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A Review
Henri Louis Bergson's Book
Time and Free Will
Chapter II: The Multiplicity of Conscious States(1) - The Idea of Duration
Topic 16: Numerical Multiplicity and Space
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
says, "You are here!")

Topic 16...............Numerical Multiplicity and Space


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

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


"NUMBER may be defined [classically] in general as a collection of units, or, speaking more
What is [definition of] number? exactly, as the synthesis of the one and the many. Every number is one, since it is brought before the mind by
a simple intuition and is given a name; but the unity which attaches to it is that of a sum, it covers a multiplicity of parts which can be considered separately."

Note (1): I had already completed the present work when I read in the Critique Philosophique (for 1883 and 1884) F. Pillon's very remarkable refutation of an interesting article by G. Noël on the interconnexion of the notions of number and space. But I have not found it necessary to make any alterations in the following pages, seeing that Pillon does not distinguish between time as quality and time as quantity, between the [conscious] multiplicity of juxtaposition and that of interpenetration. Without this vital distinction, which it is the chief aim of the present chapter to establish, it would be possible to maintain, with Pillon, that number may be built up from the relation of co-existence. But what is here meant by co-existence? If the co-existing terms form an organic whole, they will never lead us to the notion of [classically lisr] number; if they remain distinct, they are in juxtaposition and we are dealing with space. It is no use to quote the example of simultaneous impressions received by several senses. We either leave these sensations their specific differences, which amounts to saying that we do not count them; or else we eliminate their differences, and then how are we to distinguish them if not by their position or that of their symbols? We shall see that the verb "to distinguish" has two meanings, the one qualitative, the other is quantitative: these two meanings have been confused, in my opinion, by the philosophers who have dealt with the relations between number and space.

Return to top of page footnote reference.

(Our brackets, 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

Similarly to Bergson's manner of starting topic 15, he amazes us here too! He infers a quantum reality where:

Timequanton(quality,quantity), and
Timequanton(interpenetration,juxtaposition), where

interpenetration is n¤nactuality's c¤mplementary included-middle mediation of multiple comtextual juxtapositions (AKA interrelationships).

We offer some number heuristics based upon his statements about time:

  • number is quantum comtextually dependent via mediating juxtaposition,
  • number is quantum associative commingling via mediating interpenetration, and
  • number is quantum animate as a quanton of both quality and quantity.

Com(n)sider how these three heuristics satisfy Bergson's earlier statements about two classical delusions of reality:

  • that reality is stable, and
  • that objects in reality are independent.

See our One is the Onliest Number.

Com(n)sider how we can proffer similar quantum analogues for classical concepts of space and mass.

Too, here, we see that, to Bergson, particulate (lisr) objectivity and space are analogous concepts. He shows us how durational (quantum real) reality is classically n¤nnumerable.



"Without attempting for the present any thorough examination of these conceptions of unity and multiplicity, let us inquire whether the idea of number does not imply the representation of something else as well.

"It is not enough to say that number is a collection of units; we must add that these units are
The units which make up a number must be identical. identical with one another, or at least that they are assumed to be identical when they are counted. No doubt we can count the sheep
in a flock and say that there are fifty, although they are all different from one another and are easily recognized by the shepherd: but the reason is that we agree in that case to neglect their individual differences and to take into account only what they have in common. On the other hand, as soon as we fix our attention on the particular features of objects or individuals, we can of course make an enumeration of them, but not a total [because each sheep is unique/omnifferent]. We place ourselves at these two very different points of view when we count the soldiers in a battalion and when we call the roll. Hence we may conclude that the idea of number implies the simple intuition of a multiplicity of parts or units, which are absolutely alike."

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

In Quantonics, in general, we deny any classical concepts of identity and identicalness! Also see difference, omnifference, and one.



In quantum reality, what we can do (theoretically) is make a Bose-Einstein Con(m)densate (BEC) of them. In such a case, all 'objects' would share common quantum phasicities. In a sense many classical 'objects' could become ¤ne quantum co-here-nt quanton. Comsider how BECs eliminate quantonic interrelationships among condensed quantons. This process is ~reversible; however, when 'reversed' each classical 'object' would, initially share common quantum phasicities as ensemble "absolutely alike" initial comditions which would then, at up to Planck-rates, evolve omnifferently from thence on.

