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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 23: The Eleatic Paradox
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 23...............The Eleatic Paradox


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

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


"It is to this confusion between motion and the space traversed that the paradoxes of the Eleatics are due; for [classicism assumes] the interval which separates two points is infinitely divisible, and if motion consisted of parts like
The common confusion between motion and the space traversed gives rise to the paradoxes of the Eleatics. those of the interval itself, the interval would never be crossed. But the truth is that each of Achilles' steps is a simple indivisible act, and that, after given number of
these acts [i.e., said number of acts which we view interrelated as an indivisible act of quantum indivisible acts], Achilles will have passed the tortoise. The mistake of the Eleatics [assuming they did n¤t understand Bergson's own issue of n¤nanalyzable process] arises from their identification of this series of acts, each of which is of a definite kind and indivisible, with the homogeneous space which underlies them. As this space can be divided and put together again according to any law whatever, they think they are justified in reconstructing Achilles' whole movement, not with Achilles' kind of step, but with the tortoise's kind: in place of Achilles pursuing the tortoise they really put two tortoises, regulated by each other, two tortoises which agree to make the same kind of steps or simultaneous acts, so as never to catch one another. Why does Achilles outstrip the tortoise? Because each of Achilles' steps and each of the tortoise's steps are indivisible acts [durational quantum processes] in so far as they are movements, and are [classically] different [spatial interval] magnitudes in so far as they are space: so that addition will soon give a greater length for the space traversed by Achilles than is obtained by adding together the space traversed by the tortoise and the handicap with which it started. This is what Zeno leaves out [Did Zeno do that intentionally?] of account when he reconstructs the movement of Achilles according to the same law as the movement of the tortoise, forgetting that space alone can be divided and put together again in any way we like, and thus confusing space with motion." [Classicists con fuse many notions without regard their omniquenessings and their unlimited comtextings. Einstein did similar when he unified gravity and acceleration. If you think about it though, acceleration is only a symptom of gravity, n¤t gravity itself. Gravity does n¤t depend upon time. Acceleration depends, classically, upon time. Classically time is a space 'identity,' a bogus means of thought. Time is n¤t space and space is n¤t time, period. To make them 'identical' is to make an enormous Error in judgment. Zeno was attempting to show classicists that. Bergson is attempting to show classicists that. As Bergson claims only a few pages away, paraphrased, time dependent "...motion...eludes space." Time, quantumly, is pure absolute~flux pr¤cess. Motion, quantumly, is pure quanton~temporal pr¤cessings. Space, classically, is pure unprocess, pure ideal 'state,' pure 'zero momentum' stoppability. Quantum reality is unstoppable! Doug - 29Jan2008.]

(Our bold, color, and violet bold italic problematics.)

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

Unfortunately classicism and its CTMs teach its adherents that classical analyticity means, "space can be divided and put together again according to any law whatever." Almost all folk of Western culture, today, early in Millennium III's infancy, believe such!!! They believe incorrectly that reality is analytic!!! Modern physics and mathematics and all hard sciences teach this bilge habitually as legacy paradigmatic, disciplinary matrix fact! They use it to 'solve' puzzles. UGH! Doug - 22May2002.


We cann¤t classically convert and map real quantum process(ings) onto state-ic numerable space! We cann¤t state-ically measure process using spatial concepts! Process(ings) are n¤t magnitudes! Processings are n¤nquantifiable. They are quantum animate, included-middle, c¤mplementary, everywhere associative Qualities!

Space as state-ic, numerable, divisible, inanimate ESQ is quantum unreal! Classical space is a delusion! Remember, in quantum reality, classical science's indefinables — mass, length/space, and time — are definable in terms of quantum flux, but then they are n¤ longer classically state-ic, numerable, infinitely divisible, inanimate ESQ.

Having said that, we must qualify how quantum reality offers a wide range of flux (and flux 'wavelengths:' notice our own inuring re-entrapment of flux in space via our use of classical 'wavelengths' — we need n¤vel language remediation here — imagine wavelengthings for now as an interim lingual substitute), from Planck's rate to almost unchanging. We call this range of flux/process changeability, "quantum variable/tentative persistence." Classicism, due greater quantum persistence of macroscopic 'objects,' Eleatically deludes itself that reality is inanimate, immutable, state-ic, etc. It is also worthwhile to note how quantum umcærtainty scales with quantum tentative persistence. Mean timings among quantum umcærtainty ævæntings grow with persistence; however, extentings/impactings of any umcærtainty ævæntings grow too. We choose to view this as Heisenberg's quantum umcærtainty interrelationships scaling all reality (Indeed, this appears to be Zeno's whole point, at least that is our heuristic hermeneutic of it, in Eleatic paradox 1.). We also choose to view Heisenberg's quantum umcærtainty interrelationships as quantum ensembles, n¤t bi-parametric dichons. Most classical physicists claim that Heisenberg's quantum umcærtainty only applies to a subatomic subset of quantum reality. See related comments in our Quantonics Immutability & Solipsism HotMeme™


