all possess it. It cannot be regarded as a distinguishing mark of\nthis class. But while a just, cautious temperament need not belong to\nthe man of science as a human being, it might be thought that, as a\nmental habit, it is necessary to his work. There is much truth in this,\nalthough it is not wholly true. Alternative explanations are not always\nexplored by scientists, and if, as sometimes happens, the alternative\nexplanations are wrong, the scientific man may have reached a correct\nresult although he worked in a partisan spirit.\n\nBut while the characteristics of what is popularly known as the\nscientific mind are not peculiar to scientific men, it is true that,\nin their actual scientific work, these characteristics have a greater\nsurvival value than they possess in almost any other kind of work.\nThe extent to which mental habits may be local, confined to some only\nof a man\u2019s mental activities, has been made apparent by the war. The\nmajority of men\u2019s minds are split up into water-tight compartments\nin a way truly astonishing, and the various eloquent addresses on\nthe moral value of scientific studies now make melancholy reading.\nWe must assume of scientific men, as of any other class, that such\nqualities of fairness and deliberation as they exhibit in their work\nare imposed upon them as conditions of success, and are not, in\ngeneral, the natural manifestations of an exceptionally delicate moral\nsensibility. If we adopt William James\u2019 classification of human beings\ninto tender-minded and tough-minded the dividing line runs through the\nscientific camp as through any other. We see this most clearly in the\ncase of mathematicians, for idealist or empiricist assumptions seem to\nbe equally reconcilable with the results. Such sciences as physics and\nchemistry seem, at first glance, to be given over to the tough-minded;\nthe official language, as it were, is the language of the tough-minded,\nbut directly controversy arises on a point having philosophical\nbearings we see the dichotomy establish itself.\n\nNevertheless, it remains true that while scientific men, as human\nbeings, are of all sorts, they do exhibit, in their own work, a degree\nof mental honesty which is unusual. It is easy to see that this virtue,\nat any rate, has a strictly utilitarian basis. A scientific man\nis honest because he cannot succeed on any other terms in the long\nrun. The experimental verification always looms ahead. He cannot,\nlike the mystic who maintains his opinion in face of the world,\ntake refuge in the deeper insight. His results are communicable and\nverifiable or they are not science. Philosophies may be constructed\nwhich no man can verify and no man can refute. Their authors may, with\ncomplete assurance, remain satisfied of their truth and lament the\nuniversal blindness of mankind, just as a poet may present a front of\nunconquerable self-esteem to the ignorant derision of the world. But\nthe whole claim of science is that it is communicable and capable of\nverification. It is found, as a matter of experience, that results of\nthis kind are not usually obtained unless a certain mental habit is\nfirst acquired. It is this mental habit which is usually called the\nscientific mind. Where it is the outcome of a natural predisposition it\nmay be classed as a moral quality, and, as such, is not peculiar to, or\nwidely distributed amongst, scientific men. But as a tool, as a kind of\ntechnique, it is of more obvious value and is more extensively employed\nin the sciences than in any other human activities.\n\n\n\n\n                      THE SCIENTIFIC CONTRIBUTION\n\n\nFor something like seventy years science has been the dominant\nintellectual activity of the Western world. During that period the\nrange of its material has greatly increased until now the scientific\nmethod is regarded as the method proper to almost any investigation.\nPhilosophy is still a partial exception, but there is a strong tendency\nto regard such philosophic problems as are not susceptible to the\napplication of the scientific method as being essentially incapable\nof solution, or else as incorrectly stated. But although the prestige\nof science is so great, and the general attitude towards it so\nreverential, there is still much confusion respecting its function and\nachievement. Its relations to other human interests and activities are\nnot yet clearly defined. The attempts to define them by allotting to\nscience its \u201csphere\u201d have proved, in the result, to be so ill-judged\nthat it is now considered safer to waive the question of limitations\naltogether. The question is not settled. Everything is left open, but\nit is not therefore assumed that science contains or will contain all\nwe know or all we need to know. Science is not yet the one object of\nour contemplation: we have a number of interests which still lead\nseparate lives. The separation is not complete. Science, if not openly,\nthen indirectly, has invaded every province of the mind, and even a\nmodern musical composition counts Copernicus as well as Beethoven\namongst its ancestors. But it is admitted, of course, that we are\nnot usually reminded of astronomy in listening to music; there is a\nsense in which music, and many other things, are autonomous. But it\nis interesting to notice that science, to a greater extent than any\nother pursuit, can be isolated, although its historical direction has\nbeen influenced, of course, by social and political accidents. Science\nhas given generously, but has taken comparatively little, and its few\nborrowings are in process of being handed back with regret as being,\nafter all, unsuitable.\n\nWhat, then, is the precise nature and extent of the contribution of\nscience to our total stock? Although we do not intend its practical\napplications by this question, we cannot wholly ignore them. It is\nimpossible completely to separate the \u201cmaterial\u201d and \u201cspiritual\u201d\naspects of life, and the sum of the practical applications of science\nhas even profoundly affected much of our abstract thinking. Where it\nhas not originated questions it has at least made them acute, if by no\nother process than by creating or transforming social conditions. It is\neasy to trace the ancestry of whole schools of social philosophy to\nthe steam engine and the dynamo, and it is probable that the influence\nof future applications will be even more extensive. The morality,\nart and philosophy of, for example, a disease-less world, where the\naverage span of human life was two or three times its present value,\nwould certainly differ greatly from our own. We cannot, then, ignore\nthe practical applications of science, although they are not, in\nthemselves, pertinent to our question. But when we turn to consider the\ndirect spiritual value of science we are conscious, at the outset, of\nsome hesitation.\n\nIt was a common article of the Victorian scientist\u2019s creed that\nscientific study was, in itself, an \u201cennobling\u201d and purifying\ninfluence. He stressed the complete detachment required, in scientific\nresearch, from all prepossessions; the man of science was completely\ncandid, completely docile in face of the facts. Until one became as\na little child it was no use entering a laboratory. We have realised\nsince then that scientific men are human, and have their full share of\nthe unfortunate characteristics proper to that state. But it remains\ntrue that the scientific ideal of detachment and the scientific ideal\nof evidence are higher than the corresponding ideals elsewhere. In\nspite of the evidence furnished by our newspapers we may, if we are\noptimists, believe that science is gradually infecting the whole\ncommunity with its conception of these ideals. If this is indeed the\ncase it must be counted a direct and very important moral gain, as an\nindisputably valuable contribution which may be set over against those\nsomewhat ambiguous practical applications.\n\nA third contribution is to be found in the large store of \u00e6sthetic\nobjects provided by science. Many of its theories are objects of\nsurpassing beauty. This is particularly true of the mathematical\nsciences--indeed, there are a number of mathematicians who have felt\nimpelled to write of their science in a kind of prose-poetry--but it is\nalmost equally true of such a science as Geology. We can contemplate\nschemes which, in their own way, are as all-embracing as that of the\n_Divina Commedia_, and it does not detract from their \u00e6sthetic\ncharm to know that they are also true. The processes by which the\ntheories are obtained are often as \u00e6sthetically important as the\ntheories themselves. A subtle, elaborate and economical piece of\nreasoning often affords great \u00e6sthetic pleasure, none the less real\nbecause comparatively few people enjoy it. The fact that the history of\na big scientific investigation, such as the Electromagnetic Theory or\nEinstein\u2019s Theory of Relativity, is not generally regarded as a poem\nis due merely to an accident of language and education. But we have to\nadmit that most people are affected by these accidents, and that the\n\u00e6sthetic objects provided by science count almost as few admirers as\ndo the \u201cbeauties\u201d of chess. If we may judge from the number of popular\nbooks and articles dealing with science, there is some hope, however,\nthat this particular contribution is receiving more attention. The\nresults of such increased attention will not be simple, but if it did\nno more than add fresh \u00e6sthetic objects, the contribution would be\nimportant.\n\nThe fourth contribution of science, both in itself and for its reaction\non other interests, is perhaps the most important of all. This\ncontribution is, put briefly, the light thrown by science on man\u2019s\nplace in the universe. Every branch of science conspires directly to\nthis end. With some the emphasis is on the universe as distinct from\nman; others are concerned chiefly with man himself. To the general\nmind the result has been to make the universe bigger and man smaller,\nand this is, perhaps, no unfair summary. It is probably difficult,\nafter hearing a duet sung by an astronomer and a psycho-analyst, not\nto feel depressed. But, such as it is, there can be no doubt that any\nconception of man\u2019s destiny that is to command attention must conceive\nthat destiny as played against the background of the scientific cosmos.\nWhether the vision be that of a prophet, philosopher or poet, it must\naccept those postulates. The cosmos revealed by science, both in\nits direct influence upon the mind and in its almost equally direct\ninfluence upon religion, philosophy and the arts, is the most important\npart of the scientific contribution to our spiritual life. So far as\nphilosophers and artists are concerned, this influence is recognised.\nIt is probably desirable that the influence upon philosophy should\nincrease, but in the case of the artist we are faced with a special\nproblem. Its discussion would be interesting, the more so in view of\nthe fact that artists themselves have contributed very little that is\nhelpful to its elucidation. We think it essential to its solution to\nremember that the artist, like the scientist, starts with facts. But\nthe system within which the facts are related is entirely different\nin the two cases. The scientific scheme must, of course, be accepted\nby the artist _en bloc_ if his work is to be more than a pure\nfantasy. But this is very different from identifying his own scheme\nwith the scientific scheme. That is to fail signally to perceive\nthe limitations of the scientific contribution. An interesting\nparticular case of this problem is to be found in the question of\nthe right relations of the psychological novelist to the science of\npsycho-analysis. A scientific investigation is often, as we have\nsaid, a work of art, but not necessarily a work of literary art. The\nscientific contribution is very considerable, but offerings from the\nolder benefactors are still gratefully received.\n\n\n\n\n                      THEORIES AND PERSONALITIES\n\n\nThat a scientific theory is, in some sense, a personal achievement,\nbecomes evident when we study a number of theories lying within the\nsame branch of science. The ordinary belief that science is completely\nimpersonal is certainly not true. And yet it is not easy to see how\na scientific theory can express the personality of its author; it is\ndifficult, that is to say, to understand in what way a scientific\ntheory can resemble a work of art. It seems that the fact that a\nscientific theory must have \u201cobjective truth\u201d renders it an altogether\ndifferent thing from a work of art. It would be more just to say that\nthe element of objective truth radically differentiates a scientific\ntheory from those works of art which are independent of all experience\nof life--as certain musical compositions may be, for instance. But\nit is not clear that, in general, works of art are independent of\nobjective truth; all those works of art which assume experience claim\nassent--they do, in their intention, claim universal assent--to the\ntruth of their assumptions. The serious artist believes his personal\nvision to be true; he will not, probably, claim \u201cabsolute\u201d truth for\nit, but neither does a scientific theory profess to be absolutely true.