Bergson apparently did n¤t anticipate our quantum description above. He just said that since all sheep are, indeed, quantumly omnifferent ¤ne another, we cann¤t classically total them, ideally-mathematically, as a sum of cloned identical classical numeric units. Ten sheep as a total is n¤t ten classically 'identical' sheep!


77 "And yet they must be somehow distinct from one another, since otherwise they would merge
But they must also be distinct. into a single unit. Let us assume that all the sheep in the flock are identical; they differ at least by the position which they occupy in
space, otherwise they would not form a flock. [Bergson's argument here is analogous one we used in our One is the Loneliest page.] But now let us even set aside the fifty sheep themselves and retain only the idea of them. Either we include them all in the same image, and it follows as a necessary consequence that we place them [classically] side by side in an ideal [classical] space, or else we repeat fifty times in succession the image of a single one, and in that case it does seem, indeed, that the series lies in duration rather than in space. But we shall soon find out that it cannot be so. For if we picture to ourselves each of the sheep in the flock in succession and separately, we shall never have to do with more than a single sheep. In order that the number should go on increasing in proportion as we advance, we must retain the successive images and set them alongside each of the new units which we picture to ourselves: now, it is in space that such a juxtaposition takes place and not in pure duration. In fact, it will be easily granted that counting material objects means thinking all these objects together, thereby leaving them in space. But does this intuition of space accompany every idea of number, even of an abstract number?"

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

Now we see Bergson actually anticipate BECs! Taken literally, Bergson's "merge into a single unit" is quantum coherence, or more specifically Bose-Einstein Con(m)densation (BEC).

Can you see what an impact this has on classical mathematics? All numerical sums, to be quantum physially real, must represent BECs! Personally, we had never intuited that Bergsonian meme prior to now (16Apr2002).




78 "Any one can answer this question by reviewing the various forms which the idea of number has
We cannot form an image or idea of number without the accompanying intuition of space. assumed for him since his childhood. It will be seen that we began by imagining e.g. a row of balls, that these balls afterwards became points, and, finally, this image itself disappeared, leaving behind it, as we say, nothing but
abstract number. But at this very moment we ceased to have an image or even an idea of it; we kept only the symbol which is necessary for reckoning and which is the conventional way of expressing number. For we can confidently assert that 12 is half of 24 without thinking either the number 12 or the number 24: indeed, as far as quick calculation is concerned, we have everything to gain by not doing so. But as soon as we wish to picture number to ourselves, and not merely figures or words, we are compelled to have recourse to an extended image. What leads to misunderstanding on this point seems to be the habit we have fallen into of counting in time rather than in space. In order to imagine the number 50, for example, we repeat all the numbers starting from unity, and when we have arrived at the fiftieth, we believe we have built up the number in duration and in duration only. And there is no doubt that in this way we have counted moments of duration rather than points in space; but the question is whether we have not counted the moments of duration by means of points in space."

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





But, but, but, ... Einstein has told us time and space are identical!!! He said, "Reality is a space-time identity!" Is this what Feynman and Dyson meant when they conjectured Einstein had become a manipulator of mathematics and numbers and thus had lost touch with concrete (i.e. real) physical reality?

In quantonics, we can easily answer this issue using QTMs. All pairs of meme interrelationships in quantonics are quantons. All quantons are uncertainty interrelationships. So we just say, "quanton(time,space)." Spaces always have temporalities and temporalities always have spaces. How much of each depends upon which we are attempting to measure. This meme is analogous a Poisson bracket of a quanton's position and momentum. Space and time are quantum c¤mplementary! Quantons are paired quantum c¤mplementary interrelationships! We can use them to express general quantum systems, because general quantum systems are nestings of animate quantum c¤mplementary interrelationships.

79 "It is certainly possible to perceive in time, and in time only, a succession which is nothing but a succession, but not an addition, i.e. a succession which culminates in a sum. For though we reach a sum by taking into account a succession of different terms, yet it is necessary that each of these terms should remain when we pass to the following, and should wait, so to speak, to be added to the others: how could it wait, if it were nothing but an instant of duration? And where could it wait if we did not localize it in space? We involuntarily fix at a point in space each of the moments which we count, and it is only on this condition that the abstract units come to form a sum. No doubt it is possible, as we shall show later, to conceive the successive moments of time independently of space; but when we add to the present moment those which have preceded it, as is the case when we are adding up units, we are not dealing with these moments themselves, since they have vanished for ever, but with the lasting traces which they seem to have left in space on their passage through it. It is true that we generally dispense with this mental image, and that, after having used it for the first two or three numbers, it is enough to know that it would serve just as well for the mental picturing of the others, if we needed it. But every clear idea of number implies a visual image in space; and the direct study of the units which go to form a discrete multiplicity will lead us to the same conclusion on this point as the examination of number itself."

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

Here, via his "...in time only," Bergson denies our view of quantonic uncertainty interrelationships among measurables in reality. Doesn't this deny his own statements about classicists' two greatest delusions that:

1) reality is stable, and
2) objects in reality are independent?

But then he shows us how "terms" in duration are unstoppable. (Note how a classical concept of "waiting" AKA "stoppability" is necessary for mathematical induction, which is at heart of Peano's counting principle which Bergson is discussing here. Unstoppable duration (quantum reality) is, as we have shown elsewhere and as Bergson is showing us in his works, n¤n-inductive, n¤ndeterministic, and thus n¤ncausal!) Study that link carefully! Doug - 25Mar2004.

We might use photographs as cinematographical analogies here. They do n¤t really make duration "wait," either! We just tend to classically thingk that they do. Classical scientists do exactly this with their mathematics and their measurement and their digital computers! All they do is take 'photographs' of reality, process those 'photographs' analytically, state-ically, dichotomously, anachronistically, inanimately and call their results "real."


80 "Every number is a collection of units, as we have said, and on the other hand every number is itself
All unity is the unity of a simple act of the mind. Units divisible only because regarded as extended in space. a unit, in so far as it is a synthesis of the units which compose it. But is the word unit taken in the same sense in both cases? When we assert that number is a unit, we understand by this that we master the whole of it by a simple and indivisible intuition of the mind;
this unity thus includes a multiplicity, since it is the unity of a whole. But when we speak of the units which go to form number, we no longer think of these units as sums, but as pure, simple, irreducible units, intended to yield the natural series of numbers by an indefinitely continued process of accumulation. It seems, then, that there are two kinds of units, the one ultimate, out of which a number is formed by a process of addition, and the other provisional, the number so formed, which is multiple in itself, and owes its unity to the simplicity of the act by which the mind perceives it. And there is no doubt that, when we picture the units which make up number, we believe that we are thinking of indivisible components: this belief has a great deal to do with the idea that it is possible to conceive number independently of space. Nevertheless, by looking more closely into the matter, we shall see that all unity is the unity of a simple act of the mind, and that, as this is an act of unification, there must be some multiplicity for it to unify."

(Our bold and color.)


Quantum reality is n¤t classically synthetic. It is, rather, durationally emerging.




Classical number exclusively complements unity and multiplicity; however, classical number denies quantum requisite c¤mplementarity of animacy and inanimacy (quantum requisite absence of classical stability), and quantum requisite c¤mplementarity of included-middle and excluded-middle (quantum requisite absence of "exclusive" classical objective independence). To be able to understand and differentiate classical reality from quantum reality, we cann¤t over emphasize importance of what we just wrote! Doug - 17Apr2002.


81 "No doubt, at the moment at which I think each of these units separately, I look upon it as indivisible, since I am determined to think of its unity alone. But as soon as I put it aside in order to pass to the next, I objectify it, and by that very deed I make it a thing, that is to say, a multiplicity. To convince oneself of this, it is enough to notice that the units by means of which arithmetic forms numbers are provisional units, which can be subdivided without limit, and that each of them is the sum of fractional quantities as small and as numerous as we like to imagine. How could we divide the unit, if it were here that ultimate unity which characterizes a simple act of the mind? How could we split it up into fractions whilst affirming its unity, if we did not regard it implicitly as an extended object, one in intuition but multiple in space? You will never get out of an idea which you have formed anything which you have not put into it; and if the unity by means of which you make up your number is the unity of an act and not of an object, no effort of analysis will bring out of it anything but unity pure and simple. No doubt, when you equate the number 3 to the sum of 1 + 1 + 1, nothing prevents you from regarding the units which compose it as indivisible: but the reason is that you do not choose to make use of the multiplicity which is enclosed within each of these units. Indeed, it is probable that the number 3 first assumes to our mind this simpler shape, because we think rather of the way in which we have obtained it than of the use which we might make of it."

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








"But we soon perceive that, while all multiplication implies the possibility of treating any number whatever as a provisional unit which can be added to itself, inversely the units in their turn are true numbers which are as big as we like, but are regarded as provisionally indivisible for the purpose of compounding them with one another. Now, the very admission that it is possible to divide the unit into as many parts as we like, shows that we regard it as extended.

"For we must understand what is meant by the discontinuity of number. It cannot be denied
Number in process of formation is discontinuous but, when formed, is invested with the continuity of space. that the formation or construction of a number implies discontinuity. In other words, as we remarked above, each of the units with which we form the number 3 seems to be indivisible while we are dealing with it, and we pass abruptly from one to
the other. Again, if we form the same number with halves, with quarters, with any units whatever, these units, in so far as they serve to form the said number, will still constitute elements which are provisionally indivisible, and it is always by jerks, by sudden jumps, so to speak, that we advance from one to the other. And the reason is that, in order to get a number, we are compelled to fix our attention successively on each of the units of which it is compounded."

(Our brackets, bold and color.)








"The indivisibility of the act by which we conceive any one of them is then represented under the form of a mathematical point which is separated from the following point by an interval of space. But, while a series of mathematical points arranged in empty space expresses fairly well the process by which we form the idea of number, these mathematical points have a tendency to develop into lines in proportion as our attention is diverted from them, as if they were trying to reunite with one another. And when we look at number in its finished state, this union is an accomplished fact: the points have become lines, the divisions have been blotted out, the whole displays all the characteristics of continuity. This is why number, although we have formed it according to a definite law, can be split up on any system we please. In a word, we must distinguish between the unity which we think of and the unity which we set up as an object after having thought of it, as also between number in process of formation and number once formed. The unit is irreducible while we are thinking it and number is discontinuous while we are building it up: but, as soon as we consider number in its finished state, we objectify it, and it then appears to be divisible to an unlimited extent. In fact, we apply the term subjective to what seems to be completely and adequately known, and the term objective to what is known in such a way that a constantly increasing number of new impressions could be substituted for the idea which we actually have of it."

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



dichon(continuity, discontinuity)



Quantum real emergent number! In "...process of formation."

Classical unreal state-ic number, "...once formed."



"Thus, a complex feeling will contain a fairly large number of simple elements; but, as long as these elements do not stand out with perfect clearness, we cannot say that they were completely realized, and, as soon as consciousness has a distinct perception of them, the psychic state which results from their synthesis will have changed for this very reason. But there is no change in the general appearance of a body, however it is analysed by thought, because these different analyses, and an infinity of others, are already visible in the mental image which we form of the body, though they are not realized: this actual and not merely virtual perception of subdivisions in what is undivided is just what we call objectivity. It then becomes easy to determine the exact part played by the subjective and the objective in the idea of number. What properly belongs to the mind [quantum stage] is the indivisible process by which it concentrates attention successively on the different parts of a given space; but the parts which have thus been isolated [quantum islandicity] remain in order to join [quantum included-middle holism] with the others, and, once the addition is made, they may be broken up in any way whatever. They are therefore parts of space, and space is, accordingly, the material, with which the mind builds up number, the medium in which the [classical] mind places it.

"Properly speaking, it is arithmetic which teaches us to split up without limit the units of which number consists. Common sense is very much inclined to build up number with indivisibles."

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

Here, Bergson offers us his rendition of quantum uncertainty. It is analogous a Poisson bracket of change and perfect clarity.



    dichon(subjective_opposite, objective_opposite)



Bergson explains how we impose tendentious classicism on a quantum reality.

Bergson explains a source classicism's grand delusion of analytic reducibility: "...a cuisinart is our best means of understanding biological constructs."

Readers might also wish to comtemplate our take on classical "common sense." Doesn't common sense imply that we all have to think alike in order to agree on what we observe? Isn't common sense an analogue of mental cloning? What do modern academic institutions all do at Millennium III's commencement? Don't they do their best to clone minds on various subjects?

Isn't it classically considered good that classical 'scientists' all share one paradigm, one disciplinary matrix, one set of exemplar hermeneutics?

Would any truly extraordinary and pioneering scientist ever want his-her mind cloned or to be/have a cloned mind of a socially constructed paradigm?

Cloned minds are but ideal social concepts.

If we want our cultures to be diverse, why would we not want minds within our paradigms to be 'diverse.' We must realize that paradigms are state-ic patterns of social value, and as such, and happily, they are their own worst threat to survival.

We believe that social value AKA "common sense" should seldom be permitted to rule intellectual, intuitional, and instinctual patterns of value! Resist, yæs! Rule n¤! Fortunately, it does n¤t and ultimately it cann¤t.

One more comment: "Common sense," to us, is font and grail of denigration trumpeted against novel memes and their pioneers who threaten those trapped in devolving paradigms. Those trapped call their threats, "...idiots, insane, fools, charlatans, fraudulent, equivocal, prevaricative, liars, etc." When we hear those denigrations, we know those emitting such denigrations are, indeed, weak and fearful. Extraordinary scientists understand that n¤vel memes are precursors of exceptional scientific breakthroughs.

See our review of Thomas Kuhn's The Structure of Scientific Revolutions.



"And this is easily understood, since the provisional
It follows that number is actually
thought of
a juxtaposition
in space.
simplicity of the component units is just what they owe to the mind, and the latter pays more attention to its own acts than to the material on which it works. Science confines itself, here,
to drawing our attention to this material: if we did not already localize number in space, science would certainly not succeed in making us transfer it thither. From the beginning, therefore, we must have thought of number as of a juxtaposition in space. This is the conclusion which we reached at first, basing ourselves on the fact that all addition implies a multiplicity of parts simultaneously perceived.

"Now, if this conception of number is granted, it will be seen that everything is not counted in the
Two kinds of multiplicity:
material objects, counted in space;
(2) conscious states, not countable unless symbolically represented in space.
same way, and that there are two very different kinds of multiplicity. When we speak of material objects, we refer to the possibility of seeing and touching them; we localize them in space. In that case, no effort of the inventive faculty or of symbolical
representation is necessary in order to count them; we have only to think them, at first separately, and then simultaneously, within the very medium in which they come under our observation. The case is no longer the same when we consider purely affective psychic states, or even mental images other than those built up by means of sight and touch."

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

Yes, we agree. In our view, quantum reality shows us that reality is n¤t substantial, material, objective, spatially immutable, etc. Rather quantum reality is flux. Space is n¤t extensible number. Quantum space is flux wavelength!

Quantum space's smallest (currently known) wavelength is what we call a "Planck length." It apparently limits quantum flux's maximum frequency, and its minimum wavelength.

Quantum space's longest wavelength is ~unlimited depending upon whether and how quantum philosophy and science ultimately discover and decide what most closely represents percept zero in Nature. It apparently limits quantum flux's minimum frequency, and its maximum wavelength.

When we grasp quantum essence that quantum flux is not classically, spatially limited, we see that a current simple, classical univalent concept of number derived from it is wholly naïve. And that is just what Bergson is attempting to show us. We emerse a n¤vel meme that any quantum number is omnivalent. We might even think of quantum number as a qubit. E.g., an atom may be QTM-thought of as a qubit of qubits (e.g., its electrons and nuclei).

