neverendingbooks

the topos of unconsciousness

Since wednesday, as mentioned last time, the book by Alain Connes and Patrick Gauthier-Lafaye: “A l’ombre de Grothendieck et de Lacan, un topos sur l’inconscient” is available in the better bookshops. There’s no need to introduce Alain Connes on this blog. Patrick Gauthier-Lafaye is a French psychiatrist and psycho-analyst, working in Strassbourg. The book is […]

May 14, 2022
Grothendieck meets Lacan

Next month, a weekend-meeting is organised in Paris on Lacan et Grothendieck, l’impossible rencontre?. Photo from Remembering my father, Jacques Lacan Jacques Lacan was a French psychoanalyst and psychiatrist who has been called “the most controversial psycho-analyst since Freud”. What’s the connection between Lacan and Grothendieck? Here’s Stephane Dugowson‘s take (G-translated): “As we know, Lacan…

April 21, 2022
The monster prime graph

Here’s a nice, symmetric, labeled graph: The prime numbers labelling the vertices are exactly the prime divisors of the order of the largest sporadic group: the monster group $\mathbb{M}$. \[ \# \mathbb{M} = 2^{46}.3^{20}.5^9.7^6.11^2.13^3.17.19.23.29.31.41.47.59.71 \] Looking (for example) at the character table of the monster you can check that there is an edge between two…

March 16, 2022
Mamuth to Elephant (3)

Until now, we’ve looked at actions of groups (such as the $T/I$ or $PLR$-group) or (transformation) monoids (such as Noll’s monoid) on special sets of musical elements, in particular the twelve pitch classes $\mathbb{Z}_{12}$, or the set of all $24$ major and minor chords. Elephant-lovers recognise such settings as objects in the presheaf topos on…

March 13, 2022
Mamuth to Elephant (2)

Last time, we’ve viewed major and minor triads (chords) as inscribed triangles in a regular $12$-gon. If we move clockwise along the $12$-gon, starting from the endpoint of the longest edge (the root of the chord, here the $0$-vertex) the edges skip $3,2$ and $4$ vertices (for a major chord, here on the left the…

March 8, 2022
From Mamuth to Elephant

Here, MaMuTh stands for Mathematical Music Theory which analyses the pitch, timing, and structure of works of music. The Elephant is the nickname for the ‘bible’ of topos theory, Sketches of an Elephant: A Topos Theory Compendium, a two (three?) volume book, written by Peter Johnstone. How can we get as quickly as possible from…

March 7, 2022
Hexboards and Heytings

A couple of days ago, Peter Rowlett posted on The Aperiodical: Introducing hexboard – a LaTeX package for drawing games of Hex. Hex is a strategic game with two players (Red and Blue) taking turns placing a stone of their color onto any empty space. A player wins when they successfully connect their sides together…

February 26, 2022
Learners’ logic

In the Learners and Poly-post we’ve seen that learners from $A$ to $B$ correspond to set-valued representations of a directed graph $G$ and therefore form a presheaf topos. Any topos comes with its Mitchell-Benabou language, allowing us to speak of formulas, propositions and their truth values. Two objects play a special role in this: the…

February 22, 2022
Yet more topos news

Every topos has its own internal language, the so called Mitchell-Bénabou language, allowing us to speak about formulas and their truth values. Sadly, Jean Bénabou died last week. Here’s a nice interview with Bénabou (in French) on category theory, Grothendieck, logic, and a rant on plagiarism among topos theorists (starting at 1:00:16). Yesterday, France Culture’s…

February 18, 2022
The hype cycle of an idea

These three ideas (re)surfaced over the last two decades, claiming to have potential applications to major open problems: (2000) $\mathbb{F}_1$-geometry tries to view $\mathbf{Spec}(\mathbb{Z})$ as a curve over the field with one element, and mimic Weil’s proof of RH for curves over finite fields to prove the Riemann hypothesis. (2012) IUTT, for Inter Universal Teichmuller…

February 13, 2022