Saturday, January 29, 2011
New or False Number Intuitions
New or False Number Intuitions
Ulla sent me an e-mail and it was a rather interesting paper:
Here is a quote:
"This paper explains why a purely mathematical argument leads to the use of adelic mathematics, discusses this in the context of epistemology and cognitive science, then shows how topological geometrodynamics applies adelic mathematic to a reconfigured model of space and time."
The idea of both the digital and analog in the explanation of the world- nothing I had not said or posted long ago somewhere in the internet but which I regarded somewhat beyond the pale of physics proper- so much lately seems to come up from my casual axioms and thoughts and like that between two lovers each thinks that they were the first ones to discover true love.
In any case, Ulla is synchronously in tune with my more epistemological planned post and I did not go too deep into the link she applied so as not to be diverted from the path of my already planned direction for this post. I see the topic hot in the posts of others- and I see Kea discussing her blog as a top mathematics blog for readers- http://pseudomonad.blogspot.com/2011/01/theory-update-43.html I find her last mathematical posting right on and most interesting and feel quite at home with her terse hints and conclusions- whatever else my epistemological crisis was last night at least from links on her blog I did finally understand things like the how of the hook function.
In which case this blog can be skipped as it is about our minds as a state of calculation and the frontier of speculations rather than the mathematics itself. I am not sure however if blogging showing the states of mind- or even the style of writing in handwritten manuscripts really tells useful things for theoreticians.
At the rate of my posting the presumed readers may not have noticed a pause- for I did come to the coffee shop last night to post- but I could not reproduce what I thought I saw. Still the intuition of it seems to me the germ of a powerful idea, one that not only needs a Ramanujan to arise to see- but Ramanujan would need a Ramanujan to explain it. We can still wonder if our world is to be based on some form of triangulation just what difference these near coincidences, all the Bogus Pi and e's and phi's make out there. Maybe something of it is in Ramanujan's notebooks.
http://matpitka.blogspot.com/2011/01/non-standard-numbers-and-tgd.html Pitkanen also has a most relevant posting today for our new concerns about number. I also recall Kea just posting a quote of the week, a mathematical one at that- concerning axioms, Riemann's hypothesis and so on- axioms are also on my mind in these ideas of the structure of space (and alas the mind itself especially if I had a false intuition or did not listen intelligently enough to a promising one) But it is this nature of the Mind as issue in its relation to the history of physics that is the subject there- there was a poem I did not write because I am not comfortable with the stark idea that perhaps the earth is alive after all. Gaea and all that. Yet there is always the question of why we can think such things.
Lampion 01-29-11 After we gave made concrete gains on a higher level of what was formerly a vague intuition, we find the frontier of speculation again of vague intuitions or even false ones on a much greater scope then we were able to be aware of. (In some ways that the universe can be a dead and purposeless place- that too can enhance the fact that we are subjectively alive- we the otherworldly. Yet who in the more advanced religions would consider to find the higher God one must accept the musings of the metaphysics of wiccans? Or that the assumption His principle is not needed for a theory is an essential stance needed in the finding of Him?)
Lampion 01-29-11 b The essential axiom of four space (Euclidean) is that two planes can intersect in a point. Of course three planes in three space do- but there is a concept to consider also: That three parallel planes may intersect in such a point.
Lampion 01-29-11 c The DNA with its useful information is said to be read fractally. Now if numbers have fractal aspects then in the inorganic realm it is clear there is an analog to the genesis code too. The Cosmic code can then be seen in a sense aware and alive in as much as we are as well physics can so define us.
But the idea of Mind, as with Hawkings knowing the Mind of God so to speak, for or against (either way these things sell books... God Particle existing or not carries a better street light than does the Higgs exist.
Astrology in the news again- what is your sign- the constellations or just the seasons (but what of the seasons in Australia then?) Let us recall our last great astrologer and first great physicist with a side interest in the Bible code- Newton!
His intuitions went only so far having to invoke the God to move the planets the same way- and for awhile later thinkers showed how this hypothesis was not needed. You know the history, see And God made the Integers edited with Hawking.