Bottom line: a naïve concept of classical number is innately incapable of representing a quantum reality whose quantons' numbers are essentially omnivalent qubits.


86 "Here, the terms being no longer given in space, it seems, a priori, that we can hardly count them except by some process of symbolical representation. In fact, we are well aware of a representation of this kind when we are dealing with sensations the cause of which is obviously situated in space. Thus, when we hear a noise of steps in the street, we have a confused vision of somebody walking along: each of the successive sounds is then localized at a point in space where the passer-by might tread: we count our sensations in the very space in which their tangible causes are ranged. Perhaps some people count the successive strokes of a distant bell in a similar way, their imagination pictures the bell coming and going; this spatial sort of image is sufficient for the first two units, and the others follow naturally. But most people's [classical] minds do not proceed in this way. They range the successive sounds in an ideal space and then fancy that they are counting them in pure duration. Yet we must be clear on this point. The sounds of the bell certainly reach me one after the other; but one of two alternatives must be true. Either I retain each of these successive sensations in order to combine it with the others and form a group which reminds me of an air or rhythm which I know: in that case I do not count the sounds, I limit myself to gathering, so to speak, the qualitative impression produced by the whole series."

(Our brackets, bold and color.)




In his Creative Evolution, Bergson refers this kind of (more quantumesque) think-king as "...think being directly." See our coined thibedir.


87 "Or else I intend explicitly to [classically] count them, and then I shall have to [classically] separate them, and this separation must take place within some [classically] homogeneous medium in which the sounds, stripped of their qualities, and in a manner emptied, leave traces of their presence which are [classically] absolutely alike. The question now is, whether this medium is time or space. But a moment of time, we repeat, cannot persist in order to be added to others. If the sounds are separated, they must leave empty intervals between them. If we count them, the intervals must remain though the sounds disappear: how could these intervals remain, if they were pure duration and not space? It is in space, therefore, that the operation takes place. It becomes, indeed, more and more difficult as we penetrate further into the depths of consciousness. Here we find ourselves confronted by a confused multiplicity of sensations and feelings which analysis alone can distinguish. Their number is identical with the number of the moments which we take up, when we count them; but these moments, as they can be added to one another, are again points in space. Our final conclusion, therefore, is that there are two kinds of multiplicity: that of material objects, to which the conception of number is immediately applicable; and the multiplicity of states of consciousness, which cannot be regarded as numerical without the help of some symbolical representation, in which a necessary element is space."

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

As we said above, "this medium" is pragmabsolute quantum flux. We can show that space, time, mass, and gravity are all functions of quantum flux. Bergson did n¤t k-now this. (Our use of "k-now" is quantonics lingo for Bergson's "...think being directly..." and our comtraction of it: thibedir. Where classicists 'know' via classical reality's state-ic, rote information on yuck-stuck status quo is the way to go know-ledges, students of Quantonics are k-now-ing via direct experience of an animate, plural, c¤mplementary quantum reality.)




Bergson's "two kinds of multiplicity" are still both classical since they are both spatial. To extend his kinds of multiplicity into a quantum realm we must first realize that quantum flux is crux. Then we can begin to fathom that, in a sense, quantum reality is unlimited multiplicity — beyond any naïve classical categorization.


88 "As a matter of fact, each of us [classically] makes a distinction between these two kinds of multiplicity
The impenetrability of matter is not a physical but a logical necessity. whenever he speaks of the impenetrability of matter. We sometimes set up impenetrability as a fundamental property of bodies, known in the same way and put
on the same level as e.g. weight or resistance. But a purely negative [classical] property of this kind cannot be revealed by our senses; indeed, certain experiments in mixing and combining things might lead us to call it in question if our minds were not already made up on the point. Try to picture one body penetrating another: you will at once assume that there are empty spaces in the one which will be occupied by the particles of the other; these particles in their turn cannot penetrate one another unless one of them divides in order to fill up the interstices of the other; and our thought will prolong this operation indefinitely in preference to picturing two bodies in the same place. Now, if impenetrability were really a quality of matter which was known by the senses, it is not at all clear why we should experience more difficulty in conceiving two bodies merging into one another than a surface devoid of resistance or a weightless fluid. In reality, it is not a physical but a logical necessity which attaches to the proposition "Two bodies cannot occupy the same place at the same time." The contrary assertion involves an [classical] absurdity which no conceivable experience could succeed in dispelling."

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

Impenetrability is a classical code word for Aristotle's excluded-middle. Classical impenetrability describes SOM's wall. But as students of Quantonics, we k-now that Quantum flux compenetrates quantum flux. Thus quantum reality is, indeed, penetrable. William James would say it is "compenetrable." Fritjof Capra would say it is "interpenetrable." Sadly, classicists, though they refer themselves 'scientists,' are just like us naught but amateurs on Nature's quantum real stage. Decline and fall of their ugly classical deign to feign is nigh. A quantum tsunami of Millennium III change shall wash our Earth clean of them. Doug - 18Apr2002.




And here, Bergson implies that classical logic misinterprets physical (to us, physial) reality. If that is what he intends, then we agree. Of course, reader, you understand that Quantonics denies classical syllogistic logic as n¤nquantum. Quantum Bose-Einstein Condensation physically demonstrates, "[~Unlimited] bodies [can] occupy the same place at the same time."


89 "In a word, it implies a [classical] contradiction. But does not this amount to recognizing that the very idea of the number 2, or, more generally, of any number whatever, involves the idea of juxtaposition in space? If impenetrability is generally regarded as a quality of matter, the reason is that the idea of number is thought to be independent of the idea of space. We thus believe that we are adding something to the idea of two or more objects by saying that they cannot occupy the same place: as if the idea of the number 2, even the abstract number, were not already, as we have shown, that of two different positions in space! Hence to assert the impenetrability of matter is simply to recognize the inter-connexion between the notions of number and space, it is to state a property of number rather than of matter.—Yet, it will be said, do we not count feelings, sensations, ideas, all of which permeate one another, and each of which, for its part, takes up the whole of the soul?—Yes, undoubtedly; but, just because they permeate one another, we cannot count them unless we represent them by homogeneous units which occupy separate positions in space and consequently no longer permeate one another. Impenetrability thus makes its appearance at the same time as number [Classical impenetrability depends upon a concept of Aristotelian excluded-middle; this concept is necessary for classicists to assure objective, numerical non-contradiction. But reality is not classical! Reality is quantum Quantum reality's middle is included! Reality's quantons are not just penetrable, they are interpenetrable!] ; and when we attribute this quality to matter in order to distinguish it from everything which is not matter [remember, Bergson has already shown us that classical negation, 'not' is subjective], we simply state under another form the distinction established above between extended objects, to which the conception of number is immediately applicable, and states of consciousness, which have first of all to be represented symbolically in space."

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

Here, Bergson puts us in pure awe of him! This is so beautiful, so prescient, so quantum...

If matter is impenetrable and we use number to describe and measure matter, then how can number be penetrable? If number is impenetrable, how can scientists use number to do sums and products, both of which we may view as penetrable quantum condensates of classically physical description? Heads up, readers! Doug - 18Apr2002.


Amazing! Bergson shows us that concepts of classical number, and classical material impenetrability classically contradict one another! Simply Awesome! Wow!

Why has science ignored this immense classical problematic! We have not tumbled to this Bergsonian perspective prior to now. To us, this is an outright denial of classical material science and its 'valid' uses of classical mathematics. Also, we see this as another tell of reality's underlying quantum nature.


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Doug Renselle
Quantonics, Inc.
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Carmel, INdiana 46033-7730

©Quantonics, Inc., 2001-2011 Rev. 24Feb2009  PDR Created: 23Feb2001  PDR
(23Jul2002 rev - Change QELR links to A-Z pages.)
(25Aug2002 rev - Add 'consensus' link to common sense above.)
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(16Jun2003 rev - Add p. 85 comments anchor 'Common Sense.')
(25Mar2004 rev - Add p. 79 comment links and red text.)
(16Apr2004 rev - Add 'number' link to page 77 comments 'numerical.')
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(24Feb2009 rev - Add link to recent QELR of 'aware.')

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