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A Review
Henri Louis Bergson's Book
Creative Evolution
Chapter III: On The Meaning of Life The Order of Nature
and the
Form of Intelligence
Topic 32: Geometry and Induction
by Doug Renselle
Doug's Pre-review Commentary
Start of Review

Chapter I II
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Chapter III IV
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Topic 32...............Geometry and Induction


(Most quotes verbatim Henri Louis Bergson, some paraphrased.)

(Relevant to Pirsig, William James Sidis, and Quantonics Thinking Modes.)


"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 [rather, and more apropos quantum reality, we would call it "tentative persistence"] of the same fact [using similar Quantonic think-king we would say that facts are Value patterns of tentative persistence and clearly not 'absolute, immutable truth'—thus we can see more vividly Bergson's intent: that neither deduction nor induction are more than patterns of tentative persistence—it is only classical thing-king methods which have crowned them absolutes]. The consciousness of the animal already does 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. [And, to our dismay and chagrin, classical mathematics takes this to its classical 'bank of know ledge' via its invalid idea of absolute modular induction.] Now, if we examine this double belief, this is what we find. 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 operations; 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 water-kettle-stove 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 given 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 me yesterday to be the only thing wanting to complete the system, will complete it to-morrow, no matter when to-morrow may be."

(Our brackets, bold, and color.)

Bergson restarts his footnote counts on each page. So to refer a footnote, one must state page number and footnote number.

Our bold and color highlights follow a code:

  • black-bold - important to read if you are just scanning our review
  • green-bold - we see Bergson suggesting axiomatic memes
  • violet-bold - an apparent classical problematic
  • blue-bold - we disagree with this text segment while disregarding context of Bergson's overall text
  • gray-bold - quotable text
  • red-bold - our direct commentary

"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 considered contains only magnitudes. If two numbers be given, I am not free to choose their difference. [See our One is the Onliest. This is an extreme indictment of classical mathematics which routinely concretizes differences which in reality are always changing.] 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 approaches this extreme case? [This determinism is never generally available to classical reason. Reality changes quantally at Planck rates. Macroscopic quantum outcomes are always based upon stochastic quantum ensemble events!] 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?(1) 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 [what we call classical "blinders"] to two essential points."

Note (1) - We have dwelt on this point in a former work. See the Essai sur les domnées immédiates de la conscience, Paris, 1889, pp. 155-160.

(Our link, brackets, bold, and color.)

"For the 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 simultaneous: 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 [coinsidence] 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 physicist legitimates this operation later on by reducing, as far as possible, differences of quality 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 transparency, a geometrical mechanism.(1) 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, so 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, intellectuality entire."

Note (1) - Op. cit. chaps. i. and ii. passim.

(Our link, brackets, bold, and color.)


This is a Bergsonian quantum epiphany! This is exactly what quantum reality does! It superposes Values. It superposes Qualities. Were reality immutable, monolithic objects, it could not superpose! However, now we know, reality is flux. What does superposition both mandate and deny? It mandates a real included-middle of that which superposes, and denies in general, any Aristotelian excluded-middle. Quantum superposition denies Aristotle's Syllogisms. For all flux, for all times, for all loci, quantons of flux superpose on quantum stages of isoflux.


Bergson, as apropos, indicts both geometrical induction, and geometrical deduction. Classical precepts, dogma and doctrine are but relics of Earth's first two tragic and opposition-filled Western cultural millennia. We may call them in retrospect, "Earth's Versus Millennia." Goodbye Greecian wrath. Goodbye dichotomous hate. Goodbye classical static hegemony. Hello quantum tsunami! Hello choices for loves of compenetrations! Hello changes everlasting!

Classical geometry depends upon its first axim for its own legitimacy:


In quantum~reality there are no identities! Period! Flux is crux! Identity depends upon state! No classical notions of state can exist in an absolutely changing quantum~reality! Say goodbye geometry.

Doug - 13Mar2009.

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©Quantonics, Inc., 2000-2011 Rev. 13Mar2009  PDR Created: 20Sep2000  PDR
(8Jul2001 rev - Correct link to page 30.)
(14Dec2001 rev - Add top of page frame-breaker.)
(15Nov2007 rev - Reformat slightly.)
(13Mar2009 rev - Update p. 216 commentary. Make page current.)

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