Back to the Cave..... the Allegory of the cave, that is......
In its postmodern setting, the Allegory becomes the metaphor of the Holographic universe. To get a handle on this topic, just look at holographic-duality.
I've been struggling with this topic for several years, and still am just scratching the mathematical surface of it. Paul Z is digging deeper.
The holographic model may also be cast into the frame of the Kantian and Bohmian dualities, i.e. the phenomenal/noumenal duality. That is where I would like to take it.
With this latter objective in mind, I am particularly interested in the more recent and mundane uses of this duality, in the context of condensed matter physics
But, right away, there is a conceptual problem......
There is the general requirement that the holographic duality must contain, as one of its elements, a gravitational component, since only thus may the Beckenstein bound be invoked, which concept lies at the heart of the duality.
But it goes further than that...... Most generally, the gravitational side of the duality contains a 'black-hole', even in these decidedly non-cosmological models of the duality. This is a strange leap of mathematical faith, which, after a day of dilligence, I have not seen addressed, other than to aver that the mathematics seems to work, so don't worry.
That mathematical leap does nothing to aid my intuitive sensibility, which is my only compass in such abstract waters. OTOH, one could infer that there is hereby granted a public poetic license wrt these models. The 'black-hole' could be the philosopher's stone, for all that the mathematicians could care.
Hey, give me an inch, and I will take a mile.
All I have to do now is get my metaphors in a row, which, to be sure, is rather like herding cats. But I do have to do something with that sore-thumb, BH, sitting right in the middle of the pie.
And, then, on top of the BH pie, like so much whipped cream, we have the renormalization-group flow. That flow generally has a source and a sink, which are the so-called UV and IR fixed points, respectively, and the flow is irreversible, although I'm not sure what that means, in this, again, very abstract context. More license, anyone?
Ok, so we have taken holography from cosmology to condensed matter. What is preventing us from extending that domain into biology and neuroscience? What do we have to lose, but our reductionistic nihilism, which is precisely nothing.
More to the point is what do we have to gain? Coherence??
11am--------
I'm looking for something more specific than poetic license. I'm looking for a physical loophole that will be amenable to, or an opening toward, metaphysical construction or extension.
Previously, all that we had was the Cartesian 'pineal gland'. After that came the quantum loophole in Newton's deistic, watchmaker universe. There developed a cottage industry around the notion of the quantum-mind. Our foot in that door was the question of whether the universe was more like a great machine or a great thought.
With the BPWH, I stood on no one's ceremony, but Gottfried's, and barged right through the door...... slam, bam, thank you, ma'am. But did anyone notice? Seems not, hardly, now does it? Even the Ronster, just last evening, asked, oh-so innocently, what is a 'moap'. I said it's a MoAPS, and he said that he had thought the Princess was just lisping. Do you think I could make this up?
And now we have holographic duality on both the cosmic and microcosmic levels. Will more people be tempted to venture through the quantum door? To jump down the rabbit-hole? To step into the Wardrobe? Take the pink pill? Turn around in the Cave to seek the Source? Crash the gates of heaven? I don't see the stampede, not quite yet. But do you hear the sibilance of the long withdrawing roar, and of ignorant armies clashing by night? What great beast slouches toward Bethlehem?
One way to understand the license of the quantum is to understand the power of the imaginary unit, 'i', or the root of -1. Up until Schroedinger wrote his wave equation, 'i' had just been a curious but powerful mathematical tool, but, now, especially with the Heisenberg uncertainty principle, [p, x] = 'i'h, that little curiosity found its pride of place at the very heart of physics. What hath God wrought?
With the advent of 'i', analytic continuation became the bedrock reality of all physics. Now, with holographic duality, we have another kind of analytic continuation. But is that all..... just another fancy tool?
noon--------
But is this continuation only analytic? Might it not also have a 'synthetic' construal?
Synthetic? Holistic?
What are the rules of the hologrphic 'continuation' game? Here is one thing that I picked out of all the mathematical noise (also preening, yes, of course).......
In the context of condensed matter, the notorious 'landscape' problem of string theory, becomes a cornucopia of possibilities for the meta-materials of solid state physics.
Well, excuse me, but, since when was biology not a meta-material?
Where string theory gets lost in the desert of the unnavigable landscape ambiguities, biology finds its teleological mana, yes, Lamark, just follow the breadcrumbs.
And let us not forget the hairless hole problem..... Could I make this up? No, Johnny W did.
On the cosmological side of holography, the black holes have no hair. But, on our side of that coin, it's the shaggier the better, for those holistic holes. Hey, could I make this up?
Man may be the Measure(r), but who shaves the shaggy mathematician? Bertrand R, or that guy from Saville, or was it on Fleet street?
Like the poor wallflower, the mathematicians are sitting on a goldmine, and they don't even know it. And, excuse me again, but what did Confucius say about the inverted pilot of that other persuasion?
Srinivasa was able to catch glimpses of the Source. We're still trying to make sense of those crumbs. To what path do they point? Where is the telos? If we are not already on that path, then someone is asleep at the switch, and I don't mean us. We are still supposed to be sleepwalking. I mean the other gal, and not necessarily Amelia, either.
2pm--------
I have a long-standing interest in the organicity of mathematics. Holographic continuation might be where that rubber can finally meet the road.
Speaking of the negative root, many folks suppose that this organicity begins with Euler's identity e^i*pi leading to z'=z^2 + C, the Mandelbrot. The next stop on that path would be Witten's monster with E8xE8. That is where the path becomes obsured in ambiguity. We then pin hopes on the Fields medal and beyond....... with Srinivasa still pointing the way.
But how can biology get into that act? With Jack S, it's all about the non-linearity of the quantum. Can we point to the insufficiency of Jack's gambit?
The fact that it does not make use of the Landscape. Or maybe it does, in his mind. Or, the organicity of math?
(cont.)
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