"Hence we do not think it necessary to admit, even after the acute and profound analysis of a contemporary thinker,(1) that the meeting of the two moving bodies implies a discrepancy between real and imaginary motion, between space in itself and indefinitely divisible space, between concrete time and abstract time. Why resort to a metaphysical hypothesis, however ingenious, about the nature of space, time, and motion, when immediate intuition shows us motion within duration, and duration outside space? There is no need to assume a limit to the divisibility of concrete space; we can admit that it is infinitely divisible, provided that we make a distinction between the simultaneous positions of the two moving bodies, which are in fact in space, and their movements, which cannot occupy space, being duration rather than extent, quality and not quantity. To [classically] measure the velocity of a movement, as we shall see, is simply to ascertain a simultaneity; to introduce this velocity into calculations is simply to use a convenient [classical] means of anticipating a simultaneity. Thus mathematics confines itself to its own province as long as it is occupied with determining the simultaneous positions of Achilles and the tortoise at a given moment, or when it admits a priori that the two moving bodies meet at a point X—a meeting which is itself a simultaneity. But it goes beyond its province when it claims to reconstruct what takes place in the interval between two simultaneities; or rather it is inevitably led, even then, to consider simultaneities once more, fresh simultaneities, the indefinitely increasing number of which ought to be a warning that we cannot make movement out of immobilities, nor time out of space. In short, just as nothing will be found homogeneous in duration except a symbolical medium with no duration at all, namely space, in which simultaneities are set out in line, in the same way no homogeneous element will be found in motion except that which least belongs to it, the traversed space, which is motionless."

Note (1): Evellin, Infini et quantité. Paris, 1881.

(Our brackets, bold, color, and violet bold italic problematics.)


Classical mathematics drives out and excludes real quantum duration!



True quantum prescience, Bergson! Bravo! And he wrote this ~100 years ago! Awesome! Brilliant!


Permit Doug to refine and simplify what Bergson is writing here:

Classically mathematics can:

Anticipate and describe dialectically and conventionally simultaneity, but

Classically mathematics cann¤t:

Anticipate and describe dialectically and conventionally duration!

When you study further, and commence a better and quantum grasp of reality, you will find that quantum~reality permits n¤ memeos of classical simultaneity! Why? Quantum~reality is all quantized~pr¤cæssings n¤næ of which may be classically scalarbated as mathematics are wont to do.

Allow Doug to push simplicity a tad further to its "...we cannot make movement out of immobilities..." boundary conditionings. Realize how Bergson omnistinguishes quantum~change (wave~based~thinkqing) vis-à-vis classical state (space-based thingking).

Let's use bullets to omnistinguish them:

  • classical state-ic, space-based thingking, vis-à-vis
    • reality is stopped
    • state is perpetually durable (durable concrete reality)
    • Classical-Absolute means:
      • Consistent state: always states 'the truth'
      • Complete state: states all truths
      • Truth is durable,
  • quantum~changings, wavings~based~thinkqings
    • reality evolves at up to Planck rates of change
    • change is perpetually durable (durable quantum~reality)
    • Quantum~Absolute means:
      • Consistent change: always changes
      • Complete change: changes all
      • Evolutionary change is durable.

Again, if reality were stopped, playground swings wouldn't. See our QELR of duration.

Doug - 23Jan2010, 5Mar2010.

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

©Quantonics, Inc., 2001-2009 Rev. 29Jan2008  PDR Created: 23Feb2001  PDR
(23Jul2002 rev - Change QELR links to A-Z pages.)
(7Aug2002 rev - Assure all colons are emboldened. Remediate some page 113 comments on quantum uncertainty.)
(11Nov2002 rev - Add QSBP&Perspicacities page 113 comments link.)
(17Nov2002 rev - Insert page 113 intratextual bracketed red comment.)
(9Jan2003 rev - Add Zenos_Paradice link under page 113 text embedded bracketed comment.)
(20Jan2003 rev - Add 'Eleatically' modifier, and paradox 1 link to page 113 comments.)
(1,20Oct2006 rev - Release page constraints. Adjust colors. Add GIF aron. Adjust colors again.)
(29Jan2008 rev - Reformat slightly.)
(5Mar2010 rev - Update p. 114 comments.)

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