\nAnd, further, works of art and scientific theories exist to serve the\nsame purpose--to aid _comprehension_. An artist\u2019s chief title to\nconsideration is to be found in the depth and extent of his vision,\nin the profundity and range, that is to say, of the comprehension he\nmakes possible. The value of a scientific theory is judged by the same\ncriteria. So far, therefore, it would appear that the chief difference\nbetween a work of art and a scientific theory is to be found in their\nsubject-matter. It cannot even be said that the subject-matter is\narranged to serve different ends in the two cases, for in each case the\nend which is aimed at is \u00e6sthetic satisfaction. Comprehension is one of\nthe elements of what is loosely termed the \u00e6sthetic emotion, and it is\nthe most important element. Even when we descend to particulars, and\nstudy the quality of similes in poetry, and, indeed, \u201cornamentation\u201d\ngenerally, we shall find the criterion we employ is still the degree\nof comprehension afforded by the device. But we cannot here work out\nthe analogy in detail. It is sufficient to show that works of art that\nhave a reference to experience, to an external world, in short, are, in\nimportant respects, similar to scientific theories.\n\nSince, then, a work of art, although conditioned by experience,\nmay nevertheless be a personal achievement, we need have no _a\npriori_ objection to conceding personality to a scientific theory.\nIn each case it is the method of transformation from what we may\ncall the raw material to the finished product which is the personal\nthing. The artist\u2019s raw material, whether it be the Thames in a fog,\na number of incidents from Holinshed, or the lives of the inhabitants\nof a Russian village, is no more and no less common property than are\nthe _donn\u00e9es_ from which a scientific man constructs a theory;\nthe end product, also, in each case, claims universal assent and\nbestows comprehension. What is personal is the law of transformation\nby which the one objective thing is changed into the other objective\nthing. The law of transformation is different for each individual\nmind, and this is as true of scientific men as of any other sort of\nmen. In this sense, then, both works of art and scientific theories\nare personal achievements. A history of science written from this\npoint of view would be instructive. It would be interesting to trace\nthe personal element in each great scientific achievement, to show\nwhat kinds of personalities have dominated us, to see what meaning\n_eccentricity_ can have as applied to the thought of a scientific\nman. But although a detailed history of this kind has not yet been\nwritten, certain _national_ differences have long been recognised.\n\nThere is almost as marked a difference between English and French\nscience as between English and French literature. The English\nscientific mind is, on the whole, intuitive, mobile, illogical, and\nvery prone to imagery of a curiously practical kind. The French\nscientific mind, on the other hand, likes to simplify the complicated\nreality to as few terms as possible, and then to build up an impeccable\nlogical edifice. Maxwell was a very fine type of the great English\nman of science, but we have Poincar\u00e9\u2019s authority for saying that the\ngreat _Treatise on Electricity and Magnetism_ awakens in the\nFrench reader feelings of distrust. So far from finding an impeccable\nlogical structure, he finds that different parts of the book are\nwritten from different points of view, and that these points of\nview are even irreconcilable with one another. Maxwell\u2019s liking for\nimmensely complicated mechanical models, designed to illustrate some\nabstruse equation, is also a stumbling-block to the French reader.\nWhat are such models supposed to prove? Surely Maxwell did not suppose\nthat the \u00e6ther contained trains of geared wheels with \u201cidle wheels\u201d\nin between? What mysterious satisfaction did he derive from such\nunnecessary and irrelevant pictures? But this curious liking for models\nis characteristic of the English school, and it is a characteristic\nthat Continental physicists have never been able to understand. It is\ndoubtless a manifestation of the English reluctance to get out of touch\nwith experience. The English man of science trusts logic much less\nthan he trusts experience. The Frenchman has much less respect for\nexperience. He is willing to simplify in a way which, to the English\nmind, is almost outrageous--to see the Universe as a collection of\nlittle billiard balls with forces varying inversely as the square of\nthe distance. And on such assumptions he is willing to proceed as far\nas logic can take him. There is, indeed, a school in France which\nasserts that all we can ever know of the Universe is its equations;\nwe can never know what they \u201cmean\u201d in the English sense. From the\n\u00e6sthetic point of view there is no doubt that the French method is to\nbe preferred. We can all share Lagrange\u2019s satisfaction when he says,\nin the Avertissement to his _M\u00e9canique Analytique_: \u201cJe me suis\npropos\u00e9 de r\u00e9duire la th\u00e9orie de cette Science, et l\u2019art de r\u00e9soudre\nles probl\u00e8mes qui s\u2019y rapportent, \u00e0 des formules g\u00e9n\u00e9rales, dont le\nsimple d\u00e9veloppement donne toutes les \u00e9quations n\u00e9cessaires pour la\nsolution de chaque probl\u00e8me.\u201d But we must remember that when the\ninterest is chiefly in the \u201cd\u00e9veloppement\u201d the assumptions may remain\nuncriticised. The English way is to hold the assumptions tentatively,\nand to be always open to the suggestions of experience. The German way,\nwhich, if we are to judge by the work of Riemann and Einstein, seems\nto be to concentrate an immense critical apparatus on the assumptions,\nis equally interesting. The \u201cphilosophic\u201d tendency which is supposed\nto characterise German thought in other departments, is certainly\napparent in its science. The three tendencies are sufficiently marked\nto constitute national differences and suggest that a detailed analysis\nof individual achievements would yield equally interesting results.\n\n\n\n\n                       THE IDEAL SCIENTIFIC MAN\n\n\nIs the scientific man really a distinct kind of man, or is it merely\nthat science is a distinct occupation? To answer the question we\nmust make the elementary distinction between the scientific man and\nthe man who practises science, and when we do that the answer is\nobvious. There is as certainly the \u201cborn\u201d scientific man as there\nis the born artist. But in saying this we are referring to ideals.\nPerhaps there has never been a perfect man of science, and perhaps\nthere has never been a perfect artist. But in order to understand\nthe distinction between one kind of man and another it is helpful to\nconstruct ideals--extreme cases which may be used as measuring rods.\nWhat, then, are the characteristics of the ideal man of science? We may\napproach the solution by trying to make precise the characteristics\nwhich have led us, vaguely, to construct the hierarchy we already\npossess. We _feel_, for instance, that Henry Cavendish, that\npassionless recluse, was a much more \u201cpurely scientific\u201d man than,\nsay, Thomas Henry Huxley. If we examine this conviction of ours we\nmake the interesting discovery that it is chiefly for his negative\ncharacteristics that we assign this greater purity to Cavendish. Huxley\nwas passionately interested in the questions which concern every good\ncitizen, in politics, in social reform, in religion; he took sides\non these questions and fought for his side. Of Cavendish we can only\nsay that it is inconceivable that he would have taken sides on these\nquestions, and very difficult to believe that he was even remotely\ninterested in them. Take another point. Huxley abounded in ordinary\nhuman affections. He was a devoted husband, a good father, a faithful\nfriend, a resolute opponent. Cavendish never manifested a vestige of\nany of these qualities. He had no wife, no children, no friends, and\nnever showed the faintest dislike of anybody. Huxley was a champion of\nwhat he thought the truth, and strained every nerve to enable it to\nprevail. Cavendish, who was one of the greatest investigators, one of\nthe clearest and most subtle minds, in the history of science, kept\nhis discoveries to himself. For years Huxley bore the brunt of the\nattacks on Darwin\u2019s theory. Cavendish blandly watched the growth in\npopularity of theories he had privately demonstrated to be wrong, and\nnever stirred a finger to rebut them. And finally, Huxley was a man who\nsuffered his alternations of high spirits and despondency, hope and\ndespair, while Cavendish, from the evidence we have, was imperturbably\nserene.\n\nNow, the interesting point that emerges from this comparison is that\nCavendish, in virtue of his scientific purity, _could not_ have\nexhibited those qualities which allied Huxley to the ordinary run of\nmen. A man\u2019s characteristics are not disconnected. Cavendish\u2019s cold\npassion for knowledge required for its gratification qualities of the\nspirit as well as of the mind. No man was ever more single in his\ndesire to _know_; no man ever was so little hindered by having\nother interests to serve; no man, therefore, had a greater measure\nof the purely scientific spirit. This is the important point for our\nquestion; it is comparatively irrelevant that very few men have ever\nhad so great a mind to place at the service of their passion. That his\nactual scientific standing should be so much greater than Huxley\u2019s\nis an accident; he would still have been more purely scientific than\nHuxley had his ability been less than Huxley\u2019s. Cavendish is all of\na piece. His very perfection as a recording and measuring instrument\ntended to deprive him of \u201cpersonality.\u201d The less personal he was,\nin fact, the more dispassionately open he could be. Other passions\nwere incompatible with his perfection; they would derange this\nexquisite instrument. Judgments of good and evil would not have been\nnatural to him. His reaction to anything was exhausted in the act of\n_understanding_ that thing.\n\nSo far as we have gone, it would seem that Nietzsche\u2019s description of\nwhat he calls the \u201cobjective man\u201d is exactly what we mean by the ideal\nman of science. \u201cThe objective man is in truth a mirror: accustomed\nto prostration before everything that wants to be known, with such\ndesires only as knowing or \u2018reflecting\u2019 implies ...\u201d he will regard\nsuch personality as he has, Nietzsche goes on to say, as accidental and\narbitrary. He cannot take himself seriously and devote time to himself.\nHis love is constrained, his hate artificial. He is only genuine so far\nas he can be objective; he is unable to say either \u201cYea\u201d or \u201cNay\u201d to\nlife; he is concerned solely to understand, to \u201creflect.\u201d He says, with\nLeibniz: \u201cJe ne m\u00e9prise presque rien.\u201d This description is undoubtedly\nthe result of genuine psychological insight. When we try to disentangle\nthe purely scientific element in a man of science we find that, so far\nas he is scientific, he approximates to Nietzsche\u2019s objective man. If\nthis, then, is the ideal scientific man, what place does he occupy?\nWhere does he stand in relation to the rest of mankind? According to\nNietzsche he is merely an instrument; \u201che is an instrument, something\nof a slave, though certainly the sublimest sort of slave, but nothing\nin himself.\u201d He is no goal, no termination, no complementary man in\nwhom the rest of creation justifies itself. As compared with the\n_true_ philosopher, the philosopher in Nietzsche\u2019s sense, the man\nwho gives a new direction to life, the ideal man of science is merely\nthe most costly, the most easily tarnished, the most exquisite of\ninstruments.\n\nWe need not quarrel with this valuation, but we would point out that\nthere is an omission in it. The scientific man is an instrument, but\nhe is an indispensable instrument. The human race has endured all the\ndifferent \u201cnew directions\u201d given to it by the \u201ctrue\u201d philosophers of\nthe past without any marked increase in its spiritual stature. The\nphilosopher, however commanding, who would really lead us in any but a\ncircular direction must have _knowledge_. This knowledge, to be\nvaluable, must be clear and trustworthy; it must be scientific. And\nif the inspirations and impulses of our leaders should prove to be\nincompatible with deductions from scientific knowledge, then we may\nbe sure that the Promised Land does not lie their way. The scientific\nman is merely an instrument. But it is this instrument alone that can\nshow to mankind which, of all the goals it desires, are possible goals,\nand which, of all the leaders it trusts, are trustworthy leaders. The\nscientific man is an instrument, but it is by this instrument that\nthose who would use it are first tested. Scientific knowledge is, if\nyou like, as dispassionate and inhuman as is the universe with which it\nconcerns itself--and it can as little be ignored.