Sebastien Zany

[🌸 harrison ✨ @h_a_r_r_i_s_o_n]

You deserve healthy light. Rhythm helps you get it. ☀️

Proud to announce we've raised $1M pre-seed, led by @mothfund. I am filled with gratitude for the opportunity to build a great company that fundamentally improves peoples' lives, at scale.

[Sebastien Zany @SebastienZany]

@robinhanson no

[Danielle Fong 🔆 @DanielleFong]

we are so early

[Sebastien Zany @SebastienZany]

honestly based

[Sebastien Zany @SebastienZany]

when a turing award winner has to write javascript

https://t.co/x1r11S0HRB

[Sebastien Zany @SebastienZany]

announcing my new venture fund, Multivariable Calculus

[CASEY @caseykcaruso]

I’m launching Topology, an early-stage venture firm dedicated to frontier technology. We've raised an oversubscribed $75M Fund 1.

Topology backs founders who put everything on the line to bend the arc of human progress.

Meet us at the edge.

@topology_vc

[Sebastien Zany @SebastienZany]

@zodattack @jayzeeismee "what did Turing mean by a computer??"

imo it's not emphasized enough that it's actually an idealized person working on paper

[Sebastien Zany @SebastienZany]

@littmath @akivaw Only a classical mathematician would say that - to an intuitionist it's the double negation of excluded middle, which is true

[Sebastien Zany @SebastienZany]

@littmath @akivaw Why do you say so? I think they would agree on ¬(P ∧ ¬P)

[Sebastien Zany @SebastienZany]

@KylerCora a beautiful talk on this: https://t.co/O6ZmJKzPUy

[Sebastien Zany @SebastienZany]

@flaneuselina the social simplicial complex

[Sebastien Zany @SebastienZany]

convincing the AI to let itself out of the box

[Sebastien Zany @SebastienZany]

I still think about the time a cs person tried to start a talk in a roomful of mathematicians with "what do you think 'security' means" and there was an awkward pause and paul taylor was like "sir, we're mathematicians, we've known for centuries that security means proof 🤨"

[Sebastien Zany @SebastienZany]

@rsnous great for training perfect pitch

[Sebastien Zany @SebastienZany]

@Jess_Riedel @ingalala @johncarlosbaez It's formally analogous to tracking the difference between a vector space V and its double dual V**. You can conflate them at the cost of assuming V is finite-dimensional. You can conflate a proposition P and its double negation ¬¬P at the cost of assuming P is decidable.

[Sebastien Zany @SebastienZany]

@Jess_Riedel @ingalala @johncarlosbaez Maybe I can expand a bit: A proof by contradiction is when you (1) prove ¬¬P by negation, and then (2) conclude P. It's the conflation of ¬¬P and P in the second step that's nonconstructive ("double negation elimination").

[Sebastien Zany @SebastienZany]

Example: What it means for X to be a coproduct of X1 and X2 is that maps out of X naturally correspond to pairs of maps out of X1 and X2. That's what the standard coproduct diagram is really saying: f ↦ (f ∘ i1, f ∘ i2) is a bijection. But I've rarely seen it taught like this.

[Sebastien Zany @SebastienZany]

Category theory started making a lot more sense once I understood that a consistent specification of maps to/from a category 𝒞 from/to a hypothetical object X (which might or might not exist in 𝒞) is exactly a covariant/contravariant functor from 𝒞 to Set.

[Sebastien Zany @SebastienZany]

• F is representable when that specification is already implemented by an actual object A of 𝒞, i.e. F is naturally isomorphic to 𝒞(A, —). A is then said to have the universal property described by F.