Category Theory for Neuroscience (pure math to combat scientific stagnation)

I have been interested in and researching consciousness on and off since 9 years ago. I searched in computer science(AI), i searched in and did research in neuroscience and studied philosophy of mind on my own. With time i began to appreciate the mathematics in the sciences more and more. Now with this video, i have been convinced a mathematical fundamental in research is the way to go forward in my sciencetific career. Thank you so much for opening a partly closed door for me.

Perfect balance between high level and technical, in this presentation.

This was an amazing introduction to both category theory and the neuroscience of visual perception.

This was playing in the background while watching porn, but from 7:04 onward my attention was fully fixed on category theory and I dropped what I was doing. The highest praise I can give you, or anyone, is listening to this managed to override my lizard brain behaviour. The way you translate math-ese to understandable language and images is amazing! Making arcane topics like the Yoneda lemma come alive not via rigorous mathematical chants but social webs and colour theory is pedagogically brilliant.

I think it's missing the point though: the inverted color perception thought experiment is one very specific way to bring attention to the main issue that no one has been able to specify how brain states determine the experience of color. More generally, no one has been able to specify how brain states determine any experience. In the best case, maybe the thought experiment is not well formed, which is very interesting in and of itself. However, what have we learned about the main issue of having no clue why the neural activity associated with red MUST BE that color? To be clear, I found the lecture to be enjoyable because I learned several new things.

If you can't appreciate the obvious usefulness of CT as an organizing language for several fields of mathematics it means you've only been working/studying in a field of math that is rather non-structural, like Analysis. There's nothing wrong with that. But, as soon as you need anything a bit structural (Idk, cohomology?), you'll immediately start appreciating CT. Ask an algebraic geometer. Ask an algebraic topologist. Ask an algebraist...

For logicians, syntax and semantic are separate. The Yoneda Lemma shows that this separation is an optical illusion, because you can embed the syntax in Set ... The true category theory was found in 1965 by Max Kelly and Sammy Eilenberg: Enriched Category Theory, where "classical" category theory reduce to Set-enriched category theory ! I am myself category theorist (Enriched, but not rich 😂!). Thank you for your talk

The talk is nice but the final conclusion is hasty, to say the least. In particular, it seems to me that you showed (albeit informally) precisely why the inverted spectrum hypothesis does makes sense! Let's take the color wheel as an accurate representation of color perception. Every color is uniquely identified by the relative distances with all the other colors. Now rotate the circle, let's say 90° clockwise. The colors are still uniquely identified by their relative distances, but the absolute positions between the two circles differ: for example, what we call "red" is at the top in the first circle, but on the right in the second one (it took the place of the first circle's "blue" after the rotation). Now let's say we have two people, the first sees according to the first wheel and the second one according to the rotated version. Remember that for the two people here "seeing" (perceiving/experiencing colors if you prefer) is determined by the position on the color wheel, NOT by the hue we used in the actual diagrams (that is colors are NOT absolute); it may be useful to replace the actual colors with string of numbers (RGB encoding) to avoid confusion. So when i show a picture whose color is registered as being on the right side of the color wheel, both people will say that the color is "blue", because that's the only color compatible with the relative distances from all the other colors. In fact the second person lived all his life hearing that the thing (feeling?) he experienced when looking at objects similar to the one shown, is called "blue", even tough what he actually sees in his mind is the same as what the other person would describe as "red". It is crucial to notice that when passing from the first color wheel to the second one, we didn't just move a single color (for example putting "red" in the place of "blue"), but all the colors accordingly, in a way to preserve the relative distances. So for the second person is actually impossible to notice any inconsistencies with his mental representation of how colors works and the descriptions given by the first person of what colors are supposed to be. We can generalize these ideas to whatever mathematical object we think is an accurate representation of color perception (like the gamut in the final slides). The point is not that given a specific gamut, a certain color is uniquely determined by the relative distances with all the other colors (this is rather trivial). But what about all the possible gamuts? How are they related? Can we uniquely determine the gamut itself (that is the model which explains color perception) for all the people? To answer this question you would need to show that there can't possibly be a map between two different gamuts that preserves the relevant structure; in this case distances between colors (so it would be a continous isometry, if we think the gamut as a metric space). I hope that by now it's evident enough that "red" and "blue" are just labels and don't actually mean anything by themselves, but only when they are put in a broader context (when they are in relation with all the other colors). The act of fixing this context (which is a model of the phenomenon "colors") is analogous to putting labels to the vertices of a graph. There can be multiple labelling that are compatible, that is we can find a way to pass from the first labelling to the second one that preserves the structure of the graph (a sort of translation). An external viewer, that is not aware of the specific labelling used (let's say we cover the labels before showing the graph), cannot distinguish which one was used to arrive to a certain claim about the graph. Moreover, it doesn't even matter because the claims that can be reached by reasoning with the first labelling must be the same as the ones reachable by reasoning with the second one. In this sense we call these two labellings isomorphic (and hence the graphs), and this is what Yoneda lemma is about. For a structuralist/constructivist/empiricist/behaviorist/ecc. (i hope i'm not mislabelling) Yoneda lemma is a pretty trivial result (from a philosophical point of view): it's just an assertion of the way we think. Since we can't have access to the metaphysical/ontological level (the essence of the objects, what they "really are"), there is no use in try to reason about what we can't observe; therefore there is no practical difference between objects that we are not able to differentiate, regardless of their inner nature (that could be different as far as we know). If when we cover the labels (that is we make inaccessible the "true nature" of the object) we can't spot signs (discrepancies/inconsistencies/whatever) that could alert us of a possible difference, then the objects are equivalent/isomorphic; that is we treat them as they were the same. In the case of consciousness, the labels are always covered by default (unless we assume we can read people minds). There are others problem in the way category theory has been applied to this matter, that i'm not knowledgeable enough to discuss, but you can read this blog post (that i incidentally found as first result googling "color map yoneda lemma"): the title is "No, the Yoneda lemma doesn’t solve the problem of qualia" on Matteo Capucci website. [i don't put the link bcs youtube]