\n\n\n\n\n                        PARALLEL STRAIGHT LINES\n\n\nGeometry, it has been satisfactorily shown, had a purely empirical\norigin. It appears that the earliest geometrical formul\u00e6 which have\nbeen discovered belong to ancient Egypt, and that all these formul\u00e6\nserved a useful purpose. The oldest of them are concerned with the\nmeasurements of areas, a class of problem which the yearly sinking\nof the Nile rendered of great importance. The formul\u00e6 obtained\nby the ancient Egyptians were usually wrong, although they were\napproximately correct; they evidently rested on no theoretical basis,\nbut were compendious statements of the results of somewhat rough\nmeasurements, a point of view which is borne out by the fact that no\nproof, nor even an attempt at a proof, is anywhere hinted at. So far\nas the evidence goes, it seems to be established that geometry, as\nconsisting of logical deductions from stated premises, began with the\nGreeks. A number of theorems of a fair degree of complexity had been\ndeveloped before they were reduced to a system; before, that is, the\nassumptions on which they were based were made explicit. The task of\ndiscovering the necessary and sufficient assumptions on which a system\nof geometry rests is one of the greatest difficulty; the necessary\ncombination of subtlety and rigour is rare. The great systematisation\nof Greek geometry was effected, of course, by Euclid, and although\nhis reduction of the system to its essential assumptions was not\nfinal, his performance was such as to awaken the admiration of great\nmathematicians in every succeeding century. But there is one point in\nwhich this great reduction is notably imperfect--the so-called parallel\naxiom. It says, essentially, that through a given point only one line\ncan be drawn parallel to a given straight line. It was felt, even\nby the earliest commentators on Euclid, that this postulate did not\npossess quite the same degree of self-evidence as was manifested by the\nothers. It was necessary, they felt, to give a proof of this postulate;\nthey attempted to improve on Euclid\u2019s work in a number of minor ways,\nbut it was the parallel axiom which they were most concerned to revise;\nthe proof of this postulate should be contained, they thought, in the\nother postulates. The attempts to supply this proof were all fruitless,\nand the sixth century was reached with this nine-hundred-years-old\ndisfigurement still persisting. For some time after the sixth century\nthe world rested from Euclid\u2019s parallel axiom; indeed, it rested from\ngeometry altogether, and the old empirical outlook of the Egyptians,\nand even their formul\u00e6, again became current. But the Greek culture\npenetrated to the Arabs, and with the Greek culture came the riddle of\nEuclid\u2019s axiom. Again proofs were attempted; a famous attempt is that\nof Nasir Eddin, who flourished in the thirteenth century. In 1663 John\nWallis made the important discovery that unless the parallel axiom be\nassumed, similar figures of different sizes are not possible, that\nis to say, that if we are to assume that _shape_ is independent\nof _size_, then we must assume Euclid\u2019s parallel axiom. Many of\nthese attempts brought out points of interest, but none of them were\nsuccessful. In the year 1733, however, the whole research took on a new\ncomplexion with the publication of Girolamo Saccheri\u2019s _Euclides ab\nomni naevo vindicatus_. The importance of this work consists in the\nfact that, although it was written to vindicate Euclid\u2019s parallel axiom\nonce for all, it contains the first real outline of a non-Euclidean\ngeometry.\n\nSaccheri was a Jesuit, and it was in 1690, while he was teaching\ngrammar in Milan, that he first studied the _Elements_ of Euclid.\nHe was a man of very great acumen, and when he, in turn, succumbed to\nthe spell of the parallel postulate, he brought to bear on it a more\nsubtle and rigorous logic than had yet been applied to it. Thirty-six\nyears before he published his treatise on Euclid he had published a\nbook on logic which gives him a high place as a logician. In it he\nis particularly concerned with investigating the compatibility of\ndifferent assumptions or postulates. His method was to determine\nwhether a member of a group of postulates is independent of the others\nby finding a particular case in which the postulate in question is not\ntrue while all the others remain true. If such a case can be found, it\nis obvious that the postulate in question cannot be deduced from the\nothers, else it would be true whenever they were true. This was the\nmethod he applied to the parallel postulate of Euclid. He showed that\nthe parallel postulate is equivalent to saying that the three interior\nangles of a triangle are equal to two right angles. He proceeds,\ntherefore, in accordance with his method, to develop the consequences\nof supposing them less than, or greater than, two right angles. In\nthe latter case he succeeds in showing that we are led to impossible\nconclusions, since he assumed, as everybody assumed for more than a\ncentury after, that the straight line is of infinite length. But in the\nformer case, the hypothesis that the interior angles of a triangle are\ntogether less than two right angles, Saccheri, although he struggled\nvery hard, did not succeed in falling into contradictions. He does not\nseem to have had the boldness necessary completely to trust his own\nlogic, but the fact remains that, accepting the rest of Euclid\u2019s axioms\nand denying the parallel axiom, he developed a logically consistent\ngeometry.\n\nThere is reason to suppose that Saccheri\u2019s work had some influence on\nsubsequent thought, although its full significance was certainly not\nperceived. The parallel axiom continued to be investigated, and the\ntotal effect of all these efforts was to induce a doubt concerning\nthe absolute _necessity_ of the Euclidean geometry. Such a doubt\nwas very daring; for two thousand years the postulates of Euclid had\nbeen accepted as absolutely true; the fact of their existence had\nprofoundly influenced philosophy, and, indeed, theology. But the\ndoubt persisted and grew, until finally, early in the nineteenth\ncentury, a perfectly logical and consistent non-Euclidean geometry,\none explicitly denying the parallel postulate, was published to the\nworld. As so often happens, the great step was taken by two men\nindependently of one another, Lobatschewski, a Russian, and Bolyai, a\nHungarian. It appeared, however, that both had been preceded by that\ngreat mathematical genius, Gauss, although he had been too timid to\npublish his conclusions. The new geometry developed the consequences of\nthat one of Saccheri\u2019s alternatives which supposed the interior angles\nof a triangle to be less than two right angles. The whole outlook on\ngeometry now assumed a new complexion. Riemann tried the effect of\ndenying the infinity of the straight line and of developing Saccheri\u2019s\nother alternative. He found he was led to no contradictions. But with\nRiemann\u2019s work we come to a yet further extension of geometry--the\nextension to space of four, five, or any number of dimensions. And\nthese investigations, which seemed for some time to constitute the most\ngratuitous, although the most profound and subtle, exercises of the\nmind, have now received their complete justification by flowering into\nthe Generalised Principle of Relativity.\n\n\n\n\n                      THE NEW SCIENTIFIC HORIZON\n\n\nAbout current scientific speculations there is one characteristic,\nsubtle, perhaps, but profound and far-reaching, which distinguishes\nthem from the scientific speculations of the Victorian age. We can\nbest isolate this characteristic by considering it as a particular\nmanifestation of something which is met with in nearly every\nphase of contemporary life--something which may fairly be called\nthe _Zeitgeist_ of our time. This spirit is chiefly a sense\nof unlimited possibilities, a sense that the radically new and\nunprecedented may be upon us; with this feeling comes a recrudescence\nof the spirit of adventure; there are unknown paths leading to vague\nbut--probably--splendid goals. In the Victorian age the main lines of\neverything were settled; the chief features of the universe were known.\nThere were matter and energy, and there was, of course, the \u00e6ther.\nThe astronomical and geological scales were known in broad outline,\nand a first survey of the march from am\u0153ba to man had been taken. The\nwork of future ages was to fill in the details. The universe of the\nVictorians was a large and rather grand affair, but it was sombre.\nThose emotional barometers, the poets, in so far as they were aware\nof the scientific outlook, either \u201ctranscended\u201d it or were crushed by\nit. Jules Laforge furnishes an excellent example of the effect of the\nVictorian scientific outlook on an intelligent and sensitive mind.\nHis reaction was to compose funereal dirges on the death of the earth\nand the extinction of mankind. The universe of the Victorians was\nobjective, indifferent, tracing a purposeless pattern in obedience to\n\u201ciron\u201d laws. It was a universe which held no great surprises.\n\nIt is obvious that a very different spirit is abroad to-day. At the\npresent time the general consciousness seems to hold that almost\nanything is possible. In part this may be accounted for, as in other\nages, by credulity based on ignorance, but there is also a credulity\nbased on knowledge, and it is this aspect of the general attitude which\ndeserves attention. The two kinds of credulity may be observed in\ndifferent believers of the same statements. Spiritualism, for instance,\nhas its followers amongst those who are unfamiliar with investigations\nin the subject and amongst those whose belief has been compelled by\ntheir very knowledge of the investigations. And disbelievers form\ntwo exactly similar classes. There is also a credulity--the most\ncommon kind--based on neither ignorance nor knowledge, but on partial\nknowledge. Thus knowledge, but incomplete knowledge, of such phenomena\nas wireless telegraphy or telephony, seems to predispose many people\nto believe \u201cwonders\u201d which have no real connection with those\nphenomena, but which are merely as inexplicable by partial knowledge.\nUndoubtedly the recent developments in science are responsible for much\nof this kind of credulity. But the new indulgence of possibilities,\nas exhibited by the man of science, is dependent on quite different\nconsiderations. To the student of physics, at any rate, the work of\nthe last two or three decades has been peculiarly disturbing. He has\nbeen called upon, not merely to revise and extend his knowledge, but to\nalter his assumptions. It is in this respect that the physics of our\nown day chiefly differs from Victorian physics.\n\nThe distinctively modern epoch began with the promulgation of the\nElectron Theory. That \u201cmatter\u201d could be \u201celectrified\u201d was easily\ngranted. The fact that the famous question, What is electricity? could\nnot be answered was no difficulty in admitting the fact that, as a\nresult of certain processes, matter could be made to exhibit certain\nphenomena which could conveniently be referred to the fact that it\npossessed an \u201celectric charge.\u201d And the discovery of particles very\nmuch smaller than a hydrogen atom presented no conceptual difficulties.\nThe fact that the ultimate particles of matter were smaller than had\nbeen supposed could easily be granted; the new assumption was of the\nsame kind as the old one. And, further, to admit that each of these\nparticles possessed an electric charge made no unfamiliar demands on\nthe imagination. But the next step, that these particles consisted\nof nothing but an electric charge--that was a very different thing.\nThe early popularisations of the idea show something of the mental\nconfusion it caused. \u201cDisembodied charges of electricity\u201d was a\nfavourite descriptive phrase; many physicists fought hard to retain\neven a nucleus of \u201cordinary matter\u201d on which this charge could be\nsupposed to be lodged. That an electric charge could exist apart from\nmatter seemed to many people as difficult to conceive as motion without\nanything which moved. But the conception speedily became familiar; that\nuseful entity, the \u00e6ther, soon made things easier. For the disembodied\ncharge, the electron, could be conceived as a local distortion of\nsome kind in the \u00e6ther, and, by endowing the \u00e6ther with some sort of\nsubstantiality, the hypothesis that matter was in some way built up\nout of this primitive substance could be tolerated. But the general\neffect of the theory was to give a more philosophical tinge to science.\nThe gross, easy assumptions of everyday thinking about \u201cmatter\u201d had\nto be revised; articles were written showing that matter was really\nimmaterial, and materialism was conjectured to have received a severe\nset-back.\n\nThe mind had barely become accustomed to the new assumptions before it\nwas again profoundly disturbed by the publication of Planck\u2019s Quantum\nTheory. The theory, which was invented to explain certain radiation\nphenomena, asserted, briefly, that energy was atomic. One\u2019s most\nintimate assumptions were disturbed. Men of science are not usually\naccustomed to philosophic exercises, and the idea that energy, which\nthey regarded as necessarily continuous, had an atomic structure seemed\nat first almost meaningless. If we consider, for instance, the energy\npossessed by a moving body, it seems natural to suppose that this\nenergy can be increased or diminished in a continuous manner; the idea\nthat its energy can only increase or decrease by finite jumps was a\nvery strange idea, and led again to a scrutiny of assumptions which\nhad appeared fundamental in science. Here, again, objections to the\nnew theory were sometimes the outcome purely of mental inertia, of an\ninability to examine and discard a way of thinking which seemed almost\na necessary consequence of the structure of the mind. The last great\n_bouleversement_ of one\u2019s fundamental assumptions has been, of\ncourse, Einstein\u2019s generalised theory of relativity. Here we are asked\nto revise our most deep-rooted assumptions--so deep-rooted that we are,\nfor the most part, unconscious of them--our assumptions regarding space\nand time.