One statement of triality is that textrm Spin ( 8) has nontrivial outer automorphisms of order 3. On the other hand, the octonions have nontrivial inner automorphisms of order 3. My question: can we ...

A light mill is also known as a Crookes radiometer: It seems like a simple thing: an evacuated glass bulb with some vanes that can spin around, black on one side and white on the other. When you shine ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...

Part of what intrigues me about reading Terence Tao’s blog is that he displays there a different aesthetic to the one largely admired here. The best effort to capture this difference is, I believe, ...

A Freyd category consists of two categories C and K with an identity-on-objects functor J: C → K, where: - C has finite products - K is symmetric premonoidal (with a functor ⊗ z ) - J maps finite ...

I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

Lately there have been remarkable developments in higher category theory. What used to have a touch of alchemy to it – in its mystery, its grand hopes, its plethora of recipes tried out in hard and ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Joseph Goguen, A categorical manifesto, Mathematical Structures in Computer Science 1 (1991), 49-67. Abstract: This paper tries to explain why and how category theory is useful in computing science, ...