A New Perspective of Entropy

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@govert72 2 жыл бұрын

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.

@laurenceboulanger55 2 жыл бұрын

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?

@-delilahlin-1598 2 жыл бұрын

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

@mohamedyosef1452 2 жыл бұрын

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.

@jonathanshafter1800 2 жыл бұрын

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!

@cheyneanderson4875 2 жыл бұрын

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!

@EricEisaman Жыл бұрын

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

@jonwoods6745 2 жыл бұрын

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

@sebastianmullerbalcazar6229 2 жыл бұрын

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

@robertschlesinger1342 2 жыл бұрын

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.

@AbdulWahab-mp4vn Жыл бұрын

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.

@dd884e5d8a 2 жыл бұрын

This is absolutely fantastic!

@firstnamelastname307 2 жыл бұрын

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.