Wednesday May 9th, Tai-Danae Bradley and I are giving talks on entropy and category theory.

Her talk will dig into the consequences of an amazing fact: the function at the heart of entropy, namely

d(x) = -x ln x ,

obeys a version of the product rule!

(1/n)

You can watch our talks on Zoom if you register: follow the directions here. Or watch them later - they'll be recorded.

Then on Friday there will be a bunch more talks on entropy and categories!

You can see them live if you're in New York.

Using the product rule for d(x) = - x ln x, Tai-Danae showed that Shannon entropy is a topological operad derivation.

Perhaps now you're thinking, "Huh?" 🤔

But luckily she's great at explaining things. So read her blog article!

(3/n)

math3ma.com/blog/entropy-algeb

Or maybe you're thinking "This is the kind of math I like!" Then take a look at her paper.

She defines derivations of operads, and shows entropy is a derivation of the operad whose space of n-ary operations is the (n-1)-simplex!

(4/n)

mdpi.com/1099-4300/23/9/1195

I find this result exciting but still mysterious. I don't think we've completely gotten to the bottom of the connection between entropy, operads, simplexes, etc. When we're there, it should all make a lot of intuitive sense. Maybe we'll be able to do new stuff.

(5/n, n = 5)

I meant to say that Tai-Danae are talking on Wednesday May 𝟭𝟭𝘁𝗵. All schedule details, and how to register, are here:

johncarlosbaez.wordpress.com/2

I meant to say that Tai-Danae and are talking on Wednesday May 𝟭𝟭𝘁𝗵. All schedule details, and how to register, are here:

johncarlosbaez.wordpress.com/2

I meant to say that Tai-Danae and I are talking on Wednesday May 𝟭𝟭𝘁𝗵. All schedule details, and how to register, are here:

johncarlosbaez.wordpress.com/2

That is fascinating! Ever since I read Penrose as as kid I have been wondering wether there is a deeper meaning to entropy. Well, the plot thickens! It is much more than a statistical effect which appears in a gas of colliding particles. It has structure and that makes it appear in a lot of other places!

Finding out about the nature of entropy helps us understand structure formation, even time itself! It's so cool to see derivations pop out, a close relative of derivatives!

@johncarlosbaez

@RefurioAnachro - The universe still holds many mysteries. I don't think we've gotten to the bottom of this one yet, but I think we'll make a lot of progress pretty soon.

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