Well, the sign of the snake handler for the 13th constellation (why do we want to divide things into say 12 intuitively then compute the Saturn and Jupiter of it all even symbolically? Such mummy wheat (Yeats)- well, with tweeter not event he ancient mummys are sacred in a cause really without revolutionaries today. What sort of snakes are these strings that can Ouroboros worm bite their tails and so seem to explain gravity? Or the 14 constellation, Cetus, the whale- after all we do not need to go into space to feel the degrees of freedom general in the sea.
Lampion 01-29-11 d Strings can be a sort of ultimate particle in theory- alternatively we might consider points as existing after all. By spacious singularity I mean- a conclusion one might glean from Kea's 54 in her tetracys- that such particles, seen as point charges, clouds of vague probabilistic things, or strings tied to the ground of the Planck scale- are really after all in a sense things that like the numbers require a fractal description of their structures.
Newton then, as above so below- did he not explain away the influence of the stars and call it a sort of disembodied and mindless thing, his alien autopsy of the Deity he served in his sense of an intelligible world, that Like Lubos posted perhaps we find there is no gravity (or perhaps gravity waves observable?). Yet if there is a history that is unique and all thru time it applies and each of us unique regardless of the tides or the delay in there flight of light unto us (that unexplained even when things are consistently constant)- then in such codes if they are intelligible such a Deity could be seen as part of history- still, as I look out at the bare branches at night rejecting a poem that I am more alive when the earth is not- oh how dangerous to live without taking note of our intuitions, we who pray or not, I know that to find God or keep the concept at the frontier for inspiration, that we have to admit the possibility the earth is alive, and that the stars have something to do with our unique birth and destiny.
Or is it just that our intuitions are not false but a little incomplete?
* * *
Is it not amazing to realize that i to the ith power is a number we can write down?
That the same number laws apply to divisions by 5 and ten as in our description of the wavelengths of the radio spectrum?
What is next after that sense of a string theory without strings but a topology theory without topology- even a number theory without numbers- and gravity without gravity? Certainly, we can pin some particles on binary numbers ultimately, say 128. We can say that there may be a computational or geometrical reason for the limit of counting the triangulations- expanding or not beyond 30? perhaps in my vague numerology this reeks of the 30 cubes- thus spaces beyond those?
Perhaps the measure of how concrete our capturing of intuitions brought down to earth is the vaster scope of what is possible to see then, full of greater errors to which it is so much easier to fall into and make.
What is intelligible then in the universe- and not necessarily so- seems to have a sort of conservation of the intelligibility. But this issue of the relation, causal and ongoing or not, is way beyond the simpler questions of discrete and continuous, digital and analog, requires a much wider scope than what we may conclude from asserting new axioms.
As illogical and unintelligible as the notions and wording of the last few paragraphs may appear- is this not the general mood of the few links posted as formal paper on ideas (such as non-Archimedean extensions of numbers) as listed in the several links in todays TGD post by Pitkanen?
Sometimes, one wonders why we share certain things- like Ulla's last useful links to me- to reinforce our stances to the world? Show them as the same old sheep in wolves clothes? Have us infer something deeper behind what actually said by the philosophy? To learn or to create? The factorial heart of our triangulation to map the possibilities of inquiry and learning seems to have that emptiness we find as part of the description- as some notions or concrete entities this calls up creatively that new things do arise.
* * *
This just mentioned by one of my friends in the coffee shop- I think I found it if it is a father and son researcher that can make any shape from lines cutting the plane in certain ways.
A friend gave me an orgami octagon of sorts yesterday- and I notice a lot of articles from time to time on this- including a chip design that folds itself by these ideas. Is this not a linear problem? I mean, even in something as seemingly simple as this we see a much vaster applications of spaces and numbers, the folding of membranes and perhaps some of these new interesting properties and maybe some old ones like a fixed point in a crinkled plane over a flat array of points numbered- and yes, the ability to better understand knots and make more efficient explosives.
So we have to sort out the intrinsic curvature abstractly in such lines as if non-linear and incommensurate string like entities.
I hope my quasic grid is helpful for it does seem to make a lot of visualization much easier- once we do have a better glimpse of at least algebra 101.
I am not sure now what new projects I may undertake here- suggestions anyone?
From a post-modern artistic concept our dreams are a folding of sorts to which we see only the surface and its parts sometimes broken, sometimes the only way in the clouds to find connections we do not see in the ordinary world.
* * *
This is an interesting Lubos posting: about three back from today's post.
These sort of diagrams do indeed look classically logical and for me a little quasic. Of course the determinate's 2x2 matrix compliments and such seems to apply even as if the Aristotelian logic of it as to what can be observed or not. (But have we considered the absolute change in what is a one or a zero or some orientation if we are to recover anything in the real or concrete?) I have issues with Lubos in general on the concepts of what is positive and negative even where I agree some space is absolutely positive or zero only. I suspect I now have very subtle disagreements with his view as to what are the complex numbers or angles involved. In any case the ideas of chirality certainly needs to be expanded into a more topological view of space- at least until we can globally see why there is a difference in masses of three generations even when quantum theory would suggest we should not prefer any of the three axes involved. Styles of logical thinking, its syllogisms and all, its threeness, may separately be only valid within their own system and invalid in the other.
Of course nature in the various experiments we undertake will make these same results and conclusions in some logical manner- deducing what we can after all see and Lubos if this is your idea it is a very high level one. Of neutrino information and the mixing matrices and so on, the Majorana or other variety as to how it relates to the totality of number information once the Riemann sphere orientation finds an axis is still a question, yes? I only suggest it requires a little more than two bits to get the full picture- at least 8 rather than four only as these binary and fractal aspects of numbers do seem now to apply to physical processes.
* * *
"Together, these data suggest that there are multiple layers of information stored in the genetic code."
For this I leave you with what is perhaps a more scientific speculation:
The Portal to A Topological Storage of Our Consciousness and Memories:
* 1 the "dancing" state of DNA in this article shows it there a significant amount of the time.
*2 I note in an old post of the Arcadian Functor blog the limit of 1 and 24 in the computations- but as I suggested in a recent post- and the realization of the core of such Pascal analogs as part of the factorial including the rotations of higher dimensional shapes- that the situation for DNA reading could be much more complex ( I used the term "Holy Crapola, if DNA is read this way."
*3 It is clear then that we have to see space and numbers, the vacua in particular, as a little more than the restrictions of two dimensional foundational (and Brane) thinking. How far can we go into the abstractions in say 120 or 720 as a core spacious singularity structured vacuum topology?
*4 In this respect I object to the trying to encode genetics and the chemistry of it all merely in terms of quantum formulism (quantum gravity looping however certainly is still in the running as a major model to consider organically and inorganically.)
*5 To some extent I agree with the spirit of TGD in Pitaken's exploration of consciousness- however, I do not see a good reason to ground it to some micro physical structures in the body and mind other than of course the ability to realize mind is secondary in general if not always to the materialist substratum. But this bit of experimental observation in the link suggests that there are physical structures, internally to the topology, which act as if a portal thru the material structures to access and relate to various topological systems as if just mental.
How else can we lose consciousness and yet upon awakening our memories are in tact- or for that matter how is it we can mask or lose memory even without the loss of physical brain material?
Of course in an even more general theory, just as the issue of mind and matter or of environment or inheritance factors may self adapt or even vanish as some imagine these as false distinctions of dualism, our theories of everything may indeed see these portals and not simply a matter of reductionist energy concerns and quantum tunneling thru some barriers. A related article today suggest muons replacing one electron can make the helium atom act as if a hydrogen, chemically. But in general these weights of things do not necessarily make a living system nonviable quasically if we say replace all the hydrogen with that of heavy water. In that sense the muon is not only a sort of catalyst but also a focus of conserving the general topology.