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conductor(generic_systems_fields): Phase 1 Acquire - transcript (885 clean segments, 30KB) + 58MB mp4
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Phase 1 Acquire for generic_systems_fields: https://youtu.be/QeMajYvhEbI
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Artifacts: C:\projects\manual_slop\conductor\tracks\video_analysis_generic_systems_fields_20260621\artifacts
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Step 1: extract_transcript (yt-dlp VTT directly)
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OK: wrote C:\projects\manual_slop\conductor\tracks\video_analysis_generic_systems_fields_20260621\artifacts\transcript.json (1751 segments)
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Step 2: download_video
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OK: wrote C:\projects\manual_slop\conductor\tracks\video_analysis_generic_systems_fields_20260621\artifacts\video.mp4 (60755152 bytes)
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{
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"status": "ok",
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"video_path": "C:\\projects\\manual_slop\\conductor\\tracks\\video_analysis_generic_systems_fields_20260621\\artifacts\\video.mp4",
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"transcript_path": "C:\\projects\\manual_slop\\conductor\\tracks\\video_analysis_generic_systems_fields_20260621\\artifacts\\transcript.json"
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}
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I want to talk today about interesting
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behavior by generic systems.
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And the first part of this will be a bit
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of a review and then the second half
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will be more u a report on new work uh
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since the last time I talked which
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uh as a general presentation was over a
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year ago. I did a couple of more
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specialized presentations last year. So
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this is in the context of the diverse
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intelligence project
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which raises these questions u how
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diverse is intelligence
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and what what are the limits of
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intelligence uh if there are limits and
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how do we find out so that's what I'm
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going to talk about today
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uh to start with um
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we can look at this definition of
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intelligence that we've been using in
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the lab from William James as as kind of
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a guideline
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that intelligence is a fixed goal
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achievable with variable means of
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achieving it. So intelligence involves
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ing it. So intelligence involves
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some level of flexibility
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and this definition itself raises
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questions. Uh does any goal count? Uh
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are many any kinds of means allowed
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and does anything fall outside this
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|
definition? Are there any are there
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systems that don't achieve this kind of
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flexibility that James was interested
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in? And um it's not clear from from
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James the extent to which he was willing
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to extend intelligence
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uh to generic systems,
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but at at least some of his writings
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suggest that that may have been the
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case.
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Um
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some sort of methodological guidelines
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uh have appeared recently. Uh, for
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example, in this paper that Mike and
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David Resnik published last year,
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uh, emphasizing that the
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diverse intelligence project or the the
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TAM framework,
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um,
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emphasizes methodologically
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a reliance on empirical research, not on
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intuition for thinking about
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intelligence.
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and um an insistence on testable methods
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for understanding uh what is and is not
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intelligent and the extent to which
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things are intelligent. So I I want to
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follow this kind of empirically oriented
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framework as opposed to making
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philosophical assumptions upfront.
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And in thinking about this um an obvious
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place to look is the literature of the
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free energy principle.
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So here's um a recent paper from Carl
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Fristen's group
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um their most recent actual technical
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elaboration of the free energy principle
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and they describe it as describing a
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simple relationship between the dynamics
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of random dynamical systems and
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inference
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and that of course has been the theme of
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the free energy principle for almost 30
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years now that random dynamical systems
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uh can be considered inferential.
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But when you look into this paper
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um here's figure two
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already we find an assumption that
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there's some systems that are inert that
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don't act on the world at all.
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And that's a problem because a system
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that doesn't act back on the world when
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the world acts on it is violating
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Newton's third law. So it's it's
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violating a very basic physical symmetry
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principle.
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So
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this picture uh at least appears to
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involve uh intuitions about inertness.
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Uh and the the trademark inert system is
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a rock uh in much of this literature
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that may not stand up to scrutiny from
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the point of view of fundamental
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physics.
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So uh in that case I think we need to
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take an approach where we look at
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physics first and worry about intuitions
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later.
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So if we have a system which I'll call a
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and it's interacting with something else
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which I'll call a bar or the complement
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of a for reasons that will become clear.
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How do we guarantee that this
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interaction respects all of the physical
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symmetries that it needs to respect to
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comply with known physical theory or
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empirically supported physical theory.
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And what we want is a generic case that
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describes any interacting system
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regardless of its scale or its
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structure.
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And um I'll add here since
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the whole talk will respect this uh
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regardless of its embedding in spacetime
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what it looks like as a as a thing in
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spacetime.
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So how do we do that? And the answer is
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we start with the generic case.
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So let's assume the simplest thing we
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can assume
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which is a system that doesn't interact
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with anything. So a system that doesn't
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have an environment.
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Um so a system that's isolated.
