platonic space

Joscha Bach’s reinterpretation of Plato’s idealism:

Plato was not actually an idealist in the sense that he believed that conscious or mental experience is primary.

Plato takes these ideal forms as starting points. The ideal table is sometimes given as an example, but that’s probably not a core arcchetype of the universe or of god itself, but tables are created by human beings in particular cultural contexts, and they are an archetype in our perception. The way in which we classify the world, there is something like an ideal table. The forms that Plato is talking about are actually dimensions in an embedding space. In some of his texts, he alludes to a world outside of our perception, our mental construction that we experience, and that world is an outside [of our?] simulated world that is isomorphic to the world that we experience in these forms.

Link to original

A table is defined by its shape and material. So in the space of shapes and materials, there’s a region we’d classify as a table. This latent space is outside of our perception, but specific instantiations are made real by our thoughts and actions.
A table that’s never built, never imagined, and not found in nature simply doesn’t actually exist.

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michael levin’s take:
Abstract properties of mathematics / geometry are true no matter the laws of physics.
A cell only has to evolve a voltage gated ion channel and it gets a truth-table for free.
There is such a space not just for mathematics, but also for kinds of minds, and life is good at exploiting it. This is not a random space, where interesting / useful emergent properties just so pop up from time to time, but it’s structured, it is incredibly vast, and we should map it, otherwise we just end up with a grab-bag, a catalog of things that hold. We need to assume there is a causal structure to it.
He doesn’t make the claim that this space is static ¹, but that it is at least partially unaffected by the physical world. We categorize the things that are constrained by these facts as “physics”, the ones
that exploit them as biology.

In his own words:

A Very Simple Argument – Michael Levin

(Transcript of: platonic space-1761908148632.webp)

1. There are specific facts of mathematics - “patterns” or forms. Examples: value of $e$, Feigenbaum’s constant, facts of number theory and topology, symmetry of $SU(2)$, amplituhedron, etc.

2. These patterns are surprising and forced on you once you choose basic assumptions (very few - just logic, apparently). You “get more out than you put in”. Start with set theory and get the specific value of $e$.

3. For some such pattern $P$:

   • There are aspects of physics and biology that are explained by recourse to the specifics of $P$. If you ask “why” long enough, you end up in the mathematics department.
   • In contrast, there is no aspect of the physical world (physical events/laws), and no amount of history (biological selection), that explain/set the properties of $P$.
   • If $P$‘s facts were different, biology and physics would be different.
   • It doesn’t work in the reverse: there is nothing you can change in the physical world to make $P$ be different.
     • Therefore, causality flows from these forms to the physical world (not in the temporal sense).
     • Therefore, these facts play important instructive roles. They cannot be ignored if you want to understand and tame evolution, bioengineering, etc.

4. Therefore:

   • physicalism is a non-viable theory: there are facts that are simply not “in” the physical world in any useful sense of “physics”.
   • Pythagoras knew this already. Let’s call the set of possible properties of $P$‘s “the Platonic Space”.

5. Optional hypotheses (optimistic metaphysical claim):

   • $P$ is drawn from a distribution that’s not a random collection but a structured space
   • Therefore, we have a research program: map the space, understand relationship between interface and which $P$ it channels.

6. Skeptical position: we cannot assume that low-agency models of math encompass all the residents of this Space. Some may be better described by behavioral science tools.

   • Therefore, some of the patterns that ingress into physics and biology may be “kinds of minds”.
   • Therefore, Dualism is viable. We already knew it was true in physics and biology; this suggests it’s also relevant in cognitive science.

7. Skeptical position: we cannot assume that biological materials, evolutionary search, etc. have any monopoly on hosting those patterns.

   • Therefore, perhaps algorithms/robots should be searched for surprising ingressions that are not just complexity or unpredictability, but well-understood cognitive competencies.
     

I think Levin's research program commits to stronger metaphysics than it needs to. We don't need to resurrect dualism.

How does a non-physical space of forms causally influence biological evolution? What’s the mechanism for “ingression”?
What empirical predictions can we make with a separate “realm” that we can’t without it?

