{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# What is an observer?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On Stories\n", "\n", "\n", "evolutionary stories\n", "\n", "entropy in the eye\n", "\n", "\n", "complementarity quantizes\n", "\n", "what we can classically communicate...\n", "\n", "\n", "\n", "\n", "deeper in the bulk: scale, etc." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the end how to be ready for love.\n", "How to love.\n", "To get everything else out of the way.\n", "To build one's statue.\n", "\n", "To bring here and there\n", "a wormhole.\n", "\n", "\n", "Niels Bohr\n", "Occasions for communication\n", "Randomness the result of:\n", "The failure of a picture…\n", "Agreement \n", "Classical concepts are just: definite rules for humans, etc\n", "Subject/object mobile\n", "As if in the case of a quantum random decision:\n", "We’ve externalized the “will” in an object\n", "Bohr was advocating for something far more profound…\n", "\n", "\n", "Classical and quantum polyhedra -> loops\n", "\n", "Symplectic -> bogoliubov -> unruh etc -> haag \n", " -> syk wormhole \n", "\n", "Law w/o law\n", "\n", "\n", "Prepare to open and not open and some\n", "Acts fit both\n", "Are ambiguous\n", "Problem is interpreting the math in specific cases \n", "\n", "\n", "\n", "Loops stories Circuits closing\n", "We’re swimming upstream \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "--\n", "\n", "In a relativistic world, two things without a relationship which interact can only lead to a random outcome, since there is literally no prior reason. We can shear of relationships and so create this situations.\n", "\n", "Even if the constellation is definite, it's still ambiguous the overall 3D orientation.\n", "\n", "--\n", "***leave to the side questions about consciousness (vs what it is possible to know)\n", "for a later section****\n", "\n", "lack of orientation w/r/t to the outside of one's \"inner world\"\n", "\n", "There remain mysterious about perception.\n", "Perceiving both possibilities. Distinguishing mind vs open mind.\n", "But we could perceive a superposition. \n", "\n", "telepathy is possible, but others can't confirm it\n", "\n", "--\n", "\n", "coming together, or the whole broken apart\n", "Maybe:\n", "\n", "It's precisely when two things are in a separable state that they are entangled *with you*--the point is that you can keep them separate. They have no relationship to each other, and yet you can define a state for them both, indeed, a separable state. \n", "\n", "When two things are in an entangled state, it's precisely when you have no relationship with them: all you can say is that if you fix this guy's axis, then this guy will respond like that.\n", "\n", "But if you have no relationship with them, this can only be defined in terms of a third observer, who is entangled with both of you, and so sees you as separate.\n", "\n", "--\n", "\n", "entangled superpositions, alternative stories...\n", "post-hoc\n", "\n", "--\n", "\n", "Neutral particle \n", "Reasons why spin isn’t classical\n", "Compact groups \n", "\n", "--\n", "\n", "The arrogance of thinking you can measure with impunity\n", "\n", "\n", "Bohm\n", "Freedom in collective\n", "Plasma metals\n", "\n", "--\n", "\n", "Carved out — embedded in something higher \n", "\n", "definite integral\n", "\n", "--\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How to make a wormhole, the ultimate \"communication\"-- aligning here and there and now.\n", "\n", "burping at the same time\n", "\n", "What provides context to the matrices? Connection to experience.\n", "The character of physics : what is invariant under perspectives \n", "\n", "lawlessness\n", "\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A word on dialectics\n", "\n", "Our narrative will follow a particular thread: the generalization of the concept of number until it's adequate to describe the numbers which appear in physics. Along the way, we'll develop all the mathematics required to make simple, illustrative models at each stage, and begin to understand the stakes of even such rarefied subjects as quantum field theory and the quantum theory of gravity. A word to the wise: mathematicians might balk at my notion of the \"dialectical unfolding of the concept of number,\" and the resulting philosophy of mathematics and physics that results. Whether the notion can be made precise or not is for me less important that its role in organizing the mathematics into a narrative progression, which is a great aid to understanding and memory.