Monday, July 25, 2011
Ray-Gun Fractals L. Edgar Otto July 25, 2011
This started out as more of a puzzle to make for the recreational mathematics community but led to some interesting ideas on number theory. In the pages I posted are the germ of some old and new ideas- some standard and some novel to the best of my knowledge. It is not always in the play with shapes and numbers we need to think of it as a formal enterprise, and yet freed up intuitive play can lead to deeper concepts of math and physics. I invite the puzzle community to expanded in the ray-gun puzzle in this way, and the number theorists to take a good look too. I call these ray guns being right angles seen everywhere as in the artist who displayed them in Chicago I saw once.
The question is in the Soma cube we can have the 3cube piece as a right angle or as three cubes linearly- the remaining pieces (24 cubes) can themselves be arranged in a right angle. In this intuitive sense we use the word fractal here, a sort of embedded recursion. (And like Kea restates and points out today on her blog these sorts of ideas apply to the elements in matrices of which I see these quasic planes.)
In these considerations such objects as applied to say string theory as a matter of partitions must also include the idea of orientation.
Clearly there is an link to the concepts of complex numbers and modular numbers as both apply to the plane as far as order goes and not clearly linear where something is less than or more than or follows something else. The same for the set theoretic extreme limits, the idea say of the last infinity or last omega point. Kea in Motives where she intuitively considers surreal numbers (like mod numbers where some things add to zero so as to make loops and cycles, the little eta and little omega ordinals). On the other hand the unique properties of an open sequence (non-looping) cries out for a relationship of the properties of prime numbers as in Pitkanen's 2^n considerations as Mersene Primes.
If we in the absolute or relatively absolute concept of structure and space, perhaps a surreal calculus of sorts, and the square root of two thus treated rationally in the 2-brane or plane we can orient or make twistors out of partition theory as used in string theory and Keas use of combinotorics, these can be treated as abstract fields or particles where the little omegas and epsilons organize space into certain assumed orders as if an assertion of strict order at least in the plane if not the factors which again are not subject to the same idea of ordering, these abstractly as particles themselves- in a sense we have made a meaningful topological discovery of what one half of potential infinity means that is not infinity in the same way if we can so treat it as a number (which we can work out the results in the more standard notation.) Moreover, Is zero an even number? Is one in a sense a prime? and as such do we assert, as with many number conjectures the quasic grid shows the proof or the way to a proof, that say any even number greater than two is the sum of two primes? Or that there is a relative infinity of prime pairs? It is no longer acceptable to me to do physics as math and feel any certainty without the better understanding of these seemingly innocuous number theory concepts.
Now Kea says, when will we go beyond the QFT view of things and "fairy fields and all" and I doubt many can understand without a leap as sorts into the questioning of our most fundamental maths- it is difficult as with the significance of Pitkanen's ideas. To this we have to add the general take on things by Lubos, not so much the application of strings as his understanding of quantum and probability concepts. From my view the quasic and other newer physics ideas such as the little omega and epsilon points being zero or half-infinity or half of unity for that matter is the very underlying fact that gives the ground for random structures and phenomena. As with Rowlands we have the Nilpotency formalism that gives the ground also for articulation of structures in some natural background or framework.
Again, although in Kea's motives she pretty well surveys the complicated expansion of things to do with trying to compute braid and like methods in higher natural dimensions. Where these, say by octonions or other such counting of some region or scale of connectivity on all scales, apply to our ideas of Bosonic theory or say the reading of the gene code- no sooner we have a whole other level of reading the genome than there are levels beyond that- and we cannot casually reduce it to say quantum chemistry alone, nor ideas of say dark matter, sting theory, black holes and so on- from my view we need the next quasic level at least to understand the physicality of mind and organism. Closer to a more total theory of everything is closer to how the natural laws of the universe applies to living things.
We can of course erect great edifices on any of these world views- things like light in the background speeding up or slowing down as fundamental : Rio Frio, or the recent poster to Pitkanen's blog on radiation or heat as the source of "gravity." These may not be wrong as much as need to be integrated into other systems all of which for now seems to make thermodynamics still a frontier for concepts.
Certainly the new physics has a refined idea of what mass is. Victory, actually it is for all around. I am not that excited in the path to declare it for some particle thru the far reaching eyes of Matti and Motl whatever the nature of the particles or why anyone can with assurance dismiss the existence of some or if any combination mathematically possible is so discovered and worthy of Nobel prizes that the masses do not really understand idea to which we may begin to see (it should be made clear to the masses the importance of science and research- I have talked to so many who from the popular reading are capable of deep ideas that are popular along the line of "time is the fourth dimension" or "in the NP hard problem to solve the minimum circuit and path the mold eating various sizes of potato chips in a maze find it!" These kids are eager to learn so we do need better popularization- that or I do not realize that all is in a sense popularization with a sense of formality in the way we approach science and is anomalies at the frontier to which there is in education not just a qualitative and quantitative view of their education and expertise to some degree of relevance- but perhaps quasicalitative in a philosophic sense as well.
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I changed the Illustration for a possible project and a victory celebration of sorts and for the sake of logo design- after all to say new science recalls newscientist yet I decided scientist was better than science society:-) July 26, 2011
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I posted a comment to Kea (a link there to a very good paper from Australia BTW) and this to Pitkanen today:
Congratulation to you - I wish I felt the excitement and I do see those particles like you do even if we do not have the benefit of details of how you did the calculations- the theory is still too hard but we all win that these theories are there.
It is just that sometimes things have to get worse before they get better, or in matters of probability if we win a battle we lose the work, if we lose a battle then we win the war... But what of those who win the war or loose the battle,- as lonely perhaps as losing the war having won the battle.
There is a lot to be done and today's glory is tomorrow's broken toys where the child in the genius has room to grow and play - and when we open the presents after the rush to take off the ribbons and packaging- finding what we really need or want! Twice the warmth and joy, cutting and burning the wood for our hearths.
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