The SUSY Wars (Elegant and Inelegant Matrices)

Another spring full of passion and martyrs, the paradox of what is the message of the gods, of what in our reality and dreams is authentic. For those, as said of old, "that the price the gods extract for a song is that we become the song we sing" or that our possessions can posses us. For all those who may care about hopes held out for such things- A happy Easter to you. "Whom the gods would destroy they first make mad..." Actually, they first eat the ears- so May your chocolate bunnies not be hollow."

Footnote on the labeling and listing of the four space super-elegant matrices:

To start with I was going to ask for help making sure I found all of them in the permutations and combination's of 8 objects. Now, Kea connects to a paper which of course I find difficult but despite that there was help there and some general statements which concludes some things showing me I am going in the right direction.
So it found already things like:
A
2 (1, 2, 3, 4, 5, 6) = A
2 (3, 4, 1, 2, 5, 6) = A
2 (5, 6, 1, 2, 3, 4)
= A
1 (1, 3, 2, 5, 6, 4) = A
1 (1, 4, 2, 5, 6, 3) = A
1 (1, 5, 2, 3, 4, 6) = A
1 (1, 6, 2, 3, 4, 5)
= A
1 (2, 3, 1, 5, 6, 4) = A
1 (2, 4, 1, 5, 6, 3) = A
1 (2, 5, 1, 3, 4, 6) = A
1 (2, 6, 1, 3, 4, 5)
= A
1 (3, 5, 4, 1, 2, 6) = A
1 (3, 6, 4, 1, 2, 5) = A
1 (4, 5, 3, 1, 2, 6) = A
1 (4, 6, 3, 1, 2, 5) .
(3.14
which would help simplify the higher case. Here are the 15 of the 30 cubes and also the ten of five label letters or numbers there too- and the greater values said straightforward (which I begin to be a little unsure of lately). But it is hard for me to think of these as 6 "gluons" in a sort of superstring theory. Nor these in a kinematic sense.

I like the recursive formula and may find some use for it- but the general gist certainly looks familiar the way it seems they too are looking at a finite sort of situation. Still, I am not sure of the tree models- nor, again, that something of higher theory is not lost by the appeal to simple Feynman diagrams.

This found on the PDF at http://arxiv.org/abs/1012.3981 through Kea's blog.

* * *

The SUSY Wars (Elegant and Inelegant Matrices)

I will have more to say about this, hopefully, tomorrow. Susymmetrix!

* * *

It is not the SUSY this is the origin of disputes, but how it is applied or perhaps how someone perceives it.

Today I glanced at the link in Kea's blog to "green book" and found many things interesting from this algebraic approach to things. Remarkably, how can such diverse theories come out with the same general patterns? Something more fundamental must be happening. But this is after all from continuous group considerations as opposed to a more finite approach. As such it seems to give me a view of the physics or physicality of things such as envisioning all these abstract structures as concrete objects with interpretations as motion and so on. That is I get a glmpse of what is talked about and the probable certainty we believe in them.

A remarkable theorem and a statement of it as if we have hints of higher realms, those perhaps of balance and commutativity and not a journey into a sort of magical higher dimensional space (this of course no more an error than the blind early worship of the tops and dice of Plato and Dionysus or more recent mystics who gaze into the symmetry of things as if instead of a cold crystal snowflake it is a portal to distant truths and seething dreams- to other lands and worlds- of course when we get down to it, the core mystery of the world, the truths in it remain amazing to which no honest soul would dismiss or claim some area as wisdom).

That just as there is a match between the finite and infinite groups, it seems, mainly due to the great Cayley, that projective principles between the point and line apply also to non-linear situations. The balanced and reversible algebra notations seem to swim in a wider sea we imagine as non-linearity, imagine it only secure in one of a more narrow views. For those who achieve the clarity of the finite the prospects of infinity, say of the world, are as unsettling to them as the ideas of absolute nothingness- and version of these notions persist ever since Pythagoras contemplated the dodecahedron and diagonal of a square. We do strive to see that frontier of the irreversible, to probe such spaces where perhaps symmetry is not a good enough guide as the the foundation of action in a static and spherical conception of the world, even as boundless but finite.

We also cite the ancients for thinking the world flat when it is round, and the usual cliche is to claim that in debates between theories. Sometimes there is a deeper motive, or a higher consequence to which our edifice of achievements and progress is threatened by that which is superstitious in religious belief so we have to support the lesser myth for the greater good. We then probe the chaos with the thought that ours is not the only special (created or not) center of the world, especially now that the universe as an analog seems flat after all. Basically we desire to get a better and general, perhaps infinite overview beyond our little vertex to which we reach out with tendrils and octopi arms so as to measure- yet still a view which declares some things of the greater beyond as a center of nothingness- one that we desire as a universal law with its finite solution itself to be the general leaving of our finite mote of being for a general unified set of solutions and their derived motions. Is the flight to such greater spaces unending?
Is there more than the short race that never reaches an end to its mysteries while the race is on?

I conclude that the mathematical philosophy of foundations in all this amounts to what is elegant and elemental, or what is recursive thus not so a priori in our idea of mathematics a Platonic structure to be discovered and not invented, encountering nothing that is truly new.

A recursive formula, of which my favorite is the volume of higher dimensional spheres, is what we use when there are no other methods- and the practical or useful in them grounds the notions and the recursions themselves- but compared with some of the logical proofs needed as a world view this is not an elegant situation- nor is it one that can convey a complete comprehension to a reasonably educated person by elementary language- or at least a common language it does not take a computer to decipher if it contains errors as assumptions in the steps taken.

There is at the core of the braid like methods- and the extension of partial systems of polyhedra in the algebraic descriptions and methods- and my own methods where our systems seem to match as finite projections into each other, that when I use a label it is a dynamic and integral part of the logic and process and not an explanation of some physical process as that is not needed nor a necessarily unique interpretation of the structures. In these brilliantly conceived knots and braid notation we have labels, but they are just that- a notation and tool to come to the underyling abstract relations. In plane geometry class, where eventually I realized a proof was a matter of art more than a strict science, the labels ABCOP and so on I regarded as an intrusion and confusion to the flow of the notions. Now while you may think this a matter of taste, is the label concrete or abstract, in the context of genetics it becomes a very fundamental question. We imagine genetic algorithms but that can be a misnomer. Yes, the DNA itself in replication can rapidly solve some very hard problems, a supercomputer in a drop of water, but this is not utilizing the concrete expression of the code itself of its labels. Nor can it but stand back in admiration as to in the splicing and repairing of DNA that the complex patterns of related genes involved are easily discerned, this too a hard problem that humans recently discovered rather than predicted by taking thought.

