MW: We’re reviewing hyperdoctrines, which are specially nice functors B: FinSet → BoolAlg. When we have such a functor, any map f of finite sets gives a homomorphism of boolean algebras, B(f). But we’ve seen this is a morphism and a functor. (“It’s a floor wax and a dessert topping!”) What do you think about the term “adjoint morphism”? It might help keep the two levels straight.
Monthly Archives: December 2024
From Kepler to Ptolemy 5
Origins of the Ptolemaic System
We’ve worked backwards from Kepler to Ptolemy. What inspired Ptolemy and his predecessors (Apollonius and Hipparchus) to come up with this scheme in the first place?
First-Order Categorical Logic 7
MW: John, it’s been eons since we last discussed First-Order Categorical Logic: not since September 2019! (I read a lot of Russian novels during the break.) But New Year’s seems like a good time to resume the tale.
JB: Yes indeed! It’s been a long time, and it’s mostly my fault. Let’s see if we can get back up to speed.
Filed under Categories, Conversations, Logic
From Kepler to Ptolemy 4
Speed Laws
In Ptolemy’s system, the point on the deferent moves uniformly as viewed from a point called the equant point, or sometimes just equant. The equant, the center of the deferent, and Earth all lie in a straight line, with the center midway between Earth and the equant.
Set Theory Jottings 2. Cantor’s Paradise
Cantor’s Paradise
No one shall expel us from the Paradise that Cantor has created for us.
—Hilbert, “Über das Unendliche” [On the Infinite], in Mathematische Annalen 95 (1925)
I used to believe these myths about the history of set theory:
Filed under History, Set Theory
Set Theory Jottings 1: Philosophy and Naive Set Theory
These notes are not a systematic “Introduction to Set Theory”. I intend them as a
blend of history, intuition, and exposition, with an occasional dash of philosophy.
Filed under Set Theory
From Kepler to Ptolemy 2
I’ll begin with Kepler’s first two laws, and work backwards to Ptolemy’s system. Seeing Keplerian astronomy recast this way will expose the bones of the Ptolemaic system.
Deferents and Epicycles
From Kepler to Ptolemy 1
Quite some time ago I started writing up notes, for my own amusement, on the history of astronomy. I’ve worked on it on-an-off over the years, but there always seems to be a bit more I should add. Eventually the pdf version will be ready for prime time. Meanwhile I’ve decided to convert what I have into a series of posts. Enjoy!
Diagonal Argument 