(Most quotes verbatim Henri Louis Bergson, some paraphrased.)
(Relevant to Pirsig, William James Sidis, and Quantonics Thinking Modes.)
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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:
|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."||
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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 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 itselfrestricted, as it is, to a measurement
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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, and not
objects; that, although the moving body occupies, one after the
other, points on a line, motion itself
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
continuous, and with no analogy
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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: