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A Review
Henri Louis Bergson's Book
Time and Free Will
Chapter II: The Multiplicity of Conscious States - The Idea of Duration
Topic 25: Velocity and Simultaneity
by Doug Renselle
Doug's Pre-review Commentary
Start of Review




Bibliography Author's
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Conclusion Index

Move to any Topic of Henri Louis Bergson's Time and Free Will,
or to beginning of its review via this set of links
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Topic 25...............Velocity and Simultaneity


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

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


"A direct analysis of the notion of velocity will bring us to the same conclusion. Mechanics gets
This is seen is the definition of velocity. this notion through a series of ideas, the connexion of which it is easy enough to trace. It first
builds up the idea of uniform motion by picturing, on the one hand, the path AB of a certain moving body, and, on the other, a physical phenomenon which is repeated indefinitely under the same conditions, e.g., a stone always falling from the same height on to the same spot. If we mark on the path AB the points M, N, P . . . reached by the moving body at each of the moments when the stone touches the ground, and if the intervals AM, MN and NP are found to be equal to one another, the motion will be said to be uniform: and any one of these intervals will be called the velocity of the moving body, provided that it is agreed to adopt as unit of duration the physical phenomenon which has been chosen as the term of comparison. Thus, the velocity of a uniform motion is defined by mechanics without appealing to any other notions than those of space and simultaneity."

(Our 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
  • orange-bold - text ref'd by index pages
  • 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
118 "Now let us turn to the case of a variable motion, that is, to the case when the elements AM, MN, NP . . . are found to be unequal. In order to define the velocity of the moving body A at the point M, we shall only have to imagine an unlimited number of moving bodies A1, A2, A3 . .all moving uniformly with velocities v1, v2, v3 . . . which are arranged, e.g., in an ascending scale and which correspond to all possible magnitudes. Let us then consider on the path of the moving body A two points M' and M", situated on either side of the point M but very near it. At the same time as this moving body reaches the points M', M, M", the other moving bodies reach points M'1, M1, M"1, M'2 M2, M"2 . . . on their respective paths; and there must be two moving bodies Ah and Ap, such that we have on the one hand M'M = M'hMh, and on the other hand MM" = MpM"p. We shall then agree to say that the velocity of the moving body A at the point M lies between vh and vp. But nothing prevents our assuming that the points M' and M" are still nearer the point M, and it will then be necessary to replace vh and vp, by two fresh velocities vi, and vn, the one greater than vh, and the other less than vp. And in proportion as we reduce the two intervals M'M and MM", we shall lessen the difference between the velocities of the uniform corresponding movements."

(Our bold and color.)

Bergson introduces a simple spatial calculus of velocity.

Perhaps most important observation to make about pages 117 and 118 is that Bergson requires no notion of time to express a classical concept of velocity. We may choose to view this as a quantum tell that some specific meme more fundamental than mass, length, and time underlies those classical indefinables. In Quantonics we call it "flux." You may then choose to view Bergson's finite, yet variable, analytic decomposition of linear space as a proxy for flux just as Irving Stein does in his one-dimensional "quantum object" models. Doug - 23May2002.



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119 "Now, the two intervals being capable of decreasing right down to zero, there evidently exists between vi and vn a certain velocity vm, such that the difference between this velocity and vh, vi. . . on the one hand, and vp, vn. . . on the other, can become smaller than any given quantity. It is this common limit vm which we shall call the velocity of the moving body A at the point [point is an extremely problematic classical concept; infinitesimal 'points' do n¤t 'exist' in quantum reality] M.—Now, in this analysis of variable motion, as in that of uniform motion, it is a question only of spaces once traversed and of simultaneous positions once reached. We were thus justified in saying that, while all that mechanics retains of time is simultaneity, all that it retains of motion itself—restricted, as it is, to a measurement of motion—is immobility.
"This result might have been foreseen by noticing that mechanics necessarily deals with equations,
Mechanics deals with equations, which express something finished, and not processes, such as duration and motion. and that an algebraic equation always expresses something already done. Now, it is of the very essence of duration and motion as they appear to our consciousness, to be something that is unceasingly being done; thus algebra can
represent the results gained at a certain moment of duration and the positions occupied by a certain moving body in space, but [mathematical formulae can-] not [represent] duration and motion themselves. Mathematics may, indeed, increase the number of simultaneities and positions which it takes into consideration by making the intervals very small: it may even, by using the differential instead of the difference, show that it is possible to increase without limit the number of these intervals of duration."

(Our brackets, bold and color.)




In other words, formal mechanical (i.e., mathematical) analysis of reality samples 'state' and classical 'state' is innately (by classical axiom) state-ic, and thus "immobile." Juxtapose this classical requisite with a quantum imperative that reality is absolute changæ/flux.


Algebra is/expresses n¤nexistent ESQ! Reality is, as Bergson told us prior, animate — instable.

Duration is animate process and as such algebraically n¤nanalyzable.

Quantum reality is both duration and motion. Bergson tells us that classical mathematics has n¤ intrinsic means of representing quantum reality. Bravo! We agree.

We also offer a heuristic that classical English language is similarly, due its own analytic state-icity, incapable of representing quantum reality and that is our motivation here in Quantonics to Remediate English Language for Millennium III.

Finally, and most important of all, we must learn to understand that mass, length/space, and time are all quantum processes, n¤t classical state-ic 'measurables.'

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120 "Nevertheless, however small the interval is supposed to be, it is the extremity of the interval at which mathematics always places itself. As for the interval itself, as for the duration and the motion, they are necessarily left out of the equation. The reason is that duration and motion are mental syntheses, and not objects; that, although the moving body occupies, one after the other, points on a line, motion itself has nothing to do with a line; and finally that, although the positions occupied by the moving body vary with the different moments of duration, though it even creates distinct moments by the mere fact of occupying different positions, duration properly so called has no moments which are identical or external to one another, being essentially heterogeneous, continuous, and with no analogy to number.
"It follows from this analysis that space alone [as a state-ic, immutable, excluded-middle, infinitely divisible classical concept] is homogeneous, that
Conclusion: space alone is homogeneous: duration and succession belong not to the external world, but to the conscious mind. objects in space form a discrete multiplicity, and that every discrete multiplicity is got by a process of unfolding in space. It also follows that there is neither duration nor even succession in space, if we give to these words the meaning in which consciousness takes them: each of the so-called successive states of the external world exists
alone [i.e., classically lisr]; their multiplicity is real only for a consciousness that can first retain them and then set them side by side by externalizing them in relation to one another. If it retains them, it is because these distinct states of the external world give rise to states of consciousness which permeate one another, imperceptibly organize themselves into a whole, and bind the past to the present by this very process of connexion. If it externalizes them in relation [juxtaposition] to one another, the reason is that, thinking of their radical distinctness (the one having ceased to be when the other appears on the scene), it perceives them under the form of a discrete multiplicity, which amounts to setting them out in line, in the space in which each of them existed separately. The space employed for this purpose is just that which is called homogeneous time." [Crux! Classical time 'is' space 'is' homogeneous time!]

(Our brackets, bold, color, and violet bold italic problematics. Symbol font required for comments on this page.)



And, dear reader, only quantum computers can offer us real analogies of our quantum stages' mental 'syntheses' of duration and motion. Formal, radically mechanistic, classical, digital computers never will! (Quantum computers have qubits vis-à-vis classical computers have digits/bits/nats/etc. Where qubits are quantons, digits are dichons:

  • Qubits are quantumly l¤gical:
    • heterogeneous,
    • Planck rate mutable,
    • quantal,
    • (per intera) everywhere-associative via quantum/quantonic ensemble interrelationships mediated by quantum vacuum flux,
    • included-middle,
    • coquecigrues(ical)
    • animate,
    • phase-ic,
    • pragmadigmatic,
    • coobsfecting,
    • (classically-) innumerable,
    • stochastic, (quanton_yf(flux))
    • c¤mplementary,
    • ensemble quantum c¤mplementarity:


      There are countless ways to show and hermeneut that script. We tried to retain part of our initial description while advancing n¤vel memes of l¤cal and n¤nl¤cal EIMA fuzzonic interrelationshipings.

      New red text effaces ,c¤mplement1 which on its face is monistically, monastically naïve.

      Doug - 20Oct2006.
    • ensemble quantum umcærtainty,
      u1 (c¤mplement1·c¤mplementsn),
      where our plural use of "c¤mplements" represents heterogeneity of other quantum c¤mplementsn which have ensemble affective quantum umcærtainty interrelationships with c¤mplement1, including complement1's umcærtainty interrelationships with itself. (Our use of classical analytic mathematics is inappropriate here, and we do so only to bequeath a heretofore and yet wanting semantic of real ensemble quantum umcærtainty.)
    • omnifference,
    • etc.
  • Digits/bits/nats/etc. are classically logical:
    • homogeneous,
    • immutable,
    • (per se, objective, denying both subjective reality and quantum vacuum flux) lisr,
    • excluded-middle,
    • inanimate/stable,
    • state-ic,
    • paradigmatic,
    • unilaterally observable (lisrable),
    • predicate logically negatable,
    • (classically-) numerable,
    • determinate, (y=f(t))
    • certain, (causation & 1-1 correspondence)
    • difference,
    • etc.)
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To contact Quantonics write to or call:

Doug Renselle
Quantonics, Inc.
Suite 18 #368 1950 East Greyhound Pass
Carmel, INdiana 46033-7730

©Quantonics, Inc., 2001-2010 Rev. 11Dec2008  PDR Created: 23Feb2001  PDR
(21Jul2002 rev - Change QELR links to A-Z pages.)
(27Jul2002 rev - Add 'ensemble c¤mplementarity' to qubit quantum logic list. Add 'omnifference' and 'difference' to respective lists.)
(7Aug2002 rev - Assure all colons are emboldened.)
(5Sep2002 rev - Remediate quantum comtextual occurrences of 'change' and 'uncertain[].')
(18Feb2003 rev - Change some Wingdings fonts to GIFs for browser compatibility.)
(22Apr2005 rev - Add 'point' QELR link to p. 119 text. Adjust colors. Release page constraints. Reset legacy red text.)
(8Jun2005 rev - Repair le.gif source linkage.)
(20Oct2006 rev - Adjust colors. Update p. 120 qubit comments.)
(5Jun2007 rev - Reset legacy red text. Slight reformat. Massive respell.)
(26Nov2007 rev - Reformat slightly.)
(29Jan2008 rev - Reformat slightly.)
(11Dec2008 rev - Replace some fonts with gifs.)

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