Friday, February 25, 2011

Linear Fractal Space

Linear Fractal Space

I had some surprising results from some of my casual thoughts last night which as in the illustration resulted in art of sorts and maybe the metrics of the octagon.

I notice Lubos and Pitkanen posts today are a form of SUSY debate- oddly, Lubos makes a second post which finally concerns the ideas of the 24-cell polytope- a rather topological concept. Again, we are converging to the same thing- but it may take contrary pairs of things like the twin primes that seem to converge to phi^2 + 1 and the square root of that. 1.90216... BTW can any of you young Einsteins explain to me what an imaginary slope is?

Superspace symmetries may not be the same thing as what we seem to mean by supersymmetry. Is this a question after all of topological symmetry? I mean along the lines of something like Kea's twistor researches? After all we have known about semi-regular solids in 7 dimensions for a long time. Is it about some sort of hidden concepts of numbers upon some fractal recurrences in space? How do we get past the ideas of Ramanujan to reach a more comprehensible Topological background if we do not understand the simplicity of it and the limits of some of our mathematics which seem to match square pegs and round holes (and conversely)?

What sort of math is it that can have 0! = 1 or 0 depending on if the equations work out. What of the imaginary slopes that give us 0/0 in the trig terms and there is nothing differentiable to so resolve this?

I thought I would find curves but found lines in the illustration. It is clear that in the plane or brane space we can have changing values over infinite depth and direction so as to make this an issue of series which are indefinite as to if they converge or not (in perhaps a fractal distinguishing of primes and other numbers) in relation to unity or not.

Clearly by calculus methods we can generate an area equivalent to a circle from a square- the grid looks rather like bell shaped curves parallel at the poles.

So, from the quasic plane view- of which beyond the "square" limits we can extend it between objects and shadow objects to measure dust and space... the holographic principle- despite the information contained equivalent in the surface to the volume, that the value of the surface circumference is zero everywhere.

Oddly, in my 13 star flag post of yesterday I left out one popular one- which in the pattern in the illustration suggests, with eight point starts, that the rows of 3 2 3 2 3 = 13 one could call the quasic pattern. It is interesting this can have analogs in three space. In the partition theory of quasic recursion of shapes I mention also that in the recursion we do not necessarily have to have the same partition shapes either in the general multiplications. Of course we can go on in one form or another to expand this as Kea does with the Cayley numbers.

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It was a little difficult typing this and trying to finish faster when a friend had to talk about a situation, romantic.

To state again an idea: the quasic plane is a region of unity in itself and cannot be seen in its circumference as if a square- it can be thought of as a circle or even a torus and so on. Now these being a zero and a rather scaleless region save for the concerns of what is happening in the region with the mathematics- these can be connected in the abstract. But in a sense numbers can reach its vague zero or infinity so to appear linear. But this raises my own question as to if between such regions or planes there is after all an underlying pixel grid of things to count between them (the epsilon honeycomb). But in a sense the region as a singularity or wildcard establishes a relative unity of sorts- for example the issue of a hierarchy of Planck volumes seen in the partition space as a limit or zero grounding that may be everywhere on a continuous scale and not necessarily a quantized concept. Or from considerations of the depth and span of things there may be such a hierarchy only a step down or up but these way beyond our concept of universe in fact if not in the paradoxes of these theories- and that would not be even a weak fractal hierarchy. I have seen people speak of these h models (for example TGD) or of such things as a problem, or in relation to scales of energy, or as a reinforcing of some idea in the measure of things to the h level and string theories (to which invariably with this as a reductionist grounding emergence things are declared a problem or mystery or the quantum ideas have no concrete relevance at all on larger scales say of biochemical organization with ideas speculated as explained as "decoherence" and so on. From a self connected and simple view with an appeal to origins at zero or infinity a problem in resolving the archetypal notions and physics is that the theory are seemingly miraculously intelligible. The questioning of the logic or of the solid grounding of arithmetic does not have to undermine its general higher utility and paradox of unintelligible but necessary reality.

Given these general notions I feel more at ease in the natural or familiar scale of things to interpret things like entropy as the merger of wildcard regions that retain a possible view of whatever external and observable structures and symmetries. But to do so is to combine vague shadows, as well as vague realities and laws of energy and dust. At least there seems intelligible reasons to which our human experience at present seems to converge and optimistically so by which we can keep in mind the unique reality and truly judge what are our delusions and misconceptions- if in the end these things in a sense matter despite our visions. The power of abstraction is as important as the power of counting, genius is to keep in mind what is the obvious that is important in what on some level overwhelmed by our archetypal and chemical structures at times, of what in our freedom of thought and enquiry as our basis of living is but chance in encounters globally but trivial.

Left to ourselves, we become the ideas we think those had before us of legend when they but the flotsam and jetsam of humans and not the saints and gods we worship as if they our first parents. That is to say, in your own quasic region of this concept of generating deep thought and its connection to the world, with fresh creativity or just the existential doing things for the hell of it, the effort is in your court to decide and direct the evolution of the game. We zeros of dust and shadow tend to default at times to the heart of things and not just go around them as nature tends to do, take advantage of the differences and perambulations along the biochemical pathways, as we then combine with other zeros in a hierarchy of learning.

Along such an expression or expansion of series and lines- it is perhaps too soon for Dirac in his go to the horses mouth assertion that there are no longitudinal forces as waves in deep nature. This too can be a matter of tastes and perspective.

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Happy spring as the waters dissolve things to Pieces again and are Phoenix reborn. We all know but do not say or consider it beyond ourselves always- like two lovers thinking they have found the ideal and first to find true love- that in the end in the archetypal zero and settling against the parameters of nature for less yet the lure of better encounters with touch in the dust- ultimately the compromises and chances of spirit, mindfulness, a little chaos to ease the boredom as a sort of entropy all its own in love as global warming unto our economics of a Cantor dust- that in us, as we hold the lantern of wisdom to find truth and honest souls as well the batons, be they hockey sticks or gnarled clubs, or elegant Bat Masterson stave's and walking sticks bring law to the lawless West, that in us is as much the Fool as the Magician.

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Where the metric in the pattern of the illustration has weakly recurring fractal shapes of octagons and even stars, this was not planed out but fell out of the drawing, most likely simply the properties of squares and the square roots of 2. It is not just the arrangement of stars on the flag but the points also. The worlds of compacted and centered dimensions and of the extended ones we project everywhere unto some idea of flatland and shared infinity- both apply to general space descriptions.

Clearly, we can use the insight of Riemann up or down a dimension, the seven to imply and eight or assume a higher or lower to explain better a picture and its needed freedoms of motion. But is this not a puzzle piece either a small part of the whole to which we can infer from the shape the global curvature of things as we can say from a geodetic triangle of Einstein? We can also take the missing shadow and make some conclusions as to the general shape of the piece. What I suggest here is that we can also do it in flatland. That the cosmos is not flat would be the problem.

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I posted this comment to:


I like this presentation I found on Kea's blog.

You might see my post today as relevant at least from the philosophy of it all. Not sure if it is an alternate theory needing experiment or not as a way to settle things. (I think Kea is on the right tract).

I suggest that we do need a balance of existentialism and pragmatism, for such a balance would raise the deeper paradox of Abbagano's synthesis: "There are no necessary realities."

The PeSla

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  1. Wau, a much more beautiful star formation for the US.

  2. It is well known that the ratio of any Fibo(n+2)/Fibo(n) will converge to a limit φ + 1 = φ^2 (an irrational number) as n approaches infinity. And so it follows that the ratios of the Fibonacci numbers indexed to the twin primes (n+2) and/or twin prime candidates in sequence converge accordingly (in other words, the square roots of the ratios of Fibonacci numbers indexed to the twin primes and/or twin prime candidates in sequence converge to φ).

    Here are some examples (square roots not taken):

    Fibo(13)/Fibo(11) = 2.617977528089887640449438202247 ...
    Fibo(19)/Fibo(17) = 2.618033813400125234815278647464 ...
    Fibo(31)/Fibo(29) = 2.618033988748203621343798191078 ...
    Fibo(43)/Fibo(41) = 2.618033988749894831892914017992 ...
    Fibo(49)/Fibo(47) = 2.618033988749894848153928976786 ...
    Fibo(61)/Fibo(59) = 2.618033988749894848204586345776 ...

    Excerpted from