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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"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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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
|
||||
which plays essentially the same role
|
||||
here that it plays in classical physics.
|
||||
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
|
||||
um corresponds to there being no no
|
||||
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
|
||||
was infinity there would be a
|
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singularity. So it needs to be finite.
|
||||
Now this theory is quantum theory
|
||||
of an isolated system.
|
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So in a sense isolation is all you need
|
||||
to get quantum theory. Uh it's a it's a
|
||||
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
|
||||
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
|
||||
has this simple representation of
|
||||
interaction and it's linear.
|
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So this is a generic symmetry preserving
|
||||
representation of interaction between a
|
||||
system and and everything else.
|
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Now we can continue decomposing this
|
||||
interaction term again additively
|
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um as a sum
|
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of operators that act on single quantum
|
||||
bits. And some some of you have seen
|
||||
this kind of picture before in uh
|
||||
previous talks, but these operators are
|
||||
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
|
||||
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
|
||||
physics that can now be imported to talk
|
||||
about this boundary. And I'm not going
|
||||
to really talk about that physics today.
|
||||
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
|
||||
each other by changing the values of
|
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cubits.
|
||||
Uh what we wanted though is to
|
||||
understand how a and a bar influence
|
||||
each other. How information flows from
|
||||
one to another.
|
||||
And these are the same uh if and only if
|
||||
one condition is met that a and a bar
|
||||
have conditionally independent states.
|
||||
So that we could talk about the state of
|
||||
A and the state of A bar.
|
||||
And that's a simple requirement. We have
|
||||
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
|
||||
state of the other system.
|
||||
And this is in quantum theory called
|
||||
separability. And it's the same as the
|
||||
absence of entanglement.
|
||||
So systems
|
||||
have their own states. if they're not
|
||||
entangled.
|
||||
And entanglement just means factoriz or
|
||||
non-entanglement just means
|
||||
factorizability.
|
||||
And of course that maps over into
|
||||
classical systems. If classical dynamic
|
||||
system has a markoff blanket then the
|
||||
then it factors
|
||||
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
|
||||
operator its dimension is well defined
|
||||
and by small it means its dimension is
|
||||
much less than the dimension of either
|
||||
of the other operators in the picture
|
||||
the internal operators for a and a bar.
|
||||
So intuitively the evolutions of these
|
||||
systems have to be almost independent
|
||||
for their states to be separable and for
|
||||
the interaction to actually capture all
|
||||
of the influence of one system on the
|
||||
other.
|
||||
So what we've done here is reconstruct
|
||||
the free energy principle from minimal
|
||||
physics. And again u at least some of
|
||||
you have seen this before.
|
||||
If uh these two systems A and its
|
||||
environment are separable, so they meet
|
||||
this dimensionality constraint on the
|
||||
Hamiltonians,
|
||||
then the Hamiltonian fully describes
|
||||
information exchange. The boundary
|
||||
functions as a markoff blanket. Uh the
|
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variational free energy is a measure of
|
||||
the interaction strength.
|
||||
uh minimizing VF VFE which is what the
|
||||
free energy principle is about is
|
||||
keeping the interaction weak while
|
||||
allowing thermodynamic exchange.
|
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So it's it's keeping the interaction
|
||||
between the system and its environment
|
||||
fairly weak while enviring allowing the
|
||||
system to eat some of its environment to
|
||||
to provide enough energy to live.
|
||||
And in this case predictability which is
|
||||
what the system is after is constrained
|
||||
interaction. So it's constraining the
|
||||
interaction in a way that's consistent
|
||||
in a way that's consistent
|
||||
with staying alive.
|
||||
So ANA bar maintain their identities as
|
||||
distinct systems only while their
|
||||
boundary um remains a markoff blanket.
|
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So there can't be any rips, there can't
|
||||
be any explosions, other sort of huge
|
||||
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
|
||||
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
|
||||
system
|
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and this follows uh just from very
|
||||
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.
|
||||
uh any system that
|
||||
persists through time acts inferentially
|
||||
uh as if it's trying to continue to
|
||||
exist. This is what Jacob Howey calls
|
||||
self-evidencing
|
||||
as an interpretation of the FEP.
|
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Are any means allowed? Well, yeah.
|
||||
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.
|
||||
And does anything fall outside of this
|
||||
definition? No. It's completely generic.
|
||||
At least it's completely generic for
|
||||
systems that are physically realizable.
|
||||
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