@maonu Locus Solum: From the Rules of Logic to the Logic of Rules
Category theory is quite useful for organizing logic, because you have different levels; some are purely syntactic rules, but you can easily label your arrows with meanings, or other elements of a monoidal product. Saying A => B is syntactic, and slightly different from the thing you might be intending to say, CT helps organize the levels
Just test-drove the topo editor that @bohwaz@mamot.fr fixed up, and it's working great, nice work!!
Scaling is a bit off; I had to scale up pretty much everything (lines, marks, text) by 200-300%, but that's due to images being so huge nowadays.
Looking forward to updating my photos of The Crag Next Door with proper topos!
Huawei believes his esoteric concept of the #topos could be key to building the next generation of #AI, and has hired Fields medal-winner Laurent Lafforgue to explore…But #Grothendieck ’s motivations were not worldly ones, as his former colleague Pierre Cartier understood. “Even in his mathematical milieu, he wasn’t quite a member of the family. He pursued a kind of monologue, or rather a dialogue with mathematics and God, which to him were one and the same.”
A larger question is whether this is what Grothendieck would have wanted.
In 1972, during his ecologist phase,
concerned that capitalist society was driving humanity towards ruin,
he gave a talk at CERN, near Geneva,
entitled
"Can We Continue Scientific Research?"
He didn’t know about AI
– but he was already opposed to this collusion between science and corporate industry.
Considering his pacifist values, he would probably also have been opposed to Huawei’s championing of his work;
-- its chief executive, #Ren #Zhengfei, is a former member of the People’s Liberation Army engineering corps.
The US department of defense,
as well as some independent researchers,
believes Huawei is controlled by the Chinese military.
Huawei insists it is a private company,
owned by its employees and its founding chairman,
Ren Zhengfei,
and that it is “not owned, controlled or affiliated to any government or third-party company”.
Lafforgue points out that France’s IHES,
where Grothendieck and later he worked,
was funded by industrial companies
– and thinks Huawei’s interest is legitimate.
Caramello, who is the founder and president of the Grothendieck Institute research organisation,
believes that he would have wanted a systematic exploration of his concepts to bring them to fruition.
“Topos theory is itself a kind of machine that can extend our imagination,” she says.
“So you see Grothendieck was not against the use of machines.
He was against blind machines, or brute force.”
What is unsettling is a degree of opaqueness about Huawei’s aims regarding AI and its collaborations,
including its relationship with the Grothendieck Institute,
where Lafforgue sits on the scientific council.
But Caramello stresses that it is an entirely independent body that engages in theoretical,
not applied research,
and that makes its findings available to all.
She says it does not research AI and that Lafforgue’s involvement pertains solely to his expertise in Grothendieckian maths.
In mid-April, dapper Parisians are filing out of the polished foyer of a redeveloped hotel in the seventh arrondissement, heading for lunch.
The first French TV programmes were broadcast from the building -- now, #Huawei is pushing for a similar leap in AI here.
It has set up the Centre-Lagrange,
an advanced mathematics research institute, on the site and hired elite French mathematicians,
including Laurent Lafforgue, to work there.
An aura of secrecy surrounds their work in this ultra-competitive field,
compounded by growing suspicion in the west of Chinese tech.
Huawei initially refused to answer any questions, before permitting some answers to be emailed.
Grothendieck’s notion of the #topos,
developed by him in the 1960s,
is of particular interest to Huawei.
Of his fully realised concepts, toposes were his furthest step in his quest to identify the deeper algebraic values at the heart of mathematical space,
and in doing so generate a geometry without fixed points.
He described toposes as a “vast and calm river”
from which fundamental mathematical truths could be sifted.
#Olivia #Caramello views them rather as “bridges” capable of facilitating the transfer of information between different domains.
Now, Lafforgue confirms via email,
Huawei is exploring the application of toposes in a number of domains, including telecoms and AI.
Caramello describes toposes as a mathematical incarnation of the idea of vision;
-- an integration of all the possible points of view on a given mathematical situation that reveals its most essential features.
Applied to AI, toposes could allow computers to move beyond the data associated with, say, an apple;
-- the geometric coordinates of how it appears in images, for example, or tagging metadata.
Then AI could begin to identify objects more like we do
– through a deeper “semantic” understanding of what an apple is.
But practical application to create the next generation of “thinking” AI is, according to Lafforgue, some way off.
„Die Umgestaltung der Kärntner Straße war in der Hinsicht revolutionär, weil sie Unternehmen klargemacht hat, dass sie nicht zwangsläufig in Konkurs gehen, wenn eine Fußgängerzone kommt“
Dass Städte jahrtausendelang ohne Autos funktioniert haben, das haben die meisten vor lauter Abgase wohl schon vergessen, gehabt,
Auszug aus dem spannenden #ORF #Topos zur FuZo Kärntnerstraße
Das Überraschende daran ist, dass es so gar nicht überrascht:
"Die Gruppe 47 war ein 'boys club' (...) , dessen männliche Dominanz das Leben und Wirken der wenigen Autorinnen – gut 200 Männer stehen 30 Frauen gegenüber – maßgeblich bestimmte."
Hello everyone!
Tonight I'll be livestreaming some livecoding with Topos again, trying to make some generative melodies. If you're curious, come check it out on my channel, 8PM on my channel!
https://www.youtube.com/watch?v=_lPN1H0VP0U
#livecoding #Topos
Hello everyone!
Tonight I'll be livestreaming some Topos livecoding again! See you on YouTube at 8 pm French time!
https://youtube.com/watch?v=iR8jnxD359U
#livecoding #Topos
The poll has spoken!
I'll be streaming my discovery of @bubobubo's Topos tonight at 20h French time.
Sehr interessanter Artikel von #topos zur Idee und Umsetzung von einem #Einküchenhaus
Küchenrevolution in den 1920er Jahren
https://topos.orf.at/vor-100-jahren-einkuechenhaus100
Just watched a characteristically great talk by @jonmsterling on Synthetic Domain Theory. It's extremely clear, and if anyone is looking for a great reason for people who care about #ComputerScience to care about #topos theory, I highly recommend it (though maybe people who follow me on mastodon are more likely to already have good reasons of their own, haha)
Lawvere's Conceptual #Mathematics. Friedman's The Little Schemer. These two books provide playful approach to their subject matter, toying with camp while stealthily introducing the reader to advanced concepts that they will only later in their journey recognize (#topos theory for CM, #compilers for TLS).
I consider them to be truly masterful & singular pedagogic demonstrations. What other works fit into this category?
Beim @neusprech mal wieder das Wort #Topos gehört. Mein Eindruck ist, dass das nur in journalistischen Kreisen verwendet wird. @kaibiermann bestätigt hier den Eindruck. 
#Geoveille #Rediff #Topos #Géographie #geography #Spatialité
À la recherche de l’espace perdu… Lecture géographique de Marcel Proust, chez MondesSociaux par Lionel Dupuy #Chôra https://sms.hypotheses.org/19303
"Nonetheless one should learn the language of topos"
- Carlin McLarty on #Grothendieck's 1973 #topos lectures