* * *

The comparison of elegant and other group algebras: BTW I notice that we cling to a lot of terms- expecting in this miracle of a time when what was very obscure to the general and better educated populace is now that expected to be known, as if a dynamic notation. Too often in the general debate are these terms thrown in to drown out what may be of value as a simple and elementary message, the use of knowledge or rumor of it as a big stick which like war may have no really good purpose nor outcome- at least for those involved in one generation. If a theory is to be negatively criticized, and not dismissed as irrelevant or unrealizable, let it be in a business like and scientific manner. What good are forums that bait people in that they can be sacrificed to the sleeping volcano of new wisdom? What gods are they that they can distinguish what is sane or madness in themselves or others, what superior and true science and methods?

Of course, the idea of Hubris as Kea mentioned in a comment to my blog, is one of those ideas which is ambiguous and its own contradiction. I certainly claim no wisdom superior to others and have even been known to distrust those who say as much of what I say as intelligent- That said, which is really a general cliche itself and not a false modesty as if a Socratic method or that of Franklin to achieve a project by letting other discover things they think they found on their own- that is the trust that just perhaps people get thru life a little better if they think for themselves. So my analysis of the permutations makes no claim to being right- indeed, what little I could read from that joint paper and understand- even that seems to for awhile come crumbling down where perhaps I did not understand anything in the paper at all! Keep that in mind if you read this- Also, the poet in me (and Kea I wrote thousands of poems most lost over the last ten years and the cold fact is that in this town you do not exist unless part of the university system- and for some mediocre poet professors theirs gets the exposure in the community and the media).

1 2 3 4 5 6 the permutation identity and standard order of which it is not simply a cyclic thing say to use these to color the faces of a cube or to examine the rotations and so on- or to use in the abstract to knot and braid particle physics.

But as concrete labels I ask, even at this 6 "gluon" level, of the 720 possible painting of the faces what is the minimum number of these cubes to be regarded as unique? There are 15 which of course there are the mirrors. But it turn out, if I read what the paper is doing with these permutations (even though the get close to or exact numbers as my musings, disconcertingly perhaps both ways) That these are not that global and reduced symmetry of unique labeling considerations.

The permutations listed in the illustration above are indeed 15. But of the 22 elements of symmetry (perhaps seen as in the crystallography) some of them are used many times and some not at all.

Down the list and with my labels or Trinomes and reading from 1 which is red for a color code, we get this: CHL (the standard, xyz) JAO OAJ BHN CHL DFN EFM FCO HCL HEJ ICK KCI LHC MBI NBH . Which means that CHL is used 4 times, BHN CIK and AOJ 2 times, BIM COF DFN EFM EHJ 1 time each for a total of 15.

This means that ANK ALM BOG DIJ DGL EKG are used 0 times or not at all. But if we sum these six to the 15 we get 21 (I begin to feel that these minor integer adjustments in the theories is after all a matter of how we center our structures in what dimensions- I will speak of the 8 color case further down Certainly we might say of the crystal cube it has a total symmetry element in the center 23).

In a given theory of eclectic degrees of inclusion of what is elegant or recursive in reaching into hierarchies of complexity our elements behave according to if it is a concrete or discrete matter of view. When a theory is recursively inelegant we are surprised when something elementary and discrete shows up in the notational chaos or particle zoo.

So, I decided to take a look at these six cubes left out or not needed by the theory. My first instinct is to put them into matrices 3 x 3, yet in a sense these are not matrices as such any more than they being magic square like planes. In fact for the first time one such arrangement I used the word determinant upon finding the old backdoor gin (BKD GIN) trinomes which as with these competing theories of symmetry sometimes claim as part of their theories a unique mixing of label interpretations into their basis which ironically may not be the same thing. In fact my Arcadian Super Elegant matrix may only appear superficially to be a PeSla to Kea translator.

So when you arrange these six you find two groups ANK BOG DIJ and DGL EGK ALM
now these can be arranged into, well, Speakese-Z's for we get 4real and 2 non-real labels (of which some may interpret as concrete or virtual particles) for 22 B4reals abstract symmetry elements. so with the first set we find the 4reals KAN BOG DJI AOJ and 2 nonreals (or from another view 2reals) which are BKD GIN. This a speakesez determinant- which I understand is a method or reduction and a whole area of mathematics as such to reach into the notions of space and thought)

Now the other three labels, ALM DGL EGK can be put into such a speakesez array where we find 3real and 3nonreal (ie concretely materialized or forceful or force receptive trinomes), that is other than the label L duplicated in the array we get the three trinomes only, this is the case to with CIK HBN AOJ as a 3 and 3 array.

Now, for 8 colors there seems to be agreement that we can represent things as a cube with its interior and face diagonals- that is a hyperoctahedron or beta4 polytope shadowed down into a cube. Each of the four colors repeated diagonally for the 16 tetrahedra that describe this polytope. We find any four of the 8 colors. But there is perhaps a distinction although the number of things taken so many times are mirrored in that level of Pascal's triangle as to the general idea of dimension that also apply in the same plane or linear consideration or if expanded to recover what might seem the information lost in such simplification and focus if it ultimately can be lost- but that beyond the scope of this posting.

To take the model literally we consider there are slices thru such a cube representation to get 4 colors 6 ways (from the edges) and six ways thru the diagonals for 12 tetrahedra these be regarded as embedded in three space. Now the surface of six cube faces have six more 2D tetrahedra, for 18. So where are the other 4 tetrahedra? Obviously as tetrahedra inscribed in such a cube representation. This gives us 20. Now since these two are to be regarded as 4D embeddings they can have each two inversions or the change of two of the colors- this then gives us the 22. But we have only considered 2 3 and 4 D, in the crystal group of a cube we might add the 8 points or the 1 of the cube itself eventually to come up with normal 3D space orthogon structure to recover our ideas of 3^3 or 27.

As a question of the elegant and not just the recursive philosophy of science is if we can understand each others paths to knowledge and know when it is only a path to a cultural perspective and perception set as a precedent? In the new physics such considerations are not necessarily distinguished as a new paradigm.