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And if we start with that, um, we know
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that we're going to respect the various
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symmetries that have to do with not
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having singularities because there's no
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there's no place for information to flow
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from into this system and no place for
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information to flow to because there's
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no environment. So there aren't going to
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be sources or syncs.
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So whatever dynamics this system has, it
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has to conserve momentum and energy and
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information.
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U so
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the technical term for conserving
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information is unitarity
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and it turns out that this is a very
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productive assumption.
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If we have conservation of information
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in other words unitarity
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then we can represent the dynamics as a
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linear operator
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um because nonlinearities
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uh don't conserve information.
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So this dynamics that I've called P of U
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the propagator of U is a linear operator
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on some state space. And in fact we can
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make the state space a Hilbert space
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which is a particularly simple kind of
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vector space. It just takes every
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possible value of every possible degree
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of freedom and makes it a basis vector.
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So if we assume some background time t
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which is just a symbol that lets us talk
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about change.
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Uh we can write this propagator
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uh as a periodic function of another
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operator which represents the energy of
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the system. That operator is the
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Hamiltonian
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which plays essentially the same role
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here that it plays in classical physics.
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It's a measure of energy
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and when we write this equation um it
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requires introducing a constant which is
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finite and which has the units of action
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and a finite value of this constant
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um corresponds to there being no no
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singularities. Clearly if that symbol h
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bar was zero
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there would be a singularity and if it
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was infinity there would be a
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singularity. So it needs to be finite.
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Now this theory is quantum theory
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of an isolated system.
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So in a sense isolation is all you need
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to get quantum theory. Uh it's a it's a
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good way to start because it gets you
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someplace that we understand
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and that we have empirical reasons to
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think is a good description of generic
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systems.
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So if everything is linear, the dynamics
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is linear, we can do a linear
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decomposition of the dynamics.
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So we can split this isolated system U
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into the components that we're
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interested in some system that we want
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to talk about uh A and and its
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environment now A bar which is just
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everything else in U that isn't A and
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that introduces the idea of a boundary
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between the two. Um and the linear
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decomposition is a decomposition of this
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operator h the Hamiltonian
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and we can decompose it into the sum of
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three terms. A term for the left side, a
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term for the right side and a term for
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the interaction.
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So a nice thing about quantum theory, it
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has this simple representation of
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interaction and it's linear.
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So this is a generic symmetry preserving
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representation of interaction between a
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system and and everything else.
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Now we can continue decomposing this
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interaction term again additively
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um as a sum
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of operators that act on single quantum
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bits. And some some of you have seen
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this kind of picture before in uh
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previous talks, but these operators are
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very simple. They're just operators that
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measure the spin of a quantum bit. And
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each one of them is equipped with a
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reference frame that says what direction
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counts as Z since this is a Z spin
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operator. And Z can be chosen to be
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anything. and it can be chosen uh in
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different ways for different cubits.
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But this turns this boundary B into a
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holographic screen. So there's a lot of
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physics that can now be imported to talk
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about this boundary. And I'm not going
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to really talk about that physics today.
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Uh we're just going to go on.
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Um this Hamiltonian now tells us how a
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and a bar act on each other. they act on
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each other by changing the values of
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cubits.
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Uh what we wanted though is to
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understand how a and a bar influence
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each other. How information flows from
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one to another.
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And these are the same uh if and only if
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one condition is met that a and a bar
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have conditionally independent states.
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So that we could talk about the state of
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A and the state of A bar.
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And that's a simple requirement. We have
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to require that the joint state the
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state of the two systems factors into
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the state of the one system and the
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state of the other system.
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And this is in quantum theory called
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separability. And it's the same as the
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absence of entanglement.
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So systems
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have their own states. if they're not
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entangled.
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And entanglement just means factoriz or
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non-entanglement just means
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factorizability.
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And of course that maps over into
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classical systems. If classical dynamic
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system has a markoff blanket then the
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then it factors
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and we know what separability requires.
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It requires sparse coupling.
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So formally this interaction has to have
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a small dimension and since it's an
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operator its dimension is well defined
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and by small it means its dimension is
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much less than the dimension of either
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of the other operators in the picture
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the internal operators for a and a bar.
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So intuitively the evolutions of these
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systems have to be almost independent
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for their states to be separable and for
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the interaction to actually capture all
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of the influence of one system on the
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other.
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So what we've done here is reconstruct
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the free energy principle from minimal
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physics. And again u at least some of
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you have seen this before.
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If uh these two systems A and its
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environment are separable, so they meet
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this dimensionality constraint on the
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Hamiltonians,
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then the Hamiltonian fully describes
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information exchange. The boundary
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functions as a markoff blanket. Uh the
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variational free energy is a measure of
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the interaction strength.
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uh minimizing VF VFE which is what the
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free energy principle is about is
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keeping the interaction weak while
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allowing thermodynamic exchange.
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So it's it's keeping the interaction
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between the system and its environment
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fairly weak while enviring allowing the
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system to eat some of its environment to
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|
to provide enough energy to live.
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And in this case predictability which is
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what the system is after is constrained
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interaction. So it's constraining the
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interaction in a way that's consistent
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in a way that's consistent
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with staying alive.
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So ANA bar maintain their identities as
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distinct systems only while their
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boundary um remains a markoff blanket.
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So there can't be any rips, there can't
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be any explosions, other sort of huge
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excesses in interaction strength.
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So that's actually what the FE is about.
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It's about keeping interactions small
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enough to maintain the integrity of a
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boundary and that's what's required for
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persistence over time as a well-defined
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system
|
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|
and this follows uh just from very
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||||||
|
minimal physical assumptions.
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|
So now if we go back to Jane's Jane's
|
||||||
|
definition of intelligence as a fixed
|
||||||
|
goal with various means of achieving it,
|
||||||
|
we can ask um is there always a goal?
|
||||||
|
Does any goal count? And the FEP always
|
||||||
|
gives us one goal continuing to exist.
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|
uh any system that
|
||||||
|
persists through time acts inferentially
|
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uh as if it's trying to continue to
|
||||||
|
exist. This is what Jacob Howey calls
|
||||||
|
self-evidencing
|
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|
as an interpretation of the FEP.
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Are any means allowed? Well, yeah.
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|
Whatever the internal dynamics are
|
||||||
|
capable of is an allowed means for
|
||||||
|
keeping the boundary intact, for keeping
|
||||||
|
the interaction uh weak but still open.
|
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|
And does anything fall outside of this
|
||||||
|
definition? No. It's completely generic.
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|
At least it's completely generic for
|
||||||
|
systems that are physically realizable.
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|
um so systems that actually respect the
|
||||||
|
sorts of symmetries that our physics
|
||||||
|
requires.
|
||||||
|
So from this point of view, intelligence
|
||||||
|
looks like something that could be
|
||||||
|
generic.
|
||||||
|
The question then becomes not what's
|
||||||
|
intelligent, but is its behavior
|
||||||
|
interesting?
|
||||||
|
Um maybe everything is intelligent but
|
||||||
|
some things are completely boring. They
|
||||||
|
don't behave in ways that are
|
||||||
|
interesting.
|
||||||
|
So our question about intelligence
|
||||||
|
really turns into a question about
|
||||||
|
interestingness. Are there limits on
|
||||||
|
what kinds of systems can exhibit
|
||||||
|
interesting behavior? And if there are,
|
||||||
|
how do we find out? How do we find out
|
||||||
|
what the limits are? And how do we find
|
||||||
|
out what sorts of systems actually
|
||||||
|
display interesting behavior?
|
||||||
|
And if we're going to ask this question,
|
||||||
|
we have to know what interesting means.
|
||||||
|
So here's some ways of characterizing
|
||||||
|
interesting behavior. Um
|
||||||
|
so if it's interesting, we want it to be
|
||||||
|
surprising.
|
||||||
|
uh maybe it's unpredictable in practice
|
||||||
|
or only predictable approximate
|
||||||
|
approximately with some amount of coarse
|
||||||
|
graining. So if we don't measure what
|
||||||
|
the systems doing with too much
|
||||||
|
precision
|
||||||
|
um maybe we can predict what's going on
|
||||||
|
but if we really look closely it's it's
|
||||||
|
going to be uh less predictable.
|
||||||
|
Maybe the system is unpredictable in
|
||||||
|
um systems seem to be interesting if
|
||||||
|
they can learn from experience, if their
|
||||||
|
um behavior depends on their memory, if
|
||||||
|
it depends on the context they're in.
|
||||||
|
Uh and we can get really radical here.
|
||||||
|
some systems may have distributions of
|
||||||
|
outcome values that actually violate the
|
||||||
|
Kaggoro vacs. So the outcome probability
|
||||||
|
distributions are undefined. That's
|
||||||
|
really interesting.
|
||||||
|
But operationally,
|
||||||
|
what this all comes down to is that
|
||||||
|
if we measure a bunch of state
|
||||||
|
transition probabilities for some finite
|
||||||
|
amount of time, they don't converge to
|
||||||
|
predictive adequacy.
|
||||||
|
So induction uh doesn't work or doesn't
|
||||||
|
work very well or only works if we
|
||||||
|
severely coarse grain things.
|
||||||
|
So the sort of mechanical expectations
|
||||||
|
that we've inherited from 19th century
|
||||||
|
science are violated
|
||||||
|
and we know that life does this. Um,
|
||||||
|
if you observe a baby for a while,
|
||||||
|
you're not going to be able to predict
|
||||||
|
what happens as an adult uh to that
|
||||||
|
person or how that person behaves as an
|
||||||
|
adult. In fact, if you observe an adult
|
||||||
|
for a while, you can't perfectly predict
|
||||||
|
what they're going to do next. So, life
|
||||||
|
life doesn't satisfy these sorts of
|
||||||
|
mechanical expectations.
|
||||||
|
But what else violates them? Uh that's
|
||||||
|
what we're going to be interested in
|
||||||
|
finding out.
|
||||||
|
And we have some hints.
|
||||||
|
So here's a old hint from the 1950s from
|
||||||
|
cybernetics.
|
||||||
|
Edward Moore showed that finite input
|
||||||
|
output experiments can't uniquely
|
||||||
|
determine the the machine table which
|
||||||
|
just means the in internal state
|
||||||
|
transition probabilities
|
||||||
|
of a generic classical black box.
|
||||||
|
And um the canonical example of that is
|
||||||
|
a a box with a clock. So something like
|
||||||
|
a time bomb where the behavior can
|
||||||
|
change abruptly after some amount of
|
||||||
|
time. And if you don't observe it
|
||||||
|
through that change of behavior, then
|
||||||
|
you can't predict what's going to happen
|
||||||
|
next.
|
||||||
|
Here's another more recent hint from um
|
||||||
|
Conway and Koken. The free will theorem.
|
||||||
|
Here Conway is John Conway from the game
|
||||||
|
of life.
|
||||||
|
They published what they called the free
|
||||||
|
will theorem
|
||||||
|
which shows that special relativity and
|
||||||
|
quantum theory together rule out local
|
||||||
|
determinism
|
||||||
|
and rules out local determinism in a
|
||||||
|
very strong form. Uh the whole pass like
|
||||||
|
cone of a system can't determine its
|
||||||
|
behavior
|
||||||
|
if special relativity and quantum theory
|
||||||
|
are combined. So their slogan in their
|
||||||
|
first paper in 2006 was if experimenters
|
||||||
|
make choices electrons do too.
|
||||||
|
So that's a pretty strong hint that even
|
||||||
|
electrons can exhibit interesting
|
||||||
|
behavior.
|
||||||
|
And then a third hint uh is this paper
|
||||||
|
from Frank Tipler in 2014
|
||||||
|
where he showed that the simplest way to
|
||||||
|
remove the singularities
|
||||||
|
from classical physics
|
||||||
|
uh actually reproduced the quantum
|
||||||
|
potential postulated by David Bone in
|
||||||
|
his formulative formulation of quantum
|
||||||
|
theory. And basically what the quantum
|
||||||
|
potential does is make the motion of any
|
||||||
|
given particle dependantly
|
||||||
|
on the motion of every other particle in
|
||||||
|
the universe.
|
||||||
|
And interestingly uh Nicholas Jesus
|
||||||
|
pointed out that back in the day of
|
||||||
|
Newton and lelass
|
||||||
|
uh before the 19th century physics
|
||||||
|
wasn't singular because it was basically
|
||||||
|
about gravity
|
||||||
|
and gravity wasn't local. Every particle
|
||||||
|
did actually behave on depend on what
|
||||||
|
every other particle in the universe was
|
||||||
|
doing instantaneously.
|
||||||
|
And it was Einstein who introduced
|
||||||
|
strict locality by requiring information
|
||||||
|
to only flow at the speed of light.
|
||||||
|
So these hints sort of suggest that
|
||||||
|
generic systems can display interesting
|
||||||
|
behavior. So the question is how do we
|
||||||
|
make this precise? How do we understand
|
||||||
|
it? How do we use it? So that's what I'm
|
||||||
|
going to try to talk about in the
|
||||||
|
remaining time.
|
||||||
|
So here's the setting again. Uh we have
|
||||||
|
a system. It's interacting with another
|
||||||
|
system which is its environment. There's
|
||||||
|
a boundary between them that the
|
||||||
|
interaction flows through. So
|
||||||
|
observations and actions live there on
|
||||||
|
the boundary. U actions of A on A bar
|
||||||
|
and actions of A bar on A.
|
||||||
|
And u A's measurements and action
|
||||||
|
choices are computed by its internal
|
||||||
|
dynamics. That's true for AA bar also.
|
||||||
|
In FE language, that computation is done
|
||||||
|
by A's generative model. Same applies to
|
||||||
|
Abar.
|
||||||
|
The system satisfies this dimensionality
|
||||||
|
constraint. So we can also think of it
|
||||||
|
as the dimensionality of the boundary is
|
||||||
|
much smaller than the dimensionality of
|
||||||
|
either system.
|
||||||
|
But the thing to keep in mind is that
|
||||||
|
inputs and outputs, so behavior is much
|
||||||
|
less complex than the computations that
|
||||||
|
generate inputs and outputs. So behavior
|
||||||
|
is less complex than the computations
|
||||||
|
that generate it generically.
|
||||||
|
So this immediately tells us something
|
||||||
|
important
|
||||||
|
that recurrence of states on B.
|
||||||
|
So seeing the same behavior does not
|
||||||
|
imply recurrence of the internal
|
||||||
|
dynamics of the system that's exhibiting
|
||||||
|
the behavior.
|
||||||
|
And in particular, the probability of a
|
||||||
|
behavior given the internal dynamics is
|
||||||
|
not the same as the probability of the
|
||||||
|
internal dynamics given the behavior.
|
||||||
|
So behavior generically depends on
|
||||||
|
hidden states um which we can think of
|
||||||
|
as memory or internal context or
|
||||||
|
something like that.
|
||||||
|
And formally we can always represent
|
||||||
|
that as an internal geometric phase.
|
||||||
|
what's also called a Barry phase after
|
||||||
|
um can't remember his first name Barry
|
||||||
|
who first characterized it almost in
|
||||||
|
general for for adiabatic systems
|
||||||
|
and as as Chris Fuches the uh physicist
|
||||||
|
who in came up with the cubist
|
||||||
|
interpretation of quantum theory put it
|
||||||
|
all physical systems have interiority
|
||||||
|
and here he's also very influenced by
|
||||||
|
William James I think interiority is
|
||||||
|
actually a Jamesian term.
|
||||||
|
So what is this geometric phase?
|
||||||
|
It's it's just an apparent phase change
|
||||||
|
that results from transporting a vector
|
||||||
|
or some collection of vectors around a
|
||||||
|
path in an internal state space.
|
||||||
|
So here's an example um the right hand
|
||||||
|
side of the screen. If you have a sphere
|
||||||
|
and you start with a planer a
|
||||||
|
two-dimensional coordinate system up at
|
||||||
|
the north pole and you transport that
|
||||||
|
coordinate system smoothly down to the
|
||||||
|
equator and then you transport it a bit
|
||||||
|
to the east on the equator and then
|
||||||
|
transport it back up north. It's going
|
||||||
|
to look like you've introduced a 90deree
|
||||||
|
phase change in the coordinate system.
|
||||||
|
But nowhere in this process have you
|
||||||
|
done any rotation.
|
||||||
|
Uh you've just transported
|
||||||
|
uh this system in a in a parallel way
|
||||||
|
without changing the system at all
|
||||||
|
around in the state space but the state
|
||||||
|
space happened to be curved. So these
|
||||||
|
are called holonomy operations.
|
||||||
|
Uh and purists call them anholony
|
||||||
|
operations.
|
||||||
|
um but physicists just call them
|
||||||
|
holottomy operations and they're not
|
||||||
|
much talked about in biology
|
||||||
|
but there is this paper from 2026 from
|
||||||
|
Marcel Blatner
|
||||||
|
that applies this sort of thinking to
|
||||||
|
plenaria
|
||||||
|
and he does it in a framework he calls
|
||||||
|
tangential action spaces but if you go
|
||||||
|
back and look what he means by that he's
|
||||||
|
really just talking about uh holomy
|
||||||
|
transfer formations.
|
||||||
|
So this is this is work that's starting
|
||||||
|
to be applied biologically
|
||||||
|
but to see why it's important
|
||||||
|
um it's important because non-trivial
|
||||||
|
honomy is actually a provably sufficient
|
||||||
|
resource for universal quantum
|
||||||
|
computation.
|
||||||
|
So if you want to build a universal
|
||||||
|
quantum touring machine, you actually
|
||||||
|
only need one ingredient and that's
|
||||||
|
non-trivial holomy in the search space.
|
||||||
|
And it works because it allows you to
|
||||||
|
construct a map from an observable
|
||||||
|
boundary state, an input and an internal
|
||||||
|
state to some other observable boundary
|
||||||
|
state, an output and some other internal
|
||||||
|
, an output and some other internal
|
||||||
|
state. for arbitrary input and output.
|
||||||
|
. for arbitrary input and output.
|
||||||
|
So you can you can implement any
|
||||||
|
computation just with holonomy and this
|
||||||
|
has been known for 25 years. Uh but it's
|
||||||
|
only really been known in the quantum
|
||||||
|
information community.
|
||||||
|
So um
|
||||||
|
computing by holom is actually stayed
|
||||||
|
basically within the quantum computing
|
||||||
|
community.
|
||||||
|
So to see why this is important um or to
|
||||||
|
see its larger implelications,
|
||||||
|
I think it's important to think about
|
||||||
|
what a physically implemented
|
||||||
|
computation is.
|
||||||
|
Uh physically implemented computation is
|
||||||
|
just a mapping
|
||||||
|
from the behavior of some physical
|
||||||
|
system. The observable behavior. So the
|
||||||
|
observable of the behavior of the
|
||||||
|
boundary of that system
|
||||||
|
to an abstract representation of a
|
||||||
|
computable function.
|
||||||
|
And
|
||||||
|
saying that
|
||||||
|
um some device implements a computation
|
||||||
|
is just saying that these kinds of u
|
||||||
|
diagrams commute
|
||||||
|
where you're either mapping the behavior
|
||||||
|
into the symbolic representation of the
|
||||||
|
computation
|
||||||
|
or you're mapping the symbolic
|
||||||
|
representation of the computation into
|
||||||
|
the behavior by either a projection or
|
||||||
|
embedding.
|
||||||
|
And obviously this only works for
|
||||||
|
computable functions
|
||||||
|
because if you can't compute the
|
||||||
|
function f, you can't determine whether
|
||||||
|
these diagrams commute. So this is a
|
||||||
|
definition of implemented computation
|
||||||
|
for computable functions.
|
||||||
|
And this interpretation
|
||||||
|
is a projection uh into the behavior. So
|
||||||
|
that's important.
|
||||||
|
Because embeddings are injective.
|
||||||
|
Embeddings are one to many.
|
||||||
|
Um you can embed lots of different
|
||||||
|
computations in any given behavior. And
|
||||||
|
that tells us something that poly
|
||||||
|
computation is actually generic.
|
||||||
|
Um and indeed managing thermodynamic
|
||||||
|
flow. So keeping your system alive uh
|
||||||
|
requires that the informative behavior
|
||||||
|
that you're you're interested in
|
||||||
|
describing computationally is just a
|
||||||
|
proper sample of the total behavior.
|
||||||
|
U and that's true even for your laptop.
|
||||||
|
You know we're not looking at everything
|
||||||
|
the computer is doing when we're looking
|
||||||
|
at the screen particular. We're not
|
||||||
|
looking at all the thermodynamic
|
||||||
|
exchange that keeps the thing running.
|
||||||
|
And the same is true for organisms.
|
||||||
|
Uh we're not necessarily looking at the
|
||||||
|
caloric content of what they're eating
|
||||||
|
when we're trying to do their
|
||||||
|
psychology.
|
||||||
|
So um we can take this a little bit
|
||||||
|
farther. Turns out that we can always
|
||||||
|
think of computation as scattering in
|
||||||
|
some sort of space of data structures.
|
||||||
|
And some colleagues and I have a paper
|
||||||
|
on this that's been in review for months
|
||||||
|
now that goes fairly far and in fact
|
||||||
|
shows that the formal representation of
|
||||||
|
scattering can always be applied to
|
||||||
|
computation. But we can just use this in
|
||||||
|
a in a fairly intuitive way. If we think
|
||||||
|
of an ideal classical computer
|
||||||
|
implementing an algorithm for f then
|
||||||
|
we're thinking about something like
|
||||||
|
this. We have an input for f and we have
|
||||||
|
some ready state of this classical
|
||||||
|
computer. And if we combine the input
|
||||||
|
and the ready state, something happens
|
||||||
|
that is some sort of implementation of f
|
||||||
|
on the input.
|
||||||
|
And at the end of that something
|
||||||
|
happening, we get an output of f on the
|
||||||
|
input and the computer returns to its
|
||||||
|
ready state. So we can do it again.
|
||||||
|
Now this is a useful way to think in a
|
||||||
|
coarse grained way but the observed
|
||||||
|
ready state which is a projection of B
|
||||||
|
of the boundary of the device that we're
|
||||||
|
talking about does not actually pick out
|
||||||
|
a unique machine state.
|
||||||
|
Um,
|
||||||
|
that's what we just saw with this
|
||||||
|
business about holomy, but it's also
|
||||||
|
just Morris theorem from back in the 50s
|
||||||
|
updated.
|
||||||
|
Uh, we don't actually know what's going
|
||||||
|
on inside the machine. It's a black box.
|
||||||
|
Uh, it's got a boundary and we have to
|
||||||
|
look at what's going on on its boundary
|
||||||
|
and that doesn't determine what's going
|
||||||
|
on inside.
|
||||||
|
And we can see this in practice. Um even
|
||||||
|
a classical operating system
|
||||||
|
uh accumulates internal state changes as
|
||||||
|
we execute it over and over and over
|
||||||
|
again with different inputs. Here the
|
||||||
|
input is some program together with some
|
||||||
|
data
|
||||||
|
and
|
||||||
|
uh we have the machine implement some
|
||||||
|
program with some data and it produces
|
||||||
|
an output. Then we give it another
|
||||||
|
program and some more data and it
|
||||||
|
produces another output. We're not
|
||||||
|
keeping track of everything that's going
|
||||||
|
on inside. We just depend on the
|
||||||
|
operating system to to stay in some
|
||||||
|
usable state
|
||||||
|
uh without saying exactly what that
|
||||||
|
state is. And after a day's use of your
|
||||||
|
computer, the final state may be very
|
||||||
|
different from the initial state. And
|
||||||
|
eventually the computer has to be
|
||||||
|
rebooted to get it back to something
|
||||||
|
like the initial state that you started
|
||||||
|
with today.
|
||||||
|
So we can think of that in in this
|
||||||
|
language of side projects. Uh the
|
||||||
|
operating system is constantly doing
|
||||||
|
side projects. It's it's rearranging its
|
||||||
|
internal memory. It's moving things
|
||||||
|
around in its long-term what used to be
|
||||||
|
a disk memory.
|
||||||
|
um it's um changing its internal state
|
||||||
|
in various other ways. So this is
|
||||||
|
inevitable in generic systems uh because
|
||||||
|
generic systems
|
||||||
|
u exhibit non-trivial honomy because
|
||||||
|
they have big state spaces and more
|
||||||
|
complicated dynamics than what they
|
||||||
|
display on their boundaries.
|
||||||
|
So we can also represent these sort of
|
||||||
|
phase changes geometric phase changes as
|
||||||
|
reference frame changes.
|
||||||
|
So for example u go back to that picture
|
||||||
|
of a generic interaction that shows
|
||||||
|
operations on cubits by spin operators
|
||||||
|
each of which has a local reference
|
||||||
|
frame.
|
||||||
|
If the system undergoes some honomy
|
||||||
|
operation
|
||||||
|
uh that introduces a phase into a vector
|
||||||
|
that's transported to some new part of
|
||||||
|
the state space
|
||||||
|
and we think of what that does to these
|
||||||
|
reference frame vectors
|
||||||
|
um
|
||||||
|
that tell the spin operators what
|
||||||
|
they're doing. Then a general holomy
|
||||||
|
transform can modify a reference frame
|
||||||
|
and in that case the output of acting
|
||||||
|
with that operator is different. So if
|
||||||
|
the reference frame is up and you act on
|
||||||
|
something with spin up stays spin up.
|
||||||
|
But if I've tilted the reference frame
|
||||||
|
then what I do is rotate
|
||||||
|
um that cubit. So it when that cubit
|
||||||
|
gets measured by another system you're
|
||||||
|
going to get a different answer
|
||||||
|
and in fact this representation
|
||||||
|
of holom as reference frame change turns
|
||||||
|
out to be generic
|
||||||
|
and um I'm involved in another ongoing
|
||||||
|
paper that's trying to sort out um how
|
||||||
|
this works in general
|
||||||
|
and Again, it involves many different
|
||||||
|
literatures that don't communicate with
|
||||||
|
each other very much to put together a a
|
||||||
|
real understanding of how holomy change
|
||||||
|
relates to reference frame change
|
||||||
|
and it all turns out to couple to the
|
||||||
|
theory of error correcting codes and
|
||||||
|
hence the theory of emergent spacetime.
|
||||||
|
So this this issue of geometric phase
|
||||||
|
and reference frame change is is
|
||||||
|
actually very deep. But all we need to
|
||||||
|
know for for now is that if the system a
|
||||||
|
bar exhibits non-trivial honomy then how
|
||||||
|
it acts on on the boundary so that the
|
||||||
|
output that it produces its behavior
|
||||||
|
it's going to change um as honomy
|
||||||
|
operations move vectors around in its
|
||||||
|
state space.
|
||||||
|
So this is important um because when you
|
||||||
|
move reference frames around
|
||||||
|
you end up with uh behaviors that don't
|
||||||
|
commute.
|
||||||
|
So in particular uh this simple case of
|
||||||
|
spin operators
|
||||||
|
uh spin operators with different
|
||||||
|
reference frames don't commute. Acting
|
||||||
|
with up and then sideways is not the
|
||||||
|
same as acting with sideways and then
|
||||||
|
up.
|
||||||
|
And this has a an overall global
|
||||||
|
consequence. Whenever you have
|
||||||
|
non-commuting reference frames,
|
||||||
|
uh they generate non-causal context
|
||||||
|
dependence in the behavior of the
|
||||||
|
system. Uh and if you're you're making
|
||||||
|
measurements with non-commuting
|
||||||
|
reference frames, they generate
|
||||||
|
non-causal context dependence in your
|
||||||
|
measurement outcomes.
|
||||||
|
And in either case, the consequence of
|
||||||
|
that is that joint probability
|
||||||
|
distributions on the outcomes are
|
||||||
|
actually undefined. They violate the
|
||||||
|
Kagoro axioms. And this is this is what
|
||||||
|
is observed in systems that violate for
|
||||||
|
example Bell's inequality that exhibit
|
||||||
|
entanglement
|
||||||
|
uh systems that violate the leot
|
||||||
|
inequalities and so um exhibit what
|
||||||
|
looks like entanglement in time.
|
||||||
|
uh systems that violate the Coke and
|
||||||
|
Specker
|
||||||
|
uh theorem
|
||||||
|
uh which is essentially a restatement of
|
||||||
|
the conditions for entanglement.
|
||||||
|
Uh so exhibit context dependence
|
||||||
|
depending on different orders of of
|
||||||
|
observational
|
||||||
|
actions yield results that can't be
|
||||||
|
given an overall joint probability
|
||||||
|
distribution. So there's tons now of
|
||||||
|
experimental data that it demonstrates
|
||||||
|
this sort of
|
||||||
|
kagorov axiom violation by physical
|
||||||
|
systems
|
||||||
|
and I've put down here a reference to a
|
||||||
|
paper that talks about uh this
|
||||||
|
non-communing QRFs generating non-causal
|
||||||
|
context dependence in general.
|
||||||
|
So what does this mean? It means that
|
||||||
|
all of these interesting kinds of
|
||||||
|
behaviors are in fact generic.
|
||||||
|
And they're all generic for the same
|
||||||
|
reason. That they're all the result of
|
||||||
|
requiring that the behaving system is
|
||||||
|
separate from the system that's exhibit
|
||||||
|
that's observing its behavior.
|
||||||
|
Uh and that separability requirement as
|
||||||
|
we saw
|
||||||
|
uh induces this dimensionality
|
||||||
|
requirement that we have big systems
|
||||||
|
with small boundaries and so behavior
|
||||||
|
has much less dimensionality than the
|
||||||
|
computation that generates it. Whenever
|
||||||
|
that condition holds
|
||||||
|
uh then we see these sorts of
|
||||||
|
interesting behaviors
|
||||||
|
and that condition holds whenever we can
|
||||||
|
separate ourselves as observers from
|
||||||
|
whatever system it is we're observing.
|
||||||
|
So this tells us in fact
|
||||||
|
that intelligence is very diverse and in
|
||||||
|
fact interesting behavior is very
|
||||||
|
diverse. Um it also provides us with a
|
||||||
|
very general and strongly empirically
|
||||||
|
validated foundation for talking about
|
||||||
|
diverse intelligence i.e. quantum theory
|
||||||
|
and it tells us that intelligence and
|
||||||
|
persistent observability so separability
|
||||||
|
between the observer and the observed
|
||||||
|
uh go hand in hand.
|
||||||
|
uh if if a system is different from us,
|
||||||
|
we're observing it, then its behavior is
|
||||||
|
going to be interesting.
|
||||||
|
And we can make that interestingness go
|
||||||
|
away by coarse graining or averaging or
|
||||||
|
the common practice of throwing out
|
||||||
|
anything that looks anomalous,
|
||||||
|
but it's actually there. And if we look
|
||||||
|
carefully enough, we'll see it.
|
||||||
|
So that's it. Thank you.
|
||||||
@@ -0,0 +1,16 @@
|
|||||||
|
# yt-dlp log
|
||||||
|
# url: https://youtu.be/QeMajYvhEbI
|
||||||
|
# output: conductor/tracks/video_analysis_generic_systems_fields_20260621/artifacts/video.mp4
|
||||||
|
# returncode: 0
|
||||||
|
|
||||||
|
stdout:
|
||||||
|
[youtube] Extracting URL: https://youtu.be/QeMajYvhEbI
|
||||||
|
[youtube] QeMajYvhEbI: Downloading webpage
|
||||||
|
[youtube] QeMajYvhEbI: Downloading android vr player API JSON
|
||||||
|
[info] QeMajYvhEbI: Downloading 1 format(s): 400+251
|
||||||
|
[download] video.mp4.f400.mp4
|
||||||
|
[download] video.mp4.f251.webm
|
||||||
|
[Merger] Merging formats into video.mp4
|
||||||
|
|
||||||
|
stderr:
|
||||||
|
WARNING: yt-dlp EJS not enabled; some formats may be missing.
|
||||||
Reference in New Issue
Block a user