\n", "\n", "The idea of a dialectic goes back to the beginning of written philosophy. One rather famous example of a philosopher who spent a lot of time thinking about dialectics was Hegel. The caricature runs like this: first, you have a thesis. Then, the thesis calls into existence its antithesis. Finally, the thesis and antithesis are overcome by a synthesis, which resolves them together, but which couldn't have been anticipated by mere analysis of the thesis and antithesis, which are by definition irreconcilable. A new cycle begins: the synthesis itself acts as a thesis, bringing forth an antithesis, etc. Hegel famously used this device to try to retell human history as part of the dialetical unfolding of ideas in a cosmic spirit. Marx tried to apply it to social and economic structures. Its reputation has risen and fallen, tracking the motion of various politics. Whether \"the dialectic\" applies to this or that complicated phenomenon is a difficult question to answer, but the mathematics of numbers is one place where the dialectical pattern can be displayed rather cleanly and persuasively.\n", "\n", "We first establish four dialectical axioms. These are not axioms in the usual sense of formal objects, upon which well defined operations act, from which we can mechanically deduce theorems. Instead, they establish the rules of the dialectic: and unlike a monologue, the results of a dialogue cannot be anticipated beforehand, because of the uncertainty of the other. We'll see in what sense they are like axioms as we go along: they are best explained by using them.\n", "\n", "But here they are:\n", "\n", "### The Four Axioms of the Dialectic of Number\n", "+ You can do something or not.\n", "+ Anything you can do, you can do again.\n", "+ Anything you can do, you can undo.\n", "+ Anything you can do in sequence, you can do simultaneously.\n", "\n", "We can actually be more specific:\n", "\n", "+ You can make a mark.\n", "+ You can make another mark.\n", "+ You can erase a mark.\n", "+ You can symbolize a sequence of marks with a mark.\n", "\n", "With that laid out, let's begin.\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " (Now there could be some restrictions on where a “cut” can take place. Here’s one idea I keep tossing around in my head. One could imagine dividing the world into SUBJECT BODY WORLD, all entangled, and we set up the formalism so that projections all take place on the BODY (including clocks if we’re working with timeless QM, and in general, including all the past choices relevant to the moment being considered), and the rule is that only cuts which are permissible are those that lead to SUBJECT and WORLD being in separable states (of course, having been steered appropriately). This is just one spin on the Heisenberg/Von Neumann cut. Is it paradoxical that the SUBJECT could itself split into multiple disconnected pieces? Finally, in this scheme, one is tempted to interpret the quantum states of the SUBJECT, in their own entangled superposition, in terms of perceptual gestalts rather than “superpositions over outcomes” (re: the theory of constellations). And yet: there is a fixed point, which is our gestalt perception of: multiple possibilities unfolding itself.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Irving’s point.\n", "\n", " Any theory of the mind has as its empirical basis a list of correlations: between the body and experience. \n", "\n", " I poke your brain with some electricity, and ask you: Did I trigger some perception, like the smell of your mother’s cooking? Or no? I’m going over your brain, poking here and there, to figure out which parts of the brain correspond to what we are actually conscious of. The thing is: I can’t directly observe your experience itself. So I have to ask you: Did my poke do anything or not? And you have to tell me.\n", " Well, you aren’t satisfied with that, so you start monitoring the neurons that control my mouth, and learn to decode what I’m about to say it just before my mouth actually moves. And then you press inward into the brain, trying to predict whether I say yes or no before I actually say it. \n", " Maybe this proves in practice impossible, if for example the signal from the poked neuron bubbles out over the whole brain, and bounces around, and then refocuses itself near the part where I tell my mouth what to do so that it would be practically impossible to actually trace the causation the full yway. Or if for example, the brain is highly entangled, so that the the relevant occurrences are taking place at a deeper level of entanglement (correspondingly larger scale of the brain). And if, whether due to quantum effects or semiclassical effects, any attempt to fully map out the firing of our neurons necessarily alters their firing pattern.\n", " But Irving makes an even more profound point about self-consciousness. \n", " \n", " So we ask you: Tell me if you feel something, yes or no. And then we poke a neuron, and then that neuron fires, and then another neuron fires … and then we hit a fork in the road, if neuron A fires, then … you say yes! but if neuron B fires, then … you say no! We’ve done the experiment many times, and have in fact observed this correlation. Great! So we don’t actually need your personal experience anymore, we just poke you, and if neuron A fires, there was a conscious perception associated to the poke; and if neuron B fires, then there wasn’t.