Overview of the Quadratic Plane

Overview of the Quadratic Plane

This will be a discussion of fractals, really- something I have not been that interested in but has come to the forefront of my thoughts as something we must get thru as a stepping stone to a more unified physics. My interest comes at a good time (what what is a good time but to be in the right universe for a change and foresee it where Green Bay wins the superbowl?) This discussion shortly will relate to very much of what our bloggers have posted and amounts to a comment on their new visions as much as it brings back some old ideas from my philosophy postings in new light.

*Lampion Fx1 - In the wider sense some say gravity is an illusion in the volume if not the surface of some space- so to we can think of mass as an illusion.

*Lampion Fx2 - The quadratic plane can be filled with certain paths that are not differentiable, but it can be filled more than once and result in intelligible coordinate motion and labeling.
**Comentary Fx1 & Fx2 - Escher drawing of water flowing up hill and down hill can be thought of as an illusion or our perceptions- or is it the realization that we can combine two three spaces in a plane? That in such a mirror world of twists and turns the Penrose Triangle is not an impossible reality but an accurate perception to which humans have evolved to abstractly understand. But in the simple counting of things, the distinguishing of grids to contain things or not, we shall not say in one extreme or the other if the substance creates the form or the form the substance.

*Lampion Fx3 - Newton defines continuity as a.consecutive, b.contiguous, c.continuous
The contiguous can have useful information fractally where the discrete or continuous may not be useful as such information. A person (or a computer) can be a genius with brute intuitive counting- or a genius on the abstract and disembodied intuitions of things imgined as continuous. Contiguity has yet to be serious studied, but my own intuitions suggest the fractal in fractal approach is useful (and as mere patterns or as mere programming I find ideas like this on line yesterday. Only, in a deep sense, where quasics transcend the quadratic plane, I had suggested a sort of continuous differentiability as epsilon-delta honeycombing or grids)
**Comentary Fx3 - It turns out (I am not saying this thought is original to me) that from Chaos to Simplicity as in the idea of the Ancient Greeks, that in fractals the simplicity leads to chaos- and in our time such chaos becomes simplicity again. (But a connection I do make as original but not necessarily useful) This mimics the idea of the vase that breaks into diasphora the returns again- as perhaps all such thesis, antithesis and synthesis patterns that ultimate represent subject-object ideas. Again, this is not a statement illusion is the source of consciousness nor that consciousness is the source of illusion or even implied so thus explained as the nature of consciousness prerequisite for that which perceives illusion.


continued today...




Communication Interlude:

I must say that some side communications from Ulla are most interesting and welcome so to see how she interprets some things and like any of us are inspired and excited by the possibility (and reality) of the new physics. Alas, it might be better to include such behind the scenes discussion on the blogs themselves. On the other hand there is no such direct (email)communications with Pitkanen or Kea. In Kea's case I can nevertheless appreciate her thinking and results from the terses of hints as such signals pass thru the night (the old ships sending bits of light and signals until they pass again into the darkness into unknowns.) Ulla sees Pitkanen as some sort of islands in the stream, an idea I must mull over that also seems relevant to the general discussion- more on this latter perhaps, more from the perspective of philosophy.

We tend to see things from certain coherent and consistent views- some commitment to a ground to set up evaluation of other views and systems. What does it ultimately mean to see so much of the world as asymmetric or see it as non-linear when the goal thru the chaos returns to simplicity again as if on the larger scale things can be reduced to linear again- of course that just raises the bar for that which we consider non-linear and asymmetric is banished to a little more remoteness for what we observe in our island of universe- even if it is a matter of general planes as the grounding.

Illusions, of these geometrical varieties, can interact with illusions, and quite aside from the question of their reality as geometry we can make analogical and intelligible systems of our general vision and descriptions.

If we imagine fractals of the Hilbert variety (remember I do not see our current best generalizations of space as fundamental, phase, Hilbert, configuration, complexification spaces and so on- nor see the resolution of them as not ultimately an imperfection of illusion. 1728 But we can, once given such an illusion of mathematics extend it to the higher cases.) or the Peano variety. In a sense the Penrose triangle idea justifies the duplication of some things as if we do this by those numbers involving turns and twists, imaginary numbers, a hierarchy of them really to what we could represent as higher planes. This can also be the relations between things in such volumes or planes as still higher solutions, albeit they more limited in a sense not close to a simpler ground, to the quadratic solutions of less faster converging integral numbers (again, much of them prime).

So, even though the quadratic plane is of that full fractal dimension we can imagine different such paths and their directionality merging at certain points in which these can be labeled as a concrete object in the doubly full quadratic plane. We can develop many such combinations of aspects of conjoining the various planes.

Where in the taxi Hardy reports that Ramanujan corrects him saying the taxi number 1728 is exceptional after all- perhaps we jump too fast to thinking he has a deep grasp that survives Hardy's insistence on proof and pure mathematics on how he sees numbers but that the number 1728 itself is a special case of such recursive views.

I would like to add, from my more general intuitive (that is subjective and the continuity of things behind the discrete recreational color cube matching and counting) Kea has put more substance into the idea that we perceive the three dimensions only of what in a real or abstract sense is the nine. Of course for me this comes from the general idea of the 24 cell in four space- after all, its group is 1152 which is three times the four dimensional 384 of orthogon rigid rotation and inversion. But the intuition comes up other places as abstract as it feels- and not to mention how things happen at nine natural dimensions and it a tenet of some of the string theories.

Clearly, with respect to higher space, at any point (Riemann really) we cannot say what direction time goes forward. It can go outward or inward, and give us ideas of its utility to describe things as going backward in time or that time travel itself may be a real possibility, at least intuitively and subjectively. Yet, as there are mass differences fundamentally (still not explained adequately) the idea of entropy of even energy, and time itself on the level of physics has variable properties at time or seemingly does so- yet we do not say time is but an illusion. On the other hand from a philosophical perspective what is the lifespan of an individual, if we could see it, no matter how short, fills up the totality of the reality of time.

Forgive me for my illustrations being too simple of cases. In matters of the practical world view, as in mathematica, we should also develop the analog concepts again to have a wider grasp of mathematics although .ma point is well taken. In a sense the shear exploration and experiment can in theory fill most of our needs and beside the caveat of np-hard, solve and enumerate things from a counting perspective alone and not the deeper abstract theory alone.

What is the difference of saying certain concrete things cannot survive the big bang and that such things cannot survive the idea of clashing brane scenarios? Insufficient data that perhaps is beyond experiment and possibly theory.

In general the illusions so to speak of the quadratic plane as a matter of more than meets the eye of symmetry, momenta, dimension, once put into a more concrete and general matrix form, the plane is subject then to all the aspects of such combining of abstract positions and motion to our group ideas, especially the Dihedral group.

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Partons for Ulla:

In partial answer to your e-mail question as to mass differences of protons and neutrons (I think, if you ask this of the particles themselves and not atoms) I give you the old parton theory circa 64 to consider. Of course by then we knew that the neutron decays into a proton, electron and a couple of neutrinos of which Kea finds room for in her pictures.

Now, in your reply to Rio Frio's post today- what a profound devil's advocacy! You suggest a contradiction here! But Ulla, if you do not think something like a black hole if one were in the center of the earth could have an effect of something like quantum flux- perhaps that is a doubting of quantum theory itself as well the doubting the alternative theory of something like black holes also a creative force.
So you doubt the idea of a wildcard at the heart of things- as well, a caution to me of separating the skeptical science from any idea of a metaphysical foundation. That in itself is good advice. But what is left at the core of some unknown say if it is ultimately emptiness? Certainly one wildcard seems to be a deep awareness as well as consciousness of these abstract physics and speculation :-) It being really too soon to assert the universe or earth or anything else can be a unified and even disembodied consciousness. Philosophy. Yet such philosophy can hold enough awareness to make some breakthru which helps a more material connection to things.

For example, the teleomeres in one of your posts. The have their own mechanism for example, a very beautiful arrangement I may add of the geometric shapes and it also suggests to me higher space connection? Is it aware? Does it not occur by the background of form and process of structures of things if not the raw geometry?

One of my earliest ideas after reading Klein's the Icosahedron and equations of the 5th Degree was the application of this structure to the DNA of which many in some for or the other have made that connection. But just as there are stable places in the elements or the general matrices of magic numbers not there save in theory, we can imagine the chromosome as a series of such shapes- they are elongated and are only from a more general view of space to be seen as a symmetrical higher analog to one of the Platonic solids. In fact between the teleomers such a "polytope" unfolds in its spacious unitary segmented direction to come back again after so many jumps and twists around the real or imaginary wildcard singularities. Thus, on a deeper level we have the paradoxes of time in all such views of a smashed higher space as the code can be read in two directions. But the structure of the code itself if we have fractals in fractals is like a maze where one way it is very difficult to solve and the other way easy to negotiate. All this to some degree of approximation can have an intelligible and predictable algebra. This is just a start really. But I do hope your skepticism aids you in your studies of DNA and finds something new in how we apply a little but of unity itself as a rather wild card to it all. :-)