I think Levin stands things on their head in points 3) and 4) of his argument: Mathematical facts don’t act on the world, they’re abstracted from it by minds modeling regularities.

What changes if we simply say the space of patterns/minds is like an embedding space? It has structure (geometry, clusters), exploitable properties (navigation, interpolation), but no causal power of its own.

An attempt to rephrase levin’s argument from a materialist perspective:

There is one material world. Because of how matter organizes, there exist objective constraint-structures (attractors, symmetries, conservation laws, control geometries). Humans produce mathematical–conceptual spaces that model those constraints. Minds, embryos, and algorithms realize and exploit them (engineers should too). Explanations run upward (composition) and downward (constraint), but all causation is materially implemented.

Read this for further elaboration on my attempt at a materialist perspective.

I was in the middle of refactoring / imrpoving the clarity of this (and the (link to the) "materialist argument" – perhaps put it here, perhaps whatever).

followed a bazillion rabbit holes, would now prlly be ready, but hav other things to do – and better if i take some more time and read the source materials in more depth
physicalism qa; hempels dilemma (pretty much done i think)
a1f120c9-ea36-46ef-b7f7-9a31b03d8a3d
main one where i was sharpening the arg; “where do patterns come from” blogpost todo; but also messages[:-3] not yet fully processed; there’s aslo a huge comment thread on the post which i should read summarized
ff26a695-ef60-4e1f-86ac-fc867ece0c62 dr-michael-levin-platonic-space-where-cognitive-and-morphological-patterns-come-from-besides-genetics-and-environment
very relevant: my observation on observer-relativity
everything is observer relative — there’s a spectrum of invariance to observers; at the very top sit mathematical facts, progressing down we have physics (some theories only hold from certain perspecticves), and so on descending narrower invariance groups, minds somewhere at the bottom.
But my hypothesis is that science progressively uncovers that these “set in stone” laws are… not so set in stone after all.
“I suspect these patterns are not static / unchanging” or sth is literally what levin said too, about the platonic space. Like the speed of light, facts of mathematics etc… some might sooner or later turn out to not hold or change, depending on the perspective.

dr-michael-levin-a-short-argument-on-platonic-space-variable-agency-patterns-that-in-form-physics-biology-computer-science-and-cognitive-science

• On the origin of the space: “I have no claims about how the Platonic space came to be” Thoughtforms
• On pre-existence: “I won’t claim patterns pre-existed the physical world — it may not be a well-posed question in this situation” Thoughtforms
• On the naming itself: “the naming is questionable; I chose Platonic Space because the mathematicians would immediately know what I mean and I could extend off of that, but I make no attempts to stick close to Plato’s views” Thoughtforms
• On whether patterns are eternal: “I don’t commit to that. There may be some, like e, but I think most of the interesting ones (like us – we are patterns on this view) are modified by their projections into the physical world (it’s a 2-way interface)”

Update: So in this discussion, Amahury makes pretty much exactly the points I was grasping at. Very insightful discussion for this perspective.

so in summary levin totally isn’t opposed to there only being a single realm. he’s kind of pushing it in a contrarian way though, the other perspective, because he thinks that crazy ideas haven’t been taken too seriously under what he calls middle positions.

the discussion about whether there is a separate realm or not could be summarised as: if it doesn’t causally interact with our world, is it really? then it doesn’t make sense to talk about it. as soon as we talk about it, we already brought it into causal interaction with our world. is it really a separate world? if it’s part of our world, yeah sure, we can apply different lenses depending on which is more practically useful.

for some reason that i have to check again … idk i guess maybe it’s just this contrarian thing to really push this idea that there’s the space that we can study still insisted on that separate realm framing making sense practically now.
I’m not so sure since it seems it spurs more confusion than what it does good. Fighting fire with acid or sth.

From Experience to Math by Chris Fields:

Footnotes

1. And generally he’s calling it “platonic space” to connect to the notion of discovering the structured space of mathematics, but for kinds of minds; but says he’ll have to change the word “Platonic” eventually because his ideas don’t actually fully align with platonism. ↩