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A Review
Henri Louis Bergson's Book
Creative Evolution
Chapter III: On The Meaning of Life The Order of Nature
and the
Form of Intelligence
Topic 30: The Geometrical Order
by Doug Renselle
Doug's Pre-review Commentary
Start of Review

Chapter I II
Introduction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 
Chapter III IV
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  46 47

Move to any Topic of Henri Louis Bergson's Creative Evolution,
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Topic 30...............The Geometrical Order


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

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


"When we consider the admirable order of mathematics, the perfect agreement of the objects it deals with, the immanent logic in numbers and figures, our certainty of always getting the same conclusion, however diverse and complex our reasonings on the same subject, we hesitate to see in properties apparently so positive a system of negations, the absence rather than the presence of a true reality. But we must not forget that our intellect, which finds this order and wonders at it, is directed in the same line of movement that leads to the materiality and spatiality of its object. The more complexity the intellect puts into its object by analyzing it, the more complex is the order it finds there. And this order and this complexity necessarily appear to the intellect as a positive reality, since reality and intellectuality are turned in the same direction. [Doug must say, just now, this is one of Bergson's most important paragraphs thus far, especially in its import to humanity for Millennium III. It shows in a few efficient semantics how classicists placed and keep their heads in a deep pile of mathematical and objective sand. 'Positive' classical objects deny their quantum complements; they negate quantum complementarity; they call non-objective reality "non-sense, and absurd." All of our current classical science 'supports' itself on this feeble pile.]

"When a poet reads me his verses, I can interest myself enough in him to enter into his thought, put myself into his feelings, live over again the simple state he has broken into phrases and words. I sympathize then with his inspiration, I follow it with a continuous movement which is, like the inspiration itself, an undivided act. Now, I need only relax my attention, let go the tension that there is in me, for the sounds, hitherto swallowed up in the sense, to appear to me distinctly, one by one, in their materiality. For this I have not to do anything; it is enough to withdraw something. In proportion as I let myself go, the successive sounds will become the more individualized; as the phrases were broken into words, so the words will scan in syllables which I shall perceive one after another. Let me go farther still in the direction of dream: the letters themselves will become loose and will be seen to dance along, hand in hand, on some fantastic sheet of paper. I shall then admire the precision of the interweavings, the marvelous order of the procession, the exact insertion of the letters into the syllables, of the syllables into the words and of the words into the sentences. The farther I pursue this quite negative direction of relaxation, the more extension and complexity I shall create; and the more the complexity in its turn increases, the more admirable will seem to be the order which continues to reign, undisturbed, among the elements. Yet this complexity and extension represent nothing positive; they express a deficiency of will. And, on the other hand, the order must grow with the complexity, since it is only an aspect of it. The more we perceive, symbolically, parts in an indivisible whole, the more the number of the relations that the parts have between themselves necessarily increases, since the same undividedness of the real whole continues to hover over the growing multiplicity of the symbolic elements into which the scattering of the attention has decomposed it. [Bergson shows what happens when we apply objective static analysis in an unlimited elemental lisr reductionism. Where objective elements are lisr, and sever their complementary interrelationships with both other non-'positive' actualities and nonactualities our quantons are non-lisr and retain their dynamic quantonic complementary interrelationships.]"

(Our links, brackets, bold, and color.)

See Doug's 'What is Immanence?' Doug - 8Aug2012.

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
  • 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

"A comparison of this kind will enable us to understand, in some measure, how the same suppression of positive reality, the same inversion of a certain original movement, can create at once extension in space and the admirable order which mathematics finds there. There is, of course, this difference between the two cases, that words and letters have been invented by a positive effort of humanity, while space arises automatically, as the remainder of a subtraction arises once the two numbers are posited.(1) But, in the one case as in the other, the infinite complexity of the parts and their perfect coordination among themselves are created at one and the same time by an inversion which is, at bottom, an interruption, that is to say, a diminution of positive reality.

"All the operations of our intellect tend to geometry, as to the goal where they find their perfect fulfilment. But, as geometry is necessarily prior to them (since these operations have not as their end to construct space and cannot do otherwise than take it as given) it is evident that it is a latent geometry, immanent in our idea of space, which is the main spring of our intellect and the cause of its working. We shall be convinced of this if we consider the two essential functions of intellect, the facility of deduction and that of induction."

Note (1) - Our comparison does no more than develop the content of the term ld gos, as Plotinus understands it. For while the ld gos of this philosopher is a generating and informing power, an aspect or a fragment of the y n c h , on the other hand Plotinus sometimes speaks of it as of a discourse. More generally, the relation that we establish in the present chapter between "extension" and "detension" resembles in some aspects that which Plotinus supposes (some developments of which must have inspired M. Ravaisson) when he makes extension not indeed an inversion of original Being, but an enfeeblement of its essence, one of the last stages of the procession, (see in particular, Enn. IV. iii. 9-11, and III. vi. 17-18). Yet ancient philosophy did not see what consequences would result from this for mathematics, for Plotinus, like Plato, erected mathematical essences into absolute realities. Above all, it suffered itself to be deceived by the purely superficial analogy of duration with extension. It treated the one as it treated the other, regarding change as a degradation of immutability, the sensible as a fall from the intelligible. Whence, as we shall show in the next chapter, a philosophy which fails to recognize the real function and scope of the intellect.

(Our bold.)
















See Doug's more recent, 2005, QELR of duration in both its classical notions and quantum memeos.

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©Quantonics, Inc., 2000-2021 Rev. 3Oct2007  PDR Created: 20Sep2000  PDR
(31Dec2001 rev - Add top of page frame-breaker.)
(3Oct2007 rev - Reformat.)
(8Aug2012 rev - Add p. 209 comments link to Doug's 'What is Immanence?')

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