* * *

Yuri,

I did look over those comments on your page- certainly something that influenced these ideas above. And thank you for your views on supersymmetry. Sometimes the clarity comes from grasping some ideas. Kea has links on her post today to which you might add your perception of the 3 and 1 essential ratios of things (of which as I have said before the vision you have has depth apparently some others do not see or care to explore directly. Also your depth may not yet be developed in ways that compel the readers to see the picture and its applications in their language. I did like your historical thoughts on some of the quantum guys who died way too soon and what their cryptic sayings may have meant. http://vixra.org/abs/0907.0022


So, today I read the link to http://arxiv.org/abs/hep-ph/0505220 which you will find most interesting I quite imagine. You can find a ratio there also which may connect to your notions but with different integers in some cases.

There is something super going on out there and yes I agree with those who as quantum physicists would welcome a good reason gravons would not exist :-) that seems like it would be one way to solve the unification problems. But in the link I just posted the idea of three things and a fourth space and so on in the associahedra it seems there is a sort of insight as to what happens in a higher space in making circuits around it. Not bad for a simpler or reduced view of symmetry and of dimensions that circumnavigate the borders of some sort of superspace.

ThePesla (also to posted in an email)

* * *

I Miss the Sea Too L. Edgar Otto April 23. 2011



I miss the sea too, and would miss it more

if my world had not slipped more toward slumber

became a desert



Somewhere under the poles, dry the ice

or in some crater on a moon, what's left of

pristine vital water



Or Saturn with his crown of hex

sends forth the narrow beams of sparks

to explain, heat my core



I lost in the sands like all who thirst

recall replete the waters, now for anyone to hear

write my last poems in blood



She has such soft and pure spring rain skin

so formal her dress in the bar at night

seeing my hidden drink, not her straw man companion



Why did she steal a glance and smile

her eyes are not dry and over shadowed nor wrinkled

worn as the spirit spent lady beside me?



I gaze out across the landscape, regrets in sweet solitude

even the concrete jungle is a desert, light and vermin

going nowhere, in shadows everywhere



Yet my heart grows brighter in the whispers of the stars

I too once daring the surf of hurricanes and undertows

fearing not the chance of sharks, insensitive the jellies stings



I shall not forget you as our waters are left only in the stones

we once a new and baby galaxy too fat so great our novas

of drama, so hungry for metallic dust, not teasing sugars taste



At a distance I loved you as no other, that you already know

As we leave the bowl of stars with wisps and whips of afterglow



* * *

I came across this while catching up with the science magazine links today:

http://www.newscientist.com/blogs/shortsharpscience/2011/04/has-the-lhc-found-a-hint-of-th.html

"The Résonaances blog by physicist Adam Falkowski has a good rundown of the possible explanations for the signal. Physicist bloggers Tommaso Dorigo and Lubos Motl have interesting discussions too."

* * *

Yuri sent this wonderful essay today: http://www.igpp.de/english/tda/pdf/paulijcs8.pdf

It gets me to thinking that the differences between the elegant and braiding-knot permutations models is one of this Pauli concept of symmetry breaking-

The difference in elegant and asymmetric results in space and time should not view such symmetries, hidden or explicit, as only in one dimension at a time- the symmetries of a general cube for example are not broken with respect to some views from a general space but are for just the two or three space case. This modeling does eventually invoke quaternions and so on, but with a wider scope of applications. If in fact we cannot see this inter-dimensional generalization in relation to time and space, if it cannot explain this subtle difference in chirality and so on (all apparently deep and original concerns of Pauli) we may not be able to totally explain how CPT may not be conserved where not as a triad they break down in pairs- that is not be able to explain the generalization of particles in nature other than perhaps to enumerate complicated pathways and space representation regardless if they are part of the objective neutral experimenter's consciousness or not. What then does this say about the energy processes in nature- By my statement, Ulla, Life is that signal we receive before it is sent, this in a sense would involve a better unification of what we mean by a coming back to the present world of the balance of symmetries and asymmetries- as I said, teleology as perhaps more a physics. That any archetype occurs including those by Jung's analysis of Pauli's dreams he still left us involving the number 32 as a trinity and clock not deciphered, be but a mechanistic thing or some sort of filled and meaningful spirit or intelligence must remain for now a deep sort of global unity across infinite dimensions to which we cannot tell if in this summation symmetry involving it is broken or not- if indeed we ever nail down what of modeling it our deeper mind, when it is humble and healthy, says about even a new theory of consciousness with a time direction of a conception greater than that of the quantum theories- here, Platonic perhaps, we cannot ask if in the notion of symmetries and action, of moving time and falling into time, there can be much said about this idea of symmetry breaking in the nothingness of spacetime, whatever grounds its apparent simplicity- such a simplicity the ultimate invariant no matter what level or dimensionless grounding of our scales of singularities.

The legitimate sense of certainty if we do not put aside our own mental jumps into the synchronous world or as Pauli said Coincidences-together world is perhaps a measure of our own consciousness and sensibility, sanity and intellect, which will remain as mysterious as what we feel and know as that property consciousness seems to be described as in itself. Somewhere what we observe in physics, while intelligibly countable, may not in some deep background, be clearly invariant to anything but our models so as to distinguish it from relative change.

* * *

Further down the page with the question of epigenes (well that was a quantum leap in the understanding of the complexity of DNA in its time) and I thought the article was finished but after minimizing it came back then continued reading- and this is a difficulty in understand where we all stand in the philosophies beyond and behind these super symmetry wars with symmetric or hidden agendas or not. I quote for those who without at least the historical interest in the development of quantum mechanics from the Pauli essay link above Yuri sent):

In an unpublished manuscript Remarks on the Psychology of the Evolution
of Scientific Concepts, Pauli made some interesting comments connecting his
ideas on final causation to human consciousness:74
“It cannot be excluded that the images, which certainly exert a strong
influence on the direction of conscious attention (even if they remain unperceived),
are not only to be causally evaluated as a backslide to prescientific
thinking but also finally directed to a goal. In the latter regard
they might contain the seeds of anticipated future developments. It is
tempting to assume that the goal-oriented direction of these background
images is similar to the approach of matter to modern psychology in the
historical disguise of alchemy. . . . Therefore I came, already some time
ago, to the conclusion that the goal of images (goal understood in terms of
teleology) cannot be a further retraction of mental projections from matter
but rather, ultimately, a reconstitution of a state (that was realized,
however insufficiently, in alchemy), whose mental and physical aspects are
described with the same scientific terminology.”
Admitting the highly speculative character of these remarks, we must leave it
to the future to show whether non-random biological mutations will one day
be associated with a modern conception of final causation. But even on the
basis of present knowledge it is clear that Pauli’s uneasiness with the straight
Darwinian picture of biological evolution was fully justified