\n", " The issue, however, is: what if we hadn’t asked the question.\n", " We asked you a yes/no question, and this prepared you to be in the mindset of answering that question, monitoring your perceptions for any change, while we poke you. And this has a neural correlate: neuron A fires if yes, neuron B fires if no. And so we think we don’t need you to introspect anymore, we can just look at your brain and guess: ah, the person associated to this brain will be experiencing this right now.\n", " But if we hadn’t asked the question, and you hadn’t been in that discriminatory mindset, then there would be no neuron A to trace and no neuron B to trace. There would just be you having an experience, and its neural correlates meanwhile in the brain, but there would be no way to tell from looking at the brain whether the poke was experienced consciously or not.\n", " In other words, we can’t get rid of introspection. The ability to assign neuron A to CONSCIOUS and neuron B to UNCONSCIOUS depends on the subject of the experiment themselves asking the question. (It’s possible that not all brains can ask themselves such questions!) If they aren’t asking themselves the question, then there won’t be any neural correlate to CONSCIOUS vs UNCONSCIOUS. And therefore, we can’t just study brains in isolation from the self. And we have to be sensitive to the fact that “asking yourself whether you are having a perception or not” is not the same experience as “having a perception per se.”\n", " Of course, this doesn’t rule out broader analysis, like: generally speaking, when the visual cortex is firing this way, people see this sort of thing. But that’s a prediction. Even if we know about convolutional neural networks, and watch an image being processed layer by layer, and see the same kinds of connectivity and activation in the visual cortex, in the end, it is self-reporting that is the basis for the study of brain/mind correlations. \n", "\n", " One might say: well, what calculation is happening when we poke you, and neuron A fires or neuron B fires. Like what computation is that the result of? If we know what computation it was, and its meaning, then we maybe could say: well, since this computes whether the poke was experienced or not, then by understanding its meaning (probably having to do with attention), we could then understand why some things are conscious or not, and then predict that directly from the brain.\n", "\n", " But that perhaps jumps the gun. Since it could be that: when we have a perception that we are conscious of, it bounces around, and gets into our rhythm, and induces all sorts of correlations are are good proxies for the thing having been perceived; but that ultimately there is no rule able to be given in the sense of a computation, but only a correlation between body and mind.\n", " \n", " It’s still not clear if actually we are conscious of our entire brains/bodies, only most of it is “folded up” in our perception, in the background, in the white noise, encrypted as it were, and what we are really doing is folding and unfolding, expanding things out, or scrambling them across, so that we are really conscious of our whole selves (even the whole world), but most of it its compressed down into the fringes of our experience, or is perceived as “scaffolding,” like “spacetime.” So that the question isn’t: what parts of our brain are we conscious of and which parts aren’t we conscious of. But the same question as in quantum mechanics: why do we have this perspective, as opposed to any other? And nothing in science offers any answer to that.\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "The book is:\n", "\n", "Transfinite Life: Oskar Goldberg and the Vitalist Imagination\n", "\n", "https://experts.illinois.edu/en/publications/transfinite-life-oskar-goldberg-and-the-vitalist-imagination\n", "\n", "and it's perhaps more interesting for its contextualization of the guy rather than the guy himself! There's an interesting genealogy of late 19th / early 20th century vitalist thinkers that evidently runs through the \"phenomenologists\" like Brentano and Husserl as well as the \"embryologists\" which I hadn't quite realized. It's the end of the 19th century. Everyone's obsessed with the mechanism/vitalism duality: physics seems mechanical and yet look at how in perception the whole comes before the parts, which therefore can't be separated mechanically question mark. Everyone's trying to define what makes an organic whole. But it's the end of the 19th century. We haven't proven atoms exist yet. There's probably an ether. No word yet on anything like DNA. One scientists takes a fertilized frog egg, lets it split for a bit, and then separates it into two pieces. Half a frog grows out of each. Another