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.
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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.
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