That's the longest "I don't know" answer to consciousness.

Great talk. From pure math to applied math. I don't have math background but I love type theory and category theory.

Yeah, I think is this why if you have a mapping from one distribution to another (F(X) => Y) you effectively have a mapping from x to y (f(x)=>y) (individual points in the distributions) when x is a high-dimensional object (which makes it very unique/specific). This is important because deep learning learns distributions, so now you have a certainty that individual data points can be mapped as well.

Absolutely brilliant video!

Excellent presentation and communication skills, was very easy to follow.

Great talk given here. Very interesting and insightful

Great video! I'm getting into category theory but got lost when I got to natural transformations, so I obviously didn't understand Yoneda Lemma, but this video helped a lot. Thanks!

I don't think this actually solves the inverted spectrum problem. Just looking at the very last figure in this talk - imagine red and green being swapped... each color would still have their own distinct set of relations, but the PERCEPTION of the color could be inverted and we'd never know.

As a scientist myself I see the main problem in the fact that you just can't afford to concentrate on high risk topics that might or might not produce groundbreaking results. You have to write several articles per year, fully aware that they're only mildly interesting. Because doing otherwise would be professional suicide. Another thing: you can't overestimate the value of discussions with top scientists. But this is not possible when 10% or more of a class go for a phd. Many of them don't even want to work in science. Some do a phd to further their career, others because they won't get a job without the title (biologists and chemists in some countries) and yet others because it's customary (medical "doctors")

In 10:07 it went from what is a set to Yoneda's lemma, first day of math degree to last day of math degree ;-)

"high abstraction, low complexity" e.g. non-wellfounded sets: astrocyte_syncytium = ( infomorphism, astrocyte _syncytium ) where infomorphism = affordance -> memory where affordance from Gibson is possibility Death modelled by running out of possibilities, i.e. possibilities go to zero. Repeatedly substituting the RHS of the equation for "astrocyte _syncytium" on the RHS produces a finite stream which ends when you run out of possibilities (affordance). The most basic possibility involving the self would be breath. (Having no possibility for breath leads to death.) The first possibility involves "hunger for air", which comes after connexin43 and other connexins flood the system during parturition. Given the difficult if not impossible instrumentation, the probable, initial situation is: parturition -> connexins -> astrocyte syncytium -> self with memory and therefore consciousness of "hunger for air" ("Infomorphism" comes from a category called "Chu space". See Barwise and Seligman "Information flow: the logic of distributed systems')

Thank you. Amazing presentation.