[Fernando Franco]:
Major topic on my list is regarding something I feel you will catch on at once. I learned of it in the sci.physics.research newsgroup, whose message archive you can find online at: http://www.lns.cornell.edu/spr/ Perhaps you already know it. At any rate, there is a thread there regarding this, if interested, I suggest you peruse it.
Do you remember normal relativity? You had X, Y, Z, and T (time)? Well, now we have X, Y, Z, T, and F !!. Where F stands for fractal dimension!!! The whole thing is called Scale Invariant General Relativity. Other keywords are Fractal Spacetime, and Scale Invariance (this last one will take you again to Dan Winter, who is there since ages ago pointing his finger to all what is relevant under the sun).
Let us review the history a little. First we thought all happened in 3 D. Then Einstein and 4D, spacetime. Then Kaluza and higher dimensions. All the way to 11, 26, or whatever dimensions. But what's wrong with all the above? Well, it assumes a few things. And that is always bad news.
Point 1: It assumes an *integer* number of dimensions. Why not a fractionary one??? Who said we do not live in, say PI dimensions (plus time). Or some specific multiple of e (logarithms), or PHI, the golden mean? Who said all the physical phenomena, like electricity, or magnetism, etc, are not the reentrance, partial effects and wigglings of an "incomplete" dimension? (Not even a "higher" one, a la Kaluza, but an "incomplete" one).
True enough, fractals are pretty new, just 30 years or so. Non linearity, chaos, complexity, and so on, will prove to be just different names for the same thing. Children of the concept of "fractional dimension". Its effects. We just upgraded our notion of "dimension" from the integers to the reals (exactly, fractally, and non-coincidentally, since All is just One process, like we did in our generalizations of the concept of "number" through math history. Furthermore, I could conceive even chances of a next revolution, if this one is not enough, leading to hypercomplex dimensions (quaternions, octonions, whatever). But even though fractals are pretty new, fractal thinking is as old a mystic teachings, going as far back as "As above, so below", and probably more, and for the most natural reasons. Madame Blavatsky's Secret Doctrine, circa 1900, is, among another things, a fractal book itself !!!. Almost a treatise on dimensionality. On cosmic branching. But still, this Scale Invariant thing, has been around for almost ten years, and mostly unnoticed. Btw, the man who kickstarted is called Nottale: http://www.daec.obspm.fr/users/nottale/ukliwo12.htm
http://www.daec.obspm.fr/users/nottale/ukmenure.htm
It was god damn time. I've been waiting for this even since I read Blavatsky, some time back. And please, do not get me wrong. There have been some critics already. And perhaps Nottale's formulation is flawed, or incomplete. Nonetheless, my hat goes off for him. THAT is going in the right direction, IMHO. In fact, I just heard that there are even newest shots at it. You might want to check Carlos Castro, from Colombia. I could not check more on him or his references, yet, but I found a most remarkable paper by him (on another subject, but, IMHO, not unrelated, and *most* interesting):
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time, by Carlos Castro and Jorge Mahecha hep- th/ 0009014 v2 12 Sep 2000 ( I assume at http://xxx.lanl.gov/ ) Note the variation, is "Cantorian" fractal spacetime, in this case, and mind-bogglingly enough for the non cognoscenti, full of references to the golden mean (he is not Dan Winter yet, but getting there, and better yet, in full math armour this time). Also please note he says explicitly his results, regarding the Riemann zeta function, are just tentative, non conclusive. Regard it as a good approach in progress. By the way, you might remember a post in Greenglow some time back about fractality found in primes and its connection to the zeta function. This shows tantalizing connections. But I digress, let me get back to the dimensionality story...
Point 2: It assumes a *finite* number of dimensions. Just some of us at this point were guessing that in fact we might be living in N dimensions, which is already a qualitatively different way of thinking. Point 3: It assumes a *fixed* number of dimensions (be it 4, 11, 26, whatever), Why not a variable one??? That is exactly what this new approach addresses. And it implies many things. It is not just that we get fractional dimensions instead of integers. More important than that, IMHO, is that we are passing "from crystalline to fluid". From discrete to continuous. And in an *orthogonal* (i.e., linearly independent) way. A true new variable. This paves the way for the dynamic aspect. True cosmology. How did all start (IFF it started)?. And how did it develop? (which is just the same questions, really, since there is only ONE process going on; it just happens to be fractal).One note on cosmology. It comes in two basic flavours: there was a start, or all is eternal and cyclical. All this new stuff, plus more to come is invariant with respect to that. Either if one conceives the universe as starting, or cycling (possibly passing at some point through a "root" of its function, something like a "ground state"), vacuum), all this holds the same. If one conceives the universe as starting, then this movement to fluidity, to continuity, fractional dimensionality, provides a way for its development to happen. And does so within the frame of a ToE, namely, that All is One, and never stops being so. If one conceives it circularly, then this describes its movements. Topological fluctuations of the vacuum, sort of. In both cases, the move to continuity says nothing regarding if there was a start or not, and IMHO, will not say anything in the future as well. Not because of this line of thinking, at least. Is independent. Just for completeness, the question remains about if there could be yet another chance to line or circle, it does not seem unlikely, given we see helixes all over, and they are a combo of both. But at the true root of that lies a question of *logic*, and it seems the time is not ripe yet for that (coming soon, though).
