1
42
In The Hitchhiker’s Guide to the Galaxy by Douglas Adams, the number 42 is the “Answer to the Ultimate Question of Life, the Universe, and Everything”. But he didn’t say wha…
John Baez
One of my dreams is finally coming true: ecological modeling with the help of category theory!
- Popular posts
- 24
- Total points
- 4,931
- HN comments
- 1,529
- Rank
- #221 personal
Visit johncarlosbaez.wordpress.com → RSS feedOn Hacker News Apr 2012 – May 2026
Science & Space 21Math & Algorithms 19History & Retro Computing 2Society, Policy & Culture 1Life, Learning & Writing 1
2
Applied Category Theory
It just became a lot easier to learn about applied category theory, thanks to this free book: • Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Cate…
3
What Is Entropy?
I wrote a little book about entropy; here’s the current draft: • What is Entropy? If you see typos and other mistakes, or have trouble understanding things, please let me know! An altern…
4
The Color of Infinite Temperature
This is the color of something infinitely hot. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range. This…
5
Planets in the Fourth Dimension
You probably that planets go around the sun in elliptical orbits. But do you know why? In fact, they’re moving in circles in 4 dimensions. But when these circles are projected down to 3-dimen…
6
Dead Stars Don’t Radiate
Three guys claim that any heavy chunk of matter emits Hawking radiation, even if it’s not a black hole: • Michael F. Wondrak, Walter D. van Suijlekom and Heino Falcke, Gravitational pair…
7
How I Learned to Love Algebraic Geometry
A more polished version of this article appeared on Nautilus on 2019 February 28. This version has some more material. How I Learned to Stop Worrying and Love Algebraic Geometry In my 50s, too old …
8
Ice
Water is complicated and fascinating stuff! There are at least sixteen known crystal phases of ice, many shown in this diagram based on the work of Martin Chaplin: (Click for a larger version.) For…
9
Tritone Substitutions
A ‘tritone substitution’ is a popular trick for making your music sound more sophisticated. I’ll show you a couple of videos with lots of examples. But since I’m mathematici…
10
Ramanujan's Easiest Formula
A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could f…
11
Mathematical Patterns That Eventually Fail
Sometimes patterns can lead you astray. For example, it’s known that $latex \displaystyle{ \mathrm{li}(x) = \int_0^x \frac{dt}{\ln t} }$ is a good approximation to $latex \pi(x),$ the number …
12
Civilizational Collapse, Part 4
This is part 4 of an intermittent yet always enjoyable series: • Part 1: the rise of the ancient Puebloan civilization in the American Southwest from 10,000 BC to 750 AD. • Part 2: the rise and col…
13
Levels of Excellence
Over on Google+, a computer scientist at McGill named Artem Kaznatcheev passed on this great description of what it’s like to learn math, written by someone who calls himself ‘man aft…
14
Pi and the Golden Ratio
Two of my favorite numbers are pi: $latex \pi = 3.14159… $ and the golden ratio: $latex \displaystyle{ \Phi = \frac{\sqrt{5} + 1}{2} } = 1.6180339… $ They’re related: $latex \pi =…
15
Quark Stars
Wow — evidence that very massive neutron stars may have cores made of deconfined quark matter! The idea of a ‘quark star’ is not new, but I didn’t know it was a serio…
16
Hardy, Ramanujan and Taxi No. 1729
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It …
17
Naturally Occurring Quasicrystals
I love quasicrystals—like crystals, but with patterns that never repeat, like Penrose tiles. But they’ve very rare in nature. They’re created only by the most exotic and violent e…
18
Dividing a Square into 7 Similar Rectangles
This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectan…
19
Random Points on a Sphere
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy R…
20
Entropy in the Universe
If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars: But stars contribute only a tiny fraction of the total entropy in the observable Universe. If…
21
The Busy Beaver Game
This month, a bunch of ‘logic hackers’ have been seeking to determine the precise boundary between the knowable and the unknowable. The challenge has been around for a long time. But on…
22
The missing digit of Stela C
One bad thing about archeologists is that some of the successful ones get a big head. People used to think the Olmecs, who made these colossal stone heads, were contemporary with the Mayans. But in…
23
The Joy of Condensed Matter
I published a slightly different version of this article in Nautilus on February 24, 2021. Everyone seems to be talking about the problems with physics: Woit’s book Not Even Wrong, SmolinR…
24
The Gravo-Thermal Catastrophe
In 1962, V. A. Antonov did some remarkable simulations showing that in Newtonian mechanics, gravitating systems can violate the usual rules of thermodynamics. Instead of reaching equilibrium they c…