Saturday, April 30, 2011
Knight Tours, Hamiltonian's, Division Topologies
A footnote. My last post of the many for April and maybe awhile. Of course we can use other methods and make other important distinctions for this puzzle like dividing the board first into quadrants.
So how can something like strings not be involved in the mystery of gravitation, and how can octonions not be involved in the mix? At least for our outdated applications and descriptions.
Four dimensional chess anyone?
A Link to the Experiments of John Baez
and My 30 cube Notations
There is obviously very much to explore and learn on these pages of Baez. Some of us are aware of higher space and the meaning of symmetry in it- and the varieties of what can occur there as in my application of Conway's matrix of color cube matching.
Here it is: scroll to bottom of page... name over this graph is Phylogenies
* * *
Well, its been a productive blogging month- and I will probably be away for awhile setting up the candles perhaps- I am not sure of computer access. So, without much to say for now, and a thin posting compared to most- my thoughts look through the science daily and playfully find these links that seem to suggest something about how we might view and organize space perceptions- at least on the nerve level:
"Box jellyfish may seem like rather simple creatures, but in fact their visual system is anything but. They've got no fewer than 24 eyes of four different kinds. "
"The UCSD researchers monitored the electrical activity of grid cells in rats that explored a small four-foot by four-foot enclosure. Grid cells, located in the entorhinal cortex just adjacent to the hippocampus, maintain an internal representation of the external environment. This representation is a grid-like map made of repeating equilateral triangles that tile the space in a hexagonal pattern. As an animal navigates through its environment, a given grid cell becomes active when the animal's position coincides with any of the vertices within the grid."
"The researchers found that rhesus monkeys can flexibly recall extremely simple shapes from memory, as evidenced by their ability to reproduce those shapes on a computer touch screen. The findings suggest that human and monkey memory is more similar than scientists knew, the researchers say."
* * *
So it has been a long ride up hill and I have surpassed myself again in my enquires although it is not a bad, but a dangerous and arrogant assumption to feel a little ahead of the race or quest for a unified theory hauntingly near and almost there. After all it is a very steep climb and can only end, as Heinz Pagels pointed out for quantum physicists drawn to mountaintops before his prescient dream of falling came true.
I was tempted to post comments other places- the news of Baez to have an article in Scientific American forthcoming, the blog suggesting it a matter of teaching the readers for such links- but I did not, because the real unification is from our various viewpoints to which, like the string theories Baez tried to bring into a unity of sorts, almost magical, as the M theory tried before him, is the unification of all our ideas to which we feel so strongly in its parts we feel compelled to push some agenda. I then will wait for the world to catch up- heck, even breaking even to our time frames is better than being behind even with the clock running out. I will wait then for another encore and the recurring dream of this work of poetry thought but another bowing out only the next book of poems surpassed, as are our visions.
But as far as the way things are going now, with our rungs and ladders, our snakes and ladders too in the morality of the game - we gentle with the new and as nature so wasteful with her acorns and stars, so said Schweitzer, our work so long in the saving of the sunlight perhaps just to vanish at its peak- I leave you with Vonnegut as far as quantum cats and string theory is concerned as we welcome, oppress, or lead the next generation to find dimensions so much wider than our present dreams:
"No damn cat, and no damn cradle."
* * *
Division Algebras and Four Space TrajectoriesL. Edgar Otto 04-30-11 Eau Claire, WI
I give you first a sort of ley rant on theories of the foundations. I suppose the quality of one's playing in a chess game depends on the quality of your opponent- in this mood it is unfortunate the intellectual challenge that inspired this defense of Baez et al comes from what some conclude is not a strong enough army to command respect and civility in undertaking science war that may lead to breakthroughs and leaps.
I present this informally to show the links that come to mind- all of this impeded by our languages and notations- but I assume some of the methods have been around long enough to be common knowledge by those in the discipline- how we derive the Lorentz transformations for example.
Since the Lorentz "boosts" are associative, those who, although standing on an immutable truth over the infinite range (perhaps excluding zero) and hyperbolic spaces, (these as identity matrices from my researches in a "quasic" ordering and zeros considered at rest or otherwise, those who consider this work of the last century to be the end all and grounds for all future developments in foundational physics including what we mean by spins and rotations in spacetime, This property then limited by that property in the division algebra limited in notions to quaternions, and the applications limited to special relativity only in a discrete quantum way in which case the concept of octonions is an irrelevant background for hoped for super symmetries, that or seen as anathema let alone a useful generalizations of the opaque that may describe the universe even beyond such algebras.
In some was we are not concerned only with even or odd functions over quasic (wave particle) space but also the natural consideration of the Lorentz treatments and absolute values of invariant spacetime shifts as vertical to the upper and lower quadrants - this the basis for deriving the transformations of such a spacetime group theory. This pattern seems, on the face of it, most evident in the evolving structure of life, provided fractal like (that is the assumption of a quasicontinuum) spaces grasp the limits of symmetry and asymmetry and other hierarchical scales and values that tries to understand an infinite regress.
Considering the order of the matrix idea leading to Lorentz transforms it makes sense in quantum theory to rotate them 90 degrees to interpret say Feynman diagrams so rotated in particle descriptions and transfers, decays. It is the 45 degrees of the absolute angles of light rays that makes the quasic plane on this dimensional level relate it as if square, and what sort of determinants and linearity involved in these fixed and general vector objects fill the square 8 space with hypersphere objects. It also may follow, if the reductionists applying reduction to this idea take these algebras and general numbers seriously- that different laws across the universe seem to be there in some cases, the inside of quasars, the shift of neutrino masses and other anomalies to their system (one that btw it is futile and false to assume it can be dismantled without consideration of its deeper axioms, or the thought of a variation of the light velocity, this is perceived as a threat that can only be resolved by a more comprehensive foundational theory.
We try of course to resolve the issues of interest, fact or myth, of our time- after all communication is a human need and is important even with some sacrifice of certitude. In these issues of simple Trinity as a model to include, perhaps the Christian tradition would understand this better or at least a Western one, for the physics, for science, as well as religion it seems these issues of triality in what factions people belong to has cause more core in depth conflict by ideas alone than most any other issue of philosophy from religion.
Apparently, the use of simple graphs and geometry, after all how do we define say a Cayley number or graph? Seems to be suspect and rejected at the heart of new theory, but this is how it was for a very long time for the status of simple geometry as taught.
* * *
Although the lecture (thru Kea's blog) concerned string theory on the atomic and then Planck level was deep into its origins and continuity of the growth of ideas from Newton to Quantum- as a creative method the lecturer asked what if someone from the future came and told Newton that his trajectory ideas were wrong or could be expanded into a more quantum view- should we not image the same state of things for a better idea that really does not undermine the old physics, just expands upon them? We certainly need more of these intuitive methods, to think about the foundations of the foundations. What do we gain by uplifting an idea, such as that of the surfaces into projection of volumes holographically, as an item of unquestioned worship- especially if we cite all the time the specially chosen saints of that discipline as if no others worthy to commune with the ultimate spirit of physics? Is that not some form of Nationalism? Some inversion that beyond the healthy egoism is a nasty self-centered egotism where both are not really defined?
* * *
Let me say a couple of things, technically, the all important fact that it is shown that in the Graceo-Latin squares there are no solutions for 2 and 6, this shows up when we make squares of things (in four space for after all we cannot extend the matrices as Cramer? does beyond three space) and it follows that there are known ones for at least ten elements to combine. Why are these global things of simple topology and counting not considered intrinsic to physical theories? Why is this the case in reality anyway as a property of space? What is the two then three and a little more in a world were our notions and notations have to deal with 2 x 6 or 12 things over space. (the consideration of these led to the 9 cubes drawn above).
The previous table (that included a Maroi title) amounts to a Keaese-to-PeSla translator where we try to resolve these models of triality which are really a sort of compliments as maybe we should expect from the new freedoms of higher space and the use of defining numbers like the Mersenne for the essential composites and thus the factoring or division of things. As the illustration states I rather sorted these axes and labels informally and not their mirrors for example- nor have I formally shown, as Kea did, these transformations in spirit do apply to the multiplication say in the case of quark mirrors. But my doing that also shows a certain ease when in parts of combinatorics the order does not seem to matter. Yet it is clear with privileged centering in a global setting artfully assumed, the properties of division algebras asymmetrically and with the associahedra and so on are useful areas to study and explore- certainly it would enhance string ideas. While we may think of such space as M theory without strings, it is true also that there are still those who think, from a recent bygone era, we can have string theory without these higher levels of number theory as spaces-string elements not explaining so many things disembodied from any idea of space and time itself.
To what extent, I wonder, is the density as defined by say the polygons and polyhedra a density as so defined by the expansion or contraction of wide space.
I remark also that while it is not looked at too deeply, the tachyon idea is alive and well or at least in the background, that to keep in mind in our explorations as either a useful principle or one that if not there explains so much as to what is there. But again, teleology is still more philosophy than science.
* * *
Ironically, I owe Lubos for an idea today for on his article:
he shows this diagram which speaks for itself- that is shows such work from the alternative views of Baez et al- but as far as I can tell this drawing comes from Tony Smith. From my view, and in struggling to see things a little alien to my views that involve the twists and turns and braids and so on of complex numbers this way of representing octonions and division space, a seven sided figure that is broken down into triangles speaks volumes to me- a way perhaps to make another set of such cubes for three space. Again we would benefit from more formal explorations or at least from those who might choose to help with the work, surely they to find something new also in the new physics,- well, a theoretical brain is a terrible thing to waste, would from an existentialist view our detractors not vanish but come on board that while we breathe the wheel is in motion and a conversion to the cause if it a better and objective direction, is to be hoped for.
* * *
Friday, April 29, 2011
Triality and Pairs ( Ko Tahi Pu Tua Toru )
In thinking about 36 again as a triangular number, and of things like Kepler's calling his book of symmetries "The Tri-cornered Snowflake" I came across this combinatorial idea by Thomas Kirkman (1847). It reminds me a lot of Kea's approach and I realize that my own may be hard to understand as it is complimentary or different.
After all my purpose was to connect the 36 colors in a different way for my calyptic puzzle. This of course leads to some variations when we try to color things as if axes or square surfaces on a cube in three space. The point is that there can be other combinatorial systems as intelligible- and these may apply to classifying particles and of course as braid theory we find the idea of pairs as mirrors.
Why did Kepler call it Tri-cornered when most of us as kids know it is six sided? I mean some kids make their snowflakes cut from paper as square- or think the clovers can have four leaves for St. Patty's Day- good luck anyway as those in the know find four more rare, even five is rarer. It was hard to find them as a child looking over the field of clover but once you found one and followed its stem down, for four and five leaves, a few more came from the same roots.
Of course a Hexagonal number is equal to a triangle number n + three times a triangle number n - 1. (take note Ulla, this has a lot to do with how we express the structure of carbon in the genes- I suspect, as per your insight). In any case these flat and mirror pairs of triality have their application as if determinants as square things, or as a right angle of three things, fractal like really but in a different way, reminiscent of Sudoko also... 27 and 36, 4 x 12 and so on as we struggle in our time to learn to count these higher patterns and find new ones or use them for measure and the understanding of higher dimensional complex space.
Actually, I am thinking of numbers as related to the article on savage numbers by the brilliant young man I mentioned earlier. That and the ultimate nature of thinking about primes and what this higher dimensional sieve might do to find them.
So, I agree that the primitives count differently but not necessarily that the achievement in the West over the developing peoples by advanced counting advanced our science. I think rather it is how we relate in our minds such a stance toward counting. The Maroi counting system comes to mind as a model.
For one thing there is evidence theirs may have had a base of 20 at one time- or that this was the early stages of such a base as say developed with the style of zero by the Mayans. It is certainly an advanced and not a "savage" idea but a different way we relate toward the patterns of numbers (indeed, of alphanumerics in general). The base ten may in fact be inferior in many ways, to count by five (as we have two hands) would be much faster in initial computations as on early computer programs applied to gaming.
Of course the 20 base is thought to be a matching of our fingers and our toes. But what sort of 4 way handedness is this if we tend to break things, like the Maori, into the more efficient counting by pairs? But like the rest of us they have a word for many after a certain point, theirs is rau and they have one for very many - mano. Interestingly, they do no do well beyond 180 but that after all suggest factors and perhaps the 20 base.
This of course is more like anthropology or archeology as a theme or topic - then again when counting, that is 1 Tahi, 2 Rua, 3 Toru, 4 Wha ... and of course variations that do suggest an ascending order (as if we imagine ascending dimensions) they have ordinal numbers 1st Tahi, 2nd Tuarua, 3rd Thatoru, 4th Wha and words are different in counting when referring to persons rather than objects- which for me justifies this more psychological or consciousness consideration of how our mathematics and perceptions relate to shed light from one to the other. For persons: tokotal, tokorua,, tokotoru ...
But most interesting, much as we can imagine mirror and virtual particles as part of a system of triality and braiding theory, the Maori had words that meant a certain amount or count and yet the meaning could convey the sense of "a little more".
Let us also recall for other places in the world we find the base 60 evolved- and for some of the savants it is thought they count this way, over focused but efficiently. It would be interesting to see what effect on our perceptions or understanding of some topology and algebra ideas a good grounded 20 base would influence the development of our pattern thinking.
* * *
Now a couple of ideas came from these linguistic thoughts which seemed to have some relation to both systems of triality (including, Pitkanen, the situation where I too regard the octonions as part of the physicality of things especially where the informational aspects have the multiplicative inverse and compliments.) The quasic grid or plane as multidimensional exceeds projective space and there is a little more that seems to be a property akin to the generalization of odd and even, but not that for also these can be reduced to one concept or formula of patterns.
This little more when we consider null or zero in the count of things tends to justify what was thought and error that Eddington made for such numeric methods of counting for the 136 dimensionless constant (adding in fact +1, so he called old +1 for awhile). Our scientists, no matter how great their experimental contributions, like him or Tesla, are given much less standing if they have dabbled in considering the spiritual or occult.
What pattern in the developing language, the goad for language itself perhaps as number may be, drive us to the one more- what leading singularity? What hidden triality that shifts the sounds of words beneath the phonemes and phenemenes? What such quark models of our protons?
I think of things like the old sieve for primes- it works for the finite counting as well that which connects as linear and beyond, in sense the idea of mult-sieve if we consider new results from the multidimensional geometry and things like Grassman vectors of subcells of orthogons... a little more to add, to integrate the areas and volumes, and the recursive method descriptions. Such planes or branes can better show what is Casimir on many scales or what is down to earth classical over modern- the quantum logic not just that between some number of planes, but beyond Gibbs even, in its multi-brane concepts of any level of the interconnected universe.
So I imagine, the poet in me (and btw Lubos, I watched as much as I could for the wedding of the royals as it was late or early... do you no know the mathematics of voting and all its paradoxes? Do your not know how much tax payer income that wedding brought in? You really need a more formal and scientific analysis of your politics- and not ask people posting to your blog if they know how stupid they are- even reading new scientist last week the multiparty system was explained. And it was not the king raising taxes that lead to the revolution, but the tyranny of the parliament! Read a little history too.) things like brushes and combs, bristles that focus from all directions on a brier or nit. Or Baleen, some idea of what is not seen as a reference frame or some particle like the Higgs we almost seen, that teaser, but then again it has hidden from us or nature conspires it does so as our frantic search accelerates- [see comment to Tommaso's blog below:] but what of velocity and that question if laws are uniform- I mean why should light have the value it has? And in the null hypothesis how can we see our errors type 1 or 2 after all? Space and Time also may be factored as separate as with all that may reach some idea of rational absolutes.
Or I imagine briers that attach to the fabric of it all or to fuzzy quantum cotton balls. And best of all Velcro- for the hooks and fibers the interlock or break apart is not that bad on some scale as a falsifiable model of the atom with hooks as some first tried to describe their bonding.
The "blocks" of elements in the accompanying illustration is a number that can be shown to be so arranged if divisible by 6 then have a remainder of 3 or 1.
Lampion- Considering the logic of polarized planes, branes, gates, universes as beyond a quantum logic in its subtle polarizations and dualities and a little more the ultimate idea of what prime means is one of fine degrees of relevance like the beads in beads of ink filled glass in Japanese ink. Primacy is the ground, irreducible or quantum dust and yet not as simple as the sieve these sub-continua to which we impose our style of counting.
* * *
I made this comment today on Tommaso's fine blog:
Of course the original paper struck me as a fine joke.
I heard he world teleology in a video about "leading singularities".
Now, today this rumor of circumstances conspiring to prevent the discovery of the Higgs came up briefly in my own creative pages today but I could not recall the source of it.
Considering the uncertainly around all the rumors perhaps that cosmic and possibly futuristic censor slipped a little and now the data on things are a little fuzzy as if the quantum cat out of the bag was put back in.
Perhaps that thinker can learn a little from the methods of Dr. Rhine of Duke who studied precognition, that the results of the telepathy came out about as expected by guessing- but if we jumped a card it was way beyond the norm for averaging good hits- however, the quality of those hits depended on if in some future time those doing the test were told of the results!
* * *
I posted this on Matti's blog after searching for a term on Google (most of the references were associated with him save one that mentioned Clifford.
I found it hard to search some of your terms like Kahler action. But that does no matter.
Of course octonions apply to all of this (and beyond that at least to 16 space of which I am not quite sure that is what you mean by hyper-octonion or some sort of complex duplications.
I do not see (as of yesterday) the idea of the primes as a concept so restricted but I do see the math forms you are adept at rather cumbersome and misleading in our less rigid ideas of hyperspace. I am not sure of the dynamics but certainly we can expand 4 into 8 and that is a condition we seem to want to explain (compactification is the germ of a good idea here) The use of Feynman diagrams and the group notation loses information unnecessarily. Classical and other differences are irrelevant as on a higher level these ideas are transitive over all systems including spinning.
I will take this as our differences in how we see finite or continuous things- in general I think the quantum terms misleading here for such a reach of your generalization.
Hopefully we can speak again in details when some of this gets sorted out better. I will be taking a break soon.
[this in reference to this pdf searched quote:
The notion of hyper-quaternionic and octonionic manifold makes sense but it not plausible that
H = M4 CP2 could be endowed with a hyper-octonionic manifold structure. Situation changes
if H is replaced with hyper-octonionic M8. Suppose that X4 M8 consists of hyper-quaternionic
and co-hyper-quaternionic regions. The basic observation is that the hyper-quaternionic sub-spaces
of M8 with a xed hyper-complex structure (containing in their tangent space a xed hyper-complex
subspace M2 or at least one of the light-like lines of M2) are labeled by points of CP2. Hence each
hyper-quaternionic and co-hyper-quaternionic four-surface of M8 de nes a 4-surface of M4 CP2.
One can loosely say that the number-theoretic analog of spontaneous compacti cation occurs: this of
course has nothing to do with dynamics.
* * *
[I came back to check mail and found Lubos post on Baez- so I was moved to post this on Pitkanen's page as a comment:]
I see Lubos too today had some comments on octonions.
"idiosyncratic bullshit" is what he referred to for Baez.
One can claim an other does not understand a theory (string theory) but where is Lubos showing his work?
The numeric properties of these various spaces- apparently many want to keep it in the old physics framework- seems to me to be done more with practical considerations than with deep theory.
The radius of nine units to a square of 8 units as the ancient approximation to pi comes to mind as engineering, not magic for the ancient Egyptians- but theory may be hidden under all this that is not as numerological as the string ideas. There is nothing magical about ten dimensions.
And for all its apparatus, the idea of powers or integration over series, or thinking of calculus from this side of things in three space now a breeze- our common language shared common errors.
i to the i for example, as if acceleration was the key to all things comes out a real number- in fact, 4n + 1 can make many of these real numbers- your strength is the practical seeing of this.
I for one found Baez to make a lot of sense, and perhaps in ways even he does not realize yet.
Well,we keep on for some reason, play with roots and all, surely you have moments to question the project and the outcome- I have- I mean such growing wisdom for me in a sense comes too late. Like St. Augustine, loving Sophia too late.
I our abandonment at least we can sense that in the end all that we are capable of seeing now in the math and physics turns our so simple after all.
As always we are punished for our discovery of fire...
* * *
Thursday, April 28, 2011
Without Design or Dust, the Bridge of Primes
L. Edgar Otto April 28, 2011 Eau Claire, Wisconsin
Long ago I thought the key to a unified theory would be ultimately how we understood prime numbers better. Something deep in our intuition draws us to such a conclusion, and it is philosophy more than science for now. A philosophy of mathematics, perhaps, although such contemplations do tend to organize systems of thought on how we apply and see such things.
If we develop quantum forms of computation what we encounter will not be as alien as some suggest explicitly, for we have hints of it already within our thoughts. Some of our cherished stances to the world will seem changed and have to be revised, but the quest to deal with numbers and patterns is very old in our history, for the new in our time it can seem surprising how long ago some ancient people broke grounds.
The seeming certainty of arithmetical laws, our ability to formulate them, find patterns, rely on their results, can come home to the point where we might ask if the universe could be any other way. This of course is a radical position for those who only choose to deal with the one world of our experience as the mysterious but only intelligible reality, one that despite the fragility for logic over changes seems to endure so through all of time.
We suspect, even prove, that some early comprehension of how these ideal or solid things called numbers works can be explained completely by say factorials encompassing the world. That becomes a problem not only to our rise to learn to count, but that the numbers are so large they are impossible to grasp in the detail, to count or compute, even by this age of help from our machines.
Perhaps, what we mean by non-linear, that world a little fuzzy and beyond the simple idea that dimensions can be more than lines and n-bodies can have vectors hard to pinpoint of objects between each other, or that we cannot predict the tides without ever more complex wheels and gears- if indeed the idea on the other side of this coin is that randomness can somewhere exist- that old philosophic thought that what we are measuring is our ignorance, some idea of growing disorder in what should be an ideal world if not one totally determined from some view, is this idea of something like mind, be it of a great and intelligent design or an ever existing indifferent clockwork.
Mind in any case seems to be receptive to the dust and the dust to it. It shows that beyond mere physical organisms that its connections and bridges, its ground of primes or they as radically different from our wide scales of experience as what may constitute our core sets of beliefs that the idea of consciousness and thought is of a higher level of complexity than living systems physical in themselves.
Our approach then to number, and to design, if these be some ideal independent objects or part of the big picture of things only, is to emphasize the methods of one ideal or the other usually. So where we find a part of reality without design or dust, without measure- we may claim that at the background of all thing is mind, that which can ground our conception of God so to supply in the dusty count some depth and certainty of meaning, some comfort beyond our frailties and mortality, and so on... The argument from design may or may not reflect our own intelligence, may or may not reflect the world as something with a Designer behind it or that totality merely the universe itself- in effect the laws of the universe where the arithmetic explains what is dust and the context or topologies as dust, albeit complex, are understood at least for this and all worlds not then grounded on mystery.
Yet if our goal is to find a unified physics based on such ideals of shape and count, and these are not as deep as say the arguments for or against a Supreme Being, our longing for perfections, our clinging to being, and especially the freshness and threat of nothingness in teleology everlasting, then how can we establish a physics of such unity when numbers and space themselves are debated, not known, if there is a solution to if these are ideal entities with a being of their own- or we invent some things appealing to the simple fact we exist and would not be able to discuss this otherwise- especially as an idea for formal theories of physics.
[Well, a little simpler in the wording but still long winded compared to the few germs of ideas that unfolded as if from a hint or mood of a wider dream for a poem, a memory- anyway I will continue here later, with relevant illustrations - the theme is after all how the quasic grid shows certain number relationships clearly and I wish I could have programmed more of this instead of the hands on computations. After all the binary bases on many levels are built into the overall design and at some point there is perhaps a difference in how we view things in a way not quite as simple as what is even or odd. It does relate as well to the halves and roots and so on. Certainly we should apply these ideas, at least logically to life- and it certainly seems to begin with matrices of the base 4 - what I regarded as the main quasic numbers are after all what one can derive from some level of the Mersenne prime identity- but even in this rich extended realm one wonders if in some local and accessible sense there are simpler ways to factor and determine where and why primes show up - if indeed this problems has some reasonable solution, especially applied to our idea of design totalities or points for physics. Again, and fundamentally, are numbers that exist to be discovered or in some sense to we invent them?]
* * *
Thinking of our frontier searches, by method or relaxed exploration, we come again to that world of a background of how things work I have called the Ramanujan background which for our traditional interests we also desire to include the Topologies as a further generalization or background ( a Phaneron as Gardner called it, after the Machian, Einsteinian, Liebnitzean and Newtonian grounding for the physics.)
We will still want answers from these views, like the formulation of things from say the relativistic viewpoint, at least in retrospect. Surely, one way to look at it- is that Einstein in the end did not throw away his diamonds, so to speak.
In the articles on Mersenne primes there was no periodicity of 24 things- and now, not claiming to see the details, such a pattern seems to have been found.
This periodicity, of course, is important for our ideas of what are the real numbers and whatever way we represent them we find cyclic patterns with the logical restrictions related to primes that things are prime known one way but not necessarily the other way for a described ordered number. For example, 89 is also a Fibonacci number and a prime, but the primacy cannot be determined from the F sub n notations. In such numbers as binary representations we do find patterns and patterns in patterns and here the important recurrence is 11. But 11 from the four base notation can be read a different way say as 2, or N in my notation 4 base, for if 11 is 2 then that squared would be 121 or four if we playfully sum the digits.
So what does 2^11 - 1 say about the primacy of that number as we think more about the structural background of bases?
Wednesday, April 27, 2011
Cheshire Grins and Other Generalizations
of Euclidean Space
Well, maybe this is all we can see of the Higgs particle, the U of the Cheshire cat's smile.
Not quiet the feisty quantum cat with nine lives but a more subtle creature. In any case one might go down the white rabbit hole- time speeds up and the white rabbit races because he is late. maybe it is not that we wonder where dreams and dust come from as if nothing, a black hole of sorts, but from some mysterious source appears the white rabbit hole.
Now, sweet Alicia playing with her little cubes written on them Latin letters, does puzzles made by the old Oxford don logician- wondering what keys he holds in the bulge as he punts along the back of the Granta in Cambridgeshire, his caterpillar blowing smoke rings and letters around hidden truths and hidden dreams in which we are always at times the Mad Hatter celebrating the un-birthdays as the clocks and planets turn, capturing but the promise of a smile in photographic light- Alice does not know yet how to get thru the doors to that kingdom of hearts as she discovers not what he is smoking but how a few mushrooms might change her perception of scale.
Let the kids play while for appearances sake, that there be no scandal as the old Don dates the chancellor's wife and Alice's mother- or fill their heads with questions like looking glass written poems and lesser quantum fires on the other side of the mirror. Or running in place as so many do in dreams challenge them with the fundamental question- How is a raven like a writing desk?
* * *
There is a fundamental principle of Intelligibility to which we explore some grounding theory or speculation- and things are not always what we expect, nor are they clearly a simple solution- or a unique one when all is understood. Of the 1100 or so areas of mathematics the great thing is when we find and understand parallels between our formulations- so to our theories of physics.
The occasion of this post is the deeper understanding- yes, something new to me but surely if we do not at least see an idea or equation how will we be able to comprehend it, even subconsciously as we read rapidly to digest the meaning later?
I now find the p-adic ideas deeper than my superficial reading and understanding thereby, thanks to a link with the ideas of TGD of Matti Pitkanen... one that was already incubating in the foundations of my mathematical pondering s on the basic nature of number itself which are issues in the background anyway to which there are many quotes and ideas held back in the teaching or presentations and publications. But, my approach is from quite a different geometry and the link seems to me not a link at some foundational place- but a link, much like the ideas behind some of the lecturers in theoretical physics I have encountered here lately- that have not accepted Pitkanen's deeper ideas, probably because like me I cannot risk the step into a purely mind description of reality without a little more data to prove it.
Of course I am not sure this theory does what I think it does from what little I have recently seen of it- although I have played in the background with these concepts and at times felt rather out of my league and my intuitions leaning more to the realm of fantasy or science fiction. Even with these links and understandings these ideas are in some ways still in their infancy, and are not sufficient alone in the complexity of merging new theories as the world's theorists seem to finally be going back to the drawing board. Even so, left to our own areas of research in which it seems few have come to recently, there are some deeper questions to be asked and resolved.
In fact, these speculations came by a small fortunate accident of drawing some grids and finding the picture and count a little off. Perhaps, this was the most rapid of transitions to my uncertainty about a theory to the sense it is a foregone conclusion to the discovery that most of the work done by others decades ago then to the realization that we in the present time are still ahead of the others in our understanding.
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The big question seems to be, and this a concern of p-adic theory, that there is in a sense a finite concern with things such as the diagonals of some squares and rectangles. I wonder then if p-adic notions for a calculus is the same as that for surreal calculus- I mean in a sense and as a grounding issue we ask if the square root of two can be seen as a rational number? But is the conclusion than the diagonal is equal to the edge of a square as a proof an error of what is the transfinite number of things? Would those who imagine gluons arising in strings, or some limit to the number of patterns of singularities not be making this error or in a way confirming some of the maths offered in the blogs, such as braiding theory and p-adics (let alone my quasic interpretations which connect many ways to those far better trained than I)?
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Let me say that the Ulam square of factored numbers is that which we mysteriously see something there, and he has put it into spirals of factoring things.
Is the p-adic physics, especially in relation to Gaussian and other primes of that nature, the same as the idea of congruence by Whitehead as a further generalization of the Euclidean plane- something that for awhile shed light on relativity theory?
Spirals, well, if we take the Ulam square we can extend it of course in the series of rectangles through higher dimensions across the diagonals, the square root of that number as if the spiral of such numbers made long ago.
We know that what evolves the galactic arms (from recent sci mag articles) is not as simple as say the theory of Lagrange and his probabilistic treatment that bypassed Newtons concerns that perhaps God sets the planets in all the same motion. In a sense we may ask of the particle world also what is the analog to this concept in the particle physics. Apparently statistical methods are not deep enough to explain things to the satisfaction of the reductionists. Thus, my long held cherished belief that there is a viewpoint I called the chiral theorem that explains the evolving structure of galaxies is also not good enough- it follows that the ideas of chirality, anti-matter and so on, to explain mass (as in the muons and weak force concepts of Rowlands) is not deep enough at the foundations. In fact this question of why matter and not more anti-matter is a big one in the sense that perhaps anti-matter exists like recent articles for an anti-helium nucleus- but this will be found as we set our experiments up to find it narrowing other areas and methods- I see no justification other than this design principle to assume that we get back to conditions of the big bang where such things were assumed symmetrically balanced.
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Consider then, the lattices of normal three space that are close to other objects and objects like the logical ones decomposing in many ways some plane, squares, matrices... for example: in a square of say 64 cubes these are equal to the volume of 8^3 tetrahedra. But seen as analogs in a cube to the 4D polytope as an octahedron we obvious count 64 x 16 or 1024 tetrahedra.
One interesting thing about this space is that we can imagine a labeling of the points in a cubic array and the coloring of them... but it would take seven colors not the five given us in the case of a plane in two space. It would be interesting to develop a higher arithmetical analog of say 10^3 with ten colors, and so on.
In Lewis Carroll's logic diagrams and his algebraic forms of them not all can be a square you see, some times there is the 8 fold problem or the odd dimensions to the powers of two... 32 128 512 and so on to which just doubling the regions does not seem as elegant in a plane as in at least a three space formulation.
Also, with the calyptic idea mentioned earlier there should be some rather ghostly particles (quasic grids to find particle resonances and hierarchies btw as they did in 95 faster than a computer could for my string theorist friend) I am not sure these do not exist in the literature (or perhaps the intuitive genius of Kea) but it does amount so some sort of extension or generalization of the Hessian polytopes and it was expected because of this even odd problem in the coloring of my quilt patterns of which there are 36 in calyptic cubes in which we make fundamental choices of patterns that if we counted them only would be in the same binary power.
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This relevant comment to Ulla on Pitkanen's blog:
Clearly when we view things from this p-adic physics of numbers and extend the spirals of factoring in some direction (where it is still important to look more deeply at the arrow of time as Matti does and some say is just a high level illusion) we find some numbers to high to analyze that can be shown not to be Mersene numbers. In which case the hex symmetry is intrinsic to number, math as superior in descriptions where we at least have no surprises today to current physics.
But I still bet memory in the structured vacuum as if in nothingness or what cannot be seen- in at least these mathematical ideas. Carbon or water it is the same geometry. It must be deeper than your link that imagines superconductive photons in a sort of Higgs condensate and so on...
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and... if we are not cluttering up his blog too much- I am wondering why he cut the value in half for the difference in 107 and 89 square roots- if not by my observation of the sort of odd logical diagrams of Carroll? And I would ask him why going down to 61 is important that it is a lesser number- then again these numbers are not always discovered in order of value- after all what do we do with a number who if seen as a coordinate is but a series of unity in all directions?
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Reply to Ulla in an e-mail (nothing personal here) that may show some context of our thinking:
Your link is most interesting as is the tone of that you have posted from this author on your zone reflex blog. Wow, you have found the frontiers in which our little planet of thinkers in the blogosphere are still linking and continuing on despite the chaos around us.
Of course, while his attitude towards how we should be doing the sciences is right on, he still does not have the insights some of our bloggers have long developed. But to supply a proof of some of this- a justification perhaps of our concerns- that alone is quite impressive.
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In these links we find deep echos of formulas and diagrams as used by Pitkanen and the work of Kea in her blog of updates.
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A couple of links for recent ideas mentioned at a distance in my blogs:
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Here are some relevant links I found today for these number issues:
(Of course we find the square root of three symmetries in 3 space numbers reduced to the complex, and other factoring planes of many dimensions.)
which discusses the magic numbers including from a quantum perspective for the nucleus- with a tetrahedral map- yet here they did not limit the elements to the 120 they describe as I long have done on this sheet of what makes the hidden and seen structures of such material objects. It is amazing that such things I found early on and rapidly, and it was so hard to connect to the information on it for so many years, perhaps even in academia. So now we need to look back on all such things in light of the new physics.
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Tuesday, April 26, 2011
April 26, 2011 Will the New Physics Bring us Useful Crafts Beyond its Art for Art's Sake?L. Edgar Otto (aka PeSla)
So it is that my blog became progressive harder to read, something I observed earlier when I joiked that I can barely read it myself. So here I come again with a new frontier of things half wanting to drop out of the hippodrome full of chariots and lions and horses, gladiators and games for the masses and kings. I can only sit back and watch the unfolding of intutions, much as a poem that seems to come at once and if we think to do it, capture as best we can a sometimes impossible mood and not always a describible or easy to describe picture.
Provided of course we are not discouraged by the dreams of others or their own centering and dealing with the circumstances of their existences- all such spirit guests or trapped as fragile ambience upon dispassionate and disinterested souls and in truth ultimately homeless.
Do not be discouraged. Hope that no time comes when you find yourself vaguely put off from your embarrased actions, once passionate desire and you cease in dreaming, abandon them.
For the new physics, if that is what our atom smashers are looking for- if there can be some reward that uplifts humanity or sustains it, defends against evils, makes existence a little better for us all, and our children's world to come, say by finding some conucopia of free and safe energy these experiments beyond hints have failed in the very method of the looking and in the very ground of chance as a measure of our ignorance ever more rigidly focused.
Ours is a world, in our souls full of quakes and longings unfulfilled, much like the earth itself pushed and pulled and spun, not quite there at a stable end to sustained and sane dreams, as all failed stars. Nor do we know yet the why of galaxies evolved flaying their arms, some force of self flagulation, some chance chaos the same as if by natural laws or by some fateful Design.
Only in the far reaches of our mental aethers can we say, once we have not dropped out of the race and battle where the play repeats again and we reinvent individually the wheels and axels
defend or tire of the same old debates and sayings, you cocky young larva in the privies of first awakenings far from the town let alone the gown, the gods caring not if we stumble and cannot get up again, the tyranny of others given only a formal reprimand, ruler on the hand, worse than the gods their spending of their own light.
Together, my idea of that hidden in the depths of motes of nothingness or that focused to vanishing of notions and ever more energetic particles or as some neutral idea at zero points- as with all complimentary ideas that may achieve some higher and explict integration beyond their contrary claims- for I have come to realize that our description of dimensions are the same only the differnce is that who can see it first and consider the new integrations of wider fields - there alone in but a smaller step up in the complexity, we almost there, this is where the difference is to be found- and the source of energy accessible there worth more than the gold talisman of prestige and social reward of prizes, the work and not promised forever later, of capital in the down to earth reach of intellect worth so much more than rumors of gold.
In this the colliders may have inspired and lain the ground for a better future, so has not failed, and in the end has done so by inspiring those already in wonder and awe at the universe to keep learning and dreaming on- somewhere such integrations occur in our time and space and dust, as subtle as a scale left on your ear from a passing butterfly's wing where all sunrises if still are confused with wisdom's sunsets.
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A comment and thought to Matti Pikanen today:
I am still having trouble trying to evaluate and see where the water memory fits in to the scheme of things.
On the other hand I have read that statistically water that had passed thru Einstein leaves a few molecules in all of us. Well, maybe you drank a few more :-)
I found this today which vaguely links some ideas of p-adic analysis and my quasics- I now know a little better the great uses of this idea, even an alternative calculus based on absolute numbers seen differently.
Check out the pictures on that link. I am giving these number ideas in general a lot of thought lately. Do you think there may be primes beyond 127 as such? or is it somehow limited and physically so?
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Geometric Analogy in Super and Sub-standard Space
After sleeping in, with normal dreams, the two lectures I viewed sink in a bit to the point where I can question some of the ideas, or see through some of the things that intend to lead the viewers toward a certain conclusion or deflect them from what is a competitive view or something the lecturer does not know, if indeed aware he does not.
There is obviously a lot of energy, and a few sink holes too, around what at first seems a glitch and of course I, being not tied to some state or institution with a career to risk, chose to ride with the assumptions of new things found in the experiments. I do not know enough to bravely deny the existence of some things but I can support those who claim they do when I so suspect it myself.
I did some rather foundational thoughts on math awhile last night, the symbols of things fluid as the range and value of the ideas- it has been awhile I took this childish approach to physics- but it is a fresh breath in the less polluted frontiers in the sense that we work somewhat for the near future beyond the current fray and heat of this golden age of particle physics and cosmology.
Hmmm, the one lecturer- through Kea's blog, used the term "teleology" which he said he had learned recently. Such an application to perhaps the term "leading singularity." So there are some things of which I am impressed and some not so impressed- for one my conception of space is much wider- and for another what I saw in this and the other lecture through Lubos blog- is after all traditional mathematics and physics- more a math and geometry than its applications, more a context of things.
For example, if we are looking for some sort of brane like entity or plane in which things occur beyond our familiar way- it is a quasic plane but it is not just a quadratic plane- That is as we understand quadratics we can solve them by the matrix of the eigenvalue diagonal.
The rather fanciful symbols and equations I scribbled down all seemed to involve our deeper conceptions of mathematics than the physics. In the world of the multiplicative inverse of Cayley number systems we can find the super-space and sub-spaces to which we are now on a tightrope with the experiment and standard particle theory.
I will try to put some of these ideas down here today, ideas or just questions rather. Some of it involves the ways Matti Pitkanen sees things as as with such theoreticians both lecturers converge to at least some of the things seen in his vision.
Basically though, the unification of physics on some level as some not seek it, a third physics of sorts or a new physics, may not be what we expect or should call quantum-gravity, after all.
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The theme of this post then is that in all the more creative theories on the frontier, especially the growing influence of the blogs and internet for a more challenging and open discussion in the midst of chance and chaos, that in the diverse theories we can find parallels in them to signposts on the way to more general or unified theories (if those in a sense exist as such.)
In particular, and it is hard to show exactly where the difference may be as to the claims to at least published priority, is not a subtle change that embellishes, illuminated, or enhances notions as originality or borrows from an others theory.
But as in the lecture thru Kea from that institute of a theoretical group, should we not use the insight and assertion that what is required between the quantum field and string concept is the need for unitary and locality in the physics? And beyond this the great question of integrability? These reflect the background of the known methods of mathematics, its number theory that in itself has abstract limitation implied and sometimes proved so. Taking the surface of things, the solutions to squares into the diagonals and diagonalizations, is perhaps a cherished tradition now which in the more infinite and continuous cases can be physically interpreted as explaining things like the emergence of time or gravity otherwise an illusion and as the lecturer said from a more general view of the evolving of physics while these sorts of questions are unsolved on the level we can not ask them they may not be relevant to the solution and actually limit any breakthroughs to a more unified understanding. Yet, some among us, even vaguely in the doing so, continue to follow down the paths of such questions, bravely or in error of misconceptions, with courage.
When it comes to the foundations of mathematics and its relationship to logic it seems to me the theoretical physicists as well as the mathematicians are rather relaxed on the interpretations of their counting.
Is the recent confusion on what may or may not be there as discoveries of the atom smashers an implication of a new physics, support for some old direction and method, a compromise as to the idea there is a sub-standard theory where the resonances of particles are there in a sort of super-standard hierarchy as non-linear and of a different level of measures to evaluate?
I would have asked of he lecturer (thru Kea's blog) So, we have established that two planes are involved here with the usual idea of quadratic solutions by eigenvalues and these are inferred or shown as perpendicular and of course are four dimensional at least Euclidean, intersecting at a point. But in the scheme of things I would ask at what grounding do these two space vector entities dwell in, say in a greater Grassman scheme of things? Or if there is more complexity in such spaces would not this reflect, as a matter of integration, as a matter of applying a stacking of dimensions along a matrix as at least quadratic in the diagonals (a V matrix) and then the global mixing of the group of all such matrices reduced to ideas of two space--- of the notation little lamba and lamba tilde- apply the Dihedral or other groups for a general dimensionless universe of discourse and then not expect that if we so limit our vision of dimensions that enhancements and proofs to our standard theory can only be verified as sub-standard, or from the multiplicative inverse and complementarity of such mirrors, even as particles, that the range of these numbers on the Cayley level goes outward in the depth rather than be a theory that is contained within the subspaces or compatified spaces of particles.
By leading singularities I give you the iota particle concept but with a wider dynamics of dimensions, and the iota complexes. The quasic field, as we have gleaned from phase angles and so on, is after all at least potentially a matrix of infinite values rather than finite ones into which we expect the summations and reasonably expect the limits can be zero or some sort of potential or final infinity.
These questions are also about the nature of transfinite numbers, and even a way in which such numbers are also their own identity and multiplicative inverses that we may say the continuum can be seen to have a relatively real mirror continuum. And as a continuum the 2^n and that inverse apply also in a four way view with all the limitations and patterns of such numbers (can we not see that Pitkanen's probing into the Mersene primes may have deep value and relevance? and that still in the game yet beyond the physics of our time? Has he also not been limited by the traditional methods when we take the square root space for solutions of our matrices and singularities?) As far as these issues of transcendental numbers go, and the crude approximation even nature seems to have to make concerning factorial expressions of binary numbers, aleph 0 as finite is subject to these same restrictions and higher degrees of freedom that we may expect from higher alephs or other continua- as if they exist perhaps between them by default or exclusion to their not non-cantorian view in such local analogies of geometric laws to which things are certainly messy but unitary and local to some extent of physicality.
Such is a view of numbers as constrained but boundless singularities (iota complexes) that is a view defining the freedoms and uniqueness in complexity.
The looping that seems to constrain these singularities is already a property or an assumption of the quasic field (Qcm the Quasicontinuum) that does not seem to go on indefinitely or will make geometric structures to which these may emerge to make other structures of wider physicality (including perhaps the focusing of mass in its densities and the general expansion of the universe or dark energy "acceleration") is then the idea of hierarchical values not without some justification as notions?
The absolute quasic dimension (Cyrillic letter D sub n) is not the same, or is not necessarily the same as the nD of familiar or vector space, nor of some idea of a more fixed and less relative notion rR dimensions as representations.
But it helps to show the steps and details. I would suggest that for those of us with aspirations to more unified theories we point out just where some of our notions do match that of others and the mathematics established in the literature.
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Monday, April 25, 2011
The Pre-Quantum Void L. Edgar Otto 04-25-11
The concept of a vector, a generalization of numbers, is also a generalization of the other subcells of dimensional space. A plane can be a vector for example. But let us analyze the ground of vector space from a less fixed view of dimensions. We shall go on to discuss the role of logs and exponential s and its mirror in use of symbols, that involving notions of probability and pi. Certainly from the methods of calculus, in P or vector space, in three dimensions in particular, at the gradient of one the exponential's meet more abstract M space beyond octonions, for these functions also are self recursive and fractal like, their own derivative in which they share with the octonions the notion of the operation of a sum and an inverse. I feel it a limitation of our notation that in the partial differentials for higher dimensions beyond three or four the structures only can be represented as sums.
Pre-evaluation of Vector Principles in Space:
*1 There is no guarantee a vector passes through and origin even in the "finite or discrete" singularity-as-complex
*2 There is not guarantee a singularity can be a zero vector.
*3 Four or more vectors and nth roots may seem to pass through a singularity in different ways, and simultaneously.
*4 A vector may have no clear direction in the depth and span of spaces
*5 Omnic limits, in phase space micro scales flat and directional, the rationality of e may oscillate between its identities as a rational or irrational number.
*6 Between to gradients at unity between log and exponential space, this property may repel or attract, resonate or average out at the interface of M-ality.
*7 Such a gradient may be multidimensional and inter-dimensional, and may relate as oscillating variable existences, even as quasi-identical singularities.
*8 As an ordered quasic space the non-existence of such omnic activity between quasi-logs is three to one existences ( a principle in multi-singularity complexes I style Yurion quadrant field or particles )
*9 Such opaque or hidden symmetries as singularity complex have relative positional structure at least unto the natural dimension number.
* If there are no Higgs-like objects to establish mass from some M-ality space, then there are no fields or mass, at least in the generals sense we think of them.
* Wormholes are not necessary in the quasic fields, but the mouths of wormholes may exist with the quasic idea of no action at a distance, nor a zero distant quantum like jump, nor the reduction by the joining of cubes in three space partial differntials of six degrees of freedom as a necessary consequence. Nor the idea of zero point from a quantum like field region, or some broken symmetry in Higgs like fields, may exist without further general theory made less ambiguous and vague.
* Dark fluid models and ideas like Preons, within P (for prime arithmetical) vector space of our reality (R), within that reality and a worthy and complicated enquirey it is, we may "gravitate" to one or the other poles of such models.
* Dark matter does not necessarily connect in a singularity complex but the opaque values or units may make n-topes or polyhedra as if made of matter and dark matter points, lines, and so on...
* A monopole like object needs no tunnel to ground or release in divergences magnetic fields, even as dipoles.
Conclusions on the human psyche for longings in cosmic understanding:
These sort of new level ideas at last begin to ground psychology more as a science.
It is clear to me that to some extent in the creation of theories that the same opaque models suggested here are at the heart of our psychological mechanisms and we as conscious creatures apply this in the soul searching within ourselves even if it may be a prioi and archetypal, these structures do apply to our projected ideas into the universe as physics, to others, and our sense of ourselves.
For example, I am aware that some of the archetypal and usual models I have pursued are things, even if they do not matter now, are too private to discuss- that is if these were known and the assumption being it discredits a theory based on perceived character, many would defecate goobers. Yet it is the nature of our minds in its messiness of diversities and evolutions, between the existing and the void or opaque, that corresponds to that we observe in the general cosmos not so ideal. But as part of development, even when such things in hindsight do not matter, we keep the ambiance of it as a metaphor to so continue the direction of thoughts if they dawn on us objectively and sanely as wise paths. This happens in development even when not aware of the fact that we if wounded by fate can get caught up in the wounds. As to our position or lack of them in society persisting such a theory of the opaque and overt may begin in our collective structure's to show where society if it does not make ultimate sense at least behaves by intelligible natural laws.
Another example is that in my poem lately concerning the Witch of Endor: The point of that being from some string of words, thought perhaps or treated as holy, we erect a culture and tradition, glorify a particular view of some minor poetry that is not just a local or tribal concern. So Samuel bands all the witches who believe in the spirits, talking to the dead, and so on- as an affront to the one and nameless God. Yet after doing so Samuel consults with the Witch of Endor himself. Is this his satanic verses?
Well, there is no point making plans over too many pitchers of beer as if anyone will recall everything (actually my long walks and poetry written down after a walk and keeping so many ideas in my head at once as memory and even if they are lost the discipline of it leading to not just coherent connections but whole themes in booklets of poems almost ran to the ground for some of the images and metaphors- has helped me immensely in keeping thoughts and not losing them in the extended typing, although the coffee shop closed early last night and I have to recall all today.) This true of my roommate who is in his nasty cycle lately, a sort of psychosis brought on by prescription drugs and reactions to alcohol. I know the cycle now. So, he comes to me aggressive, I see some of what he says is really about his own view of himself in the world. But what is the point of debate with someone in that state of mind? Still, he tried, apparently with some sense of clarity and even superiority in that state of mind, schizophrenic if that means anything, to ask if I believed in the spirits around us. A trick question actually, for if I so believed then I too would confirm that such voices he at least hears are real and even compelling. But if I say there are not such spirits then he must as the priests interpreted for Samuel later about the Witch of Endor that all such does not exist and it the work of but one great evil one, one devil. He is caught in such a strange loop, one that unraveled into himself when even his logic of confabulations made no more sense to him and he went off to sleep. Let us hope, while I know he at least knows there are no such spirits in this building as he now locks the door, let us hope that he does not dream again of his father the anti-Christ as if only the devil exists to torment him if he does not heed or believe in the spirits.
A Metaphysical Resource on the Frontiers of New Space Insights:
*One thing about the idea of Void or absolute nothingness, to be welcomed or avoided in our concepts of history and our ideas as such in relation to philosophy and science where these are inspired as metaphors from religion- if that not the actual case to some level of wisdom of concrete grounding for religion itself, is that intuitively it surpasses the ideas of space- that is it can fill all of space to the furthest reaching of infinity- nothingness and infinity the omnic poles as well in the living world experienced the philosophy of limits and changes in themselves.
*Another thing is the idea of quasic space which like the nothingness may extend beyond the idea of scale and measure, beyond the idea of any singularity complex to which we might if limited by fixed vector and geometry ideas.
*The new and creative religious metaphor then is that our concept of God when taken to the ultimate we can now, as well is thought to extend the cosmos and in a sense be that- the God Particle an apt pun in fact, is that the wider God is outside the encompassing of vector cosmic space even as multiverse as well beyond the encompassing of null space and most importantly greater than quasic space structures. God, as the archetype for physicists needs to go beyond his useful conception as the ultimate inertial system and fixed frame of reference.
And as we have suspected from even an opaque and nameless God, beyond the null in a way that we still do not fully understand as we face higher theoretical models and the foundations, the World itself perhaps beyond the creating of that, quasi-opaque. Our lives but a footnote that contains a large volume to be read and is quasi complete and unique as in the omnium we point toward the potential infinite and the zero in some as yet untapped vector space and its dust and fluid dynamics.
Reading some speculative and formal papers with the new physics approach, the presentation of the mathematics is almost trivially standard, only in the suggestion of its application might someone object. The use of e periods and Fourier transforms for example, and loops when we negotiate higher space, are part of the standard undergrad curriculum and are expanded further in courses. As physics, and as the language of differentiation, the grad, div and curl of things we see that these are not powerful enough or trivial enough to truly understand the nature of Maxwell's equations, and their extension say in to gluon stings, nor the edifice of the relativity's- as if physics is a subjective thing only with an objective and usually reductionist background- and yet in reading recent biographies and articles we see that in the creation of a new physics the characters involved were very much dramatic dreamers more than experimenters and interpreters of experiments. (I see no errors in Kea's paper, so why is this not understood, why does it not get a voice? Why is the simplification so artfully grounded genius not recognized by those who speak the language?)
Footnotes for Thermodynamic and other Models of Entropy and Dimensions:
* A sort of thermodynamic glue when two 6 degrees of freedom object meet and only quasi lose some properties for these would suggest quasi-gluon like objects only restricted perhaps by the dimensional limits of the inverse square in general three space (which btw as virality of Rowlands is not the cause of three space but the result of it)
* From my view of these omnic, quasic, and abstract principles, scientific or philosophic, it seems that the notions evolving in our various blogs are converging more and more even when the bloggers are lagged to admit it.
* Or I may state a simple theorem with a little more faith in my intuition:
By advanced structures of mathematics, it makes sense to jumble and match the color cubes so as to get results that teaches such maths- and perhaps maths beyond this. Or asserted simply: Playing with the little labeled colored cubes can be seen as a deep and useful recreation (as if the true enthusiast needed justification for a foundation for his hobby). But even here this is a shorthand for wider spaces of discovery that can see into the depths and span of complexity of which our notions and symbols and equations are somewhere stable and grounded in the quasi-finite and quasi-contiguous in a space that within the world of the natural existence of numbers
we can intuit beyond our self what is truth as intelligible.
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So, we come again to this question of what is after all a quasi- (continuous and combinatorial discrete) view. Thank you for the link Ulla on the part code that without loss encodes the infinite whole in the algorithms. And to Kea's paper today on matroids although I can hardly regard 1991 as a classic paper, its too new. Guess I have considered such things already, in a way, and from my view of inter-dimensionality would give them a better concrete grounding in whatever application we use to describe real particles and how in the varieties of manifolds we may circumnavigate the knots and loops and quasi-directionality of time dimensions. But I just read on this idea, glad the braid stuff confirms some of my intuitions.
But I am not exactly speaking from a quantum view here, although we might question what is a path or point with some idea of uncertainty that certainly sounds like the quantum world. Again one has to consider the whole polywhatsit as well as build up from some idea of a vertex- and we need better to count the singularities and the contiguity of the lesser and global matriod dimensions of a space structure. And lastly we need to enhance and revise all ideas of looping integrations in higher space around such structures. Would such laws hold intelligibly in structures that were composed of both normal matter (including virtual matter) and that opaque or dark for the elements? BTW the matroid idea for me can be corpuscular, of that sort of absolute but at rest space in which point of sorts move between fixed curves.
But after all, the fundamental idea of quasic space is the ultimate, or seemingly considered ultimate, concept of the sum and the multiplication one logical unity in the description of our ideas of motion- if our calculus cannot explore such manifolds except by sum only in the higher space we need to change the calculus. From and Euclidean view, as with that of Coxeter, ultimately the sum of orthogons is the same description as the product of said orthogons.
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I just posted a comment for Kea to read I post here (but not my email in other areas to Ulla) as it may not be appropriate in length or subject matter. But as a creative endeavor it from my perspective is certainly dramatic.
I watched the first hour of Arkani-Hamed but did not get to the above figures, just a few minutes ago.
I am surprised no one has worked in this area for so many years.
The third physics of which he speaks then goes on to explain, as far as I can tell and with no exceptions is what I have shown by "Quasic Physics".
Thank you for the link for something that I can say I totally understand in pictures if not in the standard language.
The key results of residues and looping, the minors and so on, even besides recursions
is also something that can happen if we try to count all trees of things in our heads faster and faster, until these grounding ideas precipitate out. But I am well beyond the obvious intersection of just two plane vectors in the fn notation.
It was a little boring but got progressively exciting. It was a bridge to what we mean by the usual ideas of measure and physics and to our abstract methods. I liked his way of looking into the foundation of things as well of what we know already on some level. Why do we do this work anyway?
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The Universe, I well imagine, will be here long after we have moved on... But I must say for those of us with such a commitment and interest for so long and in such interesting times- it was quite a ride...
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Sunday, April 24, 2011
Extending General Number Systems (N Q O M
Beyond the Complimentarity of the Quantum and General Relativistic Systems, Nature solves our notions full of contradictions. L. Edgar Otto Eau Claire, WI
Some of the ideas in this paper I found from anna as a comment in Motl's blog today comes at a time when reaching the limits of the mathematical operations involved in notions and thinking, the loss of them in more generalized number systems left me with little to post or write. Consequently, my notes of last night were rather sparse. Yet, I am not now surprised at this for I begin to see we, when of all the changes of systems happen, find ourselves, our awareness in at least one circle or pehaps fixed point as a reference to our reality in existence.
What I noticed was the idea of quadraples, that is in the number theory formula (2^n x (2^n)! / n!2^n) = (4n -2)! , that this is also (2(2n-1)) ! which recalls the magic numbers of electron shell configuration, ideally. thus we have the sequence 1 2 6 10 14 18 22 ... and so on (with of course a view or actual limitation of the number sequence for general number system reasons intrinsic to the algebra and numbers themselves. This multiplied out results in the sequence 1 2 12 120 1680 30240 665280... any successive two divided together gives the magic sequence.
This would seem trivial but I was trying to count some combinatorial relations in higher space and coming up with some interesting integers such as 5040 in the counting from other considerations of what sort of matrix we have that applies a group rotation if the diagonals are 1 to 9 and we simply add the elements together- being the sum of 25 x 20 or 500. This is 168 x 120 which are both important numbers in such theories of some background of general space.
As with all things at the limit of our comprehension so limited by say mathematical operations we are in an area of speculation which seems rather wild to me then and this morning which after all is about our concepts of Higgs-like, gravity-like, mass-like analogs, monopolel-like entities which is the professional and crackpot propaganda of the day in the SUSY or dark matter war. I may put the down at the end of this post as background to my more concrete philosophic considerations.
The simplicity of all this, as well the complexity when we explore, develop, or ignore some path or view to an idea of a more unified system - how this differs when committed to a method or system is the issue and is one about the foundations of mathematics and physics. To start with we note that these issues are stated as theorems which exclude the zero vectors. This is the origin when we try to extend our number systems (of the imaginary variety) of concepts like zero-point energy, or like the differences between phase and position space. It asks or explains also the unanswered question concerning neutrinos if they are Majorana- this itself a question of information that can be transferred non-locally for finite values or any number in the entire Riemann sphere- including of course the zero and the infinity poles themselves involving rotations at this last property of octonions and beyond that into an inferred or hidden system without complementarity at all- that of course only thought existing if at all as a structural background. We can claim from some view many physical properties as illusions or for some objects that they only exist- despite the same information there, from an alternative reference.
