Creative Evolution — Henri Bergson (trans. Arthur Mitchell, 1911)

certain measure. Very soon appeal has to be made to common sense, that is to say, to the continuous experience of the real, in order to inSect the consequences deduced and bend them along the sinuosities of hfe. Deduction succeeds in things moral only metaphorically, so to speak, and just in the measure in which the moral is transposable into the physical, I should say translatable into spatial symbols. The metaphor never goes very far, any more than a curve can long be confused with its tangent. Must we not be struck by this feebleness of deduction as some- thing very strange and even paradoxical? Here is a pure operation of the mind, accomplished solely by the power of the mind. It seems that, if anj-where it should feel at home and evolve at ease, it would be among the things of the mind, in the domain of the mind. Not at all; it ia there that it is immediately at the end of its tether. On the contrary, in geometry, in astronomy, in physics, where we have to do with things external to us, deduction ia all-powerful 1 Observation and experience are un- doubtedly necessary in these sciences to arrive at the principle, that is, to discover the aspect under which things must be regarded; but, strictly speaking, we might, by good luck, have hit upon it at once; and, as soon as we possess this principle, we may draw from it, at any length, consequences which experience will always verify. Must we not conclude, therefore, that deduction is an operation governed by the properties of matter, molded on the mobile articulations of matter, implicitly given, in fact, with the space that underlies matter? As long as it turns upon space or spatialized time, it has only to let itself go. It is duration that puts spokes in its wheels.

Deduction, then, does not work unless there be spatial intuition behind it. But we may say the same of induction.

It is not necessary indeed to think geometrically, nor even to think at all, in order to expect from the same conditions a repetition of the same fact. The consciousness of the animal ah-eady docs this work, and indeed, independently of all consciousness, the living body itself is so constructed that it can extract from the successive situations in which it finds itself the similarities which interest it, and so respond to the stimuli by appropriate reactions. But it is a far cry from a mechanical expectation and reaction of the body, to induction properly so called, which is an intellectual operation. Induction rests on the belief that there are causes and effects, and that the same effects follow the same causes. Now, if we examine this double belief, this is what we f5nd. It implies, in the first place, that reality is decomposable into groups, which can be practically regarded as isolated and independent. If I boil water in a kettle on a stove, the operation and the objects that support it are, in reality, bound up with a multitude of other objects and a multitude of other oper- ations; in the end, I should find that our entire solar system is concerned in what is being done at this particular point of space. But, in a certain measure, and for the special end I am pursuing, I may admit that things happen as if the group vxUer-keitle-atove were an independent microcosm. That is my first affirmation. Now, when I say that this microcosm will always behave in the same way, that the heat will necessarily, at the end of a certain time, cause the boiling of the water, I admit that it is sufficient that a certain number of elements of the system be ^ven in order that the system should be complete; it completes itself automatically, I am not free to complete it in thought as I please. The stove, the kettle and the water being given, with a certain interval of duration, it seems to me that the boiling, which experience showed

Geometry and Induction

me yesterday to be the only thing wanting to complete the system, will complete it to-morrow, no matter when to-morrow may be. What is there at the base of this belief? Notice that the belief is more or less assured, according as the case may be, but that it Is forced upon the mind as an absolute necessity when the microcosm con- sidered contains only magnitudes. If two numbers be given, I am not free to choose their difference. If two sides of a triangle and the contained angle are given, the third side arises of itself and the triangle completes itself automatically. I can, it matters not where and it matters not when, trace the same two sides containing the same angle: it is evident that the new triangles so formed can be superposed on the first, and that consequently the same third side will come to complete the system. Now, if my certitude is perfect in the case in which I reason on pure space determinations, must I not suppose that, in the other cases, the certitude is greater the nearer it ap- proaches this extreme case? Indeed, may it not be the limiting case which is seen through all the others and which colors them, accordingly as they are more or less transparent, with a more or less pronounced tinge of geometrical necessity?' In fact, when I say that the water on the fire will boil to-day as it did yesterday, and that this is an absolute necessity, I feel vaguely that my imagination is placing the stove of yesterday on that of to-day, kettle on kettle, water on water, duration on duration, and it seems then that the rest must coincide also, for the same reason that, when two triangles are superposed and two of their sides coincide, their third sides coincide also. But my imagination acts thus only because it shuts its eyes to two essential points. For the

We have dwelt on this point in a former work. See the EaaaitUT lea donrUea immidiatea de Ut coiunence, Paris, 18S9, pp. 1S5-160.