\n\nIt is this thorough overhauling of primary assumptions which\ndistinguishes the modern progress in physics from all the progress of\nthe Victorian age. Physics has not merely been extended, it has become\na radically new thing, and there are very good reasons for supposing\nthat it is going to change still more. A certain sense of unknown\npossibilities is therefore natural, even if it be the product merely of\nbewilderment. The total effect of the new ideas is to make the universe\nof physics less objective; to an unsuspected extent this indifferent\nuniverse, with its iron laws, is a product of our own minds. To some\nextent this fact was always recognised, particularly by the Continental\nphysicists, but as a general persuasion it is comparatively recent.\nWe cannot escape the structure of our own minds, it is true, but we\ndo not yet know what that structure is; we do not know what barriers\nare breakable; we do not know what thoughts are thinkable by man. A\nuniverse in whose construction so plastic and mysterious an entity as\nthe mind of man collaborates, may very well hold great surprises.\n\n\n\n\n                          THE HOPE OF SCIENCE\n\n\nIt is not an unfair judgment, we think, that decides, on a survey\nof contemporary intellectual activities, to grant science the first\nplace. Whether we consider the quality of the work which is being\ndone, its importance to mankind, or the spirit in which the work is\ndone, we think science earns that place. Our age is a scientific age\nto an extent which is certainly not generally realised. Contemporary\nscientific work is of a quality fully comparable with that of the\ngreatest periods of its history; it is inevitable that our age should\nemerge, in the history of the future, as an age of science. It has,\nindeed, already established a perspective which leads to a revaluation\nof the Victorian age. There have already been many writers who have\nthought that age more memorable for its science than for its other\nachievements, that its significance to humanity lay more in the work\nof Darwin, Faraday, and Maxwell than in that of Tennyson and Matthew\nArnold, or even in that of Mr. Gladstone, but the perspective we have\nnow obtained puts the matter almost beyond doubt. With most of us our\noutlook is the result of a decrepit tradition. Our orientation towards\nlife, so far as we are conscious of having one, is based upon the\nvalues we attribute to the various objects of our thoughts, and these\nvalues are determined partly by our instinctive desires and partly by\nthe suggestions of our education--using the term \u201ceducation\u201d to include\nall converse with the minds of our fellows. Education, so defined, is\nthe result very largely of a long and widespread tradition, a general\ntradition of European culture. It is a curious fact that, although\nthe history of science goes as far back as the history of the arts,\nscience is not an integral part of this, nevertheless, very catholic\nculture. There are periods, it is true, when some scientific theory\nis sufficiently dramatic, or appears sufficiently pertinent to man\u2019s\ndestiny, to secure general attention; Newton\u2019s theory of gravitation,\nDarwin\u2019s theory of evolution, and Einstein\u2019s theory of relativity have\neach given rise to such a period. Einstein\u2019s theory, we are informed,\nis now the favourite topic of enlightened conversation in Parisian\nsalons, as Newton\u2019s theory once was. Some of this interest, no doubt,\nis the product of disinterested curiosity, and in that respect is\nvastly different from the once general interest in Darwin\u2019s theory.\nBut we fear that many of those who are curious about Einstein\u2019s theory\nwould, if they understood it, find it uninteresting. We dare not\ninterpret this curiosity as a sign that people are beginning to be\nas naturally interested in science as they are in literature, for\ninstance.\n\nNevertheless, we believe that the old culture is moribund in the sense\nthat its particular scale of values is undergoing revision. Science\nis becoming less an affair for specialists; it is acquiring a \u201chuman\u201d\nvalue. An increasing number of people are beginning to realise that a\ngreat science, such as Physics, may offer objects for contemplation\nwhich are as delicate, as subtle, as exquisitely harmonious as the\ndreams of Plato--and much better founded. And in relation to man, his\npresent state and possible future, science alone, to those who are not\nsatisfied with less than verifiable knowledge, speaks with the accent\nof authority. The great constructions of science are grandiose without\nbeing chimerical; they are beautiful but not deceiving. Indeed, one\nsometimes has the feeling that it is only in science, nowadays, that\none still meets with the spirit of adventure, the sense of boundless\nand glorious possibilities, with an exultant hope. Our poets and\nmen of letters generally are extraordinarily tame and disillusioned\ncreatures compared with our romantic and daring men of science. It is\nrefreshing to turn from the lamentations of our literary men to such\na book as the _Space, Time, Matter_ of Hermann Weyl, if only for\nthe fervour, the immense enthusiasm with which that highly accomplished\nmathematician writes. Einstein is his Columbus, with the difference\nthat his America has indicated the existence of yet vaster continents.\nAnd this enthusiasm is justified by its fruits; it has inspired Herr\nWeyl to make what is unquestionably the greatest advance on Einstein\u2019s\nown work which has yet been made. It is not in Physics alone that we\nfind this note. To the biologists, also, the world has become young\nagain. Should our ignorant and unimaginative politicians, and our\nstill more ignorant and unimaginative business men, succeed in turning\nthe whole heroic effort and age-long struggle which has produced our\npresent culture to a mockery, they will put an end to a curiously\ninteresting and promising transition age, to an age which is at once\n_fin de si\u00e8cle_ and at the morning of a glorious renaissance.\nBut if they do not succeed, if the ordinary man shows himself even a\nlittle worthy of the immense travail of his species, then we prophesy\nthat science will become an integral part of the culture of the future.\nThe new physics, the new biology, the new psychology, will be too\nobviously pertinent to all man\u2019s chief preoccupations for us to be\nable to pretend that the present narrowly conceived _humaniora_\nfurnish a liberal education. We even believe that if the old arts are\nto become youthful again, it must be by a transfusion of blood. It will\nnot be sufficient that the philosophy and literature of the future\nshould \u201caccommodate\u201d themselves to the scientific outlook; they must be\ninspired by it.\n\nMeanwhile, scientific men must be charitable; they must believe the\nbest. If science is to become an integral part of culture, scientific\nmen must help to make this possible. We believe that much of the\npresent interest in science is genuine; that it springs from a serious\nattempt on the part of many people to find out what science can tell\nthem about themselves and the Universe they live in. Science is not\nhunted purely for its dividend-earning capacities or for its power of\nproviding new thrills. Einstein, we understand, is suspicious of the\npopular interest his theory has evoked; \u201ca mere fashion,\u201d he says. And\ndoubtless his suspicion is largely justified. But we believe there is\nmore in it than that--that there are many who, besides valuing the\ndelightful dreams of the poets and philosophers, have an affection for\n_knowledge_. And when they find that the constructions of science\nare not one whit less delightful than the dreams of the poets, this\naffection may give rise to a permanent attachment. And with these new\nobjects of interest will come a change in values. Men will learn to\ndifferentiate in their beliefs between those which are mere indulgences\nof emotion and those which correspond to objective truth. This is the\npath by which the mind becomes mature. It may not be, in all stages,\na pleasant process, but it leads to increased freedom and increased\npower. The impossible will no longer be attempted, but the region of\nthe possible will be seen to be vastly greater. Man will see in what\ndirections he can shape his destiny, and he will be able to enter on\nthe task with a rational hope. All his courage and endurance will have\na chance of victorious achievement; he will know that he is not engaged\nin a forlorn hope; the world will become young again.\n\n\n\n\n                         THE RETURN OF MYSTERY\n\n \u201cIt is a universal condition of the enjoyable that the mind must\n believe in the existence of a law and yet have a mystery to move about\n in.\u201d--JAMES CLERK MAXWELL.\n\n\nThat our thinking, and with it our feeling, is largely conditioned\nby assumptions which have no logical necessity, is a commonplace of\nphilosophy, and is indeed apparent to the slightest introspection.\nCharacteristic of any age is a body of beliefs, resting on more or less\ngood evidence, and a group of feelings associated with those beliefs.\nThe German language, so rich in indefinite but valuable general terms,\nafforded the word _Zeitgeist_ for this complex, a word we have\ndirectly translated into the Spirit of the Age. The name is a good\none; it indicates that we are dealing with something which is widely\ndiffused and also subject to change. It is subject to change, but it\nplays a dominating r\u00f4le in the age to which it belongs. The Spirit of\nthe Age is something that practically all the intellectual life of the\nage has in common. It is not manifested only in philosophical treatises\nor in works of art; it is often manifested even more strikingly in\nstatesmen\u2019s speeches and a country\u2019s domestic and foreign policy. It is\na kind of intellectual and emotional atmosphere of which everybody is\naware, but which probably nobody could define. We see, however, that\na very important part of it consists of a sense of probability, of a\ntendency to accept certain kinds of explanation and to reject others.\n\nFor the last few decades, at any rate, Science has been the chief\nfactor in forming this omnipresent sense of probability. As a matter\nof fact, it is probable that the influence of Science in forming\nthe Spirit of the Age can be traced a very long way back, as far\nback as Copernicus. Not that we assert the existence of a close\nconnection between the Science and the other intellectual activities\nof Copernicus\u2019s own age. The influence of which we speak is likely to\nmanifest itself gradually; in particular, it may take a long time to\naffect the arts. And by the time it has percolated so far its origin\nmay be forgotten; it may appear as a subconscious rather than as a\nconscious group of assumptions. By the time a scientific discovery\nbecomes part of the mental furniture of an age, many of what were\noriginally its possible implications will have become an integral part\nof it. The original discovery will then be merely the nucleus of a rich\nintellectual and, possibly, emotional complex, of which the parts are\nno longer envisaged separately. The work of Newton, for example, and\nthe great body of exact investigations he made possible, influenced the\noutlook of the nineteenth century chiefly in the direction of making\ndeterminism plausible. Such lecturers as Tyndall could confidently\nappeal to this mental predisposition on the part of their audience,\nalthough they had no need to postulate any direct acquaintance with the\nwork of Newton and of his successors. The fact that Newton successfully\nformulated exact laws for the description of natural phenomena is\nthe important aspect of his work from our present point of view. The\ninfluence of Copernicus was rather different. From the point of view of\nthe history of Science his importance is that he made Newton possible;\nfrom our present point of view his importance is that he made Darwin\npossible. Copernicus\u2019 destruction of the isolated position of man\u2019s\nplanet in the solar system prepares the mind for Darwin\u2019s destruction\nof the isolated position of man in the animal kingdom. They each\nshocked the same set of prepossessions.\n\nThe \u201cmaterialistic philosophy\u201d which was so marked a feature of the\nlatter part of the nineteenth century, and which still forms, we\nbelieve, the prevalent intellectual complexion, owed the whole of its\nplausibility to its supposed scientific backing. Its basis was not\nmerely biological; physics played quite as great a part as biology.\nThe notion of determinism derived its strength, as we have said,\nchiefly from physics; biology was not in a position to demonstrate the\nexact correspondences required. The ultimate grandiose vision of the\npurely natural and inevitable march of evolution from the atoms of\nthe primitive nebula to the British Association for the Advancement\nof Science, as outlined by Tyndall in his Belfast Address, assumed\nthe results of physics and astronomy as much as Darwin\u2019s _Origin\nof Species_. It was because biology was not the only science\ninvolved that it was possible to found a \u201cmaterialistic\u201d philosophy\non Darwinism. One primary assumption of that philosophy, that life\narises from \u201cdead\u201d matter, not only had no biological support, but had\nbeen decisively refuted by the experiments of Pasteur. But, as related\nto the general movement of Science, the hypothesis had the necessary\nplausibility. Considering the then existing evidence, this hypothesis,\ntogether with the hypothesis that mental states are produced by atomic\nmovements in a strictly determinist manner, are, indeed, striking\ninstances of the way in which the _Zeitgeist_, as much as the\nevidence, determines the direction of our thinking.\n\nThe importance of such conceptions cannot be over-estimated. Directly\nor indirectly they influence the whole life, if not of their time, then\nof an age which succeeds them. The philosophy in question had existed\nfor centuries, of course; what made it influential was the scientific\nbacking it received, for, in these matters, Science has for some time\npast played the dominant r\u00f4le. Neither religion nor philosophy has been\nable successfully to oppose it; nowadays, indeed, they seem concerned\nonly to agree with it. And if, here and there, a few artists have\nfelt themselves outraged by what were supposed to be the teachings\nof Science, their influence has not been sufficient to deflect the\nstream. Such isolated protestants have had nothing but their feelings\nto oppose to what were considered to be facts, and the world, with what\nmay have been a stupid honesty, has followed after the supposed facts.\nBut the influence of Science on the arts would require a separate\ninvestigation. A certain stability is given to some serious art by\nits own tradition, and this may lessen its sensitiveness regarded\nmerely as an indication of the spirit of its age. It is, nevertheless,\nvery sensitive. In a history of modern literature, for example, it\nis impossible to exclude direct references to Darwin; it is usual,\nindeed, to devote some space to such \u201cinfluences.\u201d And the artist who\nis not at home in his age may be reduced to impotence by it. Dostoevsky\nis a magnificent example of a writer who, extremely sensitive to the\nspirit of his age, and profoundly understanding it, strove to transcend\nit. A smaller Dostoevsky might well have been nothing. And is a\npost-Darwinian Beethoven, or a post-Darwinian Dante, really conceivable?\n\nNow it is unfortunate that, so far as scientific discoveries form\nthe Spirit of the Age, they do so at second-hand. The _Origin of\nSpecies_ happens to be easy to read, but even so that body of\nthought known as \u201cDarwinism\u201d owes its influence chiefly to such\nexpositors as Huxley and Tyndall. The thing becomes set; it assumes\nhard, bold outlines; the issue has to be presented with something of\nthe simplicity of an election cry. The universe of Science becomes\nfinally a universe from which all mystery is banished and where the\nonly ultimates are small, incompressible spheres whose movements and\ncombinations produce--everything. The chasm separating this conclusion\nfrom the actual scientific evidence is not realised. Very tentative and\nalmost fantastic hypotheses become dogmas, and it is as dogmas that\nthey become influences. As a matter of fact the scientific evidence,\neven of Darwin\u2019s day, suggested quite other possibilities than those\npopularised as a \u201cmaterialistic\u201d philosophy. James Clerk Maxwell,\nwho had a profounder insight into physical reality than any other\nman of his time, in a very little known essay, draws attention to\nthe \u201csingularities\u201d characteristic of certain natural phenomena, and\nsuggests that there are more singular points the higher the rank of the\nexistence. \u201cAt these points, influences whose physical magnitude is too\nsmall to be taken account of by a finite being, may produce results\nof the greatest importance,\u201d and he warns his readers against \u201cthat\nprejudice in favour of determinism which seems to arise from assuming\nthat the physical science of the future is a mere magnified image of\nthat of the past.\u201d\n\nMaxwell\u2019s remark is now seen to have been prophetic. The\nextraordinarily profound and far-reaching philosophical implications\nof the theory of relativity have hardly yet begun to be investigated,\nbut we have already a general sense of their direction. Hermann\nWeyl\u2019s _Raum, Zeit, Materie_, for instance, the most thorough\nmathematical exposition of the whole theory which has yet appeared,\nhints not obscurely at the philosophical bearing of the new\ninvestigations. Now that, by Weyl\u2019s own work, Maxwell\u2019s electromagnetic\nequations are included by the theory, it seems to be scientifically\ncomplete. It presents us with a picture of the universe which is wholly\nunlike the picture of the early physics. In particular, an altogether\ndifferent r\u00f4le is assigned to the human mind. So far as the exterior\nuniverse and the laws of nature are concerned, we see that the primary\nentity is the mind itself. It is the mind which has created, not only\nspace and time, but the matter it has put within that framework. The\nmind has not created the universe out of nothing, it is true. But it\nis almost impossible to say anything intelligible in the old sense\nabout the fundamental entities to which Einstein\u2019s theory leads us.\nProfessor Eddington suggests that they may be \u201cthe very stuff of our\nconsciousness,\u201d a somewhat mystical remark which nevertheless shows\nthe trend of the new speculations. And, as a striking confirmation of\nMaxwell\u2019s view of the possible development of physical science, we may\nquote one of the last sentences of Weyl\u2019s profound discussion: \u201cIt\nmust be emphatically stated that the present state of physics lends no\nsupport whatever to the belief that there is a causality of physical\nnature which is founded on rigorously exact laws.\u201d Unfortunately not\nall men are mathematicians. The great and wonderful vista now opened\nup by Science--greater and more significant, we believe, than has\nexisted at any previous time in the history of thought--is at present\na consequence of highly abstruse investigations. The sheer technical\ndifficulty of these inquiries will long hinder them from exerting their\ndue influence on philosophy and, through philosophy, on the whole of\nthe intellectual life of the age. But the new conceptions exist, and\nthey derive their unshakable strength from the fact that they are the\nresult of the severest Science. And surely no one can fail to see\nthat they promise not only fascinating regions for thought, but a new\nliberation of the human spirit. Mystery, but more wonderful and full of\npromise than ever, has been restored to the universe.\n\n\n\n\n                         MATHEMATICS AND MUSIC\n\n\nIt is possible that the old heading \u201cArts and Sciences\u201d has been\nresponsible for some of the barrenness which is so conspicuous a\nfeature of \u00e6sthetic theory. For the heading seems usually to have\nsuggested, not only that there is a difference between the arts and the\nsciences, but that the difference is of a fundamental kind. For the\npurposes of \u00e6sthetic theory the various arts are assumed to have more\nin common than any one of them has with any of the sciences. We find\nthe writer on \u00e6sthetics expounding his principles in chapters headed\nPainting, Sculpture, Poetry, Music; but it is rare indeed to find the\nargument extended to mathematics and physics. Yet there is no evidence\nthat such omissions are due to deliberate reflection; the philosopher\nhas not decided, after examination, that the sciences are un\u00e6sthetic\nobjects; we must assume that accidents of taste and education have\nprevented him from paying attention to what may conceivably be useful\ndata for the formulation of a theory of \u00e6sthetic. Within the last two\nor three generations scientific men have been thinking and writing\na good deal about the philosophic basis and implications of their\nstudy, and it is significant that this inquiry has led many of them\nto insist on the \u00e6sthetic character of the satisfactions that science\naffords. The late Henri Poincar\u00e9, in particular, has shown that\nscientific theories are akin to works of art, and in this country, Dr.\nNorman Campbell has asserted his belief that great men of science are\nessentially great artists. The point of view is an interesting one,\nand suggests that fresh light may be thrown upon \u00e6sthetic problems by\na new grouping of their subject-matter. Instead of putting the arts\nand the sciences on opposite sides of the fence, it may be helpful to\nsee whether certain members of these two groups have not a natural\naffinity with one another, and so gain hints for a different and more\ncomprehensive classification.\n\nIt is noteworthy, in this respect, that music has always occupied an\nexceptional position among the arts. Pater tried to relate it to other\narts by saying it was the art to which all others aspire:\n\n The arts may be represented as continually struggling after the law\n or principle of music, to a condition which music alone completely\n realises; and one of the chief functions of \u00e6sthetic criticism,\n dealing with the products of art, new or old, is to estimate the\n degree in which each of these products approaches, in this sense, to\n musical law.\n\nIt is characteristic of Pater\u2019s criticism, and of much of the criticism\nof his school, that it exists, as it were, within a world of its own.\nThe meanings to be attached to his most important terms are always\nsuggested or insinuated; they are never defined. The method is useful,\nperhaps even necessary, in dealing with a complex and elusive object,\nand where appeal is made to perceptions which lie on the fringe of\nconsciousness. But it runs the grave danger of becoming altogether\ntoo tenuous to be intelligible when we make direct reference to the\nobject it is supposed to illuminate. When, for instance, Pater says\nof the best music, \u201cthe end is not distinct from the means, the form\nfrom the matter, the subject from the expression,\u201d we become acutely\naware of the absence of definition in each of these primary terms\ndirectly we think of any actual composition. We feel, indeed, that the\nterminology is not natural; in contemplating a poem the mind may be\nnaturally impelled to distinguish between subject and expression as a\nkind of first effort in analysis; it is doubtful whether, in listening\nto music, this direction for analysis ever presents itself. So that\nto say that in music subject and expression are identical is not to\nsay anything useful about music, but merely to declare that that kind\nof analysis is irrelevant. It is very probable that nothing is to be\ngained by first making distinctions which have a meaning for other arts\nand then bringing music into the scheme by saying that for music such\ndistinctions become meaningless.\n\nBut if we are to maintain that this kind of criticism is irrelevant,\nthen music becomes not only an isolated art but the art of which we\nknow least. If it cannot be accommodated as an example within the\ngeneral body of \u00e6sthetic criticism, the criticism that uses such terms\nas Pater uses, then whatever general conclusions the multifarious\nwritings of the last two centuries on the \u201cbeautiful\u201d may be considered\nto have reached are not applicable to music. In this extremity it is\nnatural, nowadays, to become \u201cscientific.\u201d Comparative studies are\nundertaken: the music of Java is compared with the music of Bach: the\nevolution of musical devices is made clear; the psychological condition\nof the patient under music is examined: the time taken for the right\ndegree of hypnosis to be induced is determined. That such methods may\none day stumble upon important facts it would be rash to deny, but\nnothing has yet been reached which illuminates the particular problem\nthat music presents. We are frankly of the opinion that, so far, the\ndifficult utterances of certain mystical or semi-mystical writers throw\nmore light on the real nature of music than do those of common sense.\n\nAmong such writers on music Schopenhauer is notorious; and it is worth\nwhile to dwell a little on his speculations, fantastic as they may\nseem, since they contain an element common to all such interpretations,\nwhich does serve to isolate the essential problem of music. In\nSchopenhauer\u2019s \u00e6sthetic the object of all arts, except music, is to\nlead, by the description of objects, to the recognition of the Ideas\n(Platonic) whose appearance in multiplicity constitutes the world.\nAll arts, therefore, have a transcendental function; their aim is to\nreveal to us the Platonic world of eternal essences or Ideas. But they\nhave to raise us to this region _via_ the objects of experience;\nin that sense they are also, therefore, concerned with the world of\nappearance and are dependent upon it. The case is different with music.\nMusic is not concerned with the external world either as a symbol or as\na reality. It is not even, in Schopenhauer\u2019s language, concerned with\nthe Ideas, but refers directly to that \u201cWill\u201d which, in Schopenhauer\u2019s\nphilosophy, underlies the Ideas themselves. The essence of his theory\nis given in the following passage:\n\n ... so ist die Musik, da sie die Ideen \u00fcbergeht, auch von der\n erscheinenden Welt ganz unabh\u00e4ngig, ignoriert sie schlechthin, k\u00f6nnte\n gewissermaassen, auch wenn die Welt gar nicht w\u00e4re, doch bestehen:\n was von den anderen K\u00fcnsten sich nicht sagen l\u00e4sst. Die Musik ist\n n\u00e4mlich eine so unmittelbare Objektivation und Abbild des ganzen\n Willens, wie die Welt selbst es ist, ja wie die Ideen es sind, deren\n vervielf\u00e4ltigte Erscheinung die Welt der einzelnen Dinge ausmacht.