For such general systems which metaphorically I designate KLMN OPQR as a token to the 120 elements from my view possible in three space for an atom, N the natural system, Q for the quaternions, O for the octonions and M and R depending on how we approach the macro or micro scales and what is within or without some structure in the depth and span of our methods and systems... M-onians for our vague conception of M theory, and R for the Ramanujan background or phaneron of space and perception. KL held in reserved for existence thus metaphysical. It would be useful to describe simpler states or transcendent sates of the physics of a World if any.
This leaves us with N Q O M the P the topology background and the order of the general number systems seemingly out of order as a reminder that some things can be mapped as braid space.
Some generalizations may exist mathematically of which we are not sure have physicality, at least for some theories in the present- of which in our time octonions may still be in that position as some papers in our blogs suggest should get into the mix of the debate. I further suggest, for theories that move the background based on arithmetic and those for topology R and P, that M is also a structure to extend into that is at least the 16 dimensional case of neutral or null effects.
Yet, even here we can have a looping back of sorts to a more unified theory of things in the level of the context background in question. This, when we in effect find a three space number system as if it a complex space by simple labeling, begins to explain the ideas of the generations of physics and analogous concepts of triality like our notions of color and flavor of particles- those a generalization of numbers in some sort of different representations in the same number if we so order them- and apply, like partitions, with rules that factor them akin to factoring spaces and numbers.
Yet, even here we can have a looping back of sorts to a more unified theory of things in the level of the context background in question. This, when we in effect find a three space number system as if it a complex space by simple labeling, begins to explain the ideas of the generations of physics and analogous concepts of triality like our notions of color and flavor of particles- those a generalization of numbers in some sort of different representations in the same number if we so order them- and apply, like partitions, with rules that factor them akin to factoring spaces and numbers.
I still do not see the magic values in nuclear shell numbers as a beautiful ideal system say as if the dual of some hyper space solid like 120 to 600 cells in 4 space for example. A great grand theory of things. But again with zero vectors and time in motion linearly in the microcosm view this side of singularities we expect in the three space variations if we insist three space as a dimension is fixed and independent of other dimensional effects and not at least a triplification. Of course the internal protons are complimentary to the electrons so octonions may suffice.
When we consider 8 dimensional objects it is as clear as pascal's triangle that when we add two from the last row we get numbers in the next and thus extend the binary value a dimension. In this sense the claim the world is 9 or ten dimensional, or 11 or 12 and so on is a matter also of specific structural computations, the row in such a 2^n in the triangle can be extended to 16 or 18 in some cases fairly close to our standard maths and so on. Here my intuitive grasp of the spaces of games and cubes finds the reason the 4 space chess was 1024, that is 2^10. I note also that if we consider 2^X as subsets intrinsically not 1 to 1 greater than X this has a compliment in the sense it is also that much smaller intrinsically in some background representation. But there is nothing to say that beyond some general number system values these cannot materialize again into some real space of our natural dimensions nor vanish to some ordered evolving existence.
The promised speculations: Some particles may exist only as exclusions or illusions where they are in other dimensional or opaque spaces and have no intrinsic existence there- in that space we may claim they are constrained in their measured value by something like quantum mixing or combinatorial considerations of the topology- these two not necessarily the same thing outside of some sort of complementarity and duality or quadrality...
So the terms Higgs-like, monopole-like, gravon like as a position of exclusion, from the view of only so many special subsets of primes, and from the extension say into p-adic lattices as primes all of which ultimately can be explicitly expressed as factorials... an idea perhaps there is no ultimate chirality for black holes where there are no such X-like objects singular or multiple, singularity or singularity complex, for the exclusion, the vacuum implies the notion as real of the unified concept of what is mass that is gravity virtually. The Higgs-like may not exist as it is one with its anti-self, similar to monopole-like entities and just like the imaginary gluons as if a particle we can expect in such proofs of valid infinite descent, probability considerations and a hierarchy of such mirrored real or illusionary illusive objects. The general idea of H and anti-H like objects is simply that in the 4ness of them the implied space and its solutions are in five natural dimensions.
And the pseudohedrons are such a description of any unification of Fermion or Bosons systems.
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Thus the elegance of super symmetric matrices determines if neutrinos (momenta and angular momenta conservers for accounting) and the relation to our notions of energy and entropy is that from some view and in some thus basis in some statistics is if it is Majorana or not. If there is a confusion speculation on the ultimate nature of some particles discovered, or even imagined it is evidence of these elegant and mathematical considerations of disembodied symmetries which in the reality of the objective experiment is the result physically of our general number systems in our existing and perception of the cosmic and atomic backgrounds.
Strings on some fundamental and measurable scale of levels and application, and an analog even if only in the form of things for life "force" or mind, also tend to divide into notions of phase and position- the over all limits to our three space as a dynamic one between its adjacent dimensions where there are asymmetries of complimentary as we know by the application of group theoretic ideas that not all of some things can be delineated in both directions of a theory- the prime example of this is as in the article in the link above, what is real and what is complex in the solutions of general numbers, vectors themselves a generalization for some physics applications. And of course what we can or cannot find as we explore matrices from one direction of an equation or another as we intuit some wider planes and landscapes.
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John Baez had this most interesting link up about fundamental constants: (Through Kea's blog, not sure why I checked this today but find it rather relevant).
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From an evolutionary point of view, this article points toward the G to C quadrants of quasic space 8x8 at least, as a matter of topology or chemistry and the extension in my view to deeper binary powers of elegant matrices. From the Omnic view it is suggested in the article that in a sense there is a "setting back the clock" with the ALT structures in tumors.
* * * There is an interesting article I could not access on newscientist without a subscription. I was going to quote the last paragraph and supply the original paper by the most interesting author there. But when I went back to find the spelling of his name a note at the header said please do not cite this as it is a work in progress. Its content is social as well as about numbers and counting. That is, I have begin to search google lately for more original sources for some articles.
Well, not since Gammow inspired a generation of young scientist with his book 1 2 3 Infinity have I seen much on this issue- our generation seems to have its savage numbers or limits to counting... can we not see beyond three space? Can we see beyond aleph 2 if that? Can we not insist like the prehistory sheep herder to divide transactions of trade into 2 if we reach the confusing number 4? In our time this reflects an attitude to more primitive man in the still to be colonized world and the literature of the time seems so politically incorrect. But there is a science issue here, well, maybe a social one, for in a sense are we not still primitive in a sort of prehistory of counting? History repeats itself in a way for not since childhood reading of the first world war has the world come back to things like a state of Serbia, or the old flag of Russia and so on... what numbers would the Hindu god count with a thousand hands? If SUSY is a noble green mansion of innocence or just a savage, either way she is not without her warts and beauty. It may not be about race really, but it is certainly in our genes.
I would like to see what he said about Cauchy and Euclid... but so many things seemed tied up and hard to access, when you try to download from the university repository it says : you do not have the right to download this document. well, what do we savage number counters know anyway?
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The Rose Between the Ages of
Poetry and Prose
L. Edgar Otto 01-24-11
Here falling up or down into the aether
its shadows a firmer ground than light
I recall my explorations through the
petals of a rose, its scent and velvet feel and taste
Oh that was another time, no noble savage place
to explore before the age of steam, then Witches of Endor
When poetry was empire and progress, that or gyres
were one cannot see the sun save its dark side fires
If this is what we take with us, shorn of thorn
life was no waste, no rose spiders for butterflies
'Tis said the hourglass figure is a sign of intelligence
I must say you were very smart
Back when Time's river flowed four fold in its floods
as did the budding stars within my heart...
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Footnotes of a sort:
The issue of Hardy's poetry
R Langbaum - Victorian poetry, 1992 - JSTOR
As we slowly emerge from the shadowing power of the age of modernism, Hardy's poems can
be felt as more durable . . . than those of, say, TS Eliot Reading Eliot (or even Yeats) one may
say, "ah, here in fulfillment is the sensibility that formed us." Reading Hardy one may say, " ...
Thomas Hardy: The Tragedy of a Life Without Christ
by AWR an Agnostic - 1997 - Related articles
Thomas Hardy had considerable biblical background. His life-dream as a child was to ... I have read 9 of his 14 novels and all of his 947 poems. ... The Return of the Native (chap 6) mentions "the witch of Endor [who] called up Samuel. ...
The Spell Of The Rose by Thomas Hardy
The Spell Of The Rose - by Thomas Hardy .. 'I mean to build a hall anon, And shape two turrets there, And a broad newelled stair, And a cool well for ...
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