From W. Heath Robinson's Hans Andersen's Fairy Tales [London: Constable, 1913]
Carpenter's words are in bold.
IT is one of the difficulties which meet anyone who suggests that modern science is not wholly satisfactory, that it is immediately assumed that the writer is covertly defending what Ingersoll calls the "rib-story," or that he wishes to restore belief in the literal inspiration of the Bible.
But, religious controversy apart, and while admitting that Science has done a great work in cleaning away the kitchen-middens of superstition and opening the path to clearer and saner views of the world, it is possible --- and there is already a growing feeling that way --- that her positive contributions to our comprehension of the order of the universe have in late times been disappointing, and that even her methods are only of limited applicability. After a glorious burst of perhaps fifty years, amid great acclamations and good hopes that the crafty old universe was going to be caught in her careful net, Science, it must be confessed, now finds herself in almost every direction in the most hopeless quandaries ; and, whether the rib-story be true or not, has at any rate provided no very satisfactory substitute for it.
And the reason of this failure is very obvious. It goes with a certain defect in the human mind, which, as we have pointed out elsewhere, necessarily belongs to the Civilisation-period --- the tendency, namely, to separate the logical and intellectual part of man from the emotional and instinctive, and to give it a locus standi of its own. Science has failed, because she has attempted to carry out the investigation of nature from the intellectual side alone --- neglecting the other constituents necessarily involved in the problem. She has failed, because she has attempted an impossible task ; for the discovery of a permanently valid and purely intellectual representation of the universe is simply impossible. Such a thing does not exist.
The various theories and views of nature which we hold are merely the fugitive envelopes of the successive stages of human growth --- each set of theories and views belonging organically to the moral and emotional stage which has been reached, and being in some sort the expression of it ; so that the attempt at any given time to set up an explanation of phenomena which shall be valid in itself and without reference to the mental condition of those who set it up, necessarily ends in failure ; and the present state of confusion and contradiction in which modern Science finds itself is merely the result of such attempt.
Of course this limitation of the validity of Science has been recognised by most of those who have thought about the matter ; but it is so commonly overlooked, and latterly the notion has so far gained ground that the "laws" of science are immutable facts and eternal statements of verity, that it may be worth while to treat the subject a little more in detail.
The method of Science is the method of all mundane knowledge ; it is that of limitation or actual ignorance. Placed in face of the great uncontained unity of Nature we can only deal with it in thought by selecting certain details and isolating those (either wilfully or unconsciously) from the rest. That is right enough. But in doing so --- in isolating such and such details --- we practically beg the question we are in search of ; and, moreover, in supposing such isolation we suppose what is false, and therefore vitiate our conclusion. From these two radical defects of all intellectual inquiry we cannot escape. The views of Science are like the views of a mountain ; each is only possible as long as you limit yourself to a certain standpoint. Move your position, and the view is changed.
Perhaps the word "species" will illustrate our meaning as well as any word ; and, in a sense, the word is typical of the method of Science.
I see a dog for the first time. It is a fox-hound. Then I see a second fox-hound, and a third and a fourth. Presently I form from these few instances a general conception of "dog." But after a time I see a grey-hound and a terrier and a mastiff, and my old conception is destroyed. A new one has to be formed, and then a new one and a new one. Now I overlook the whole race of civilised dogs and am satisfied with my wisdom ; but presently I come upon some wild dogs, and study the habits of the wolf and the fox. Geology turns me up some links, and my conception of dog melts away like a lump of ice into surrounding water. My species exists no more.
As long as I knew a few of the facts I could talk very wise about them; or if I limited myself arbitrarily, as we will say, to a study only of animals in England at the present day, I could classify them ; but widen the bounds of my knowledge, the area of observation, and all my work has to be done over again. My species is not a valid fact of Nature, but a fiction arising out of my own ignorance or arbitrary isolation of the objects observed.
Or to take an instance from Astronomy. We are accustomed to say that the path of the moon is an ellipse. But this is a very loose statement. On enquiry we find that, owing to perturbations said to be produced by the sun, the path deviates considerably from an ellipse. In fact in strict calculations it is taken as being a certain ellipse only for an instant --- the next instant it is supposed to be a portion of another ellipse. We might then call the path an irregular curve somewhat resembling an ellipse. This is a new view.
But on further enquiry it appears that, while the moon is going round the earth, the earth itself is speeding on through space about the sun --- in consequence of which the actual path of the moon does not in the least resemble an ellipse ! Finally the sun itself is in motion with regard to the fixed stars, and they are in movement too. What then is the path of the moon ? No one knows ; we have not the faintest idea --- the word itself ceases to have any assignable meaning.
It is true that if we agree to ignore the perturbations produced by the sun --- as in fact we do ignore perturbations produced by the planets and other bodies --- and if we agree to ignore the motion of the earth, and the flight of the solar system through space, and even the movement of any centre round which that may be speeding, we may then say that the moon moves in an ellipse. But this has obviously nothing to do with actual facts. The moon does not move in an ellipse --- not even " relatively to the earth " --- and probably never has done and never will do so. It may be a convenient view or fiction to say that it would do so under such and such circumstances --- but it is still only a fiction. To attempt to isolate a small portion of the phenomena from the rest in a universe of which the unity is one of Science's most cherished convictions, is obviously self-stultifying and useless.
But you say it can be proved by mathematics that the ellipse would be the path under these conditions ; to which I reply that the mathematical proof, though no doubt cogent to the human mind (as at present constituted in most people), is open to the same objection that it does not deal with actual facts. It deals with a mental supposition, i.e., that there are only two bodies acting on each other --- a case which never has occurred and never can occur --- and then, assuming the law of gravitation (which is just the thing which has to be proved), it arrives at a mental formula, the ellipse. But to argue from this process that the ellipse is really a thing in Nature, and that the heavenly bodies do move or even tend to move in ellipses, is obviously a most unwarrantable leap in the dark.
Finally you argue that the leap is warranted because, by assuming that the moon and planets move in ellipses, you can actually foretell things that happen, as for instance the occurrences of eclipses ; and in reply to that I can only say that Tycho Brahé foretold eclipses almost as well by assuming that the heavenly bodies moved in epicycles, and that modern astronomers do apply the epicycle theory in their mathematical formulae. The epicycles were an assumption made for a certain purpose, and the ellipses are an assumption made for the same purpose. In some respects the ellipse is a more convenient fiction than the epicycle, but it is no less a fiction.
In other words --- with regard to this "path of the moon" (as with regard to any other phenomenon of Nature) --- our knowledge of it must be either absolute or relative. But we cannot know the absolute path ; and as to the relative, why all we can say is that it does not exist (any more than species exists) --- we cannot break up Nature so ; it is not a thing in Nature, but in our own minds --- it is a view and a fiction.
Again, let us take an example from Physics --- Boyle's law of the compressibility of gases. This law states that, the temperature remaining constant, the volume of a given quantity of gas is inversely proportional to its pressure. It is a law which has been made a good deal of, and at one time was thought to be true, i.e., it was thought to be a statement of fact.
A more extended and careful observation, however, shows that it is only true under so many limitations, that, like the ellipse in Astronomy, it must be regarded as a convenient fiction and nothing more. It appears that air follows the supposed law pretty well, but not by any means exactly except within very narrow limits of pressure ; other gases, such as carbonic acid and hydrogen, deviate from it very considerably --- some more than others, and some in one direction and some in the opposite. It was found, among other things, that the nearer a gas was to its liquefying point, the greater was the deviation from the supposed law, and the conclusion was jumped at that the law was true for perfect gases only.
This idea of a perfect gas of course involved the assumption that gases, as they get farther and farther removed from their liquifying point, reach at last a fixed and stable condition, when no further change in their qualities takes place --- at any rate for a very long time --- and Boyle's law was supposed to apply to this condition. Since then, however, it has been discovered that there is an ultra-gaseous state of matter, and on all sides it is becoming abundantly clear that the change in the condition of matter from the liquid state to the ultra-gaseous state is perfectly continuous --- through all modifications of liquidity and condensation and every degree of perfection and imperfection of gasiness to the utmost rarity of the fourth state.
At what point, then, does Boyle's law really apply ? Obviously it applies exactly at only one point in this long ascending scale --- at one metaphysical point --- and at every other point it is incorrect. But no gas in Nature remains or can be maintained just at one point in the scale of its innumerable changes. Consequently, all we can say is that out of the innumerable different states that gases are capable of, and the innumerable different laws of compressibility which they therefore follow, we could theoretically find one state to which would correspond the law of compressibility called Boyle's law ; and that, if we could preserve a gas in that state (which we can't), Boyle's law really would be true just for that case.
In other words, the law is metaphysical. It has no real existence. It is a convenient view or fiction, arising in the first place out of ignorance, and only tenable as long as further observation is limited or wilfully ignored.
This then is the Method of Science. It consists in forming a law or statement by only looking at a small portion of the facts ; then, when the other facts come in, the law or statement gradually fades away again.
Conrad Gessner and other early zoologists began by classifying animals according to the number of their horns !
Political Economy begins by classifying social action under a law of Supply and Demand.
When people believed that the earth was flat, they generalised the facts connected with the fall of heavy bodies into a conception of "up and down." These were two opposite directions in space. Heavy bodies took the "downward" ; it was their nature.
But in time, and as fresh facts came in, it became impossible to group animals any longer by their horns ; "up and down" ceased to have a meaning when it was known that the earth was round. Then fresh laws and statements had to be formed. In the last-mentioned case --- it being conceived that the earth was the centre of the universe --- the new law supposed was that all heavy bodies tended to the centre of the earth as such. This was all right and satisfactory for a while ; but presently it appeared that the earth was not the centre of the universe, and that some heavy bodies --- such as the satellites of Jupiter --- did not in fact tend to the centre of the earth at all. Another lump of ignorance (which had enabled the old generalisation to exist) was removed, and a new generalisation, that of universal gravitation, was after a time formed. But it is probable that this law is only conceived of as true through our ignorance ; nay it is certain that belief in its truth presents the gravest difficulties.
In fact here we come upon an important point. It is sometimes said that, granting the above arguments and the partiality and defectiveness of the laws of Science, still they are approximations to the truth, and as each fresh fact is introduced the consequent modification of the old law brings us nearer and nearer to a limit of rigorous exactness which we shall reach at last if we only have patience enough.
But is this so ? What kind of rigorous statement shall we reach when we have got all the facts in ? Remembering that Nature is one and that if we try to get a rigorous statement for one set of phenomena (as say the lunar theory) by isolating them from the rest, we are thereby condemning ourselves beforehand to a false conclusion, is it not evident that our limit is at all times infinitely far off ?
If one knew all the facts relating to a given inquiry except two or three, one might reasonably suppose that one was near a limit of exactness in one's knowledge ; but seeing that in our investigation of Nature we only know two or three, so to speak, out of a million, it is obvious that at any moment the fresh law arising from increased experience may completely upset our former calculations.
There is a difference between approximating to a wall and approximating to the North Star. In the one case you are tending to a speedy conclusion of your labours, in the other case you are only going in a certain direction. The theories of Science generally belong under the second head. They mark the direction which the human mind is taking at the moment in question, but they mark no limits. At each point the appearance of a limit is introduced --- which becomes, like a mirage in the desert, an object of keen pursuit ; but the limit is not really there --- it is only an effect of the standpoint, and disappears again after a time as the observer moves.
In the case of gravitation there is for the moment an appearance of finality in the law of the inverse square of the distance, but this arises probably from the fact that the law is derived from a limited area of observation only, namely the movements (at great distances from each other) of some of the heavenly bodies.
(It is not generally realised how feeble a force gravitation is. It is calculated --- see Encycl. Brit., Art. Gravitation --- that two masses, each weighing 415,000 tons, and placed a mile apart, would exert on each other an attractive force of only one pound. If one, therefore, was as far from the other as the moon is from the earth, their attraction would only amount to (1/57,600)th of a millionth of a pound. This is a small force to govern the movement of a body weighing 415,000 tons ! and it is easy to see that a slight variation in the law of the force might for a long period pass undetected, though in the course of hundreds of centuries it might become of the greatest importance.)
The Cavendish and Schehallien experiments do not show more than that the law at ordinary distances on the earth's surface does not vary very much from that of the inverse square ; while the so-called molecular forces compel us (unless we make the very artificial assumption that a variety of attractions and repulsions co-exist in matter alongside of, and yet totally distinct from, the attraction of gravitation) to suppose very great modifications of the law for small distances.
In fact, as we saw of Boyle's law before --- the Newtonian law is probably metaphysical --- true under certain limited conditions --- and the appearance of finality has been given to it by the fact that our observations have been made under such or similar conditions. When we extend our observation into quite other regions of space, the law of the inverse square ceases to appear as even an approximation to the truth --- as, for instance, the law of the inverse fifth power has been thought to be nearer the mark for small molecular distances.
And indeed the state of the great theories of Science in the present day --- the confusion in which the Atomic theory of physics finds itself, the dismal insufficiency of the Darwin theory of the survival of the fittest ; the collapse in late times of one of the fundamental theories of Astronomy, namely that of the stability of the lunar and planetary orbits ; the cataclysms and convulsions which Geology seems just now to be undergoing ; the appalling and indeed insurmountable difficulties which attach to the Undulatory theory of Light ; the final wreck and abandonment of the Value-theory, the foundation-theory of Political Economy --- all these things do not seem to point to very near limits of rigorous exactness !
An impregnable theory, or one nearing the limit of impregnability, is in fact as great an absurdity as an impregnable armour-plate. Certainly, given the cannon-balls, you can generally find an armour-plate which will be proof against them ; but given the armour-plate, you can always find cannon-balls which will smash it up.
The method of Science, as being a method of artificial limitation or actual ignorance, is curiously illustrated by a consideration of its various branches. I have taken some examples from Astronomy, which is considered the most exact of the physical sciences.
Now does it not seem curious that Astronomy --- the study of the heavenly bodies, which are the most distant from us of all bodies, and most difficult to observe --- should yet be the most perfect of the sciences ? Yet the reason is obvious. Astronomy is the most perfect science because we know least about it --- because our ignorance of the actual phenomena is most profound.
Situated in fact as we are, on a speck in space, with our observations limited to periods of time which, compared with the stupendous flights of the stars, are merely momentary and evanescent, we are in somewhat the position of a mole surveying a railway track and the flight of locomotives. And as a man seeing a very small arc of a very vast circle easily mistakes it for a straight line, so we are easily satisfied with cheap deductions and solutions in Astronomy which a more extensive experience would cause us to reject. The man may have a long way to go along his "straight line " before he discovers that it is a curve ; he may have much farther to go along his curve before he discovers that it is not a circle ; and much farther still to go before he finds out whether it is an ellipse or a spiral or a parabola, or none of these ; yet what curve it is will make an enormous difference in his ultimate destination. So with the astronomer ; and yet Astronomy is allowed to pass as an exact science !
As another instance of the same thing, let me quote a passage from Maxwell's Theory of Heat, p. 3 1 ; the italics are mine :
"In our description of the physical properties of bodies as related to heat we have begun with solid bodies, as those which we can most easily handle, and have gone on to liquids, which we can keep in open vessels, and have now come to gases, which will escape from open vessels, and which are generally invisible. This is the order which is most natural in our first study of these different states. But as soon as we have been made familiar with the most prominent features of these different conditions of matter the most scientific course of study is in the reverse order, beginning with gases, on account of the greater simplicity of their laws, then advancing to liquids, the more complex laws of which are much more imperfectly known, and concluding with the little that has been hitherto discovered about the constitution of solid bodies."
That is to say that Science finds it easier to work among gases --- which are invisible and which we can know little about --- than among solids, which we are familiar with and which we can easily handle ! This seems a strange conclusion, but it will be found to represent a common procedure of Science --- the truth probably being that the laws of gases are not one whit simpler than the laws of liquids and solids, but that on account of our knowing so much less about gases it is easier for us to feign laws in their case than in the case of solids, and less easy for our errors to be detected.
Well then, as in Astronomy we get an "exact science," because the facts and phenomena are on such a tremendous scale that we only see a minute portion of them --- just a few details so to speak --- and our ignorance therefore allows us to dogmatise ; so at the other end of the scale in Chemistry and Physics we get quasi-exact sciences, because the facts and phenomena are on such a minute scale that we overlook all the details and see only certain general effects here and there.
When a solution of cupric sulphate is treated with ammonia, a mass of flocculent green [sic] precipitate is formed. No one has the faintest notion of all the various movements and combinations of the molecules of these two fluids which accompany the appearance of the precipitate. They are no doubt very complex. But among all the changes that are taking place, one change has the advantage of being visible to the eye, and the chemist singles that out as the main phenomenon.
So chemistry at large consists in a few, very few, facts taken at random as it were (or because they happen to be of such a nature as to be observable) out of the enormous mass of facts really concerned : and because of their fewness the chemist is able to arrange them, as he thinks, in some order, that is, to generalise about them. But it is certain as can be that he only has to extend the number of his facts, or his powers of observation, to get all his generalisations upset. The same may be said of magnetism, light, heat, and the other physical sciences ; but it is not necessary to prove in detail what is sufficiently obvious.
But now, roughly speaking, there is a third region of human observation --- a region which does not, like Astronomy (and Geology), lie so far beyond and above us that we only see a very small portion of it ; nor, like Chemistry and Physics, so far below us and under such minute conditions of space and time that we can only catch its general effects ; but which lies more on a level with man himself --- the so-called organic world --- the study of man, as an individual and in society, his history, his development, the study of the animals, the plants even, and the laws of life --- the sciences of Biology, Sociology, History, Psychology, and the rest.
Now this region is obviously that which man knows most of. I don't say that he generalises most about it, but he knows the facts best. For one observation that he makes of the habits and behaviour of the stars, or of chemical solutions --- for one observation in the remote regions of Astronomy or Chemistry --- he makes thousands and millions of the habits and behaviour of his fellowmen, and hundreds and thousands of those of the animals and plants.
Is it not curious then that in this region he is least sure, least dogmatic, most doubtful whether there be a law or no ? Or, rather, is it not quite in accord with our contention, namely that Science, like an uninformed boy, is most definite and dogmatic just where actual knowledge is least.
It will however be replied that the phenomena of living beings are far more complex than the phenomena of Astronomy or Physics --- and that is the reason why exact science makes so little way with them. Though man knows many million times more about the habits of his fellow-men than about the habits of the stars, yet the former subject is so many million times more complicated than the latter that all his additional knowledge does not avail him.
This is the plea. Yet it does not hold water. It is an entire assumption to say that the phenomena of Astronomy are less complicated than the phenomena of vitality. A moment's thought will show that the phenomena of Astronomy are in reality infinitely complex. Take the movement of the moon : even with our present acquaintance with that subject we know that it has some relation to the position and mass of the earth, including its ocean tides ; also to the position and mass of the sun ; also to the position and mass of every one of the planets ; also of the comets, numerous and unknown as they are ; also the meteoric rings ; and finally of all the stars ! The problem, as everyone knows, is absolutely insoluble even for the shortest period ; but when the element of Time enters in, and we consider that to do anything like justice to the problem in an astronomical sense we should have to solve it for at least a million years --- during which interval the earth, sun, and other bodies concerned would themselves have been changing their relative positions, it becomes obvious that the whole question is infinitely complex --- and yet this is only a small fragment of Astronomy.