\n\nOr, as he says a little later on, the world may be regarded as embodied\nmusic.\n\nIt is not likely that anyone will take Schopenhauer\u2019s philosophy of\nmusic seriously; and even those who are sympathetic to his general\nview are not likely to find their sense of the ludicrous undisturbed\nby his identification of bass notes with the planets, tenor notes with\nthe vegetable world, and so on. The intensity of his response to music\nand his humourless courage have led him to what are perhaps the most\nfantastic statements in all his writings. But what is worth noting is\nthat so imaginative and fertile a speculator, because he was genuinely\nsensitive to music, had to give it a profoundly isolated position in\nhis \u00e6sthetic. In so doing we think he recognised one very important\ndifference between music and the other arts. It is true that music is\nindependent of the world of experience in a way that other arts are\nnot. It is true that there is a sense in which Schopenhauer is right\nwhen he says that music would exist even if the world did not. We\ncan see what is meant if we compare the development of a \u201cdramatic\u201d\npiece of music, such as the first movement of Beethoven\u2019s C minor\nSymphony, with a great tragedy. The tragedy, as a condition of success,\nmust make reference to our experience of life. The ostensible matter\nof the tragedy, the characters and incidents, must not violate our\nconception of reality if they are to be accepted. The tragedy must be\nplausible. Such considerations obviously do not apply to music. It is\nmeaningless to say that the development of a composition must satisfy\nour sense of probability. Yet there is a meaning in saying that its\ndevelopment seems either arbitrary or inevitable. The analogy that\nimmediately presents itself is a chain of logical reasoning, as in\nthe sustained development of a mathematical theorem. Such development\nis independent of all experience; the mind is obeying none but its\nown laws, and is paying no attention to any alien elements. And it is\nthis characteristic of mathematics which seems responsible for the\nfascination the study possesses for its devotees.\n\n Remote from human passions, remote even from the pitiful facts of\n nature, the generations have gradually created an ordered cosmos,\n where pure thought can dwell as in its natural home, and where one, at\n least, of our nobler impulses can escape from the dreary exile of the\n actual world,\n\nsays Mr. Bertrand Russell in a typical passage. A strain of romantic\neloquence seems, indeed, to be inseparable from the writings of\nmathematicians on their subject. But the analogy can be pressed more\nclosely. There are elegant and inelegant mathematical demonstrations,\nthose which merely \u201ccommand assent,\u201d as Lord Rayleigh said, and those\nwhich provide a very high degree of \u00e6sthetic satisfaction. In these\nlatter demonstrations the mind seems to be moving with more swiftness\nand freedom; the whole demonstration seems to flower in a natural\nand spontaneous way; we have the impression of _inevitability_.\nMathematical elegance, as Poincar\u00e9 has put it, \u201cn\u2019est autre chose que\nla satisfaction due \u00e0 je ne sais quelle adaptation entre la solution\nque l\u2019on vient de d\u00e9couvrir et les besoins de notre esprit.\u201d It is\nas if there were a mode of living natural to the human spirit, an\n_unadapted_ life, a life free from the necessity of accommodating\nitself to the elements, so largely alien, of the actual world.\nMathematics is the expression of this life so far as the intellect is\nconcerned. Is it too much to say that music is a fuller embodiment of\nthis free life?\n\nIf we are to say this we must acknowledge that more than the intellect\nis capable of this free life, that there is a logic of the emotions as\nwell as of the mind. This assumption is not difficult to make; indeed,\nif we reflect on our experience of some compositions, such as, to take\nthe same example, the first movement of the C minor Symphony, it is\ndifficult to avoid making it. And, in considering the matter from this\npoint of view, we may gain some results useful for musical criticism\nin general. The theme of the movement in question is characteristic\nof many of Beethoven\u2019s themes in that it does not serve merely as a\nkind of structural skeleton on which a composition is to be built. In\nthis respect it differs from, for instance, many of Bach\u2019s themes.\nThe theme immediately, in its ominous and arresting quality, throws\nthe mind into a certain state of expectancy, a state where a large\nnumber of happenings, but only the happenings belonging to a certain\nclass, can logically follow. As an analogous vague yet restricted\ninitial preparation we may instance the entry of the witches at the\nbeginning of _Macbeth_. As the music proceeds this rich, but more\nor less definite, state in the hearer becomes more and more precise,\nmore and more subtle. It is, as it were, explored and shown in all\nits height and depth. What was pregnant in the theme is exhibited\nto us in all its extent, its definiteness, and its force. The theme\nwas the entrance to a world. And we have the consciousness of logic,\nof _inevitability_, because at no point are we constrained. We\nexult because we are free; this is how we, too, would move but for\nour fetters, our alien, arbitrary fetters from which, for this time,\nwe have been freed. And in none of this, unless we have incurably\nliterary minds, are we ever reminded of experience. This life is no\nlife that we have lived or that, on this planet, we could live. Music\nis as independent of the world as mathematics, but it cannot, like a\nsystem of geometry, even be applied to the real world as an hypothesis.\nIt is even doubtful how far the emotions it expresses, when it is\nmerely expressing emotion, correspond to those of real life. The\nsorrow of the bereaved father is not the same thing as the sorrow\nof the bereaved lover, but music can express sorrow with thousands\nof _nuances_. It is customary to say that the emotions of music\nare generalised emotions; that its sorrow, for instance, is a kind of\ncommon denominator of all sorrows. But the exact opposite seems to be\nthe case. The situations of real life, like the resources of language,\nare probably too limited to afford correspondences to the immense\nvariety of emotions expressible in music. The musician is as free as\nthe non-Euclidean geometer to create worlds which have no objective\ncounterpart.\n\nIt is natural, therefore, in comparing the arts, that we should class\nmathematics and music together, since they resemble one another by\ntheir most intimate characteristics and differ, in these respects,\nfrom all other arts. It is worth noting, in this connection, that it\nis only in mathematics and music that we have the creative infant\nprodigy. Experience and learning, compared with what we vaguely call\n\u201cinstinct\u201d or \u201cgift,\u201d play a comparatively insignificant r\u00f4le; the\nboy mathematician or musician, unlike other artists, is not utilising\na store of impressions, emotional or other, drawn from experience or\nlearning; he is utilising inner resources so obviously independent of\nexperience that, like Plato\u2019s slave, he seems to have brought them\nwith him from some anterior life. And the artistic progress of a\nmusician, if it be a true progress, means primarily that he is making\never more accessible the riches of this inner life. It is difficult\nto avoid mysticism, or at least Platonism, at this point. But here\nagain it seems to us that Schopenhauer understood something essential.\nWhen he says that music, like the Platonic ideas, is an embodiment\nof the \u201cWill\u201d that underlies all things, he does at least say that\nwhat is revealed to us by a composition is something other than the\n\u201cpersonality\u201d of the composer. The function of music is not, like\nthat of literature, to illuminate this world, but there is a world it\nilluminates--a world at least as vast and independent of this one as\nthat mathematical \u201ccosmos\u201d described by Mr. Bertrand Russell.\n\nThere is much music, of course, which suggests no such mystical\nfancies. With most of Wagner\u2019s music, for instance, there is no hint\nof other worlds, but rather a gorgeous colouring of this one--or of\nthose aspects of this one which excite romantic poets with strong\nbodily appetites who can assume the background of the vigorous\nmaterial prosperity of the nineteenth century. Such music is fully\ncomparable with a certain kind of literature; all it lacks is the\ndefiniteness of statement, and hence the intellectual clarity, which\nthe use of language affords. It may be even more powerful and subtle\nthan literature can be--_Tristan und Isolde_ expresses certain\nemotions with immense adequacy. But it is not doing something which\nmusic alone can do; and, for that reason, it throws very little light\non the peculiar problem of music. For the peculiar problem of music\nconsists in its independence, in its power of transporting us to a\nworld which is not otherwise revealed. To Schopenhauer, to whom both\nthe world and music were embodiments of the same Will, there was a\nmusical equivalent for every experience; and, it would seem to follow,\nfor every musical utterance there is a corresponding experience.\nThe two worlds are independent, but there exists between them, as a\nmathematician would say, a one-to-one correspondence. Yet he very\nstrangely goes on to accept the theory that a musical utterance is a\nkind of generalisation of a number of distinct experiences. He points\nout that the musical setting of a poem, for instance, will serve for a\nnumber of similar poems. It is the \u201ckernal\u201d of all these poems which\nis given directly by the music. But it is equally true that the same\npoem will serve for several musical settings. When Beethoven, as one\nof sixty-three composers, composed his setting of Carpani\u2019s poem \u201cIn\nquesta tomba oscura,\u201d he probably composed the best setting, since it\nis the only one that has survived; but among the other sixty-two there\nmust have been many which, in Schopenhauer\u2019s phrase, were expressions\nof the \u201ckernal\u201d of the poem. The fact seems to be that, unless music\nis deliberately illustrative, it is not concerned with what is\notherwise expressible. That is why musicians are always dissatisfied\nwith \u201cliterary\u201d descriptions of music. However good in their own kind\nthey may be, they are always felt to be irrelevant and even, in some\nway, a degradation of the actual musical utterance. It is felt that\nthey exhibit a certain insensitiveness or lack of taste, as in that\ncuriously popular image which likens twin hills to a woman\u2019s breasts.\n\nAs compared with literature, music is abstract. It is independent, as\nliterature is not, of the facts of life. But just as there is some\nmusic which approaches to the condition of literature, so there is some\nliterature which approaches to the condition of music. Such literature,\nwhile it is concerned with the world of experience, as literature must\nbe, is concerned with that world as symbol and not as reality. Such\nliterature, we might say, is not concerned to illuminate the world\nof what we here call experience, but to reveal something about the\nsoul of man itself--or, if we prefer scientific jargon to mystical,\nto deal with the normally subconscious rather than with the normally\nconscious. Both kinds of literature have been called realistic, but\nthey are realistic from entirely different points of view. Dostoevsky,\nfor instance, regarded the realism of such writers as Zola as trivial.\nAnd can _Macbeth_ be regarded as a realistic work, on the basis of\nthe French conception of realism? _Macbeth_ is, indeed, a striking\nexample of the extent to which literature can approach the condition\nof music. The whole apparatus of the play, the witches, the characters,\nthe incidents, are so obviously not presented for their own sakes, but\nas symbols through which an overwhelming perception was to be conveyed.\nHere the fact that the literary artist must accommodate himself to the\nlaws of the real world, that he must satisfy our sense of probability,\nseems hardly a hindrance. Our sense of probability is, indeed,\npurposely lulled by the entrance of the witches at the beginning. We\nare made aware that not the real world alone is concerned. In this\nrespect the supernatural \u201cmachinery\u201d of _Macbeth_ performs an\naltogether different function from that in _Hamlet_. The whole of\n_Hamlet_ is perfectly realistic in the tight sense. But the fact\nthat literature must always use symbols differentiates it utterly from\nmusic. And just as we have seen that real life may present no analogies\nto what is revealed in music, so it may happen that the literary artist\nwho has access to a wide and deep inner life may find no symbols, such\nas are essential to literary art, to convey his perceptions. Mr. T.