Maxwell’s Relations (Part 1)
The Maxwell relations are equations that show up whenever we have a smooth convex function They say that the mixed partial derivatives of commute, but also that the mixed partial derivatives of various functions constructed from commute. So in a sense they are completely trivial except for the way we construct these various functions! Nonetheless they are very important in physics, because they gi
Applied Category Theory Course
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 Category Theory. I’ve started an informal online course based on this book on the Azimuth Forum. I’m getting pretty sick of the superficial quality of my interactions on social media. This could be a way to do so
Open Petri Nets (Part 1)
Jade Master and I have just finished a paper on open Petri nets: • John Baez and Jade Master, Open Petri nets, Mathematical Structures in Computer Science, 30 (2020), 314–341. Abstract. The reachability semantics for Petri nets can be studied using open Petri nets. For us an ‘open’ Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri
Large Countable Ordinals (Part 1)
I love the infinite. It may not exist in the physical world, but we can set up rules to think about it in consistent ways, and then it’s a helpful concept. The reason is that infinity is often easier to think about than very large finite numbers. Finding rules to work with the infinite is one of the great triumphs of mathematics. Cantor’s realization that there are different sizes of infinity is t
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-dimensional space, they become ellipses! This animation by Greg Egan shows the idea: The plane here represents 2 of the 3 space dimensions we live in. The vertical direction is the mysterious fourth dimension. The
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 what the question was! Since today is Towel Day, let me reveal that now. If you try to get several regular polygons to meet snugly at a point in the plane, what’s the most sides any of the polygons can have? The answer is 42. The
1
リリース、障害情報などのサービスのお知らせ
最新の人気エントリーの配信
j次のブックマーク
k前のブックマーク
lあとで読む
eコメント一覧を開く
oページを開く
Categorical Semantics of Entropy
The Madelung Rules
The Koide Formula
Hypernuclei
Categories of Nets (Part 1)
A Second Law for Open Markov Processes