scientist takes a sea urchin and lets a fertilized egg split for a bit, then gives it a shake to separate it into many pieces, each of which grow into their own smaller sea urchin. The latter is taken by some people to be evidence that the sea urchin is contained \"holistically\" in each of its cells in an \"organic\" non-mechanical way. Well, now we have a more mechanistic explanation in terms of DNA. But at the time, it was seen as part of the argument for holistic, top-down causation--along with the nonseparability of the perceptual gestalt, where the whole perception of seeing you sitting on a chair comes prior to being analyzed into its component pieces, and the pieces only make sense with regard to the perceptual whole. Remember we're converging on whether the world is made of \"atoms\" or not in the science of the time. It's a very live possibility that it isn't, that actually perhaps some kind of \"continuous\"/\"organic?\" math governs the world. Then some Jewish/very neoKantian German thinkers get excited by that and also Cantor's discovery that there are transfinite numbers, where are kinda like \"organic wholes\" in the sense that they \"contain\" for example \"the completed infinity of 1,2,3,4,...\" or \"the completed infinity of the continuous line,\" and also by the late 19th / early 20 century obsession with myth in the context of the colonial era which made all Europeans fantasize about what made them so different in their bourgeois lives from the tribal peoples out yonder, and speculate about \"organic\" forms of collective social organizations, tribes, etc. Our Oskar Goldberg decides to tell a post-WW1 story about how the nation-states lost their way, turned into capitalistic killing machines, divorced from their origins in the holistically unified tribal state, each Nation a God to its people, but sort of in an almost to me comic book like setting, where YHVH manifests in the world at Sinai, the one true God, but the way God set up the world was that if He could Enter it, Any Other Transcendental Powers could also enter it, and so they do, and gather up people of their own, whose lives become holistically organized around sacrifices to that God, etc (I suppose you don't have to read this as a \"racist\" story per se, although he tries to suggest that this is the origin of ethnicities, which in his mind grew up around charismatic leaders in touch with the relevant Transcendental Power, and helping holistically organize the people)--and anyway the one true God YHVH who is the One True God because he is the only Unique One cleaves his people to him, and he's on a metaphysical war against the false gods. 5000 years of civilization go by, and all the old Tribes are scattered and lost, and although the Transcendental Powers are still active, they aren't organized in an obvious tribal fashion, and we still have to join YHVH on his mission to save the world by having everyone appreciate how transcendentally unique YHVH is re: the other gods. And so now we need an organic politics in the aftermath of the Great War.\n", "\n", "Meanwhile, I'm thinking:\n", "In other news, James Joyce shows you can have your cake and eat it two, walking around Greece and Dublin simultaneously. It's the 1920's. And on the other side of the stage, the physicists are just then actually answering the question. Is the universe continuous or discrete, vitalist or mechanical? And the answer is drumroll: both! The universe is actually quantum mechanical! It's made up of quanta, in the sense that measurements always reveal some definite number of quanta, but the math that governs how they evolve in time is continuous! The quanta can join together into complexes called atoms that explain all of chemistry and familiar matter. And in fact, you can have holistic organic wholes in the other sense too! That's just entanglement: there is more information in two entangled particles together, than there is apart. The two parts are defined in terms of the whole; rather than the whole being defined in terms of its parts. So that at its deepest level, the world is not \"mechanical\"-- but there are good arguments that you can use to show why the world looks mechanical in many common circumstances! In other words, the organic-ness is generically *very fragile*. And yet evolution is very powerful... Am I holistically contained in each of my cells? I'm still not sure! But a lot can be explained mechanically via DNA at least with regard to embryos, as I said, so the proof will be trickier. We're probably going to discover all sorts of funny entanglement effects across our bodies. But no one has yet really figured out how to relate all this to perceptual gestalts although of course that is the dream. Von Neumann had his interesting thought about \"psychophysical parallelism\" but I say no one has really been able to unpack it in a truly satisfying way.