One final comment on this. Once one has such a mechanism (either of evolution in the sense of creation, or just of cyclical evolution, there is a word that comes to mind to describe this process. That is *decoherence*. It so happens that that particular word seems to be being used at the time by physicists. I tried to check, but even though I read a few things, it remains unclear to me at the moment. The context seems to be similar (wave collapse, for instance), but I strongly suspect they refer to something different. Let me clarify a bit what I mean by it...
It is the old philosophical problem of the One and the Many. How does One thing become Many? By division, seems the obvious answer, does it not? However, let us remember that we are seeking a ToE. A unified field. So we should rephrase the above question to... How does One become Many without stopping being One? Still seems a bit of a contradiction, unless we change it again to..."How does One *apparently* become many?", which is much more logical, since it never stopped being a One thing and One only. This new formulation takes into account the fact that the very question is asked by observers, which are immersed in the very process. That is, takes "perception" into account. The relative with respect to the absolute, the part with respect to the whole, if you so wish. Note that it still is incorrect, though, because the "observers" are part of the whole as well, and not distinct from it. But even though I could go into the geometry and topology of consciousness...let me not digress. *Coherence* seems to me something much more basic in itself that most of the concepts used more commonly by physics nowadays. We have seen it in action in things like coherent light, lasers, cutting through metals, so is officially no longer just mystics talk, thank god, and we can proceed on it. Coherence: co-here, the capacity to occupy the same space at the same time (or the same state, like in quantum physics, if you wish). Things in phase. Harmonic. No auto-interference. In short, the result of phase conjugation. And the way to *warp*. To co-here the vacuum. the opposite process than that of "creation". Decoherence, as I mean it, at least, would be just its opposite. To go out of phase, to bifurcate, etc., etc. It is not difficult to see how it relates to dimensionality. One can conceive the cosmic process as a departure from a starting state (linear case), or from a ground state (circular case). Today we speak of vacuum fluctuations. Of course, that was what Pythagoras was all about, and Hermes, and everyone else.
May I share with you a little gem it just downed on me? I was rereading, as I do constantly, Blavatsky's Secret Doctrine. In the middle of describing an ancient manuscript's account of how and why it all happens, and how next "things" sprout from the former, she says something like...> and those globes have children...which are at the same time their children and their brothers< !!!! Most curious expression, wouldn't you say? I wondered for years what the heck she might be talking about. A few days back, then, I was thinking...is the number one an integer, or a rational? Is it 1, or 1/1? Does it not have children (rationals) which are at the same time its children and its brothers? Note that exactly the same pattern we find each time we expand (should I say "quaternionically bifurcate"?) our notion of "number". Same thing I said about 1, could be said for the complex (1,0). Or for any unit, for that matter, be it quaternions, octonions, or whatever. In short, she spoke of laya centers, or neutral centers (in Keely's parlour). We would say today " nested relative zeropoints ", or invariant longitudinal or scalar waves, or a dozen more. "That which splits both intra and inter dimensionally". of which the golden mean is, of course, the golden path...and unique. Invariant both transversally and longitudinally at the same time. Keeping its information (its angle) both intra and inter dimensionally. etc., etc. I assume you notice all the same regarding neural nets, and I assume that's what's behind Hnet, either in its original form, or in your own improvement. Perhaps I could improve as well. Anyway, decoherence. I reckon we will be using that word much more very soon (in the described sense).
Which leads me to a side thing.
I was probably following the eikonal/moebius thread as intensely as you did. As you know, though, I do not post, by principle, in Greenlgow, so there was no feedback from me there, but, yes, I did. Furthermore, I did not fail to see your references to being working on it and Maxwell. At some point, as well, neither did I fail to see you somewhat tired. Most understandable, trust me, I know as well. And I understand you very well. I Did not fail to see, finally, some references to "getting ark and going aside". (in that case, count me in, please). In short: Any progress? Care to share? I remind you I'm not a mathematician, nor a physicist. But I have been reading many convergent things for quite a time, now. And I feel perhaps I could feed back some.