16,918 karma · joined July 13, 2015
1) someone might have paid them to do a real poll and they faked it, which is just straightforward fraud with a clear victim.
2) (the fun one) they might have done it to manipulate political prediction markets, which gets into securities fraud questions.
I am in favor of deporting people that have not been here long, but there has to be a way to fine people and get them documented after a certain amount of time.
OTOH, my borrow checker is provably sound, which is why I am using it.
The only ethical way to do it is better security at the border and making legal immigration and visits much easier. You can’t just snatch people who are established in communities and put them into camps without leading to a thoroughly justified moral outrage.
for all n there is some natural number x such that BB(n) = x
x like all natural numbers is trivially computable.
But BB(n) as a function that you could run and _find_ x, is not computable in general, because it would entail solving the halting problem.
I actually think it would be very smart for the big AI labs to get together to fund an independent organization to manage such a thing, and hire mathematicians to run it.
What is happening now is that some aspects of mathematics are turning into essentially an exercise in software engineering. It is well known that proofs and computer programs have an isomorphism, and I think the eventual merger is more or less inevitable.
That's not to say that there isn't an infinite amount of work remaining for mathematicians to do. There are only so many problems that are going to be amenable to this approach.
No, the other way around. The natural language proof was derived from the lean code, badly. This is my experience with using claude and lean to prove things. Its natural language explanations drift a lot from the lean, both before and after. But the lean code is the lean code.
The formalization went through, but there were _several_ mistakes in the original paper that it uncovered, from type setting errors to (many) formulas that quantified over all resources as printed, but actually applied to only arising resources in the calculus..
So the formalization did give me a formally verified borrow checker that I could use to build a programming language on top of, but it was _not_ exactly the borrow calculus that was printed in the paper.
I expect this is the most common experience when mechanizing a printed paper. There are a lot of skipped steps and handwaving.