\nS. Eliot has stated that _Hamlet_ is an artistic failure because\nthe whole play, considered as presentation in terms of symbols, does\nnot adequately convey the emotions or perceptions we confusedly feel\nShakespeare is trying to express. Whether or not Mr. Eliot is correct\nin his instance, his general thesis is perfectly sound. Even if\n_Hamlet_ could be re-written so as to satisfy Mr. Eliot, it is\nstill true that there are some perceptions, states of mind, emotions,\nor whatever one likes to call them, which it is very difficult to\nbelieve are expressible in literature at all. Santayana gives a neat\nbut somewhat trivial instance in one of his essays where he says that\nthere is no human incident or group of incidents which can serve as a\nfitting symbol for pure radiant joy--a sort of prolonged, exultant,\ncelestial state of joy. A shadow, to the mature mind, lies over the\nbrightest and most delightful of life\u2019s happenings. He suggests that a\npoet who should try to imitate music in this respect could do little\nbut write the word \u201cJoy!\u201d with exclamation marks. He could write\nnothing else that was unambiguous. And, indeed, a symbol is always\nambiguous unless, like the symbols of the mathematician, its meaning is\ncompletely exhausted by its symbolic intent. The symbol distracts; it\nbrings with it a crowd of irrelevant associations, and for that reason,\neven when the symbols are most superbly handled, as in _Macbeth_,\nthe resultant communication is less definite than with music. But the\nvery great, the immense, importance of literature lies in the fact that\nit can, partially at least, shape the facts of life so as to make them\nconsonant with the nature of man. If experience can furnish symbols\nwhich express the deepest needs and aspirations of the soul, then life\ncan be, at least partially, illuminated. For man can understand nothing\nwhich is not consonant with his own nature. The literature which truly\nilluminates life is the literature which interprets life most fully\nin terms of our own emotions and aspirations. In this sense not only\nall literature, but all science, is anthropomorphic. Science is only\npossible in so far as it is logical. That is to say, the universe can\nonly be understood in so far as its happenings are obedient to the laws\nof man\u2019s own mind. In its relation to mathematics, where the mind pays\nno attention to the arbitrary conditions of experience, physics plays\nsomething of the same part as is played by literature in its relation\nto music. Both physics and literature, in their universal function,\nare concerned with a world which _need_ not obey the laws native\nto the spirit of man. Such illumination as they can give is dependent\nupon, as it were, what correspondences they can find. The revelation of\nlife afforded by _The Brothers Karamazov_, for instance, consists\nin relating the phenomena of life to the deepest impulses of the spirit\nof man. Only so does life become in any measure truly comprehended;\nand it is in this respect that such works differ from those reports\non life where we may recognise and assent to everything, but where\nour comprehension of anything is not deepened. Such works as _The\nBrothers Karamazov_ may be called philosophic, if we use the word to\ninclude something other than purely intellectual understanding.\n\nWe have suggested that, if mathematics may be taken as the intellectual\nanalogue of music, then it is not perhaps too far-fetched to say that\nsuch a science as physics may be taken as the intellectual analogue\nof literature, since both are concerned to interpret what we call the\nreal in terms of what we call the ideal, while the two former arts\nare not concerned with the real. And the question arises whether the\narts, mathematics, and music, which are not concerned to illuminate\nexperience, are worthy of serious attention. In the case of mathematics\nthe answer is not doubtful, since it has repeatedly shown itself\napplicable to real happenings, however little notions of utility may\nhave played a part, or need have played a part, in its creation. Even\nthe most remote mathematical theorems are not certainly immune from\npractical application. But no such claim can be made for music, and\nit is for that reason that to some philosophers music is a pleasing\nbut essentially trivial art. To such philosophers music, while it may\nsuggest spiritual profundities, is, after all, saying nothing of any\npossible significance. The adventures of the soul that it depicts are\nless significant even than a stage fight. Its one justification is the\npleasure it affords; it takes us out of ourselves in a way no other art\ncan do, and after this refreshing interregnum we return to the things\nthat matter. It may be so; we can give no proof that it is not so; we\ncan only say we find the point of view incredible. On this point,\nagain, we certainly find the mystical view of Schopenhauer, if less\nintelligible, at least more convincing than that of common sense.\n\n\n\n\n                            HUMAN TESTIMONY\n\n\nEverybody normally acts on the assumption that the value of human\ntestimony is an extremely variable quantity. The rules by which we\nassess the value of testimony, in the ordinary affairs of life, are of\nthat thoroughly habitual kind that hardly involve conscious processes;\nthey repose on two judgments, which we are always making. Our belief in\ndirect testimony to an event is conditioned by the nature of the event\nand by our estimate of the \u201cpersonal equation\u201d of the witness. These\ntwo factors are not quite independent; it is very seldom, for instance,\nthat we attribute \u201cgeneral untrustworthiness\u201d to anybody who is known\nto us. Our experience usually teaches us that there are certain classes\nof statements--e.g. his breaks at billiards, the number of miles\nhis motor-car runs on a gallon of petrol--for which that particular\nwitness\u2019s credibility is at a minimum. For some other classes of\nstatements we may have learnt to take his word without hesitation. What\nthe mathematicians call the \u201ccredibility\u201d of a witness is not, in the\ncase of any witness of whom we have personal knowledge, a constant\nfigure. It varies with the event, often in an extremely complicated\nway. When Brown is listening to Jones talking about the enormities of\nSmith the extremely delicate and rapid weighing of probabilities being\nperformed by Brown beggars any mathematical description. When the\nwitness is personally unknown to us the matter becomes simpler. Our\nconclusions, one way or another, will be held with less confidence, but\nthey will be more simply arrived at. We may, on the evidence supplied\nby the testimony itself--the tone of the letter, the man\u2019s manner in\nthe dock--class the witness as a man of a certain type. Corresponding\nto each type we have a rough scale of credibility for different types\nof events. In cases where we know nothing of the witness beyond his\nbare statement that he witnessed the occurrence of the event our\nestimate of his credibility is based on very general and usually\nrather vague considerations. We are guided by two things: the initial\ncredibility of the event and our estimate of the general value of human\ntestimony. Both of these criteria, and in particular the second, are\nexcessively ill-defined.\n\nIn the first place, what do we mean by the initial credibility\nof an event? There are very few cases where this notion can be\nprecisely defined. The simple instances dealt with in the elements of\nmathematical probability do, it is true, permit of precise definition.\nThe chance that a white ball will be drawn from an urn containing\nfive black balls and one white ball can be exactly estimated, for we\nare in possession of all the very simple relevant factors. But the\nprobability that Romulus founded Rome obviously belongs to a very\ndifferent category. And what is the initial credibility of a miracle?\nHume, as is well known, thought that the _a priori_ incredibility\nof a miracle was so great that its occurrence could not be established\nby human testimony. He is here trying to establish a ratio between the\ninitial credibility of a class of events and the initial credibility\nof human testimony to such events. He is taking some kind of average\nin both cases, but it is difficult to see how such an average can\nbe arrived at. Vague considerations of this kind are of no value in\nforming conclusions on matters of real interest to us, although they\nmay be sufficient to warrant a lazy scepticism regarding what William\nJames calls \u201cdead hypotheses,\u201d or may form the basis for amusing and\ningenious mathematical exercises. But we have no notion of an average\ninitial credibility which is of any use in practice; each case must\nbe judged on its own merits. And if, to take the second point, we\nreached some average for the value of human testimony in general, we\nshould never, in practice, apply it. The utmost we can hope to do is\nto establish a more or less constant relation between the testimony\nof classes of witnesses and classes of events. We have to divide\nwitnesses into types, and for each given type estimate the value of\nits testimony to different classes of events. We must investigate the\ndifference it makes when the witness is taken as isolated and when he\nis taken as a member of a group of witnesses. In this way we may hope\nto reach results which are of value in judicial procedure, in the study\nof history, and in various particular investigations, including those\nmodern substitutes for miracles, the phenomena of spiritualism. We\nare, in fact, to investigate man in his capacity as a truth-recording\ninstrument.\n\nThe result of such researches as have been made may be said, briefly,\nto show that human testimony has much less value than is normally\nassigned to it and, in particular, much less value than it is held to\npossess in a Court of Law. The experimental results obtained in this\nfield are, indeed, often startling. It is hardly too much to say that\none\u2019s first impulse, on becoming acquainted with the results hitherto\nreached, is to fall back on a general and dismayed scepticism regarding\nthe value of human testimony to anything whatever. But a closer\nexamination of the results show us that this attitude is unwarranted,\nand reinforces the common-sense assumption that the value of human\ntestimony is a matter of degree, varying from complete worthlessness\nto a very fair presumption that the event occurred as stated. The\ninvestigation is useful chiefly in showing us what factors influence\nthis value.\n\nIt is convenient to separate out these factors according to the scheme\nrecently employed by Dr. Edmond Locard, in his analysis of police\nrecords over a number of years. The statements made by a witness\nrepose, in the first place, on sensations which he has experienced. It\nmight be thought too obvious to be worth mentioning that we require\nthe witness who heard a sound, for instance, to have reasonably\ngood hearing, and yet there are many cases where simple preliminary\nconsiderations of this kind are not taken into account. Professor\nZ\u00f6llner\u2019s famous book _Transcendental Physics_, for instance,\nalleged marvels that occurred in the presence of Slade, the medium;\nand these alleged marvels, of great influence in spreading a belief\nin spiritualism, were witnessed to by four professors, Z\u00f6llner,\nFechner, Scheibner and Weber. But a member of the Seybert Commission,\nMr. George S. Fullerton, as a result of personal interviews, found\nthat two of these professors, Fechner and Scheibner, were partially\nblind at the time. Their sensations, therefore, in this respect, were\nuntrustworthy. But defects of this kind may usually be determined and\nthis factor conditioning the witnesses\u2019 credibility allowed for. Where\na witness makes appeal to a sensation which may be checked the check\nshould always be imposed. Thus Dr. Locard gives an instance where a\nwitness stated that an event occurred in a mill at a certain hour.\nHow did he know the hour? By hearing a clock strike at the time the\nevent occurred. A test was made, and it was found that the noise of\nthe mill made the striking of the clock quite inaudible. The witness\nthen remembered that he did not hear the clock strike until he had\nleft the mill. Similarly, witnesses have testified that they saw a man\nleave a doorway, their post of observation being one from which the\ndoorway could not be seen. Sensations may often be checked, however,\nand, to a careful inquirer, they need not be a grave source of error.\nBut the next stage is concerned with the witness\u2019s perceptions. Of his\nsensations he will single some out for attention and neglect the rest.\nHe singles out those which, for some reason or another, interest him\nmost. It may quite easily happen, therefore, that the sensations most\nrelevant to the inquiry in hand have been neglected. They have been\nfiltered, as it were, through the medium of the witness\u2019s interest;\nand it is often the case that his interest has not been excited by the\nsensations most pertinent to the subsequent inquiry. It is on this fact\nthat conjurers very largely depend for their success. The attention\nof the audience is distracted; they are invited to dismiss certain\nsensations as being of no importance, and, in general, it is remarkably\neasy to ensure this distraction of attention. Dr. Hodgson\u2019s case of the\nEnglish officer and the Hindu juggler well illustrates this point:\n\n Referring to the movements of the coins, he said that he had taken a\n coin from his own pocket and placed it on the ground himself, yet\n that this coin had indulged in the same freaks as the other coins.