So, are our sorties into the battle a confusion of allies and enemies? Of civilians and professional mercenaries? But we should expect friendly fire sometimes. It does not good in the exploration in such realms of space and time as archetypal to squander our sanity in grandiose megalomania thus sink to the lowest level of those so certain of themselves as who outside sees their coherence and intelligence- a risk of philosophizing on the frontiers on the fundamentals- give us the strength not to try to reason with those unfortunately wounded in the mind or too drunk to make concrete plans and decisions- and occasionally we with others who are confused because they do both. If I am not seen awhile, it is because I am going elsewhere and not sure of the computer access, for a month anyway. It has been a rather long and creative month- and creativity can be a passion as with Nietzsche, or a madness perhaps as with Cantor as we worship the gods behind the gods of theoretical physics those by the way not as philosophical nor spiritual as Dirac and Pauli, in the end we agnostics who commune perhaps with Dionysus and his laughter.

* * *

Quasiphysical Consciousness

Quasi-physical Consciousness

*1 - The Combinatorial Spectrum As with the general debate between the continuous and discrete, so too a spectrum and laws of colors meet. Globally, and locally there are the paradoxes of non-necessary relations.

*2 - The Mind as Singularity - The metaphysical principle (of Rowlands) of what exists and not-exists as all else (said of muons) is so defined together if coming into existence, especially with rules of chirality, applies at that interface of our awakened state and dreams.

*3 Deep Loops and Layden Jars - The mind as a principle of "induction" and "complex number amplification" including the accumulation of charge or the physical limits of a spinning system. This is also the possibility of a grounding in the replete and not absolutely empty vacuum.

*4 Carbon Chemistry and Atom Substitution- The transition between a sleep and awakened state has a corresponding chemical model that may be seen as the complete explanation as all the models are intelligible. We should expect to find such concrete explanations that do not necessarily encompass the whole picture.

*5 The general division- of the mind-brain into a topological model as to what is the dream and awakened state is mirrored by the fermion-boson structural context.

*6 The Discontents of Such Systems - Clearly this same interface can be cited as the source of mental states of confusion that may be expressed in the physical state in the awakened world.

*7 Mind and Dimensions - The reduction of a mental "field" or duplication or joining of its descriptions as if surface to volume depends on centers of combining. The most intense visions is between the state of sleep and awakening and is a flatland of the mirror of compressing dimensions. (Brane?)

*8 Particle Analogies to Heat - We still have to consider the brain-mind, and consciousness in itself, in relation to thermodynamics, its laws and entities and extensions beyond its laws in more complex or simpler directions. As well the compass of synchronicity and non-locality.

*9 Puzzle Piece and Intuitions - Consciousness may complete a picture by puzzle piece clues or by those left out in both a universal or existential viewpoint of their context describing, embedded in.

*10 Degrees of Freedom, Restrictions - In a dialectical way we can observe a reversal of levels of complexity as to degrees of freedom. A tetragonal crystal unit motif while more limited than a full spherical symmetry of a cube may combine to a larger set of such units arranged together.

*11 Super-elegant Backgrounds - the substance of something like consciousness or mass or gravity, even as a neutral context of descriptions, may oscillate in the combinatorial discrete spectrum in that beyond three space there are new senses of what is parity and chirality of the count and privileges possible of more axes.

*12 Intelligibility - There is an intelligible but not necessary connection implied between physical and opaque structures.

*13 Memory - The accrued measure of memory and awareness of teleology is a learning unto future action and the recovery of that memory so freely and easily set down requires much more energy to recover.

*14 Health - The physical repair (or chemical) which is caused by faith in a theory may cause more damage than healing.

*15 Quasi-determinism - Of chance and necessity, and of non-necessity, free will and determinism can also be quasi-deterministic. The accumulation of a scaffolding and edifice of quasi-deterministic structures may not (as learning) accrue irreversible errors yet may lead down several quasi-finite paths. (Not necessarily a question of one or multi-paths.)

*16 A specific individual- in all of these senses could be unique in all of reality and thus no clear justification that in the collective no person is special. This is not to say something like the notion we are specially created- yet the mechanisms of physics is rich enough to describe, even transcend such a level of diversity in the laws of nature.

* 17 It is not clear at all, when the opaque is the mirror to the real- , if in a sense all such theoretical entities are to be taken, if not as positive, as real- nor that hidden to be considered empty beyond a reflection. But in a sense a dream is a mirror and mirrors in mirrors and so on. In fact it can be vaguely thought of as a compact and centered mirror in the dream state on that side of it- as well the external reading may be as if a post-modern jumble and entropy of themes. It is not enough in philosophic dualism to define consciousness simply there evidenced by dream or awakened states- but to distinguish aspects in both states.


It occurs to me, that these concepts (inspired by Matti and Ulla's contemplations on consciousness) can have immediate application to many issues of what constitutes our best mental states- or better what is the cause of slower thriving in some of our children. Today the news showed the drawings of children raised more with insecticides (organo-phosphates) as not as coherent of others their own age not so exposed in the food or in the womb. We need to ask such questions from a more general physics a a deeper level. When the surface chemistry of atoms seem the same but others are substituted the volume effects shielded may yet have some influence on the topological and arithmetical development of at least the individual organism if not the species. Understanding of such physics may better let us understand our perceptions and concepts of law real or imagined as necessary to heed without and within. The chirality, a spurious distinction or not of matter and anti-matter for example, is not the only thing that describes some special global attributes of our bicameral brains.

* * * *

Arcadian Elegant Matrix

Arcadian Elegant Matrix

I came back at night to post for this afternoon I was thinking about how 36 comes up so much lately in the simple arithmetic so I played with the matrix thinking it was a page I probably would not post. But the results seemed to give me better understanding of some of the more intuitive things I have done over the years with the color cubes as recreational math. I am very good at the design of such puzzles but not as good with the solutions, that is I usually allow those who are very good at the solution of such puzzles to solve them faster than I can. The arrangement of all 30 cubes for example in a row for plus or minus labels on the three axes. A lady made a set for this solution of the 15 cubes, but 30 were needed when we consider the sign of the axes. I immediately saw there were five other alphabetical solutions merely by permutations of the three letters and alphabetizing them.

After a meal and a nap I awoke from the chair and recalled how two other of my puzzles related to all this. One important one is the Calyptic Cubes, 6 cubes of 9 color patterns each used four times on one of the faces. But I do not have time to discuss that yet, and it seems to lead to some interesting speculation in general. But seeing the reduction of the four quadrants it dawned on me that when I exclude the diagonals of the conway label matrix it looks a lot like Kea's transforms. So I reread the one paper of hers I have in hard copy Quark Lepton Braids and Heterotic Supersymmetry. Now the amazing thing is that I understand a lot more than my first reading and surely this is because the patterns are universal although in different languages. This elegant matrix is thus a PeSla to Kea translator. I can see a couple of points not understood nor balanced where she suggests things I am sure she worked out in further papers- and those errors could be my own.

In my Backdoor Gin post of last year I made a six color cube of only three colors per cube which proves more than a mathematical recreation after all. For to understand the structure where in a sense particles are real, as real as the actual physical turning and twisting of cubes, the 15 three letter labels are so and the BKDGIN seems to match her sets of other types of particle numbers.

In fact I am impressed such a structure can be seen by such a different method. I am not sure by what she meant by cosmological factors unless that means gravity. I understand the accumulation of charge idea, a Machian and Diracian idea. Are we doing some sort of string theory here? I mean are there gluons in the end as we interpret them? I saw also that I have been using the terms generation and flavor interchangeably which is a good thing because there are after all two distinct ideas to which I have interpreted generation. Flavor and Color I do not use the same way nor as just a matter of partitions. Yet, I do use the general ideas presented in the paper in cases where recently she has posted on some methods of flattened topological objects. I wonder also what this paper may say about a Z' idea.

* * *

Next Morning- footnote: I had to revise the illustration twice for typos. Notice in particular H and -H seem to cancel out a neutral, a center, with small degree sign over it in the three fold axes letter combination's.

I tried again to extend this to the super-elegant level of a matrix of 4 x 4 but I will have to find the general formulas or perhaps just list them the hard way- maybe a color map of them. I should check Kea's later work on such matrix transforms too.
Why not the z' idea (in the future notation I will use the repeater pennant system with four numbers 1 2 3 4 each with a degree sign rather than st nd rd th for some listings of such cubes. Interestingly, we find the 1 8 28 56 70 56 28 8 1 here again and in a real sense of a sort of positive duplication of elements we add the two wildcards to make 72 and so on- but in general we need to work out this informational and binary numerology better where there are useful but different possibilities to consider when they are so close. We can extend the flat representations also in real space- something I dub tetrahelication or in some ways of combining singularities with inversions metatronication. Which are words that will probably not survive in my pantheon- yet, as I said some of my terms like quasic and calyptic are easy to use, hard to represent otherwise, and are indispensable for the notions they carry with no need for disambiguation- let's face it in my next post quasi-physical is not a clear and is a cumbersome word.

The idea of "flagelation" the flare or rim comes up in the intuition mentioned in Kea's paper that in these structures and matters higher space functions do seem to have effects or observations in the lower particle space- the idea that our ability to see pure n-dimensional spaces reflects how nature herself would do so. I cannot say that matter and antimatter are not an important distinction ultimately without the reason for this of some structures if viewed from the outside (as we seem to be viewing the atom.) I suspect like that result of the last face of a hypercube that there are a few more surprises when we combine these matrix label elements in higher space as if they in a sense were particles or classes of them.

Happy Earthday, everyone!

Pseudemys Scripta Elegans

Pseudemys Scripta Elegans

Which was a very big string of words for a child with a small one for a pet. The magic of it, the kids who could say and spell triceratops but not average words.

In the illustration I wanted to emphasize that the numbers (here decimal) are not simply fixed to the plane- nor are representations say of arrays of partitions withing partitions. I am not sure of course if the general idea of this space exists already or is conveyed in my posts- but I do know that as hard as some links for me are to follow, like in links to general articles in wiki- that there are paths in which from one simple link the hint of but no further links are there. I imagine because the knowledge is too esoteric or lacking somehow. On the other hand this strikes me as a measure of the depths of the higher space and math conceptions.

So, choosing for now Sel' and so on, beginning with El for elegant and super-elegant space, I tried to take the next step of exploring beyond the dimensions so far. I cannot say that these stacked Conway matrices explain the generations of particles but it does seem to intelligibly fit into the general picture. So on some scale of these spaces or state of them we find a vast world full of surprises- some of which are not visible nor expected and some that go beyond our ability to fundamentally define- for beyond just axioms invoked those who work on the foundations seem to need a theory of foundations for the foundations.

This suggests to me that there may be further particles of a sort to which we really have no idea how to imagine them- or have some idea, what for example we would expect of a Higgs. It supplies mass and mass is like the foundation on which the world rests, a sort of infinite regress, an idea logically that it can find or lose mass or can give or take mass away depending on our grounding vision of what mass or physics is. It does not seem a bootstrapping, a remixing of what is that self-defines- but this too on the absolute level is a question of metaphysics.

So, do we need now to question the metaphysics underlying the metaphysics? Surely where these abstract matrices are seen as an intelligible stereonometry we might just begin to imagine other principles of physics, levels that explain things more deeply and differently.

Of course the map of particles considering their parameters and so on if we were to make a graph of them, especially where these are finite and not a straight line or easily describable curve or fairly accurate distribution of things, how these particles and energy levels behave even with discontinuities in the graph speak for a quasi-continuous result from the expected in other directions of modern physics standpoints- including string like theories.

Like the fabled turtle, unlike him rather, we quite imagine a lowest level, a Planck level of sorts, to which all things must be held up, stand. But this case is not clearly the case anymore than the infinite regress. It does seem on the face of it to be a reasonable case, a reductionist one. But even in the first few dimensions and levels of exploration of these space structures and color cubes we can get a glimpse of even stranger worlds of foundational ideas. How far can the Sel primes go? What does it ultimately mean if a unit structure or a complex structure can be classified as we do singularities?

Metaphysically, I think we should look a little deeper at say the idea of muons and all else not a muon- that is the metaphysical idea of Rowlands. Some things we may find from our atom smasher experiments on some super-elegant but not necessarily super-symmetrical space may not be something we know what we are seeing. This seems to be the case with some recent data suggesting new particles and forces which are either the same as very old particles or different enough to be an anomaly.

I suggest that it is not necessarily possible to distinguish such a higher Sel' particle from a black hole. It is a question of this idea of multiplicity or indempotency at singularity. This merged or opaque exist, not-exist entity could be a whole new level of the grounding of physics in what we mean by space and mass.

The problems with say trying to find in space of a 3 x 3 x 3 arrangement or other such restrictions in the numbers themselves and their patterns- from the viewpoint of quasic space grids are a boon rather than a problem so they define dimensions as well some may interpret things as what are the particles and energies of things.

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http://www.ncbi.nlm.nih.gov/pubmed/3445484

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Here is the poem (almost a good song from my "I am the Weather" series) in which I actually take up the issue of touch and sight as geometry and action at a distance where the robin's red is some sort of cosmic afterglow.

Through Blinds, Glass-ly L. Edgar Otto April 2011



Another snow on the Robin's back

Cruel month of spring, false starts, new loves



But I cling to your red breast

distant your touch, my cradle second best



I will trade our hugs for light that

your shining glow sleeps not alone at night



Your heart in frozen creeping time

Builds up to storms of fire and ice



Dancing in your skin, talking to the air

As I pick my nose, you muss up your red shift hair



In this world or in some other, further

pretend we do not see, so close our dance together



Oh, you've dyed your hair in compliment

to robin's egg blue, too late to make it true



You who take our light for hugs

where nature's drapes matches the rugs...



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a comment on the graph at http://www.science20.com/quantum_diaries_survivor/blog/guess_plot-78246

In the back of my mind it reminds me of densities or packing in spaces maybe of particles on certain levels. I did not think about this a lot but it keeps coming back and a graph of this would be interesting anyway. Why indeed would there not be a straight line or an interesting curve or for that matter some scattering of data points- and not these plateaus and discontinuities and so on. A picture that perhaps has said a thousand words if we only knew how to sort them and expand them when it is but a narrow outline of which we do not know if information was lost nor if we can improve our instrumentation's and theories. Or is there still something deeper in those lines that appear horizontal?

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The astronomer Stubbs from Kea's link today and his philosophy of dark energy is most interesting. Inspiring really, (I am up to where is is pushing for more experimental gravity measures on all scales).

On the other hand, I think we will resolve this, a shorter period of dark ages, as he mentions what happened just before the discovery of quantum mechanics- in fact, some of us have already broken thru to the next theoretical golden period for the new physics. ahh its over, well- where should we look? he asks as he closes:
I suggest more closely at the way we do mathematics and topology with perhaps a little more creative interpretations. Good follow up questions and honest answers about fine structure constants and suggestions to explore them with experiments and observations- and for the quasars and dark matter that still an open question (especially "anthropic cop out philosophies and paradigms" in relation to this sort of theory and so on...)

What about 10^n! , 10^720 for example? Let us found reductionism better before we declare it as the foundation- I say... But is such experimenting possible to be falsified? In the end what can be regarded as real, the physicality, eventually merges intelligibly theoretical and applied mathematics. The ultimate antropic principle is that we are observing the light and insights from this anthrope- not yet thru an analog of some gravitational non-reductionist lens.

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Super-elegant Space

Super-elegant Space L. Edgar Otto April 20, 2001

The generalization of our ideas of space and dimension as represented in claims for a standard theory or a unified theory can be made clear by a deeper view of elements in a space array where the colors, labels, and the arithmetic with relevance of operations sensible between them have logical topological structure models in which our normal space is embedded within. This space is best seen by alphanumeric's and the interpretation of the arrangement of elements matches closely natural principles of physics.

[ I call this space, grounded in a certain order of binary cells in a "quasic" plane "elegant" in honor of John Horton Conway who remarked to me upon my giving him an arrangement of labels of five matching things on the faces of a dodecahedron which was my solution as an inversion thru the center rather than just a few possibilities of surface solutions he deduced. His comment to me was that it was very elegant. I do not know if he ever explored what he called the non-standard arrangement of the "Conway Matrix" of which I now propose a general space for all such solutions, a space with coherence and to some level of understanding our looked for unification. I regard Conway as the greatest mathematician in our time. ]

The Conway matrix is a 6 x 6 array embedded in an 8 x 8 array. In the binary ordering as this procedure can be viewed as in superelegant space as four dimensions embedded in five in a geometric analogy to the matrix of 6 matching faces of the color cubes of Malhon in the 6 x 6 array as three dimensions embedded in four where the 28 surrounding cells are permutations and crossovers in four space.

As it involves 5 and ten fold symmetry we can demonstrate the coherence of the matrix relations which are orientation and matching in all directions considered of three and four axes of space, we can use the decimal base numbers as well.

Thus for the array we have these decimal integers. I begin at 1 in the upper left hand corner but it does not matter except that with the compliment at the lower left end of the cell it sums to 65. We can begin at zero, or for that matter there are cases where some pattern intrinsic to integers are seen if we begin by a prime or if we extend the notation at that first cell into some negative integer directions.

[see illustration above]

In the illustration above we observe there are four quadrants of integers. In one of the quadrants, the upper right, we have nine numbers and these can be added as compliments together to find a number that fits the quadrant. this gives four other numbers adding across the sub-quadrants to 102 as complimentary compliments.

These numbers I have labeled with my own matrix notation by alphanumeric letters that describe pairs of complimentary colors, thus as with Conway we exclude from the 36 the main diagonal that gives the cells of pairs of the same color. This leaves the 30 cubes and the problem is to match them in three space as well as Conway has done in two space. This is a hard and super-elegant problem.

But as the quasic plane already arranges the sub-elements, the points and edges, faces and volumes, of orthogons, we should not be surprised that such a more generalized and higher dimensionally interpreted grid will simply this problem.

Where then I label these cells in the 3 x 3 quadrant and give them a three axis name like LHC DIJ GKE and so on, we find that the sum of these labels for the six possible cases (and eventually the other nine) sum to 76.

Reading across a quasic matrix those things in a line, either in the up or down direction, represent the relation of vectors of a symmetrical space system or its relations. In this sense the significant number is 24 for three and four space. It is also the number of orientations of Malhoons color matching square of four colors. I is also the number of 2D faces in a hypercube.

Reading across the grid [in my illustration of yesterday as a series of red dots in an array] I observe that there are five standard alphanumeric label matrices to consider- in fact there are 15 or 30 of them in general reading the totality of the plane in a plane and each element a unique thing, beginning at triality such that the diagonals, both of them, of the plane have spatial and computational significance. Three of the labels are in a sense excluded as only used once and not in pairs leaving the arrangements of 12 things.

The reading across the superelegant (or hyperconway) array gives the unique conditions for a positive orientation of color objects each a unique state. Of course if we take one of the six colors of these five hyper arrays as the center we establish one of the five (or 15) standard Conway arrays. In this extension from simplicity we may begin to realize that things like the number of cubes or tetrahedra or rhombuses across polyhedra of icosahedral symmetry goes a little deeper in our conception beginning with asking what exactly a cube is and is it the most fundamental of structures. [This, with all such questions on the foundation of physics, is not an obvious one to ask and harder to find proof and acceptance by those who so fundamentally cannot understand, or may understand a different tradition.]

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[ A Bit of Philosophy: Of Vertigo and Algorithmic Man this part of the post also informal between intrusive brackets and partly inspired by Ullas post today.] [ . . .

1* One amazing thing about the Omnic view as to the improbable preservation and uniqueness of the soul, about the spirit of philosophy and science that unearths and grounds it in a totality, is that a direct proof of God or gods is not needed for the mechanisms (where one might conclude or believe pre-set being as intelligent design) in reality that precipitates out, records, such structures. But it is still in our evolved core superstitions and intuitions dwells our rituals for the dead and for souls. There may well be, insisting on some faith or warring philosophy that not the best of character we may take with us in the here or hearafter.

2* A finite intelligible accounting does not necesssarily distinguish the depth or span but can arrange structure with some distinctions such as partition theory (that is of teleoscoping quasic structures information theory -wise.)

3* The complexity of the new physics and possibly the generalization to an omnic background while vaster in relation to organism encoding even more than we now suspect is a diversity manageable by the new physics as far as I can see for now.

4* The relation of notions of physical theories have parallels as if they too a quasic matrix or superelegant space of their intelligible connections.

5* A hCw matrix encodes 5D axes as 3D in 8 dimensions of vector variance. Is it the Pentality of Coxeters delta honeycombs and general orientations not broken but are 5-cyclic over some superelegant linear array of all the possible orientations? Would their then not be a further generalization of such flat honeycombs?

6* 25x30 = 750, 750-720 = 30, (6!+ 300)/6 = 5^3 ; 4 x 136 = 2^9, 2^5 = 4^2.5 ;

7* The integer weights of some crossovers of integers are invariant (quasi-partitions)

This second, informal creative philosophy section came before the more formal parts posted above- also another attempt for a song as a break called Through Blinds, Glass-ly.

So, the EILNO stands out against the 10 of A BF CGM DHJK by which around the five we can generate the 15 color cubes, this where the flat 45 or 90 orientations come up on two space in three space as if we distinguish the z axis but do not know which to color in a standard system before hand. That is for example: HCADB in an array with EILNO then JKMFG giving HEJ CIK ALM DNF BOG but these shifted such that instead of say ALM we set AJO or ANK for the 45 for such a 3 x 5 set of axial arrangements.

This found by considering "counter clockwise complementarity of reversed color sequence spectra to encode and place the letter labels giving a reduction in three space over one letter like E red violet for the face pairs AJO AND BIM ;
BHN and CHL where the significant reduced 3 x 3 matrix is FEM CHL OJA, that is the other way FCO EHJ and MLA to choose one of the 5 or 15 from superelegant space matrices.

Interestingly one can discover the triplification of natural dimensions either from a higher or lower view of the natural dimension in regards to surfaces and volumes.

These ideas preceded the more formal parts of the post above.

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Nuclear Metabolistic and Peripheral Replication Space

Nuclear Metabolistic and Peripheral Replication Space
I thought I would make it a little clearer just what I was counting. I imagine a sort of biological origins of space (still an open question) as in the debate if it can come from replication or metabolism processes- are simple molecules and more and more complex rings of them with an energy source a precursor to say RNA or DNA. I imagine this is a matter of cosmic philosophy also.

Does the cosmic code in a sense have such an idea of replication, Like Smolins baby multiverses or the professor mentioned above who originated the idea of 10^500 or so different sting universes with different string laws (and which one fits us?)

Of course the comment I took out of spam strikes me today as a contradiction in that only string theorist were recognized being alternatives requires some sort of restrictions- what sort? cosmic censoring? What could be more unrestricted than this string landscape? This was an interesting era, the prime or first work of these physicists, a sort of inflation era hoping for some Brane like resolution.

BTW the calculations in a couple of dreams were more detailed and logically pursued than shown here, this is not much different in those places of hypermnemic dreams (a Freudian term) than if we gave our whole mind to endless branching as a core replication- but even then the quasic view allows rings to precipitate out from perhaps a great sea of fundamental general singularities, a crystal lattice of sorts with quasic coherence's and echoes of resonances, iota primes which can shift the music scales fixed high and low and movable with some flats and sharps and naturals and so on. No wonder some might imagine a hierarchy of Planck like values as a natural part of the picture in action or spin ideas. But the background of things is not just a zero infinity or one but also the open wildcard as if the absolute null.

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Dimensionless Constants Top Down

Basically I considered in the quasic grid a count of the contents as if a series of Conway matrices in a sort of hyper relation to each other and their dimensionality, that is the more general idea of mixed, covariance, and so on from the symmetry in the grid. The numbers come out intelligible.

The relate specifically to the Triaconway puzzle of the 30 cubes- but the diagonal of the Conway matrix as with any matrix has special meanings and uses including the wild-card primitive initial cell of all quasic matrices at the grounding finite or infinite region or pixel. This as with Eddington's insight helps to explain what the value seems to require +1 to some accuracy (other than Eddington's more relaxed philosophic explanation).

In a sense these "quasi-scale constants" can be found from a general counting of group numbers and symmetries in much higher topological spaces than from the Pascal triangle considerations in the very low dimensions. These are then able to act with the usual mathematical operations. We might regard for example of the 6! six color cubes hypersets of 6 of them (12 with inverses) describing the 60 group of the dodecahedron (in ten binary coordinate quasic space =1024). That is of the six colors one is the center (or outside shell) of the singularity status of the other.
Thus we have the six pairs of inversion axes through the dodecahedral faces as a way to interpret some of the properties of numbers and higher crossing spaces and topologies- in any case the fixed space of these six cubes even when expressed as all possibilities does not cover the non-dimensionality- but it is a vague mistake only justified by a quantum interpretation that such effects are necessarily active on structures because they are "non-linear" - rather, it is a cop-out to which like with all faith that one might find the shamans sometimes use tricks and magic and part truths as lies to lead the student into either an understanding or the priesthood.


But, with the snow and all and still not access to my old work in storage, I do not have the time nor inclination to recompute the symmetries of Triaconway today.

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A Footnote on Mirrors and Non-mirrors in the Standard Physics from the traditions of Maxwell and symmetry unto particle and field theory descriptions as strings:

I still do not think many have grasped the wider generalization and complexity of the idea of chirality in the twists and mirrors for a foundation of physics.

Although many have stated the problem- for example that of the question of where are the monopoles. A few have understood this problem by the postulating of say a discrete system of some sort of particles, asymmetric or neutral or otherwise.

It seems intimate to our current speculations on dark matter-energy and the behavior of anti-particles. But we have taken an unsolved problem in the realm of physics as general relativity, frames involving space and matter and so on, and applied it as still an unsolved problem at the subatomic level and at what may be happening on the string level to which some things are still outside our experimental observations and may forever be so. It is really this tradition and agenda of physics that is to be defended or adjusted to what we say we mean by physics as concrete and not say its extensions into things like string theory. That theory only keeps its seriousness as science in that it supports the old applications of the old physics- even if in a sense the quantum theory trumps that of the relativity's, at least to the point we ask relativistic questions, like Dirac brilliantly did so on the scale of electrons and so on... The cost of defending such science as faith to to leave its progress to a great extent in formulations that remain mystery and faith. It also undermines from a slightly greater generalization or unification if that is possible, where clear applications of quantum and GR (Qlassical) notions do and will always apply if it maps to the functions and phenomena of reality.

The question brought up on the blogs lately is that of matter and antimatter being an attractive force- they certainly can annihilate and we can compute the resultant energy which may be the greatest method possible short of perhaps creative states of vacua like the black holes. Is this not a logic question? Someone had said, in some book I forget among the popularizations of the time soon obsolete and growing dusty in used book stores today, and in little diagrams, that antimatter and antimatter in a sense gravitationally repel. Why could matter and antimatter not in a sense attract or repel, but only from one of the poles of such a direction? At what level may we say that an atomic string might break into isolated quarks? Is the universe expanding as such its space or in a sense is it pushing away to distant structures or places and times what is after all the rare antimatter in the universe?
Or again is this a matter of the logic of possibilities where that logic is intelligible?

Surely there are already theories that question or eliminate the need for theories of dark energy, if not opaque matter virtual, continuous or discrete or not. One would be the universe as a whole spinning. Sooner or later, in the tradition of the last century's physics we might tweak the values as reductionists in style- even prove and not hold off the question to remote times and distances, if for example some particle such as the proton are our everlasting grounding of the real. That many have this faith already, one day we may show the material cause, one day we may understand the brain for example by the nerve connections. One day we may but it may also only reach a level where there are still mirrors of doubt and mystery of what is understood but remains hidden. One day something entirely new, and as physics, could arise for there is no reason to assume we now the pinnacle of science and philosophy and not but here in the beginning of a longer life of such if our world survives natural and man-made disasters.

In a sense if a path can return but in the process become its opposite, or objects in return and facing each other in direct seeing in effect look away- if after infinite time and speed some idea of acceleration becomes rest- how might we really distinguish what is the matter and what is the antimatter in an ultimate theory?

What does it matter from the omnic view or prove if in saying some state, discrete or continuous is but a unity of some measure of dimension if ultimately any such unity of scale or not are known to be composed or break down into the still vague but inductive confusions of the zero and potential infinite? In this sense the speculations on ideas of dark matter, even as just a notion, is good for physics.

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Yesterday, Lubos had a youtube video of one of the founders of string theory lecturing at Stanford. To that I make a comment, not his post today as political concept on "feminazis" (yet his posts state from the start a right wing bias.) Perhaps that level of bias between philosophies of gender colors our ideas on what is matter and anti-matter, handedness and so on. The old French saying goes, "a man without a woman is half a man, but a woman without a man is nothing at all." Surely we may claim some benefit to a woman from an evolutionary stance that even if pregnant sperm stimulates her immune system, or we can say socially that the closeness or intimacy of sex during pregnancy helps socially bond the family.

But I have to admit that the part of the lecture I saw, up to where he describes the difference of strings on the nuclear level then to the Planck level- that the ideas in a way game me things to think about the reading here and there did not clearly convey. But thru my eyes and now a long history of speculations, if you could see the lecture thru my eyes perhaps some of you would not fall asleep. Not to be unkind to the effort and awakening of that part of physics- even if once something is achieved early on the old guys (and some gals in the same field, a married couple in particular as biochemists who dismissed my more topological ideas on the gene code and who said it was just a matter of electromagnetic induction) seem to sit on their early laurels forever. Some of course, like Stasheff, continue in a fire of discoveries.

Well, some parts of the lecture - and I really do not know what they teach in schools- and by no means do I not respect the noble profession of teaching as opposed to research- struck me as historic developments with commentary- like the discovers of the resonances being linear were lucky in the guess- two points determine a line the professor said they discovered, jokingly. Now, I suppose humor is a good way to teach, at least entertaining as if the professor had read deeply from the Holy Book of Seinfeld. But it is a way to educate, lead to an idea rather than educat to lead what may be thoughts from within the student innately. This seems to me done by glossing over certain ideas or at least questioning their case logically. But I must say the quality of the questions the students asked him and the disruption in the flow of the presentation seemed to me to be of a very low level, perhaps embarrassing for them to ask. He seemed wise and old- but the result of this as ancient as I am I felt much younger.

I think, as in the simplification by Feymann's diagrams as to say turning them at right angles, that such simplification, loosing some field information I suspect, is only possible because of an underlying new physics. The intelligibility of quasic and topological fields- in fact the linear resonances are a direct result of this as well the significance of diagonals. But some lost information is really that which was not there- perhaps there are no gluons or gravons or Higgs and so on, not even in the artificial grounding of physics could we make a world more than one of notions only based on it. It is clear that in the reading of some matrices as some of our new physics theorists here in papers point out, there is the up and down, sometimes asymmetric result when we reach the two space in which these reactions occur- this is most evident in the new theories as to how the physical structures of the gene code evolves, is expressed, and is read. These theories have not envisioned the quasic space save perhaps the first inclination of it as a disembodied M theory. Nor have they yet to explicitly apply the arithmetic ideas and topological ideas assumed vaguely in the background of theories that after all must progress in the expediency of publication and discovery.

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