\n", "\n", "Quantum mechanics unifies the continuous and the discrete, the vitalist and the mechanical, but it doesn't pretend yet to have all the metaphysical answers. In fact, it spends most of its time worrying about the difference between what it doesn't know and what it can't know. Anyway, that's what I was thinking about as I was reading this book! It's a little repetition in a disseration kind of way, but contains lots of interesting details." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "One is reminded of the \"negative theology\" of late Antiquity and the Middle Ages. For example, Maimonides urges us only to define God in negative terms, never attributing some positive quality to God, since after all, all our ideas of qualities are relative human ideas gained through comparison, which can't apply absolutely to God. So it's best to say, instead, what God isn't. In other words, one chases after one idol after another, confusing them each for God, but soon enough the realization sets in that God is (as always) beyond: Well, *that* wasn't God, after all! And so we break our idols, and start over. We can't actually get a positive idea of God; we can only try and fail to capture God's image, realize how we failed, and thus ever so slowly characterize God by *how God can't be pinned down*.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "\n", "\n", "You could ask how much of our general reflections on quantum mechanics are unduly influenced by the particularly nice theory of spin? \n", "\n", "It's very satistifying to be able to say, for example, with regard to a spin-$\\frac{1}{2}$: A superpositon of $\\uparrow$ or $\\downarrow$ in the Z direction is just a spin oriented in the $\\leftarrow direction$. But there seems like a disanalogy in the case of position... \n", "\n", "But what about a position state, where the particle is in a superposition of being at location A and location B? I ask, is it at A? And it's a dumb question because it's at A *and* at B, but I forced it to choose, and so maybe it's there or not. But in the spin case, the equivalent of being at A *and* B was a perfectly comprehensible, classical, if you will state: it was just pointed in some direction on the sphere. But classically, you can't have one thing in two places at once, even if we can describe the wavefunction as a superposition of classical-like coherent states. And so it seems like our luck has run out. \n", "\n", "Arguably, we can't answer this question until we have a final theory of quantum gravity, and really nail down what we mean by \"position\" anyway. But here's something I was thinking about.\n", "\n", "Maybe it's like, if the particle is at A *and* B for me, whereas I'm definitely here, then perhaps symmetrically for the particle, it's definitely \"here\", and I'm the one at two possible locations.\n", "\n", "On that same note, one could (and some have tried) to replace the idea of a position with that of a \"view.\" Whereas I can't imagine a superposition of \"particle at A\" and \"particle at B\" being itself a classical ordinary state of a particle's position, I could imagine that a superposition of a particle being seen from the left, and a superposition of a particle being seen from the right, is just: particle being seen from head on. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "closedness of phase space...\n", "\n", "Equilibrium... and yet complex \n", "Heat equation vs Schrodinger equation\n", "statics vs dynamics\n", "cf baez\n", "\n", "expanded atiyah\n", "electron?\n", "quantum polyhedron\n", "\n", "nlp / tensors\n", "\n", "spin helicity / twistors\n", "\n", "the symbol: \n", "\n", "crypto : error correcting\n", "\n", "quantum game theory : evolution\n", "\n", "horizons\n", "\t\n", "\tcontinuous evolution is like falling thru empty time\n", "\tcollapse is like a boundary in time\n", "\n", "\tfree fall is falling thru empty space\n", "\thorizons are boundaries in space\n", "\n", "--\n", "\n", "find that ellipse code\n", "\n", "multiple polynomials: variety...\n", "\n", "the solar system analogy, and the old quantum mechanics\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "I think if there's a conundrum here, it's like... I was talking to a guy studying category theory and he was going on about making a clear distinction between the \"logical\" and the \"ontological\": in the logical setting, we are dealing with representations, and whether something can be proved to be true in some representation; in the ontological setting, we try to reason about the thing itself in its own terms, independent of representation. If we were feeling in a certain mood, we could try to define the latter in terms of reasoning about the relationships between representations, and then argue that any metaphysics beyond that is a fools errand if we only have access to things via representations: first of all, since if we were working without the mediation of a representation, we wouldn't even be able to articulate the so called \"truths\" aka \"equations\" about it. (Of course, one could imagine a hybrid situation, as seems to be the case, as we have degrees of self-consciousness.) But the situation gets starker when we imagine \"infinities,\" for example: the classic example: are we to imagine the numbers 1, 2, 3... infinity all really exist ontologically in a completed sense, or is it enough to say that any \"logical reasoners\" who agree about the rules for numbers, will agree on what the symbol \"...