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Ed J. Pedraza-Robles proslijedio/la je TweetHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Prediction: In the future, graph complexity measures and graph decompositions (both the pure sort coming from combinatorics and the applied sort coming from network theory), adapted from graphs to string diagrams, are going to be *incredibly* important in applied category theory
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Informatics elevates constructivism from being a mere philosophical position, to the much higher status of being a tool that's actually demonstrably useful in some situations Parts of category theory do the same service for some other positions, including pluralism
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Interesting, 'A Functorial Excursion Between Algebraic Geometry and Linear Logic', by
@pamellies, https://www.irif.fr/~mellies/papers/Mellies20submitted.pdf …: "the guiding idea here is that linear logic should be seen as the logic of generalised vector bundles, in the same way as Martin-Löf type theory ...Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
Ed J. Pedraza-Robles proslijedio/la je Tweet
tl;dr If your philosophy of mathematics is so naive that it can't distinguish between proofs (which are written and read by humans, in human languages) and proof-objects (which are combinatorial things with metalogical soundness properties) then, well, sucks to be you
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Ed J. Pedraza-Robles proslijedio/la je Tweet
One perspective on how topoi generalize classical logic? The internal logic of Set is classical logic so the functions determine the rules of classical logic. In a topos you can still think of the objects as sets but now the maps between them are restricted or expanded.
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Richard Feynman found trigonometry notation to be ambiguous and confusing. "If I had sin f, it looked like s×i×n×f" So he decided to create his own notation. See below.
What do you think?pic.twitter.com/61ByeX7LMz
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Il y a visiblement deux types de topologues algébristes : celleux pour qui une preuve par chasse aux diagrammes est "une preuve par incompréhension" et celleux pour qui c'est la chose la plus naturelle au monde.
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Do you believe in the Holy Trinity? Logic, Languages, and Categories are but Three Manifestations of One Divine Notion of Computation — (Saint) Harper
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Take a 600-cell in 4D with 120 vertices ±v_i, i=1…60 Define F(x)=𝚷_i v_i·x Stereographically project F from a 4-sphere to 3D, then Fourier-transform from momentum space to position space. Result: this hydrogen wave function, with energy level n=61. https://www.gregegan.net/SCIENCE/SymmetricWaves/SymmetricWaves.html …pic.twitter.com/DdYMD55XsY
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Calls: Formal Grammar 2020: Call for Papers: AIMS AND SCOPE: FG provides a forum for the presentation of new and original research on formal grammar, mathematical linguistics and the application of formal and mathematical methods to the study of natural…http://dlvr.it/RMYgQH
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Ed J. Pedraza-Robles proslijedio/la je Tweet
A "spin ice" is made of tetrahedra of magnetic ions. In the lowest-energy states each tetrahedron has 2 ions with spins pointing in and 2 with spins pointing out. There are many ways to achieve this, so there's built-in randomness - entropy - even at absolute zero! (1/n)pic.twitter.com/jwMnQCJcne
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Partially Annotable (Unexpected) Counter-Memes, Glyph-Resultatives, and 'Upward Entailing' Phono-Clicks and Why This is Fatal for NLP
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Let 2020 be the year you push back against postmodern physics: learn what derivatives are before trying to debunk climate science. (dude found a paper showing that the derivative of x is decreasing and interpreted it to be saying that x is decreasing lmao) https://twitter.com/mynameisjerm/status/1212646012428398592 …pic.twitter.com/Bg32FFZbBO
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Knowing a little physics, like knowing a little economics or maths, can be dangerous. It’s the threat from physics 101. You’re likely to make mistakes that neither laypeople or experts would. If you can’t model a quark/graviton properly, how can you model planetary dynamics?https://twitter.com/ATomalty/status/1212625480718987264 …
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Ed J. Pedraza-Robles proslijedio/la je Tweet
There is so much beauty in the mathematical pages of Wikipedia
https://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb …
This gif shows how to create a rhombic dodecahedron honeycomb by adding a pyramid to each face of an alternating cubic lattice ...pic.twitter.com/E1tTgmImrwHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
Ed J. Pedraza-Robles proslijedio/la je Tweet
Killing the Hydra. Cut off head at step n, replicate at lower node (if possible) with n copies of the Hydra through original node. Theorem 1. There is a winning strategy to kill the Hydra. Indeed, every strategy is winning. Theorem 2. Theorem 1 is not provable in PA.pic.twitter.com/XCqSiJMQ40
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Happy New Year! A bunch of us are trying to develop "applied category theory" - and now we've started a new journal on this subject, called "Compositionality". It's free to publish in, and free to read. The first issue just came out! (1/n)https://johncarlosbaez.wordpress.com/2019/12/30/compositionality-first-issue/ …
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Ed J. Pedraza-Robles proslijedio/la je Tweet
I love these notes. I particularly like the emphasis on drawing categories as directed multigraphs. Categories are often thought of as these huge abstract things but to really understand them you also need to think about their underlying graphs.https://twitter.com/PaoloPerrone8/status/1209354792746864641 …
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Ed J. Pedraza-Robles proslijedio/la je Tweet
Is there a set with 2.5 elements? No! But here's a "groupoid" with 2.5 elements. To get it, just take a set with 5 elements and fold it in half. The point in the middle gets folded over, and becomes half a point. Sounds wacky, but you can make this into rigorous math! (1/n)pic.twitter.com/vJttTq29S4
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