it's so fun seeing the physics side of something that seems related to stuff i've been learning about lately: planar algebras and free probability also thank you so much for making this accessible to a broader audience, I wish all technical fields were taught and explained like this

Hi, thank you for this very interesting video. I think what you talk about here might be an explanation as to why LLMs like ChatGPT are so good at understanding language. The idea that there is real understanding under an LLM has been criticized because LLMs are purely statistical. But if I understand this video correctly, you are making an argument based on category theory that the statistical relationship between a word and the rest of the words in language is homomorphic to meaning. I need to read your actual thesis to be sure, but if that is the case I think it could explain why LLMs work so well.

I don't understand it all, yet it makes my brain happy. In terms of fiction: I bet all this will be part of a future SciFi work that postulates a machine that uses the "Bradley Structure" to compute what will happen in the future. Like Isaac Asimov's Foundation series.

Thank you. You have a most amazing gift of communication to compliment your broad based technical insight.

It’s an advertisement, not an explanation 😢

I wish the algorithm sent this to me a year ago.

Kindly start a playlist for mathematics. I watched your maths video on tensorflow and it really inspired and motivated me to learn mathematics (not just solving questions but the concept behind it). Linear Algebra (with its relation with computer technologies like ML DL etc) , calculus , statistics probability etc.

Absolutely amazing video!

Great thesis summary!

What are you using to animate?

A preview overview like this for your paper is a great idea. I recently came across your work on Infinite Series and you are one of the most brilliant explainers of complex ideas for a generalist audience I’ve come across. I look forward to reading this paper. Thanks!

What system / software did you use to create this video? The presentation is excellent. (Still wondering, 3 months later...)

Epic

This was really great! I'm glad to see you posting more content here; I hope you'll consider posting more :)

Goog Idea to make a video about a paper.

Thank you

Hi Tai-Danae, I read your Entropy paper when it came out. Basically, as I understand it, you looked at the chain rule of entropy and said "This looks a lot like a derivation. Can I frame this whole ordeal in a way where entropy indeed turns out to be a bona fide derivation?" And you did. Very cool. To me this parallels the story in the Baudot-Bennequin paper (which you cite). While they are not as transparent as you in their train of thought (they are French mathematicians after all), I imagine that it went like this. Looking at the chain rule of entropy they said "This looks a lot like the equation da=0 for a 1-cochain in something like Hochschild cohomology. Can I frame this whole ordeal in a way where entropy indeed turns out to be a bona fide 1-cocycle?" And they did. They constructed a cochain complex in which H^1 is generated by entropy, thus proving again in an abstract way that the chain rule characterizes entropy. And although they only mention it briefly, their cohomology is actually the cohomology of what they call the information topos (=the category of partitions with the trivial Grothendieck topology), so you got your (albeit weak) link to topology there as well. Have you thought of possibly linking your results to theirs?

Very good baby.... 😎🤔🤔

This is absolutely fantastic!

Great video

You are a treasure. I’m thankful to have stumbled onto your channel today. Great stuff:)

please teach abstract algebra on youtube ;o

I wonder if (and where) conditional probabilities and correlations fit in the formulas. Or do they not? I see Bayes' formula as some sort of Leibniz formula as well. But that could just be my imagination.

Excellent video. Very interesting, informative and worthwhile video. I'll soon watch your other couple of previously posted videos and look forward to your forthcoming videos.

That you cared enough to make both a more accessible version of the paper, and this awesome little video about it, is a most compelling advertisement for the original work.

So are you still with the iirc Google (or other tech company) research group?

Loved....and indeed, theres is a relationship and you formalized it . . . the power of Category and your capability for abstraction and pattern identification great!

I really enjoyed your thesis and am looking forward to reading this new paper! Thank you so much for making your work accessible; I find these topics to be very interesting, but they're a bit above my current comprehension, so I really appreciate it!

I'm a first-year maths student from Gothemburg and I really enjoyed this video and also "At the Interface of Algebra and Statistics" video. Thank you for writing the papers in such way that you can understand the broad picture without getting too confused by the high-level maths.

Wow amazing theory. I can see applications in NLP.

I'm so inspired by your work and can't wait to apply it to the music theory 🤩

Thank you for sharing this. It is wonderfully illustrated and annotated. Beautifully done. Kudos.

Thank you, Dr. Bradley, for a fantastic video that makes a highly complex topic much more accessible to those not in your field. I’m a cancer physician but am fascinated by your thesis and now will have to read it in its entirety.

This is brilliantly presented.

Promising thesis, great introduction and summarization.

The blog post is unavailable now :(

I think the phrase “orange idea” is gonna catch up and it could no longer be used to describe something that occurs rarely in language

Nice work, understood like 1% of it, how long did it take you to finish your thesis?

Wow the initial idea is just brilliant !

I'm really excited to read your thesis! I don't know that I've ever said that about a thesis!

wow. got here from grant sanderson. cant wait to start !

This really is genial. Not only the thesis, but the way you brought the story to laymen like myself. THANKS !!!!

Amazing presentation! Did you do the animation yourself?

This is amazing!

Universal Construction 1. Find patterns 2. Find the ranking 3. Choose the best 'tis what I learned from Bartosz Milewski. The Section 3.4 of what you presented presents the idea of Universal Construction well.

527 likes, 0 dislikes. The most liked undisliked video I've ever seen.

Congratulations, Doctor!

I just came here from your website. I had seen many of your videos for PBS Infinite Series and just discovered that you have your own channel !

Woaw !!! That seems incredibly ingenious ! Good job !

I am now your fan after reading this blog (www.math3ma.com/blog/understanding-entanglement-with-svd). Hopefully, I will get something from your thesis.