the chapter lead figs in Elementary Applied Topology are amalgams of mathematical & literary images, sprinkled with my own pet theories on literature. this one, from "Sheaves" is based on the Inferno. there are three famous episodes of a pair of sinners, trapped:
* francesca & paolo : mede : in flame
* ugolino & ruggieri : in ice
the sins & the sinners get progressively worse...
to this i added a fourth -- dante & virgil : in earth, then past satan, descending/ascending to escape up to the final image of stars...
this is a satisfying mapping onto the 4 elements (+ quintessence). did dante intend this? not clear, but it's a pretty clear pattern once you see it...
* francesca & paolo : mede : in flame
* ugolino & ruggieri : in ice
the sins & the sinners get progressively worse...
to this i added a fourth -- dante & virgil : in earth, then past satan, descending/ascending to escape up to the final image of stars...
this is a satisfying mapping onto the 4 elements (+ quintessence). did dante intend this? not clear, but it's a pretty clear pattern once you see it...
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prof-g retweeted
Drag-and-drop makes the digital graspable, but building it well is fiddly enough that many don’t bother. Declarative Dragging (with Josh Horowitz & Jeff Heer, #uist2026 best paper award), lets you make an element draggable just by listing the states dragging it can reach.
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publication in mathematics may soon align with the humanities: the unit of progress is the definitive book -- not articles, not proofs -- but a comprehensive framing of and advance in a specific area of mathematics, the reading of which would be a slow educational journey.
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i built an interactive gpt-Site for CTLN's (combinatorial threshold-linear networks) of Morrison-Degeratu-Itskov-Curto. simple neurons with weak/strong inhibition indicated by a digraph. simple ReLU nonlinearity. nice [sometimes chaotic] dynamics!
…ural-choreography.prof-g.chatgpt.site
…ural-choreography.prof-g.chatgpt.site
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teaching the SVD this week.
some historical elements i've learned...
beltrami wrote the decomposition down in 1873.
jordan found it independently the next year.
sylvester called the stretches canonical multipliers in 1889.
schmidt proved the best low-rank approximation he time eckart & young put the same theorem in psychometrika in 1936, it was already decades old.
what was missing was a way to compute it that didn’t square every number in sight: golub & kahan fixed that in 1965. the version that ran for the next twenty years was golub & reinsch, 1970.
golub drove a car whose license plate read PROF SVD. lol...
some historical elements i've learned...
beltrami wrote the decomposition down in 1873.
jordan found it independently the next year.
sylvester called the stretches canonical multipliers in 1889.
schmidt proved the best low-rank approximation he time eckart & young put the same theorem in psychometrika in 1936, it was already decades old.
what was missing was a way to compute it that didn’t square every number in sight: golub & kahan fixed that in 1965. the version that ran for the next twenty years was golub & reinsch, 1970.
golub drove a car whose license plate read PROF SVD. lol...
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i once (back when i wrote EAT) mapped the pantheon onto fields of mathematics...
⚡ Zeus: algebra (king of all, regal, has his way)
🌊 Poseidon: analysis (ruler of waves & winds)
👑 Hera: algebraic geometry (king's consort)
🦉 Athena: logic (sprung from the mind)
💀 Hades: topology (invisible; fundamental, diabolical)
🔨 Hephaestus: applied math (forged, kinda lame)
🏹 Apollo: category theory (arrows)
🎲 Ares: probability (war is stochastic)
🐚 Aphrodite: geometry (lascivious manifolds)
🌙 Artemis: number theory (pure, untrammeled)
🪶 Hermes: combinatorics (quick & clever)
🌾 Demeter: statistics (domestic, earthy)
⚡ Zeus: algebra (king of all, regal, has his way)
🌊 Poseidon: analysis (ruler of waves & winds)
👑 Hera: algebraic geometry (king's consort)
🦉 Athena: logic (sprung from the mind)
💀 Hades: topology (invisible; fundamental, diabolical)
🔨 Hephaestus: applied math (forged, kinda lame)
🏹 Apollo: category theory (arrows)
🎲 Ares: probability (war is stochastic)
🐚 Aphrodite: geometry (lascivious manifolds)
🌙 Artemis: number theory (pure, untrammeled)
🪶 Hermes: combinatorics (quick & clever)
🌾 Demeter: statistics (domestic, earthy)
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i asked claude for their take (w/o sharing mine)... claude's mathematical pantheon:
⚡ Zeus: logic & set theory (axiomatic; Gödelian)
👑 Hera: algebra (guardian of structure)
🦉 Athena: geometry (sprang fully formed)
☀️ Apollo: analysis (rigor, harmony, limits)
🍇 Dionysus: topology (dissolves rigid form)
🎲 Hermes: probability (god of luck)
🏹 Artemis: statistics (Apollo’s twin; bias vs variance)
🌊 Poseidon: dynamical systems (turbulence)
💀 Hades: number theory (hidden wealth below)
🌾 Demeter: combinatorics (counting the harvest)
🔨 Hephaestus: computation (builder of automata)
🐚 Aphrodite: category theory (relationships)
⚔️ Ares: game theory & OR (born of war)
⚡ Zeus: logic & set theory (axiomatic; Gödelian)
👑 Hera: algebra (guardian of structure)
🦉 Athena: geometry (sprang fully formed)
☀️ Apollo: analysis (rigor, harmony, limits)
🍇 Dionysus: topology (dissolves rigid form)
🎲 Hermes: probability (god of luck)
🏹 Artemis: statistics (Apollo’s twin; bias vs variance)
🌊 Poseidon: dynamical systems (turbulence)
💀 Hades: number theory (hidden wealth below)
🌾 Demeter: combinatorics (counting the harvest)
🔨 Hephaestus: computation (builder of automata)
🐚 Aphrodite: category theory (relationships)
⚔️ Ares: game theory & OR (born of war)
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this is a fun one... a site for investigating spectral graph theory of the philly road network -- you can put various streets "under construction" & see what the effect on the graph laplacian eigenvectors is...
…nder-construction.prof-g.chatgpt.site
…nder-construction.prof-g.chatgpt.site
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