\n His wife ventured to suggest that the juggler had taken the coin and\n placed it on the ground, but the officer was emphatic in repeating\n his statement, and appealed to me for confirmation. He was, however,\n mistaken. I had watched the transaction with special curiosity, as I\n knew what was necessary for the performance of the trick. The officer\n had apparently intended to place the coin upon the ground himself, but\n as he was doing so the juggler leant slightly forward, dexterously and\n in a most unobtrusive manner received the coin from the fingers of the\n officer, as the latter was stooping down, and laid it close to the\n others. If the juggler had not thus taken the coin, but had allowed\n the officer himself to place it on the ground, the trick, as actually\n performed, would have been frustrated.\n\n Now I think it highly improbable that the movement of the juggler\n entirely escaped the perception of the officer; highly improbable,\n that is to say, that the officer was absolutely unaware of the\n juggler\u2019s action at the moment of its happening; but I suppose that,\n although an impression was made on his consciousness, it was so slight\n as to be speedily effaced by the officer\u2019s _imagination_ of\n himself as stooping and placing the coin upon the ground.\n\nWe have here an instance of erroneous testimony by a witness to his own\nactions; testimony to the actions of other people is usually much less\ntrustworthy. In this matter of direct perception we may discriminate\nstill further. Tactile perceptions are of almost no value whatever. If\na witness be blindfolded and asked to determine, by touch alone, the\nnature, the volume and the material of an object, it will be found that\nthe responses are very inaccurate. Experience of tactile sensations is\nrelatively small and deductions therefrom are practically valueless.\nThus the shock of a bullet entering the body may be interpreted as a\nslight blow, several dagger thrusts in the back as one thrust, and so\non. A piece of ice drawn across the neck of a blindfolded man and warm\nwater simultaneously poured on his chest have been stated to cause\ndeath by fright, the man having previously been informed that he was\ngoing to have his throat cut. Perceptions of odour or of taste are even\nless trustworthy; and here the difficulty of expression in precise\nterms, in the lack of a precise vocabulary, is complicated by the fact\nthat the witness primarily perceives odours and tastes as pleasant or\nunpleasant, and pays attention only to that aspect of them. In cases of\npoisoning, therefore, evidence of this kind should be given very little\nvalue.\n\nIt is only when we come to the senses of hearing and of sight that\nwe enter the region where perceptions may have evidential value. In\nthe case of hearing, however, we must still proceed very warily.\nExperiment has shown that estimates of direction, for example, are\nquite valueless, since the different estimates made by different\nobservers obey the laws of pure chance. Training can do a little, but\nvery little, to render these perceptions more trustworthy; in general,\nhowever, evidence as to the direction of a sound may be neglected.\nEstimates of the distance of a sound, also, are of very small value.\nThe intensity of a heard sound depends on the intensity of the source,\nand also on its distance; and these two factors may be apportioned\nby the observer in the most arbitrary manner. In the case where the\nsound is articulate, as in overhearing a conversation, we are in the\npresence of still other sources of error, due to illegitimate inference\nand the association of ideas. For words which are not heard will be\nsupplied by the witness in all good faith. He will have a theory of\nthe purport of the conversation, and will arrange the sounds he heard\nto fit it. Edgar Allen Poe\u2019s example, in _The Murders in the Rue\nMorgue_, of the cries of an ape which were interpreted as remarks\nin different languages by different observers, is judged by Dr. Locard\nto be not at all fantastic. The same general source of error applies\nto visual perceptions. Not everything is observed, and the lacun\u00e6\nare filled in by the witness in what seems to him the most probable\nmanner. Oversights in proof-reading furnish a familiar example of this\nkind of error. But psychological experiments have produced much more\nstriking examples. Clapar\u00e8de arranged for a man, wearing the mask of\na clown, to enter his lecture room while a lecture was in progress.\nThe students were afterwards asked to pick out this mask from a series\nof ten, and out of twenty-three who attempted the task five only\nwere successful--and even these successes were probably due, largely\nor wholly, to chance. The appreciation of distances, measured by the\neye, is also very likely to be erroneous, the rule being that large\ndistances are under-estimated and small ones over-estimated. A similar\nrule holds good of estimations of intervals of time. Errors of this\nkind are not pure errors of perception; they are due chiefly to lack\nof experience. A carpenter or builder would usually make a much more\naccurate estimate of the dimensions of, say, the side of a house than\nwould the ordinary person; and astronomers who work with transit\ninstruments have, as a class, very accurate perceptions of small\nintervals of time. It is chiefly lack of experience, also, which is\nresponsible for the absurdly different estimates different observers\nwill make of the number of people in a crowd. Dr. Locard states that,\non questioning the policemen employed to keep order during a procession\nas to the number of people they estimated to be taking part in the\nprocession, he obtained the figures five thousand, ten thousand,\ntwenty-four thousand. The actual number, he states, was three thousand.\nAnd during another procession two middle-aged, intelligent, educated\nParis journalists gave as their estimates for the number of people\nengaged, the one thirty thousand and the other three hundred thousand.\n\nBut now let us suppose that our witness, through the medium of his\nimperfect senses and his partial attention, has received a certain\nimage. What deformations may it suffer before it is produced as his\nevidence? If his memory of the incident has \u201clapsed\u201d the image will\nundergo comparatively little alteration, but if it has often been\ncalled to mind it will probably suffer a very considerable change.\nEach time the image is recalled it will suggest others; the creative\nimagination gets to work, altering the emphasis, adding particulars,\nobliterating others, and the result will be as much a work of art\nas the reproduction of a fact. This tendency is particularly to be\nnoticed with women, and with certain \u201cexcitable\u201d types; it may be\nalmost a national characteristic, as with Gascons and Sicilians. But\nall witnesses are prone to this kind of inaccuracy. Where the event has\noften been narrated by the witness the deformations become even more\nserious. For he is here exposed not only to the suggestions of his own\ncreative imagination, but to the suggestions of other people. Every one\nwishes to make a success of the story he is telling, and the perception\nof what points to stress and what details to add is wonderfully ready\nand alert. It has often happened that a witness of perfect good faith\nhas changed from the simple spectator of a drama to a prominent actor\nin it under the influence of repeated narration. Finally, we reach\nthe point when the witness has to bear his formal testimony. His\nobservations were imperfect, he has imperfectly remembered them, his\nimagination has distorted them, and he is now to express them. A very\nconsiderable additional source of inaccuracy is likely to enter here.\nThe witness probably cannot express his complete image--words may not\nbe sufficiently precise to render the fine shades of his remembered\nperceptions. The nature of a sound, the kind of emotion expressed by\na voice,--he may have no words for such things. And, in any case,\nthe witness will not express his complete image. He will select--in\naccordance with his own estimate of what is pertinent and what trivial.\nHe will do this even if he be allowed to talk to his heart\u2019s content;\nbut the method of question and answer as pursued in our Law Courts\nleads to even more imperfect expression. For he is forced to be precise\nwhere his recollection is vague, and he will either give a false\nprecision to his answer or else profess complete ignorance. More often\nstill the witness sins by exaggeration, and these exaggerations, in a\nthousand subtle ways, usually tend to add to his own importance. And\nit is important to notice that, besides tending to import fictitious\ndetails, the witness will tend to exaggerate his degree of conviction.\nWhere he was originally doubtful he is now perfectly sure.\n\nSo far we have been considering the witness in isolation, and we have\nnot considered the reaction upon his testimony of the emotional state\nproduced in him by the event. Yet the emotions accompanying the event\nhave a great bearing upon the value of the witness\u2019s testimony. During\nthe war it was noticed that the evidence of soldiers freshly wounded\nwas often of the most fantastic description. They would testify to\nthe details of catastrophes which had never occurred; they would\nassert that so-and-so had been decapitated in front of their eyes, and\nso-and-so buried by an explosion, when, as a matter of fact, nothing\nremotely resembling these events had taken place. And, under the\ninfluence of the comparatively slighter emotions of a spiritualistic\ns\u00e9ance, people will identify the same \u201cmaterialised\u201d mask as the\nfeatures of their husbands, wives, sons, daughters. Under the influence\nof such emotions it may be taken as a general rule that perceptions\ndeteriorate, and illegitimate inference, \u201cunconscious reasoning,\u201d\nbecomes more marked. Unconscious reasoning, indeed, plays a very great\npart in nearly all cases of mal-observation. It is well exemplified\nin the statement of the man sitting in a dark wood: \u201cThat dog\u2019s bark\nis not really a grasshopper, it is the squeaking of a cart.\u201d And Dr.\nLocard tells of one experiment he made, while in the Army, with a\nbarometer which bore a remote resemblance to a clock. His suggestion\nthat it was a clock was invariably accepted, even by the most eminent\npeople, and several of them acquired their knowledge of the time of\nday from its indications, even when the hour so indicated was highly\nimprobable. The testimony of great and commanding figures, even to\nthe time of day, may therefore be open to suspicion. But the immense\npart played by unconscious reasoning is best seen in the psychology\nof conjuring, under which head it is fair to group the great majority\nof alleged spiritualistic phenomena. In this latter case we have\nfurther to recognise what Freud calls the \u201cpleasure-pain principle,\u201d\nas distinguished from the \u201creality-principle.\u201d In other words, the\nwitnesses are seldom disinterested; they strongly desire to witness\ncertain events rather than others, and in such cases the slightest\nsuggestion is sufficient to produce conviction.\n\nWhen the witness is not isolated, but is a member of a group, the\ndefects we have before noted, due to the creative imagination, are\nlikely to be accentuated. The event will have been discussed and a\nuniform version gradually prepared. It is almost impossible, from\nthe unanimous testimony of a number of witnesses who have been in\nconsultation, to extract the original perceptions. The phenomenon of\n_mim\u00e9tisme testimonial_ makes its appearance, and may assume\nabnormal dimensions. A kind of collective hysteria may be induced, and\nthere can be little doubt that some of the collective denunciations of\nwitches which took place in the Middle Ages were manifestations of this\nform of mimicry.\n\nSuch are some of the results that have been reached by the modern\ninvestigations of the value of human testimony. They tell us little\nwe did not know before, for mankind has had an immense experience of\nhuman testimony; but they make our knowledge more precise and enable us\nto see what kinds of testimony are most open to suspicion. The effect\nof these researches on judicial procedure should be considerable, and\ntheir influence on the study of history not less marked. On this latter\nsubject their influence can only be indirect, and in the direction,\nprobably, of throwing still more doubt on the accuracy of historical\nrecords. The \u201ccredibility\u201d of a witness still remains a vague quantity,\nbut the chances are that it is something less than the value hitherto\nassigned to it. The investigation can claim no such precise results\nas those enunciated by Craig in 1699 in his _Theologi\u00e6 Christian\u00e6\nPrincipia mathematica_, where, after proving that the suspicions of\nany history vary in the duplicate ratio of the times taken from the\nbeginning of the history, he shows that faith in the Gospel, so far as\nit depended on oral tradition, expired about the year 880, and, so far\nas it depended on written tradition, would expire in the year 3150. The\nnew investigations of the value of human testimony start from humbler,\nbut surer, foundations.\n\n\n       _Printed in Great Britain by_ Butler & Tanner, _Frome and\n                                London_\n\n\n\n\n                          =TRANSCRIBER\u2019S NOTES=\n\nSimple typographical errors have been silently corrected; unbalanced\nquotation marks were remedied when the change was obvious, and\notherwise left unbalanced.\n\nPunctuation, hyphenation, and spelling were made consistent when a\npredominant preference was found in the original book; otherwise they\nwere not changed.","title":"Aspects of science","tradition":"philosophy-ethics","translated_text":null,"word_count":41332}