dddbbb

'Verified' ticks in general are so bizarrely mismanaged. See also Twitter removing the status of controversial political figures. I feel like they should be totally open access to anyone who can provide irrefutable proof of identity, rather than these odd status symbols.

Maybe it's different in other countries (I am in the UK), but I feel as if there isn't enough content for a recommender system to even be useful. I feel like after browsing through the catalogue a few times, I have a rough idea of most things I would ever possibly be interested in. There's just not that much there. Either that, or the recommender system is working too well and I never see anything beyond what Netflix wants me to.

I would nominally agree with this logic, but surely the exact same applies when voting? Should people not bother voting because they are just one in a sea of many?

Buying the cheapest Casio can also be a status signal, similar to the CEO of Goldman Sachs wearing a Swatch. Buying a truly cheap watch is a signal of 'I don't care' (which may be true, or may be affected), whereas getting into expensive watches can get very complicated. There's plenty of stories from investment banking about the signals that watches send, from my understanding people are more likely to poke fun at a Tag Heuer than a Casio.

To ask a very amateur question, why do people think Bitcoin specifically will succeed? Aren't there dozens of coins out there which have fixed some of it's most glaring flaws?

> This shouldn't be so controversial, given that they work for us,

Pretty suspect line of reasoning when you apply it to literally any other scenario.

They didn't set out to explicitly prove 1+1=2, they just got around to it after 2 volumes, it didn't require 2 volumes of background. A direct proof of 1+1=2 is pretty short in most logical systems.

Great talk. The definition of observational equivalence is very elegant. I instantly thought it made no sense or must be a partial definition, then the simple example given on the next slide explained it perfectly.

For many roles at a hedge fund, being able to do mathematics quickly and intuitively is a valuable skill. Not sure why an economist applying for an MD job would need to be tested on that, though.

It seems to me like Lean has a lot of the momentum at the moment. It's clear that other projects like Coq suffer from a lack of traditional mathematicians formalising modern, fashionable topics. Kevin Buzzard's implementation in Lean of perfectoid spaces is a great example of that boundary being broken, as far as I can tell the most advanced Coq proofs are the four colour theorem and Feit-Thompson theorem, which have analogue proofs from the 60s and 70s.

Increased assurance that the proof is correct and the various standard benefits of digital over analogue data. This software automatically checks the validity of the proof (with a very small, manually verified core of code doing so), it does not automatically generate proofs wholesale. The proof itself is written by the mathematician interactively, which is still a manual process that requires skill, creativity and thought.

Totality is optional in Idris. Also, the big dependently-typed languages like Coq, Agda, Idris all support corecursion, so they can run programs infinitely provided the program does something productive.

I'm not sure what Turing completeness has to do with such a problem. There's a theoretical non-Turing complete subset of HTML+JS that has all the problems you claim, meanwhile Markdown with a built-in lambda calculus interpreter is Turing complete yet much less problematic. I think you're overcomplicating things for yourself by bringing terms like 'Turing-complete content' into the discussion, surely it just suffices to explain that the more powerful the system, the more open to abuse it is?