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October 22, 2021

The Kuramoto–Sivashinsky Equation (Part 1)

Posted by John Baez

I love this movie showing a solution of the Kuramoto–Sivashinsky equation, made by Thien An. If you haven’t seen her great math images on Twitter, check them out!

I hadn’t known about this equation, and it looked completely crazy to me at first. But it turns out to be important, because it’s one of the simplest partial differential equations that exhibits chaotic behavior.

Posted at 4:07 AM UTC | Permalink | Post a Comment

October 20, 2021

What is the Uniform Distribution?

Posted by Tom Leinster

Today I gave the Statistics and Data Science seminar at Queen Mary University of London, at the kind invitation of Nina Otter. There I explained an idea that arose in work with Emily Roff. It’s an answer to this question:

What is the “canonical” or “uniform” probability distribution on a metric space?

You can see my slides here, and I’ll give a lightning summary of the ideas now.

Posted at 4:06 PM UTC | Permalink | Followups (16)

October 19, 2021

Topos Institute Postdoc

Posted by John Baez

The Topos Institute is trying to hire a postdoc to work on polynomial functors! Here is the ad, written by David Spivak.

Posted at 7:57 PM UTC | Permalink | Post a Comment

October 15, 2021

Dynamics of Reason Revisited

Posted by David Corfield

A couple of years ago, I mentioned a talk reporting my latest thoughts on a very long-term project to bring Michael Friedman’s Dynamics of Reason (2001) into relation with developments in higher category theory and its applications.

While that Vienna talk entered into some technicalities on cohomology, last week I had the opportunity of speaking at our departmental seminar in Kent, and so thought I’d sketch what might be of broader philosophical interest about the project.

You can find the slides here.

Posted at 10:19 AM UTC | Permalink | Followups (4)

October 4, 2021

Stirling’s Formula

Posted by John Baez

Stirling’s formula says

n!2πn(ne) n \displaystyle{ n! \sim \sqrt{2 \pi n} \, \left(\frac{n}{e}\right)^n }

where \sim means that the ratio of the two quantities goes to 11 as n.n \to \infty.

Where does this formula come from? In particular, how does the number 2π2\pi get involved? Where is the circle here?

Posted at 2:52 AM UTC | Permalink | Followups (45)