John C. Baez's Blog, page 38

Applied Compositional Thinking for Engineers

Hey! Theres a new online course coming up!

Applied Compositional Thinking for Engineers. January 7, 8, 11-15, 20-22, and 25-29. Taught by Andrea Censi, Jonathan Lorand and Gioele Zardini.

Its not a coincidence that the acronym for Compositional Thinking is CT, just like Category Theory.

The course is free but registration is required. During the sign-up process you will be asked for the most convenient times for you; the instructors will choose what works best for a majority of participants....

Great Conjunction

Ive been seeing Saturn and Jupiter coming closer to each other in the sky lately. Jupiter passes by Saturn every 19.6 years, and its called a great conjunction. But I just learned that on December 21st theyll look closer than they have since March 1226! Theyll be just 0.1 degrees apart: 6.1 arcminutes, to be precise. Thats less than a fifth of the Moons apparent width.

Jupiter and Saturn were even closer on July 17, 1623just 5.2 arcminutes apartbut the glare from the the Sun made them...

Graph Transformation Theory and Applications

I love graph rewritingthe study of ways to change one graph into another by changing one small part at a time. My student Daniel Cicala did his thesis on this! So Im happy to hear about the new virtual seminar series GReTA: Graph TRansformation Theory and Applications.

It aims to serve as a platform for the international graph rewriting community, promote recent developments and trends in the field, and encourage regular networking and interaction between members of this community.

Seminars...

Shinise

 

The Japanese take pride in ‘shinise’: businesses that have lasted for hundreds or even thousands of years. This points out an interesting alternative to the goal of profit maximization: maximizing the time of survival.

• Ben Dooley and Hisako Ueno, This Japanese shop is 1,020 years old. It knows a bit about surviving crises, New York Times, 2 December 2020.

Such enterprises may be less dynamic than those in other countries. But their resilience offers lessons for businesses in places lik...

The 600-Cell (Part 4)

I get really bored some evenings these days, after I run out of energy to work on my own projects, and before I lie in bed and read Whittaker’s mammoth tome, A History of the Theories of Aether & Electricity. So I’ve taken up browsing the arXiv. It can be quite entertaining! Here’s something I found last night:

• Tomme Denney, Da’Shay Hooker, De’Janeke Johnson, Tianna Robinson, Majid Butler and Sandernisha Claiborne, The geometry of H4 polytopes.

It mentions some cool facts that call for a ne...

Ramanujan’s Last Formula

When I gave a talk about Ramanujan’s easiest formula at the Whittier College math club run by my former student Brandon Coya, one of the students there asked a great question: are there any unproved formulas of Ramanujan left?

So I asked around on MathOverflow, and this is the result:

George Andrews and Bruce Berndt have written five books about Ramanujan’s lost notebook, which was actually not a notebook but a pile of notes Andrews found in 1976 in a box at the Wren Library at Trinity College, ...

The Swinomish

The Swimonish are Native Americans who live in the southeastern part of Fidalgo Island in northern Puget Sound, about 110 kilometers north of Seattle.

They’ve been doing interesting things about climate change and ecosystem restoration. So have other tribes:

• Jim Morrison, An ancient people with a modern climate plan, The New York Times, 24 November 2020.

For 10,000 years, the Swinomish tribe has fished the waters of northwestern Washington, relying on the bounty of salmon and shellfish no...

The Tenfold Way

I now have a semiannual column in the Notices of the American Mathematical Society! I’m excited: it gives me a chance to write short explanations of cool math topics and get them read by up to 30,000 mathematicians. It’s sort of like This Week’s Finds on steroids.

Here’s the first one:

• The tenfold way, Notices Amer. Math. Soc. 67 (November 2020), 1599–1601.

The tenfold way became important in physics around 2010: it implies that there are ten fundamentally different kinds of matter. But it g...

Ramanujan’s Easiest Formula

A while ago I wanted to figure out how to prove one of Ramanujan’s formulas. I figure this is the sort of thing every mathematician should think about at least once.

I picked the easiest one I could find. Hardy called it one of the “least impressive”. Still, it was pretty interesting: it turned out to be a puzzle within a puzzle. It has an easy outer layer which one can solve using standard ideas in calculus, and a tougher inner core which requires more cleverness. This inner core was crac...

Octonions and the Standard Model

I avoid talking about fundamental physics or pure math here—I do that on the n-Category Café. I also avoid talking about category theory, except for its applications to electrical circuits, chemical reaction networks and the like. I discuss more ‘pure’ aspects of category theory on the n-Category Café and the Category Theory Community Server.

Anyway, those of you who like fundamental physics might be interested in these posts:

• Octonions and the Standard Model 1. How to define octonion multipli...