system of to-day actually to be superimposed on that of yesterday, the latter must have waited for the former, time must have halted, and everything become simultane- oiis: that happens in geometry, but in geometry alone. Induction therefore implies first that, in the world of the physicist as in that of the geometrician, time does not count. But it implies also that qualities can be superposed on each other like magnitudes. If, in imagination, I place the stove and fire of to-day on that of yesterday, I find indeed that the form has remained the same; it suffices, for that, that the surfaces and edges coincide; but what is the coincidence of two qualities, and how can they be superposed one on another in order to ensure that they are identical? Yet I extend to the second order of reality all that applies to the first. The ph>'sicist legitimates this operation later on by reducing, as far as possible, differences of quaUty to differences of magnitude; but, prior to all science, I incline to liken qualities to quantities, as if I perceived behind the qualities, as through a trans- parency, a geometrical mechanism.' The more complete this transparency, the more it seems to me that in the same conditions there must be a repetition of the same fact. Our inductions are certain, to our eyes, in the exact degree in which we make the qualitative differences melt into the homogeneity of the space which subtends them, 80 that geometry is the ideal limit of our inductions as well as of our deductions. The movement at the end of which is spatiality lays down along its course the faculty of induction as well as that of deduction, in fact, intel- lectuality entire.

It creates them in the mind. But it creates also, in

things, the "order" which our induction, aided by de-

< Op. eit. ch&pi. i. «Dd il. patiim.

Physical Laws

ductioD, finds there. This order, on which our action leans and in which our intellect recognizes itself, seems to us marvelous. Not only do the same general causes al- ways produce the same general effects, but beneath the visible causes and effects our science discovers an infinity of infinitesimal changes which work more and more exactly into one another, the further we push the analysis: so much so that, at the end of this analysis, matter becomes, it seems to us, geometry itself. Certainly, the intellect is right in admiring here the growing order in the growing complexity; both the one and the other must have a positive reality for it, since it looks upon itself as positive. But things change their aspect when we consider the whole of reality as an undivided advance forward to successive creations. It seems to us, then, that the complexity of the material elements and the mathematical order that binds them together must arise automatically when within the whole a partial interruption or inversion is produced. Moreover, as the intellect itself is cut out of mind by a process of the same kind, it is attuned to this order and complexity, and admires them because it recognizes itself in them. But what is admirable in itself, what really deserves to provoke wonder, is the ever-renewed creation which reality, whole and undivided, accomplishes in ad- vancing; for no complication of the nrnthematical order with itself, however elaborate we may suppose it, can in- troduce an atom of novelty into the world, whereas this power of creation once given (and it exists, for we are conscious of it in ourselves, at least when we act freely) has only to be diverted from itself to relax its tension, only to relax its tension to extend, only to extend for the mathe- matical order of the elements so distinguished and the in- flexible determinism connecting them to manifest the inter- ruption of the creative act: in fact, inflexible deterraitusm

218 CREATIVE EVOLUTION [ghap?*

and mathematical order are one with this very interruption.

It is this merely negative tendency that the particular laws of the physical world express. None of them, taken separately, has objective reality; each is the work of an investigator who has regarded things from a certain bias, isolated certain variabJes, applied certain conventional units of measui'emcnt. And yet there is an order ap- proximately mathematical immanent in matter, an ob- jective order, which our science approaches in proportion to its progress. For if matter is a relaxation of the in- extensive into the extensive and, thereby, of hberty into necessity, it does not indeed wholly coincide with pure homogeneous space, yet is constituted by the movement which leads to space, and is therefore on the way to ge- ometry. It is true that laws of mathematical form will never apply to it completely. For that, it would have to be pure space and step out of duration.

We cannot insist too strongly that there is something artificial in the mathematical form of a physical law, and consequently in our scientific knowledge of things.' Our standards of measurement are conventional, and, so to say, foreign to the intentions of nature: can we suppose that nature has related all the modalities of heat to the expansion of the same mass of mercury, or to the change of pressure of the same mass of air kept at a constant volume? But we may go further. In a general way, measuri'ng is a wholly human operation, which implies that we really or ideally superpose two objects one on another a certain number of times. Nature did not dream of this superposition. It does not measure, nor does it count. Yet physics counts, measures, re- lates "quantitative" variations to one another to obtain laws, and it succeeds. Its success would be inexplicable,

' Cf. MpecUlly the profound Btudioa of M. Ed. Le Koy in the Revtu d» mtCaph. tt de morale.

Pffmc.

if the movement which constitutes materiality were not the same movement which, prolonged by us to its end, that is to say, to homogeneous space, results in making us count, measure, follow in their respective variations terms that are functions one of another. To effect this prolong- ation of the movement, our intellect has only to let itself go, for it runs naturally to space and mathematics, in- tellectuahty and materiality being of the same nature and having been produced in the same way.