\" means, which is that you can just keep counting if you want: in other words, we've turned something ontological into something logical: the rules for the '...' symbol. Then again, is it that '\"feeling of opportunity\" that all of us \"counters\" agree on? And then again again, to treat the numbers ontologically is to imagine their completion: the world from the perspective of 1,2,3... itself as it were, irrespective of anyone's perspective on them. Maybe you can attain that mentally. But there's an even more interesting issue there. Since for us, what it means to view the world from the perspective of 1,2,3..., is as much to view ourselves distorted by 1,2,3...'s POV: to wit, it's like our string must get tangled to the extent that we straighten 1,2,3's...\n", "\n", "In the end, however, the basic dilemma is that by definition, you can't prove that things are ontologically complete using logical reasoning. Even if \"ontological perfection\" were true, you could never prove it in terms of some representations. Instead the relationship is direct: all who perceive beauty participate in it, all who wiggle around participate in stringhood: but any confirmation that we both stood there seeing the same thing together requires the mediation of representations which are incapable of making an absolute distinction between the logical and the ontological.\n", "\n", "One interesting wrinkle in this whole story, which became the main subject my conversation with this category theorist, is the status of quantum indeterminism. One could try to imagine the *logical representation* of the *ontological completion* of something like quantum mechanics (aka the quantum state of the universe as a whole for all time), and paradoxically you'd get a representation of the universe as some timeless entangled state with all actual choices TBD, but without any freedom to change the law of the universe-- The first thing to say is that there's kind of complementarity between local and global: to the extent you take a global perspective, the individual choices made by individual subsystems become invisible to you. To the extent you take a local perspective, the entanglements between these choices become invisible. Seeing as we experience ourselves as subsystems in the universe immersed in the circumstance of \"actual choices,\" the relevant question for us w/r/t the \"meaning of our choices\" is: is the law globally fixed for all time, or do these choices (which I regard as my choices, your choices, the choices of electrons, nature's choices) change the very space of possibility? Is all the \"indeterminism\" in the world, all its \"incompleteness,\" the result of not having filled in the \"individual outcomes of experiments,\" while the structure between them, the laws governing them, remains fixed? Or does the incompleteness, the *becoming* of the world, unfold at an even higher level? Due to entanglement, choices across space and time, while random, depend upon each other in the way predicted by standard quantum mechanics, but does the law itself depend on our choices? The issue is that if it did, and I made a choice, whose outcome I couldn't know before hand, I'd have to change my representation of the \"universe as a whole\" to accommodate the change in law. Was I just wrong before about how the universe was already? And this change in possibility space was already taken into account in a higher possibility space? Or was I right before, and now we're all in a new universe because of me! To wit, I could imagine: okay, imagine I make all possible choices, leading to all possible laws, and that's the whole universe, completed. But on the other hand, you could say: as all these \"quantum states of the universe\" are merely provisional representations *for us*, do we actually need to imagine that the whole universe is one big quantum state *for real* beyond all representation? \n", "\n", "On the other other other hand, the only real peril, of course, in rushing to infinity is that you might accidentally hypostasize some accidents-- and attribute to the ALL something inappropriate. It's just that transcending all mistakes to reach the thought of perfection is easier said that done." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "VPython", "language": "python", "name": "vpython" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }