A Review of

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

**Chapter:****I****II****Bibliography****Author's**

Preface**1****2****3****4****5****6****7****8****9****10****11****12****13****14****15****16****17****Chapter:****III****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**

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

**COMMENTs**(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 **:**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 A _{1}, A_{2}, A_{3}. .all moving uniformly with velocities*v*_{1},*v*_{2}*, v*_{3}*.*. . 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}, M_{1}, M"_{1}, M'_{2}M_{2}, M"_{2}. . . on their respective paths; and there must be two moving bodies A_{h}and A_{p}, such that we have on the one hand M'M = M'_{h}M_{h}, and on the other hand MM" = M_{p}M"_{p}. We shall then agree to say that the velocity of the moving body A at the point M lies between*v*_{h}and*v*_{p}. 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*v*_{h}and*v*_{p}, by two fresh velocities*v*_{i}, and*v*_{n}, the one greater than*v*_{h}, and the other less than*v*_{p}. 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.

**119**"Now, the two intervals being capable of decreasing right down to zero, there evidently exists between v _{i}and*v*_{n}a certain velocity*v*_{m}, such that the difference between this velocity and*v*_{h}*, v*_{i}. . . on the one hand, and*v*_{p}*, v*_{n}. . . on the other, can become smaller than any given quantity. It is this common limit*v*_{m}which we shall call the velocity of the moving body A at the point [point is an extremely problematic classical**con**cept; 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**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.'

**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**, andobjects; that, although the moving body occupies, one after the other, points on a line,*not***motion itself has**; 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,*no*thing to do with a line**duration**properly so called hasmoments which are identical or external to one another, being essentially*no***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**con**cept] 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**, if we give to these words the meaning in which consciousness takes them*nor*even succession in space**:**each of the so-called successiveof the external world exists*states*of the external world give rise to*states*of consciousness which*states***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
**:**qubit

quantons(c¤mplements_{n},quantons(c¤mplement_{self},c¤mplements_{others}))

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¤mplement_{1}which on its face is monistically, monastically naïve.

Doug - 20Oct2006.

- ensemble
quantum umcærtainty,

i.e.,

u_{1}(c¤mplement_{1}·c¤mplements_{n}),

where our plural use of "c¤mplements" represents heterogeneity of other quantum c¤mplements_{n}which have ensemble affective*quantum umcærtainty*interrelationships with c¤mplement_{1}, including complement_{1}'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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(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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