To debate, therefore, whether the infinite complexity of the movements of the stars is greater or less than the infinite complexity of the phenomena of life, is like debating the precedence of the three persons of the Trinity, or whether the Holy Ghost was begotten or proceeding : we are talking about things which we do not understand.
Nature is one ; she is not, we may guess, less profound and wonderful in one department than another ; but from the fact that we live under certain conditions and limitations we see most deeply into that portion which is, as it were, on the same level with us. In humanity we look her in the face ; there our glance pierces, and we see that she is profound and wonderful beyond all imagination ; what we learn there is the most valuable that we can learn. In the regions where Science rejoices to disport itself we see only the skirts of her garments, so to speak, and though we measure them never so precisely, we still see them and nothing more.
There is another point, however, of which much is often made as a plea for the substantial accuracy of the scientific laws and generalisations, namely that they enable us to predict events. But this need not detain us long. J. S. Mill in his Logic has pointed out --- and a little thought makes it obvious --- that the success of a prediction does not prove the truth of the theory on which it is founded. It only proves the theory was good enough for that prediction.
There was a time when the sun was a god going forth in his chariot every morning, and there was a time when the earth was the centre of the universe, and the sun a ball of fire revolving round it. In those times men could predict with certainty that the sun would rise next morning, and could even name the hour of its appearance ; but we do not therefore think that their theories were true.
When Adams and Leverrier foretold the appearance of Neptune in a certain part of the sky, they made a brief prediction to an unknown planet from the observed relations of the movements of the known planets ; that does not show, however, that the grand generalisation of these movements, called the "law of gravitation," is correct. It merely shows that it did well enough for this very brief step --- brief indeed compared with the real problems of Astronomy, for which latter it is probably quite inadequate.
Tycho Brahé, excellent astronomer as he was, kept as we saw to the epicycle theory. He imagined that the moon's path round the earth was a fixed combination of cycle and epicycle. Kepler introduced the conception of the ellipse. Later on the motion of the perigee and other deviations compelled the abandonment of the ellipse and the supposition of an endless curve, similar to an ellipse at any one point, and maintaining a fixed mean distance from the earth, but never returning on itself or making a definite closed figure of any kind. Finally the researches of Mr. George Darwin have destroyed the conception of the fixed mean distance, and introduced that of a continually enlarging spiral. Certainly no four theories could well be more distinct from each other than these ; yet if an eclipse had to be calculated for next year it would scarcely matter which theory was used. The truth is that the actual problem is so vast that a prediction of a few years in advance only touches the fringe of it so to speak; yet if the fulfilment of the prediction were taken as a proof of the theory in each of these different cases, it would lead in the end to the most hopelessly contradictory results.
The success of a prediction therefore only shows that the theory on which it is founded has had practical value so far as a working hypothesis.
As working hypotheses, and as long as they are kept down to brief steps which can be verified, the scientific theories are very valuable --- indeed we could not do without them ; but when they are treated as objective facts --- when, for instance, the "law of gravitation" --- derived as it is from a brief study of the heavenly bodies --- has a universal truth ascribed to it, and is made to apply to phenomena extending over millions of years, and to warrant unverifiable prophecies about the planetary orbits, or statements about the age of the earth and the duration of the solar system --- all one can say is that those who argue so are flying off at a tangent from actual facts.
For as the tangent represents the direction of a curve over a small arc, so these theories represent the bearing of facts well enough over a small region of observation ; but as following the tangent we soon lose the curve, so following these theories for any distance beyond the region of actual observation we speedily part company with facts.
All our thoughts, theories, "laws," etc., may perhaps be said to touch Nature --- as the tangent touches the curve --- at a point. They give a direction --- and are true --- at that point. But make the slightest move, and they all have to be reconstructed. The tangents are infinite in number, but the curve is one. This may not only illustrate the relation of Nature to Science, but also of Art to the materials it uses. The poet radiates thoughts : but he sets no store by them. He knows his thoughts are not true in themselves, but they touch the Truth. His lines are the envelope of the curve which is his poem.
END OF PART A
CONTENTS: