Wildcard Coordinates ****

Wildcard Coordinates****

Looks like this was a rather creative blogging month. So I end it with the consideration of how these new ideas may affect us and what we are in this world. What will be the next level of our social institutions and technology- especially if these are not to evolve from the promising new quantum ideas as our mainstream technology.

There is little doubt that our cosmic view has influence on how we think of our sense of self. Science, in general can reassure us and arm us against our superstitious fears. Yet, science comes with initial doubts which brings with it a new set of threats and fear. Still, in its later promises we can awaken to new possibilities and an even deeper appreciation for what we are, collectively and individually.

Why respect endangered species when we can resurrect the Mammoth, let us just make an heirloom bank- or better yet assemble these and species never here from scratch. What does it mean to have a respect for living things far away and in the vagueness of what we are supposed to discern in our hearts from awareness of the processes of living?

[I have probably lost the interest of some readers, not quite able to put these thoughts into the clearer words at the time I found in last night's dream.]

So,

A wildcard coordinate is * one that can = 1 or 0. What is significant here from the standard view of dealing with matrices and vectors (note I have never in my posts used the word eigenvalue- where these apply the edifice of worthwhile mathematics was independently found or assumed- but certainly these apply in some of our arguments here.)

The standard zero vector set is regarded as "finite". Please see links in formal papers to the blogs I follow- the realization that aleph 0 for example has a certain sense of the reality of points. For me, for a long time, the idea that the primes are a sort of transfinite thing on their own (I called the yod transfinite '72?) becomes more and more a critical issue in applying such ideas of numbers to space.

It should be clear that stings alone without such points may not define things completely. Nor would it seem an M theory unless perhaps the attachment to such a point on a brane is what is needed to have a material reality of say, gravity or mass. Yet, without consideration of such points- that these do not technically exist we can see mass not as a function of energy, force or inertia as such but more like the ideas of falling, of general relativity only in a zillion dimensions. This is to say in the new physics the old relativity's and quantum theories have their analogs so the question is are they are can they be a unified theory even there? I wonder for those making apologies for string theory and so on how they decide to use on one hand an advanced quantum argument and on the other hand an advanced relativistic stance? Is this obvious or not from their own steps and state of thinking?

I think we should look back at Rene Thom now and his Universal Topology or catastrophe theory. After all it was a method of describing several higher spaces by embedding Riemann spheres into Euclidean spaces- Perhaps the knots and such as if compacted 6 dimensions is that they loop and relate to each other as if these a point of attachment as if a wildcard spacious point. Such a mixture of wildcard and normal matrix relations in a sense is the fact of our ideas of substance and mass so it could have a wider topological space of connections. Pitkanen posts this I think as one of his questions today to consider, how these (apparently minor spaces may globally connect).

But the wildcat philosophy I discuss here is not a final answer that is clear as to how all these things loop and connect- nor how we internalize the record a the end of the music such that we can ask again of being itself of the collective and individual (but certainly the state is now inadequate, and the corporations not capable of replacing it efficiently to smoothly run the earth.) Where does such information go? Certainly a viable state wants concrete coordinates of his history and the heros and villains who compose it in the chance summation of their song viewed after the fact of its recording and fixed judgment, evaluation, existentially, and that the accidental and individual catastrophes are of some relevance as cause and history- and meaningful purpose as if being like gravity does not in the main fail not matter what the twists and turns of our labyrinth without walls and bottomless pits into which the sand flows and the doors seal and we wonder at what treasures we have lost forever as we build upon dust again and reach at last for the stars.

* * *

Dreams, in a sense where they contain memories, while in a dream it does not take say the heat causing energy to recover them that it does in computers. It is like a reverse process where it is much easier in computers to lay down memories than bring them back. Recollection in dreams can be like a current with no resistance.

Dreams, moreover, can be no only mangled and compressed or compacted into spaces of which the surface reads rather like a post-modern description, but to enter such a dream and its volume we find the memories of previous dreams a sort of fractal in fractal collection of such post modern crumpled and mangled surfaces.

So it is that in our wakened world if we think about the consequences of some of our physics speculations, that is evoke the emotional element, it can be a fearful place where on some level we are merely machines again including emotions of which we may program to some extent in the inorganic world. This vision can make it so that we really see how irrelevant any individual of us is and what we do- we can be ready to accept our short lives and unfulfilled lives, and pointless worship of loving others or even think we know others, or hope those who follow us will meaningfully evolve beyond our crude but complex monkey dreams.

In other words, after some realizations and achievements a little more than usual most likely inspired by all the keen sense of the drama and revolution in the air by those linked here- what comes after that? Maybe some sort of let down, maybe some sort of despair, maybe given the sight still far away what we regard as of the utmost value must frustratingly vanish- as we who are not much of anything in the heard and worse are ready to accept this and give up our dreams- for we have walked into the shadows knowing it is the end- we do not even care if those with lesser mentality rant and rave and think the damage they do to even thousands means anything more than how comical they act and how less than pointless their lives.

Well, I may have captured this enough in the negative- but let me say that in the end the knowing of possible new physics came out as even more positive than this in the depth of its mirror measure.

In the dream I was able to recover a few poems of what was lost of my couple of thousand- at first I found the titles of the booklets - The Color of Love, The story of the Bird symbols for my children, The ghostly meeting by the river with a former lover, the gazing down into the river wondering if it were deep enough not to break a fall, Sagittarius looking over me at night, my explorations of the driftless area and the great Inland Sea... The five and the Eight and the mirror gods of Olney on his adventures with the fisherfolk- He the Spheredream.

But is it but wish fulfillment to recover this or is it some statement of our psyche or soul? We move on, for although it takes no energy it takes time away from the living in the world and the new dreams.

Something inevitably emerges? That certainly seems the case for life, for sentient things. When one considers the concept of the Omnium and its relation to the analogous idea of iota particles rather than pure strings it is possible to see the unity of any one psych or soul and life in such a way that our lives were of significance and what is the world is a consciousness of sorts as we are so conscious but this makes sense only over the finite and infinite unity of the Omnium.

I wish I could tell you this story better, or that I had wrote it down upon awakening as I was so sure in my dream I would recall the details of all of this.

Can the idea ultimately of matter, of gravity and such, stringly or looping or not, not be this fundamental metaphysical unity as of our private souls and dreams that resides somewhere in the wildcard coordinates fixed or moving as the invariant of what or that we just are? So to speak.

* * *

I may consider what sort of thing to explore in February- looking back as some ideas where I just casually explored some things, unconcerned really if their utility would be of interest to anyone else- like in a dream so much can be forgotten or not readily in the forefront of mind in the mass of information in the awakened world. Some of the things I was doing with non-standard color cubes comes to mind. I found two such charts in earlier posts on the philosophychatforum in my stored data on a flash drive.

So, Kea talks on quandles today- and googling it (as I am trying to see what else is out there) I find that it is hard to distinguish the threefold knots as to their handedness. One old reference with the color cubes assumed this could be done but I did not know the applications were of any value. It requires a principle of what can be described as a rather simple natural space encoding that applies to a given dimension and not some exotic turns and twists and loops or hidden fractal values behind the lattice motion changes of coordinates between cubes. It is worth a look I suppose. Interestingly in four space it requires nine distinct cubes, in three space but seven (thus I called it diatonic and labeled them cdefgab as in music. In two space there are five of which I made matching puzzles. The question in general of chirality is still a most deep one and I am not sure partition theory will add that much to the final picture. But this could be too simple an approach. But I have to say, now that I can see some of what is there in the body of learning, that from a distance and a first blush superficial level of comprehending the significance of some of the ideas- as if they set in stone as theory- that I have very much underestimated the need to be exposed to the nuts and bolts of these ideas. On the other hand we make heroes or saints of those who not that long ago were just one of the students or teachers. Let us hope those who inspire us are worth our admiration.

* * *

Of course it helps in trying to communicate some idea to another to get the words right- the back and forth of it makes things clearer in general.

http://pseudomonad.blogspot.com/2011/02/theory-update-48.html that links to:

http://home.lu.lv/~sd20008/papers/essays/Clifford%20group%20%5Bpresentation%5D.pdf

It occurred while reading this wonderful paper of 08 supplied by Kea that we might question if Dirac matrices are to be conserved. I am not sure what the 11520 means other than ten times the 24 cell group of rotations- that interesting from a mere counting view- certainly Clifford's approach seems to deal with the real and finite and I do agree that somewhere the functions have to distinguish but not always with what it the addition and what the multiplication of things.

So, maybe we should develop the matrix algebra to include the wildcard notation *. In which case if * can replace 1 or 0 (and in some sense we can make compliments replacing all the 1's and 0's) what do we do about -1 or more some complex values? Will this tell us anything via notation of the symmetries? Let me emphasize that the * notation is that in the skeleton of a grid between quasic cells as abstract 0 or 1 motions, too. But there is no intuition or guarantee this method will be intelligible. Certainly all the other ideas of matrix products, reductions and such would have analogs to interpret. Perhaps new forms of what we are no longer restricted in dealing with sums and products with this idea of eigenfunctions within the diagonal itself. After all, so much of this is to do with square matrices and how in some wider view they may interrelate.

In matters of vibration ideas as a sort of geometric structure dualism and in relation to assumed filled vacua on a hierarchy of levels I will label this area as concerning Daldala theory (from the Arabic for swinging back and forth).

* * *

Perplexities in Geometry

Perplexities in Geometry

I cannot say I really understand some of these theories. The occasion of this posting is my thinking about the last statement of yesterday's post and questioning its role as a philosophic or mathematical principle.

I think my calculator, and what a task it is to use it for such explorations when the factorial button is not working, has become a string theorist. That or she is sinking deep into dementia for her level of intellect. I think my post on bogus pi was the product of bogus pi and bogus e. In any case the calculator keeps telling me slightly different things- there must be something simple and fundamental I do not know about numbers or maybe the programming- do such large and small numbers round off at infinity to whole numbers somehow?

So my friend invents a way to see space and it is hard to understand- I only know that when I give him a problem say in higher space geometry he draws some strange patterns and out comes the correct answer in the way I had expected it.

How can I who have relied on counting so much not see in the expected structures and answers that this is about a higher physics and not just mathematical recreations? This is not like going to some universal library in the sky where one can read the cylinders of data no matter what language one speaks.

To be or not to be - the philosophic question of existence. What occurs and is useful information is the space or spirit between the absolutes of nothingness and full yet tautological something. As we set design our logic systems anyway. So it may be that we should consider removing from continuous honeycomb grids in some absolute sense (that is the compliments of matrices **** of 0000 and 1111 for example not excluded from the logic of things).

The symmetry issue, at least across the quasic plan from the xy or beta-alpha directions, is one of natural bilateral symmetry. It is not clearly an infinite flat space or honeycomb to which removal of one point and its edges results in a polytope or polyhedron. Obviously this sort of making things finite can be a double operation- in an analogous sense the cube in cube or sphere in sphere mapping in lower space of say the hypercube. We should understand this duality before we try to explore higher such n-alities.

* * *

There are issues to as to what we see as if on the surface of compactified spaces as the metaphor. (what could it mean in Kea's post of three things as holes in the "pants" configuration?)

Such things do convey suggestions to us of which we see some intelligible patterns and either think the ground for them is valid or not- just how different really are these topological and string theories anyway? It is like we from our own cultural perspective try to analyze some alien script to run some machines that may be light-years ahead of our deeper understanding as goes some of the sci-fi today, certainly that sort of speculation evolves- but not very far beyond the frontier of the concerns of scientists. Otherwise it is all just another genre of space opera.

I suspect but am not able but to intuitively explain it that this hypercube without the **** two points can form as a structure in sweet perfect symmetry if we put 8 of them in a cube structure- in which case we get 24 such compactified holes- and moreover the Truncated Octahedron of 8 hexagons and 6 squares (and I only vaguely suggest this structure as it is already vague a a statement of four space viewing and in fact it is a problem of 7 space. I only know that when we make circles of things from lines and these circles are polyhedra that we get such a truncated octahedron (Lord Kelvins space filler) only it is smashed as only one 4x4x4 space. Now this space filler is after all useful to describe the surface motion mechanism of the electron flow in say wire. So it must have something to do with ideas of physics like electric charges.

* * *

This sort of perplexity (btw... it would be nice to have a calculator or at least a program that could do some of these new math discoveries- and for my quasic maths save the effort of hand writing so many ones and zeros) which I may now use as a specialized term, raises the logic questions of how we might view the excluded middle as the case or not of a logic design system.

Again, a key quasic idea is the distance between cells in an omnic space which regards not the fact of some existing 0 or 1 but the absolute change of them between two such cells. A change of all such coordinates is a linear motion thru a diagonal and of 2^n a statement of rest in a given dimension. In the former we might say that there is a flow or process which can be seen as directional into which we ascribe as the ground for asymmetry and symmetry breaking. Such breaking then a quasical or perplexing thing in some aggregate of real or virtual concrete structures. We still do not know for example just when we enter some event horizon as this seems a mysteriously relative thing to which some may imagine certain organizations can be actually alive and dead at the same time.

Let us then speculate a little on these two related links as to what is happening if we assume such logic on the local level applies to DNA.

http://www.newscientist.com/article/dn3548-electrifying-claims-for-dna-are-dashed.html

http://www.newscientist.com/article/mg20927973.500-stretchy-dna-shows-off-its-elastic-qualities.html

To start with at a certain scale the DNA behaves the opposite of how we observe a rubber band to come back to a rest state.

We know that there is room within the DNA in which to put a lot of other things and some (of the sacred geometers) have speculated, way beyond our abilities to resolve things on the DNA level that this stretchability of DNA responds to emotions.

Let us recall earlier links posted that the code may be read as multiple levels of code, intrinsically, as well as fractal like over the extent of a gene.

These two links discuss the idea of electron flow over the structure and what causes such stretching. (an other article in science daily suggests that magnetic forces can enhance our ability to learn- but why? This seems still too speculative for formal science and yet it does consider the magnetism as we should in investigating the electric properties.

The conclusion of the article is that it is likely that the codon base bonds stretch or break to reduce or destroy the helicity of the total structure. More importantly DNA as if a wire is ruled out and that any such transfer of electromagnetic like units are to be thought of in terms of things like quantum tunneling.

I repeat that the deeper topology between these codon bases is there to work out atom by atom, individually- and that fits the overall compass of these topologies of organisms. But here we address the mechanism of flow over a length as if the surface phenomena (much like we say in a wire the truncated octahedron seems to apply). Let us put aside for now the idea of memory in the topological space something to consider through such portals of "dancing" DNA (see previous links and posts). Certainly, a model of RNA memory of flat worms with bases shot out seems an analog or simpler intuition than what happens with the more complex DNA bases.

One way to think about this observation is to imagine the information to periodically or irreversibly to read the 0's and 1's in the standard way and thus focused into a sense of the weights or gravity of certain effects of topological mass or perhaps inertia ideas a better terminology, or that at times things are to be read more from the quasic idea of the absolute changes in these bases as if coordinates of a wider space structure.

What is interesting then, from the recent links and comments to a sort of water memory by which the organism may recover from such an imprinting a sort of topological field to reconstitute the information in a chromosome deleted is that these links I just posted rule out simple electromagnetic physics to explain things- but I suggest that just the quantum aspects of this as a biology is not enough either.

It must seem rather magical that certain frequencies of magnetics target certain brain cells. Then again as if an action at a distance over the field of an organism the self programming developing in the organism in each cells has a certain coherence by which there is a specific target or connection to some area of the body to which the cell finds and relates but does not know where the other is for such an effect- a sort of global distance tunneling multiple reentry of the density in the Riemann like manner.

I note also articles on bacteria where they incorporate other bacterial genes to adapt to environmental toxins. Thus these mechanisms may (even if we do not insist on a physical explanation for all such topological ideas) return "mangled" that is imperfectly reproduce the imprint DNA helical shadow- that too can be a survival mechanism as well as a defect and chance evolution of some overall inheritance structure. It may also follow that the mechanisms of immunity as learned or not and some reserved for unknown assaults to come is a difference in this quasic and natural code reading of abstract matrix coordinates.

Certainly then, we are applying questions of fundamental logic to structures be they strings or pure space and undertaking real experiments to aid our vision of things. We like the bacteria probe into the dark at times in perplexity, driven maybe in the general flow of things and the mysterious self organizing of tissue as if to be in concert with the heart beat and its electricity. Our speculations then on what we accrue from what we cannot show clearly we understand save it seems to make sense intelligibly, on the higher or lower levels of our symbols and language. But is this not the issue now when we imagine the questions of the logic of realism in matters of what we think of as local or non-local and entanglement? Our stance to causality and the flow of time? The getting around our passing of electrons from one atom to another as if to treat it as a fluid flow?

* * *

Teleomnium

I decided to look again at some older ideas and terminology. I am somewhat constrained by the realization that some people may be reading this. A poet should not really censor himself in general. Of course all this could be just something in my mind and its sense of certainty more or less enduring and self contained- but it seems that it may be true that the complexity of information we internalize being after all very complex organic creatures could be vastly more complex than what we imagine of our most general inorganic laws.


As Creative Philosophy:

*That which becomes predetermined after the fact is balanced to some degree by that which is not determined before the fact.

*Absolue determinism of all paths across the Omnium and its states of existing fact I style the Plutomnium.

*The Omnium is that which exists as if it the most general description of space as facts of absolute rest or motion.

*From this the change of constellations of facts move as if the totality, taking time, has purpose, the Teleomnium as the collection of movement and action.

*Information into creative entities, spacious singularities, as if it returns "mangled" does so everywhere and when on all scales and dimensions of universe if not multi-verse.

*The duplication or replication of an organism taken to its fullest principles of complexity is a good initial model to visualizer or contain Omnic space and its possible opaqueness or substance of shadows.

*To ask the wave equation of the universe is as incomplete a question as to ask this quantum consideration in just matrix formulation.

*The arrow of Omnic action, the interplay of the quasic grids, pixels, subgrids, branes, cells, and so on, expanded into any natural idea of dimension, abstractly, needs not be a fixed conception or system, but a difference or quasi-preferred set of facts of determinacy.

*Subsystems erected on a standard Omnic space may reletively become independent as quasi-isolated systems to which the interactions evolve over the Omnium with its quasic states of facts of possible patterns and path determinism.

*Thus, using the metaphysical principles here stated we now strive to put it into an adequate mathematics to expand our vision of physics generally.

* * *

As Creative Physics and Mathematics:

*Let us model an 8x8x8 naturally dimensioned quasic coordinate space where the 8x8 faces are quasic planes of any binary grid or dimension here considering the finite.

*Clearly, a path between any of the 512 cells may not be totally described by the x y or z set of lines from a pixel thru the space (we adjust things for the color dimension although in theory we could describe the paths in black and white or even assume near but hidden dimensions affecting such paths). Such a path, considering numbers or such planes and cells at least a class of numbers and now intelligibly fractally patterned can be mapped after the fact.

*The order in the quasic plane sides may shift to find solutions for the space coordinates collectively (or show no such solution or near solution) to describe, partially of the dimensions applied, ideas of coincidence and probability, or such an Omnic system may have patterns of random initial states and facts of pure probability.

*The sorting of the order in random systems, even in steps that may temporarily decrease the order, is a measure of and accelerating direction toward the effects and facts of entropy.

*A "gene" may in a sense describe layers or "tissues" systemically, and in concert together over quasic shifts and omnic (as topological) coherence. Genes then are to be read also as quasi-fractal.

*In general ideas of entanglement and non locality are verified in experiment only to the extent we understand or include the 0 cases and unity generators of Pascal triangle relationships. (Of what do we measure as a proof between the 16 p's and q's of implication if we rely on 0000 and 1111 as excluded contradiction and tautology?)

* * * *

New or False Number Intuitions

New or False Number Intuitions

Ulla sent me an e-mail and it was a rather interesting paper:
http://fqxi.org/community/forum/topic/815
Here is a quote:

"This paper explains why a purely mathematical argument leads to the use of adelic mathematics, discusses this in the context of epistemology and cognitive science, then shows how topological geometrodynamics applies adelic mathematic to a reconfigured model of space and time."

The idea of both the digital and analog in the explanation of the world- nothing I had not said or posted long ago somewhere in the internet but which I regarded somewhat beyond the pale of physics proper- so much lately seems to come up from my casual axioms and thoughts and like that between two lovers each thinks that they were the first ones to discover true love.

In any case, Ulla is synchronously in tune with my more epistemological planned post and I did not go too deep into the link she applied so as not to be diverted from the path of my already planned direction for this post. I see the topic hot in the posts of others- and I see Kea discussing her blog as a top mathematics blog for readers- http://pseudomonad.blogspot.com/2011/01/theory-update-43.html I find her last mathematical posting right on and most interesting and feel quite at home with her terse hints and conclusions- whatever else my epistemological crisis was last night at least from links on her blog I did finally understand things like the how of the hook function.

In which case this blog can be skipped as it is about our minds as a state of calculation and the frontier of speculations rather than the mathematics itself. I am not sure however if blogging showing the states of mind- or even the style of writing in handwritten manuscripts really tells useful things for theoreticians.

At the rate of my posting the presumed readers may not have noticed a pause- for I did come to the coffee shop last night to post- but I could not reproduce what I thought I saw. Still the intuition of it seems to me the germ of a powerful idea, one that not only needs a Ramanujan to arise to see- but Ramanujan would need a Ramanujan to explain it. We can still wonder if our world is to be based on some form of triangulation just what difference these near coincidences, all the Bogus Pi and e's and phi's make out there. Maybe something of it is in Ramanujan's notebooks.


http://matpitka.blogspot.com/2011/01/non-standard-numbers-and-tgd.html Pitkanen also has a most relevant posting today for our new concerns about number. I also recall Kea just posting a quote of the week, a mathematical one at that- concerning axioms, Riemann's hypothesis and so on- axioms are also on my mind in these ideas of the structure of space (and alas the mind itself especially if I had a false intuition or did not listen intelligently enough to a promising one) But it is this nature of the Mind as issue in its relation to the history of physics that is the subject there- there was a poem I did not write because I am not comfortable with the stark idea that perhaps the earth is alive after all. Gaea and all that. Yet there is always the question of why we can think such things.

Lampion 01-29-11 After we gave made concrete gains on a higher level of what was formerly a vague intuition, we find the frontier of speculation again of vague intuitions or even false ones on a much greater scope then we were able to be aware of. (In some ways that the universe can be a dead and purposeless place- that too can enhance the fact that we are subjectively alive- we the otherworldly. Yet who in the more advanced religions would consider to find the higher God one must accept the musings of the metaphysics of wiccans? Or that the assumption His principle is not needed for a theory is an essential stance needed in the finding of Him?)

Lampion 01-29-11 b The essential axiom of four space (Euclidean) is that two planes can intersect in a point. Of course three planes in three space do- but there is a concept to consider also: That three parallel planes may intersect in such a point.

Lampion 01-29-11 c The DNA with its useful information is said to be read fractally. Now if numbers have fractal aspects then in the inorganic realm it is clear there is an analog to the genesis code too. The Cosmic code can then be seen in a sense aware and alive in as much as we are as well physics can so define us.

But the idea of Mind, as with Hawkings knowing the Mind of God so to speak, for or against (either way these things sell books... God Particle existing or not carries a better street light than does the Higgs exist.

Astrology in the news again- what is your sign- the constellations or just the seasons (but what of the seasons in Australia then?) Let us recall our last great astrologer and first great physicist with a side interest in the Bible code- Newton!

His intuitions went only so far having to invoke the God to move the planets the same way- and for awhile later thinkers showed how this hypothesis was not needed. You know the history, see And God made the Integers edited with Hawking.

Well, the sign of the snake handler for the 13th constellation (why do we want to divide things into say 12 intuitively then compute the Saturn and Jupiter of it all even symbolically? Such mummy wheat (Yeats)- well, with tweeter not event he ancient mummys are sacred in a cause really without revolutionaries today. What sort of snakes are these strings that can Ouroboros worm bite their tails and so seem to explain gravity? Or the 14 constellation, Cetus, the whale- after all we do not need to go into space to feel the degrees of freedom general in the sea.

Lampion 01-29-11 d Strings can be a sort of ultimate particle in theory- alternatively we might consider points as existing after all. By spacious singularity I mean- a conclusion one might glean from Kea's 54 in her tetracys- that such particles, seen as point charges, clouds of vague probabilistic things, or strings tied to the ground of the Planck scale- are really after all in a sense things that like the numbers require a fractal description of their structures.

Newton then, as above so below- did he not explain away the influence of the stars and call it a sort of disembodied and mindless thing, his alien autopsy of the Deity he served in his sense of an intelligible world, that Like Lubos posted perhaps we find there is no gravity (or perhaps gravity waves observable?). Yet if there is a history that is unique and all thru time it applies and each of us unique regardless of the tides or the delay in there flight of light unto us (that unexplained even when things are consistently constant)- then in such codes if they are intelligible such a Deity could be seen as part of history- still, as I look out at the bare branches at night rejecting a poem that I am more alive when the earth is not- oh how dangerous to live without taking note of our intuitions, we who pray or not, I know that to find God or keep the concept at the frontier for inspiration, that we have to admit the possibility the earth is alive, and that the stars have something to do with our unique birth and destiny.

Or is it just that our intuitions are not false but a little incomplete?

* * *

Is it not amazing to realize that i to the ith power is a number we can write down?
That the same number laws apply to divisions by 5 and ten as in our description of the wavelengths of the radio spectrum?

What is next after that sense of a string theory without strings but a topology theory without topology- even a number theory without numbers- and gravity without gravity? Certainly, we can pin some particles on binary numbers ultimately, say 128. We can say that there may be a computational or geometrical reason for the limit of counting the triangulations- expanding or not beyond 30? perhaps in my vague numerology this reeks of the 30 cubes- thus spaces beyond those?

Perhaps the measure of how concrete our capturing of intuitions brought down to earth is the vaster scope of what is possible to see then, full of greater errors to which it is so much easier to fall into and make.

What is intelligible then in the universe- and not necessarily so- seems to have a sort of conservation of the intelligibility. But this issue of the relation, causal and ongoing or not, is way beyond the simpler questions of discrete and continuous, digital and analog, requires a much wider scope than what we may conclude from asserting new axioms.

As illogical and unintelligible as the notions and wording of the last few paragraphs may appear- is this not the general mood of the few links posted as formal paper on ideas (such as non-Archimedean extensions of numbers) as listed in the several links in todays TGD post by Pitkanen?

Sometimes, one wonders why we share certain things- like Ulla's last useful links to me- to reinforce our stances to the world? Show them as the same old sheep in wolves clothes? Have us infer something deeper behind what actually said by the philosophy? To learn or to create? The factorial heart of our triangulation to map the possibilities of inquiry and learning seems to have that emptiness we find as part of the description- as some notions or concrete entities this calls up creatively that new things do arise.


* * *

This just mentioned by one of my friends in the coffee shop- I think I found it if it is a father and son researcher that can make any shape from lines cutting the plane in certain ways.

http://www.pbs.org/newshour/updates/science/jan-june09/origami_03-04.html

A friend gave me an orgami octagon of sorts yesterday- and I notice a lot of articles from time to time on this- including a chip design that folds itself by these ideas. Is this not a linear problem? I mean, even in something as seemingly simple as this we see a much vaster applications of spaces and numbers, the folding of membranes and perhaps some of these new interesting properties and maybe some old ones like a fixed point in a crinkled plane over a flat array of points numbered- and yes, the ability to better understand knots and make more efficient explosives.

So we have to sort out the intrinsic curvature abstractly in such lines as if non-linear and incommensurate string like entities.

I hope my quasic grid is helpful for it does seem to make a lot of visualization much easier- once we do have a better glimpse of at least algebra 101.

I am not sure now what new projects I may undertake here- suggestions anyone?

From a post-modern artistic concept our dreams are a folding of sorts to which we see only the surface and its parts sometimes broken, sometimes the only way in the clouds to find connections we do not see in the ordinary world.


* * *

This is an interesting Lubos posting: about three back from today's post.
http://motls.blogspot.com/2011/01/hardys-paradox-kills-all-realistic.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+LuboMotlsReferenceFrame+%28Lubos+Motl%27s+reference+frame%29

These sort of diagrams do indeed look classically logical and for me a little quasic. Of course the determinate's 2x2 matrix compliments and such seems to apply even as if the Aristotelian logic of it as to what can be observed or not. (But have we considered the absolute change in what is a one or a zero or some orientation if we are to recover anything in the real or concrete?) I have issues with Lubos in general on the concepts of what is positive and negative even where I agree some space is absolutely positive or zero only. I suspect I now have very subtle disagreements with his view as to what are the complex numbers or angles involved. In any case the ideas of chirality certainly needs to be expanded into a more topological view of space- at least until we can globally see why there is a difference in masses of three generations even when quantum theory would suggest we should not prefer any of the three axes involved. Styles of logical thinking, its syllogisms and all, its threeness, may separately be only valid within their own system and invalid in the other.

Of course nature in the various experiments we undertake will make these same results and conclusions in some logical manner- deducing what we can after all see and Lubos if this is your idea it is a very high level one. Of neutrino information and the mixing matrices and so on, the Majorana or other variety as to how it relates to the totality of number information once the Riemann sphere orientation finds an axis is still a question, yes? I only suggest it requires a little more than two bits to get the full picture- at least 8 rather than four only as these binary and fractal aspects of numbers do seem now to apply to physical processes.

* * *

http://www.sciencedaily.com/releases/2011/01/110128104244.htm

"Together, these data suggest that there are multiple layers of information stored in the genetic code."

For this I leave you with what is perhaps a more scientific speculation:

The Portal to A Topological Storage of Our Consciousness and Memories:

* 1 the "dancing" state of DNA in this article shows it there a significant amount of the time.

*2 I note in an old post of the Arcadian Functor blog the limit of 1 and 24 in the computations- but as I suggested in a recent post- and the realization of the core of such Pascal analogs as part of the factorial including the rotations of higher dimensional shapes- that the situation for DNA reading could be much more complex ( I used the term "Holy Crapola, if DNA is read this way."

*3 It is clear then that we have to see space and numbers, the vacua in particular, as a little more than the restrictions of two dimensional foundational (and Brane) thinking. How far can we go into the abstractions in say 120 or 720 as a core spacious singularity structured vacuum topology?

*4 In this respect I object to the trying to encode genetics and the chemistry of it all merely in terms of quantum formulism (quantum gravity looping however certainly is still in the running as a major model to consider organically and inorganically.)

*5 To some extent I agree with the spirit of TGD in Pitaken's exploration of consciousness- however, I do not see a good reason to ground it to some micro physical structures in the body and mind other than of course the ability to realize mind is secondary in general if not always to the materialist substratum. But this bit of experimental observation in the link suggests that there are physical structures, internally to the topology, which act as if a portal thru the material structures to access and relate to various topological systems as if just mental.

How else can we lose consciousness and yet upon awakening our memories are in tact- or for that matter how is it we can mask or lose memory even without the loss of physical brain material?

Of course in an even more general theory, just as the issue of mind and matter or of environment or inheritance factors may self adapt or even vanish as some imagine these as false distinctions of dualism, our theories of everything may indeed see these portals and not simply a matter of reductionist energy concerns and quantum tunneling thru some barriers. A related article today suggest muons replacing one electron can make the helium atom act as if a hydrogen, chemically. But in general these weights of things do not necessarily make a living system nonviable quasically if we say replace all the hydrogen with that of heavy water. In that sense the muon is not only a sort of catalyst but also a focus of conserving the general topology.

Questioning Our Philosophy of Mathematics

Questioning Our Philosophy of Mathematics

Today, a couple of poems- one that certainly was a mix of the snow series and arithmetic- possibly a result of the "running" of two creative moods at the same time.

I did some reading in Elementary linear algebra in a complimentary copy of a discarded book and some things dawned on me- after all it has been half a century or so since I had some brief contact with them going thru the motions of solving systems of equations with determinants and what not- but not in the way done in this book- nor its separation and emphasis on the more abstract use of matrices.

But such thoughts casually in the background of my thinking have raised some rather interesting questions on our philosophy of mathematics.

Note: Lubos has an especially interesting post today (maybe he is coming around to this wider view or role of the geometries) and Kea has discerned and counted some things of which by a different path and philosophy I found does indeed apply to asymmetric values and mirror directions of counting over a totality of systems.

Lampion: 01-27-11 In the presence of a central inversion (a singularity) of a structure, or as that singularity is approached and passed thru, we find some sort of mirror image which changes the directions and thus the chirality of the of these structures. This of course to be seen in the higher dimensions, their relationships, and so forth... [What is this sort of information and where does it go?]

What made me consider this [and what is conserved or invariant- in ideas of fluid turbulence] was the mapping of the idea of incidence matrices for the Soma cube. Such a model suggests to me a certain distinction between consciousness and awareness in that these abstract structures do not necessarily define consciousness but in our consciousness we do seem to make models that match the physical word and the understanding of them is something of which we may use for deeper comprehension.

I am not emphasizing the Soma cube especially beyond other such models- even though it is intriguing that Piet Hein invented it while attending a quantum lecture by Heisenberg- I would like to see the content of that lecture. I first thought to study this cube thinking that the Egyptians had toys with wheels and axles long before they used anything but rolling logs to move adult sized things. What significant toy might be in our civilization that could have more advanced use?

Apparently, this skeleton of our matrix notation covers a very wide scope of mathematics. It seems to underlay and contain most everything. I am amazed that determinants can be used to solve some sets of differential equations. I am amazed that they can be used to integrate and give volumes of vector parallelepipeds. I am amazed that these terms (some of which I assumed the meaning taken from the context) cover such things in a simple form to convey say, relativity. (skew symmetric is an example of how different the terminology can be perceived.) Where Lubos states in the article geometry gets hard in the remote distance- that is the beginning of deeper insights- that is a reconsideration of the varieties of the proofs of the Pythagorean theorem and its variations applied to dimensions of reference frames.

Now the nature of reading for me is not an instant continuity of comprehension, especially if that goal of comprehension is to direct in dialectics to some view or if the assumption is go thru the motions and the understanding will come. Some ideas are more simple than we have imagined and some much more complicated. So it seems there are levels of reading of which our initial comprehension radically transforms and exceeds what we thought was a complete understanding. Alas, I do not know what in the outer reaches of dimensions awaits in this complexity. What understanding I have is most likely equivalent to a hand held calculator. Of course one needs a BS in mathematics not using the calculator as a teaching tool as much as to know what buttons to push already! This paragraph applies to philosophy itself way beyond our considerations of mathematics.

I have said that I took a cue from Fermat with his recondite observations of what happens in number theory- some regard him as an amateur and a second rate mathematician. Well, I feel I am in good company then. Looking back from new connections of the background of trivialities I wonder, given his initial insights for space itself so limited in holding the perception but so much wider in the application to the idea of dimension- that after all a simple proof of his last theorem in not far away. The discrete can give us hard geometry also on the familiar scale of things and high vague languages we set up as models and for communication. After all, to some approximation of the abilities of a calculator in the distant higher calculations it will spew out that a cube can be the sum of two cubes- infinite descent is a sort of mirror of which such proofs seem to apply but lose comprehension in the process of applying it. This, like infinite regress where the exact analogies of geometry may apply, is in the end a matter of taste.

Lampion 01-27-11b The issue is our ideas of the discrete and continuous- I question, given a wider view of the role of matrices (that some can be unsolvable yet not describe some physical reality) if in general the square can be a sum of two squares even if the sides of the triangles are say triangles. I wonder if we can really say this of fractals on the sides of a triangle if they are not on the same level of being a fractal. Virtual photons can have a structure that suggests they can have a discrete collective measure of contributions by looping.

A fractal after all, complex or in some other form of pure recursive shapes, is that quantum idea of fractional dimensions. The question of fractional charges or not will be found an inherent property of the general arithmetic and geometry as dimensions.

[the mirror ideas, as made manifest, I thought I would designate as smell- thus there are caramel, melot, and horse flesh (to which like said of Fuller someone would call his touch geometry- Singh defines geometry as touch and sight- his work was horse hockey- but alas, very high grade horse hockey.) but these poetic ideas are not things I am sure I need to incorporate into the body of my mathematical philosophy.]

I am amazed, but not surprised, that these elementary matrices can work with probabilities such as Markov chains. I am not surprised because after all Pascal devised and applied all this because of theories of probability.

Now in the quasic grid, I leave it again up from yesterday if anyone wants to print one off but it would take 64 sheets of them to describe the 16 dimensional case. I know in the 9 dimensional case what I was looking for, the validity's of sorts to which the 24 is so important in three and four space, was not quite the answer I expected. It is always possible my own level of comprehension will be viewed as below some higher level of what can be obtained by self or others. I realized that some of the numbers I have called quasic or rather important for quasic structures are really the simple 1's and 0's of the diagonal matrix notation. 16 or 17 depending on how we count would be included in 8 or 2^8th dimensional resolution of the grid. Thus what we do on the line of numbers, one side of the quasic grid, is what we do with matrices- now what of the quasic plane itself and its numbers?

In another important realization is the idea of complementary or inverse matrices that is intrinsic to the quasic encoding- as if these, the absolute change in coordinates of 1 and 0, rather than these taken as absolute and then operations require multiplicative and additive distinction, are in a sense real and absolute space. However, in reducing things to one quadrant, or to one octant, we should take the others into consideration as we explore the spaces of interrelated higher dimensionality.

I found it rather interesting, the incidence matrices used for programming and to which I realized could be considered quasic coordinate notations, and yes there are more complex forms of this, the K circuits and so on of Coxeter, which considers all the subcells of things connecting or not- that we have to define a node as not connected to itself. Perhaps there are intermediate ideas of such connectivity in higher spaces, perhaps this again is a problem of looping virtual photons or even how in some way things can connect intelligibly at a generator of the null. We can proceed with caution in handling such cases but one day have to understand them from a more general view- not just the ability to build up, from flat brane like planes computation from a seemingly connected string at some point, or to compute in so many of some preferred step the end of calculations from the corner of a structure.

It is ok in such a view of matrices to perform a reductionism of the local and global information of general matrices if the result is one of a logic and its philosophy- for in doing so we at the same time expand to the theories of everything.

I suppose that covers about everything in my casual stray thoughts- I am most amazed that I can come here almost every day with so little to say then somehow type out so much. Walking, or taking a break outside, moments of easy thinking, something that I developed writing poetry in the street and but rarely having to stop and sit on the sidewalk to write a line down lest I forget- I mean, it just takes practice to have a global survey of what you recall and want to say and it gets easier.

* * *

Feathers, Seeds and the First of Stars L. Edgar Otto 01-27-11

Overcast the sky's pink glow
unnaturally returns the city's light
That ate the Milky Way long ago

The air so thick I drink it in refreshing me
I did not notice when the first icy star fell
Noticed at some point the slippery road

The profusion of them in all directions of the wind
the loon peeped, owl screeched, unconcerned as if
Snow itself was but a sandy beach

The Masked bandit peeked out from the rusting gutter drain
warily eyes me holding still, sniffed, went back again
His underground highways, snowmobile trails and rain

Tomorrow piles up mud and slush again until great floods
Nature bursting at the banks, brings back the rainbows.

* * *

Pebbles before Sand, Raindrops before Snow L. Edgar Otto 01-27-11

My calculator seems alive tonight
less the wires and glass bead game, an abacus
How I wanted one, then crude and costly prototype
freedom from the slide rule and when
They ruled the world, the first word of my first born

Oh, it needed sunlight or carbon and zinc to feed its
eerie dimming day glow eyes to help me think, discern the skies
Do long divisions and square roots not by hand so wise a babe
no more than I understanding the spewing out at creation
Reaching the pesky inverse of zero

Although it could not dance beyond two to the three three oneth power
The fractal shadow ghost of Ramanujan welcomed its poetry lost while its program error.

* * *


Perhaps it was not the dead end of trying to apply across my quasic grid the idea of the direction in one way a factorial thing and in the other way the powers of things, for to solve this we needed to work in a much higher concept of the complexity of space. Of course this apparently is what some now explain as one of Ramanujan's insights on numbers where they do seem rather fractal.

In the notation of the incidence matrices for the C++ program to generate the Soma cubes from the x direction there cannot be more than three 1's in the rows over the whole of the seven pieces. But this property in the quasic grid, that and the chirality of it in the incidence and direction of the pieces, tends to establish the four quadrants in the formalism that applies in even and odd spaces but especially to the squares of powers of this fundamental 3+1 or 2+2 Fermat-Ramanujan structure and how we understand, distinguish, or get around the relevant bilateral symmetries across the quasic grid- that important for the quasi-reductionism at least in lower orders of quasic space for the gene reading.

Of course a clue or insight such as Kea's in her post today may be a geometrical version of this number thing where vast generalizations await us and perhaps a still deeper understanding of particles and dimensions. How else could any of the powers of things act as strings without the strings? How else can such ideas as the nature of point like nodes in general space imagine or see things in the quantum world like in a sense all electrons are one electron?

In questions of the surface of that which in volume, scaleless, we note the structured central spacious or not singularity is it not obvious that somewhere the nodes can be of more than a plane? And yet if the ideas of quasics apply to such planes in what sense can we intertwine and relate to the general natural space wherein we may now describe the totality itself as naturally quasic? This perhaps a whole new area for inquirey to make what is still intuitive concrete.

Somewhere, as in my poem and apparently science news concerning the first stars, this sort of geometry in the background slowly develops them until their profusion. As vast as this vision of higher space is- in my remote awareness of it I must note also that the panorama of it can be as much humbling.

* * *

Apples, Oranges, and Pears ( 9D Chess )

The above illustrations are repeated here but are temporary until the new results are posted.

My mind has taken a quasic leap or a quantum loop and I have to follow down the paths of looking at my old ideas in the light of new connections. Essentially, I am considering a playable nine dimensional chess. Sometimes the map and grid of things is discovered or comprehended as a triviality- but sometimes when some trivialities are understood it connects to relevant other ones where some of our vague ideas makes more sense. In this case perhaps we can see the salvation of those parts of the standard theory that cannot be easily questioned.

Having found the fit of square pegs and round holes, or conversely, I now take on the mix of apples and oranges (hey I am in a poetic mood, in fact at the same time I am contemplating a poem: When Last did it not Snow. Poetry, after all, is the meaning in the cold grids of calculation and an objectivity that makes the object of its dreaming vanish into empty information. It remains to be seen, only known to the gods or perhaps myself- if doing both will in some ways enhance or diminish either, or other than intensity of mind these are closely linked.)

... returning shortly (and Kea you answered one question in your post I had not found a way to ask you yet.)

* * *
Damn, in trying to draw the picture of this I realize that the steps to see it are rather intricate and should be detailed- not to mention that a few of the some numbers and colors are used but in different ways which at times even when familiar with them I have to be aware of the possibility of errors. So, maybe this is a case where a word description of this model may help:

Normal 2D chess is played on a 2^6 or 6D board (I think this idea is akin to Clifford algebra but I have not studied that.) 3D chess in an 8x8x4 board and 4D chess in an 8x8x4x4 board. With this in mind it is clear (in a two player game) that an 8x8x8 board in three natural dimensions is playing in 9D space.

If we consider the orientation of each piece as if our natural 3D reality is really 9D of which we can only see the vectors of a third (or two thirds) we have a remarkable resemblance to the idea of quarks. (I really do not imagine even the geeks constructing and playing this game as chess even though it is possible to play it as a real construction. But as a particle idea it demands the "apple,orange, and pair production direction" of the idea of particle generation including where one imagines any fourth or partial fourth generation. In fact, I suspect the labeling as if 4 base rather than three base of this 9D quasic grid is the possible source of the idea of E7.5 intuitively but I do not know- nor have I had much luck in intuitively considering only 14 of the 15 or 16 points as associahedra in one direction. In any case the missing or implied cubes of the 6 tetracubes equaling 24 in the above grid is within the first cell or the zero cell- note also that if we do divide this 512 graph into quadrants the 240 soma solutions tend to remain within the first three quadrants.

[note: I find Kea's post on the digraphs (directed graphs) a good method to perhaps apply to this 9D grid, but do not plan to explore that key area.]

Despite the apparent complexity of all this- we really should begin with 16D space of which it will take considerably more quasic grid paper to do so.

I have a thought in the back of my head that we either have to have a new concept of complex units in multiplication or a better understanding of them in relation to the natural and real rotations and reflections of these soma cubes. But I do want to get around to plotting Peter Rowlands notations on Dirac on this 32 x 32 quasic grid.

And Holy Crapola, what if this sort of 9D particle reading applies and is extended to how we read the genetics?

* * * *

Sometimes I have doubts putting the physics before the poetry. I can only say that in my head the original while the walking seemed sweeter in the details, but here it is:


When Last did it not Snow L. Edgar Otto 01-27-11

I walk by the flower garden in the recurrent dream of arctic snow
recalled the flowers there, past and for to come, my dream last night

The Christian is out in it again with his snow plow and I
can walk easily around his house, he knows no other life

Perhaps in dreams of life to come his all the more real, at peace,
taking care for the blades and belts, winter's harvest of fingers

Three or four the seasons, more so three as my time on earth
becomes the bare bones, the last autumn leaves of trees

Somewhere in the antipodes it is summertime and yet things
stand on end when it is till Christmas in July, Orion ever horizontal

Eight the stances of the martial zodiac, then the shifts, then sixty-four
runes of my thoughts flow and coagulate, sideways blowing snow

The cities have no funds for salt, like the poor they think of sand
collect fines, only our sidewalks clear, wide enough for wheelchairs

* * *

When it rains it pours- another installment on the accidentally growing I am the Weather series of poems. This inspired from a fb chat with the poet teacher from Jordan Sultan-Ratrout who thought I knew his situation from his poems which I read as the universal human condition. Sometimes we lose more from accidental or long term relationships- and there is no cure for it, nothing to be said save the world is still wider to come, and the deepest poetry of live is its tragic losses. We do lose our desire to eat, and ability to read, at the time. But in the end the little things lost that count a great deal is the often taken fore granted simple friendship. Yet we know from the poet Kahil that lovers need some distance to grow and address our doubts and our cup of change circumstance of decisions- well, some of us are not at fault in breakups as there is not always two sides to some story. But this is not to be seen as comedy, we know, somewhere, we are all better than that. Character and judgment is still for us faced ever generation a work of art in progress.



Becca L. Edgar Otto 01-27-11

Becca you are still the most beautiful person in my world
but I was never worthy of you, not exceptional enough to fill your needs

You really did not know how beautiful you were, young lady
oh you flirted, priming and presented to the world, like anyone else

Still, felt so alone in paradise, not to build up your hopes
the bronze sea salt glistening will come for you on his surf board

I dreamed about you the other day, no lust, no tension in the dream
our short window for a short time together for it to work now gone

What is left in our pot bellied stoves against our winter but what
was lost that stoked the fires of which cold from behind we turn to face


Save that we were friends and in the sooty smoking love's embers
longs for that past thing too beyond glossed over evils that you do


Surely we were beyond all this, the prying plans of broken others
I did not think if you would steal from them, you would from me.

* * *

Arithmetica

Arithmetica

I had a most marvelous idea on the way back from the coffee shop- which I cannot post here yet because the details despite a dozen pages are not worked out- in any case this is "My Sputnik Moment" (who is the enemy this time?) So I still write in code, usually poetry (so that things I write could eventually be translated as intelligible) being a child of Kennedy with traces of the cold war mentality for secrets of which lately I have no such claim on important new ideas as not better shared. The question we should all ask ourselves, in the intuitive exploration of vague new enquiry- is if we in the search for some thought from an author and the process or steps leading to it- the claim of some puzzle answered- was it an actual solution that the author leads us to- or did he only understand the direction to find the answer, intuitively the final formulation left vague after translation?

But, as mathematics along the way grows- answers there or not- I offer this today which amounts to part of the new vision in the simple way we can map these things of my recreational concerns to the 81 elements of the hypercube. I begin to not only answer why the world is three dimensional but what happens at the ninth dimension.

In consideration of this I offer some new concepts for arithmetic, a metaphysics of thought that may be the key to some of the decoding and disambiguation of how we see number.

I note today Lubos has an excellent defense of string theory. Clearly his defense is valid to the point it again seems to confirm some of the ideas as alternative that could better generalize that sort of theory (and most likely not make it obsolete). Maybe more on this later when I fully understand some ideas from the other alternative bloggers as they go mainstream in the new physics.

* * *

Constantly running out of symbols or having to overuse them I recalled a post on philosophychatforum where I labeled the subcells of a hypercube by the Cherokee syllabary as I am part Cherokee. This pattern became clear in relation to the Pascal analogs where they trivially seem to add up in the squared formations.

Lampion 01-26-11

Although for every infinite group there is a finite group it is not clear why this should be the most general case. It is possible when an ordinal transfinite number precedes 0 and the natural numbers that from such a presumably non-linear infinity that not a diffuse but a specific ordering or individual value or pattern precedes zero and thus its successors.

* * *

I have to understand the ideas of Looping better but feel it is close to the topological ideas (provided there is a more general treatment of M like theory. But this possibility is worth looking at again even if the terms quantum gravity or sheets of things in TGD theory are still too vague. The same perhaps for any sort of existential view of twists and turns in such theories. But I ask this vaguely.

* * *

The codon bases are part of the structural understanding individually in this sort of encoding by arithmetic and geometry. (this idea from another way came up again)

* * *

Information theory (as with physical effects, numbers, and patterns) itself may present or be an aspect of triviality. The underlying theory invisible to he who makes the computation to which one may imagine a reason for not finding a pattern but cannot in logical principle say that is why we find no such pattern (Lubos).

* * *

The counting of things should consider the internal point as there or not or as a singularity complex or not- which implies the next dimension- even in orthogons.

The information is not only there in the line to a plane but for any such general and more or less disembodied abstract concept of such subcell dimensions. This amounts to a generalization of M theory as it assumes to be not a description of a multiverse. Is it then string theory anymore or closer to a more general physics?

* * *

I may add later an illustration for the above recreational diagram to which we show that the hypercube subcells are broken into three cubes of 27. But the sum of things by this sort of division is different for even and odd dimensions- that is the alternative division is as power one and not the symmetrical Pascal line one.
The 4 space can break into four cubes of 4^3, the sum of such cubes generates the rigid rotations and inversion numbers unto the dimensions in question (ie n!!'s).

The computation of a 2x2x2 matrix in relation to the supercolor pairs can have variations of which the triality and unity is reduced to duality and numbers mixed on the outside of a "geomatrix" of the next higher (perhaps complex) dimension.

* * *

In the exercise of classification of the Soma cubes, 480 or 240 from consideration of the inversion centers and not the surfaces or corners, that is a center singularity- is the C++ notation of zeros and ones usefully non-trivially to generate the cubes by visualization and not blind computation? Are they a quasic notation? In any case whatever the n-omino the grid direction say from xy (if not the notation xy yz zx from three directions) cannot exceed tricube triality. But of course the first piece of the somacube, a trionimino, may like some particles in that zoo of ghostly things, actually be 6 or 9 and so on... Soma More would express in the corpuscular flesh a 30 or 36 cube puzzle to subunfold such things.

* * *

And this was the sort of vision, that and the idea of three sets of five things when they share a point- that is 8 becomes 7. We map the soma cubes to this answer I long sought not in the back of my book but now with the wider view of higher space find it within reach and a matter of calculations, busy work. The realization is that we can map these cubes in higher space so as to see them readily, something we feel we might be able to do with numbers as to their primacy and digits- but that is a much harder problem.

If it is amazing when different areas of math magically seem to be connected, especially if we do not have the opportunity to explore or access to our earlier works, then it is all the more amazing that works of art and mathematical methods seemingly so different and each my independent discovery so magically fits together.

* * * *

From Today's post by Luboš Motl :

"What could happen - although it is extremely, extremely unlikely - is that a consistent, non-stringy competitor to string theory that is also able to predict the same features of the Universe as string theory can emerges in the future. (I am carefully watching all new ideas.) If this competitor began to look even more consistent with the observed details of the Universe, it could supersede or even replace string theory. It seems almost obvious that there exists no "competing" theory because the landscape of possible unifying theories has been pretty much mapped, it is very diverse, and whenever all consistency conditions are carefully imposed, one finds out that he returns back to the full-fledged string/M-theory in one of its diverse descriptions."

I agree pretty much with Luboš here with the exception of the part I placed in bold type- for there are those in the string field who imagine "a string theory without strings". I offer such a unifying theory as do many bloggers here. Let us not confuse the map with the terrain they say... The consistency of things like 2+2=4 or the reference frames does seem to allow for phenomena that are physical but not observed or observable directly- that does not mean there is no gravity or Higgs (well, it but one minor particle and not the all pervasive field idea) and yes I did suggest iotas which one could in trying to see the world as some sort of conservation and symmetry in terms of energy and its encompassing reality (while still not all there is of the physical let alone possible metaphysical like consciousness as a real and maybe independent source and phenomenon we experience). One can be assured there is no challenge to the string view, it in a sense is a steppingstone but like quantum and relativity itself not the isolate be all TOE.

I am glad the line calling some idiots is revised I think- an emotional rant not fitting of formal science but perhaps a good political tool in the blogosphere culture. But I do have a problem with his statement concerning the old "where does the information go into black holes?" This as a classical as well as relativistic concern for today's physics. So, it does not vanish, does not return to us to churn up the "swampland"? Loops in somewhere else in say some other action at a distance or parallel universe? Where does this information go- into braneworlds that lose their stringy origins? Perhaps, it goes (all these issues of dark or opaque matter aside) into a much greater theory, with I agree our mathematics at hand) well beyond even its marriage to what we imagine of the various dimensions, symmetries, and topologies. As Luboš foresees but does not see, this a proof of sorts of a challenge to the now established string-like framework. This only looks like a paradox or complimentary contradiction- I can agree that quantum theory and general relativistic ideas, being a little less emphasized in the pursuit of physics, will not go away either. Perhaps the information goes into the various TOE's in the great external black hole we call the blogosphere.

In the face of swampland (perhaps a more general uncertainty principle if all is Otto-Motl statistics) does a statement, while reasonable in our scientific skepticism, like his " extremely, extremely unlikely " have any meaning or relevance to the new unified physics at all?

Even in the vast and deeper dimensional worlds beyond our ability to observe or disprove as measure, things intelligibly arithmetical at least over infinity, we find alternate levels of dimensions or things like them where we may distinguish what in a group of objects has increasing discrete mass or what has mass of a more symmetrical variety. This issue is a vision of mass that is not that easily dismissed as magical or metaphysical at all- if we desire physics as a primary description of the world. Let us not into string theory bring the same old confusions and contradictions of our ideas of uncertainty and the reference frames as if on steroids- such complexity is a challenge but does not explain the omnium.

* * * *

Soma More

Soma More

We find a quasic or z-code order in the reading of dimensions- dimensions are then the same description as quasicity. These moreover are the same description as that of the fractal triangles. All of this arithmetic and algebra of the finite and the infinite. The quasicity as powers of 4 is evident from the right or left of these graphs- also the easy visualization of the orthogonal structures.

The supercolor, that is the expansion of information in the quasic dimensions is binary base representations and not just mere, but ordered duality. To reach the colors involved in 16 dimensions we have to imagine a grid of 32 x 32 which contains in each pixel 8x8 sub-pixels. 32x32 is of course the ten dimensional case.

The need to add further dimensions for that case assumes that we cannot distinguish in itself in graph theory that a line for example separates a plane into two regions and thus its existence as a grid element cannot be self contained. Upon this and with the division of the powers of 3 and 4 we have to generalize the idea of holographic and matrix algebra into some line as to what is the outside boundaries and to what extent we interpret or decipher information contained in them and the space(s) they contain.

Lampion: 01-24-11 To Kea's observation that a value is close to pi which I suggested was 256/81 I note this ratio can be the squares of each also...

Using these orthogonal representations it is an easy effort compute the combination's of some things like color visually. The Dihedral group in a sense is an overgroup fractal like to the others where they are treated factorially.

Thus in the diagram above we note on the 15 + 15 color level that all the spectrum is is represented linearly at the 8 corners of a cube or one side of the quasic grid, while the diagonals of those 6 spectral colors (6!) break into BKD or the other side from the center of the cub GIN or half the colors.

Interestingly, 9 +28 +27 = 64, which is to say something about the 36 inner squares of the 6D grid and 28 which with the nine in a reversal of global signs is the left over squares after the color fills; and of course 28+28 = 56 as all of this does relate algebraically and topologically and arithmetically to these triangular numbers.

Sometimes, as in the classification of the Soma cubes, the concept of abstract quasic motions as the power sums of two is the topological combination's of groups.

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An Overview of Fourier Methods in the Description of Physical Phenomena

It is clear that we can construct physical things (our sense of the solidity of things or force of things) by taking literally our intuitionist notations. Is this the fundamental question we are asking and seeking for a unified theory?

In effect we imagine exploration into concepts of space where in general there is no central singularity (multiple or not) or there can be seen one by the notation.

To start with the idea of transformation of assumed prime and simple solidity of three space is what happens when we transform with linear matrices into coordinates using the trig functions. This reductionist view works but does not really tell us about deeper theories of space from a more general and real grounding. We can then only assert a connection between quaternion like numbers and natural vectors when we can already examine or observe the duplication of spaces so to define these as a doubling of the grounding dimensions. This is a powerful tool but can leave us blind to the deeper reasons for measurement as the complexity of our theories fall down the rabbit hole- alternatively we can assert deviation from the methods is merely an Alice in Wonderland hope or dream.

We can divide space into so many regions over a region, say to the approximation of 64 subcells in a division to compute the Fourier transform so to find an approximation on the quasic level to things like matter distribution or any other key concept so far to describe what we see in the cosmic background.

I have to question things there at the creation of these method which is not wrong but not as a profound and historical all in all breakthrough in our methods. I want to keep in mind in the ideas of heat transfer explained it may not be the best or only thing to separate the values which are real from the imaginary so as to compute these separately.

If, as in Kea's excellent link today on braids, we utilize the 12 of things [actually we see only 6 of them with the 9 empty squares make 15 from one view rather than my vague sense of the 21] and what is within them- I imagine in the triangular orthogonal notation if we exclude the outer boundaries we have twelve things on the inside- as if a triangular geo-matrix cited yesterday on new scientist. But I only feel this for now vaguely and intuitively. Part of the game is getting ahead of our notation to see it from a more complex or even from a simpler (as if consciousness but objective view) as well as our search for a unified theory. Color then may be a composite thing or it may be that the spectrum of Newton does indeed reduce to single frequencies as per his experiments with prisms- or in some sense Goethe's color theory still has some points- especially those of asymmetric complements of subjective proportional areas.

Of course for the 3D elements of which 12 are the center the missing elements of 4D added make 21 in the three quadrants. [Note: when we go up to much higher pixel spaces into sixteen dimensions ( a sort of Fourier transform on things here divided as each pixel into 64 of 32x32... eventually in the complexity the number seven can become a divisor where it is not if the ratio of values in a lower conception of the dimensions is not that between squares. ) In this sense we may have to generalize a little bit that region from small groups to very large simple ones for some physical properties in between in this long plateau of measures. These things we should visualize after all we are indeed asking questions that eventually relate our ideas of mass and gravity to what we think about the symmetries of thermodynamics. Still, even if some of these laws are abstract they can have real consequences. The idea of a center singularity or not is essential to explain certain differences of the photon count to further explain as space properties in directions away or toward it so as to realize a difference in the stored energies. Perhaps the iota behaves like this as a theoretical subparticle not quite a string as if a general quantum like analogy to these leptons.

Interestingly too, the threefold structure's can make thee dimensional puzzle games in their own right and may have been discovered first. We can slice through the Soma cube and the slices do form so many structures based on the combination of hexagons and triangles which from that view make intelligible puzzles.

Sometimes, if we make an error in counting it is instructive to know why, a sort of doubt in the cross checking. In playing with these numbers when the calculator works- that is the factorial button now gives me error message- I have the distinct feeling there are things like quasi-rational numbers which sort of divides things intelligibly as if integers - that is certain repeating decimals of which it is not clear to me where and how they may ultimately approach the value of pi. Unless the products of pi itself makes more complex the totality and expression of its contained information in binary description. In this sense also we might find some unity somewhere in our concerns with the ideas of fractional charges although I do feel they will prove, at least on the lower dimensional levels, integer values if not binary (of which some authors like Rowlands already hints).

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Some years ago the mall had a puzzle store which sold such cubes and I had grown tired of finding one again on paper so I memorized one. Ever once in awhile I would go into the store ask what this was and accidentally knock it apart. It's OK the clerk said to me, we can put it back again like we did this morning. I'll fix it I said and rapidly put it back on the shelf.

One kid exchanged two corner tapped colors of a Rubik's cube and asked me to solve it- I cannot I said, for it is impossible you must have rearranged the colors.

I was helping another child read for my boss as he had failed the 4th grade and would do so again. He was very good putting these cubes together so I knew he was not slow. But he did not want to read so I said what the hell and played hide and seek in the college green- I thought he was tricking me when he should have seen me finding him- turns out he needed glasses and when he got them and moved up to the front of the class he had no trouble at all. I sometimes feel that the study of geometry is one of the few things that can or seems to raise our intelligence.

* * *

Clearly, it is worth stating again, that in the 3+1 or 2+2 formalism we need to consider both options that apply and one not preferred to the other. TGD as I understand it is the latter only, and for Lubos I imagine the former. So it amounts to sorting out what we mean in the dimensions of things by orthogons and simplexes when we try to calculate the global view if by any one view we may resolve things to the vague idea of 5 or ten space intuitively- but at the higher and better idea of the complexities involved in defining what we mean by such dimensions. It is not enough to divide a fivefold polyhedron into vectors that are confined only to our familiar ideas of three space for it misses more refined and general topology. Let us not forget that at whatever level of complexity the simplexes (as if a continuum in itself- the Celestic continuum in my conceptions) and orthgons(antiorthogons) have analogs on the familiar intelligible level into n-dimensions. Of course in the application of this to the genetic models this complexity has to be dealt with there too. It is not enough either to ignore exceptions like the C groups in which we conclude there are infinite numbers in the duality (viriality) applied of polyhedra. This combination of vector and octonian like spaces leave far behind the most general descriptions of space we now have- like configuration or phase space and even those purely a matter of complex space- all of which have their place in the bigger picture.

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Note: Duh, I have just read Kea's (MDS) various papers and find them clear reading with several conclusions I agree with or speculations on concerns I have thought about. It will take a little longer to digest all of it but what a beautiful person behind this paper, what a clear and intense mind with no nonsense objectivity- and what a good time for her to be here in this golden age of cosmology. Note, nothing I wrote above was intended to challenge or critique her presentation.

With the Shepherd Moons and their braids, the discovery at the time suggested to a few people that we had to go back to the drawing board of our foundations of physics.

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Well, so much more is on line since 95 or so and so many have investigated things like the soma cube puzzles and other geometrical structures. So I spent the afternoon googling a lot of things. In a lot of this I feel so obsolete, that is compared to who was on line doing certain things when I was there alone or almost alone- some of the original people have sights now (some whom I corresponded with or did an email) that have vastly grown. I especially liked the C++ generation of the soma cube and the debate as to if there were 240 or 480. Note: the inversion of such a cube will invert the handedness of those two pieces but not the color! I note that Conway seemed especially active or creative long about 95.