Figurate Number Space

Figurate Number Space



Recondite Systems Theory

Questions in a comment posted to Pitkanen:

Matti,

From comments relating to you posts I am not sure I understand your key insight, and I feel you have not seen mine- perhaps because of the complexity of the language and the subject.

There are whole journals on Pascal's triangle and its properties. There is new evidence relating to Ramanujan. So in an attempt to understand you better I took an interesting diagram from my last post and put it into my "quasic" framework.

So, if you would look at today's diagram maybe we could reach some common and new ground. In many ways yours to mine is a more reductionist or scientific theory but perhaps not a pure as Kea's math.

In this top quark idea lurks further generalizations at but the beginning of such hierarchies. Could this have been predicted in the main by our theories as it seems the 3+1 concept involved here at least in the ideal form?

This chart of course can be extended into very high dimensions the one here only goes up to ten. In this notation as a help to visualization (the intuitive structural seeing of it as our friend desires) the values of some rather large figurate numbers are reduced to a cell in the search for patterns. Is there a limit to say 64K dimensions with these Fermat numbers involving the elegance of primes? 11n + 6 = 17 ?

Could you clear up a bit your insights involving 89 - all our theories seem to have haunting parallels. 89 = Xn + b

The PeSla

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http://www.brooksdesign-ps.com/Code/Html/pin2.htm

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By recondite systems I mean the word from a comment by Fermat on 4n+1 being among the most recondite of number properties. Now in the arithmetic we need to relate this to the topology of all, that too a rather recondite study.

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I wonder in fact, on what level of quasic dimensions of our quality and quantity of insight, if they can be compared within a general theory overview, so we exceed the epiphanies of Ramanujan- or since we are aware of new directions may we now do so?

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I speculate btw that in the Gamma function, a sort of square root of factorial like things- we reach the limit of -1 (that is the way Brooks counts here beginning at 2 which is explained as a method of shifts in quasic counting) that this barrier in some form of complex space, independent of ideas of spin networks and so on, that we do not necessarily find a barrier here because of division by zero- the idea perhaps that space gets fuzzy near this singularity or at -1 it is full to infinity for both the positive real and the zeta numbers. Can we reach into such vague spaces that in effect are thus unseen but have dynamic structure's to even that of the virtual and the laws of such structures on the dark or opaque properties of these? As the boundaries of a quasic plane are zero (or one way to look at it, infinity) in what more general sense can we regard these boundaries- Brooks here uses the boundary as unities as these are in a sense the 1's in pascal's triangle as generators- such that the holographic principle informational makes sense even at these negative singularities. Can in these anomalous spaces and their looping and uncertainty of their complete closing in a sense generalize this holographic idea and its inverses?
Does not the physical content of the brain use this sort of structure as well in some holographic ways? Can an event in such mental and biological space in one place not show up thru no known paths or possibly many of them so as to become concrete differently at a distance at least within the bounds of the organism? Hawking's idea in this sense is not so much a mangled return nor is something in such abstract space lost and asymmetrical.

But I see these issues of the background or phaneron of things, Newton, Einstein, Mach and Leibniz in terms of mass like and gravity like things, recondite fields of a sorts if you will- to which I add this Ramanujan background that comes before the new physics of all this topological approach- and then philosophically the general background of reality itself dubbed the Omnium as further possibility of structure. I do not know about the 200K or so dimensions or why as some limit- nor how we derive the monster groups and so on... But, at a certain level of comprehension and awareness of it, and the limits and fact of the significance of it- I would rather be shown wrong than to be spinning in a loop of error having come so close to a total theory and not quite there at the peace of its absolute zero.

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Now, to consider Orthogonal Figurate Space and see what it parallels in thoughts of spin topology and numbers in motions concrete and abstract in our natural dimensions.



Trying then to interpret the structure of such space. Consider also when these dimensional motions are composite from shadows of higher abstract dimensions, that is here assumed to deal only with the prime triangles.

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