leifmetcalf

I especially liked the proof in that book that looks at the action of a group on its Cayley graph to show a subgroup of a free group is free.

This is a trade that is already done by trading businesses. It doesn’t even need to be this explicit; you could for instance dispose one side of a trade to reduce exposure to insiders.

Why do we have that E[max_k alg(k)/opt(k)] is equal to max_k E[alg(k)]/opt(k) ?

Gemini 2.5 at least replies that it seems unlikely to be false without hallucinating a proof. From its thoughts it gets very close to figuring out that A_4 exists as a subgroup.

My mistake, I said unique path when I should have said unique shortest path.

Also, there are trivial solutions with odd cycles and complete graphs which must be excluded. (So the answer to the prompt as originally stated is wrong too)

Let G be a group of order 3*2^n. Prove there exists a non-complete non-cyclic Cayley graph of G such that there is a unique shortest path between every pair of vertices, or otherwise prove no such graph exists.

This seems pretty convincing to me.

At the very least, the story that NVDA dropped because the Deepseek announcement reduced expected demand for cpus seems inconsistent with typical market behaviour. I wonder if we’ll see a correction of the narrative in mainstream outlets.

I was wrong about this. Case is a macro (a special-cased macro even, defined at https://github.com/elixir-lang/elixir/blob/4def31f8abea5fba4...), not a function. It works with pipes because in the AST it's a call, unlike in Haskell where case is its own thing.

Elixir doesn’t even need a special syntax — it gets Haskell’s LambdaCase as a natural consequence of case being just another function, and the pipe operator always chaining by the first argument.

Haskell’s >>= is doing something slightly different. ‘getThing >>= \case…’ means roughly ‘perform the action getThing, then match the result and perform the matched branch’

Whereas ‘getThing |> \case…’ means ‘pattern match on the action getThing, and return the matched action (without performing it).

The >>= operator can also be used for anything satisfying the Monad laws, e.g. your actions can be non-deterministic.

This is according to ‘climate damages compared to market value’.

Haskell gets compiled to core (https://hackage.haskell.org/package/ghc-9.2.1/docs/GHC-Core....) which is pretty similar to lambda calculus, but it has some additions like literals, let expressions, and case expressions.

Huh. If I move my mouse fast enough I can escape the lock.

Back now in NZ

Heat pumps are more than 100% efficient

Auckland Transport does the same thing

I'd be interested to see how effective algae and mosses are at cleaning air, too, since they are so easy to grow and propagate.

I just switched from GSuite to https://www.pobox.com. For $20 a year they manage your email address and forward anything sent to it to another account. I have a gmail free account set up to send emails via smtp through pobox, which works great. It's the service a lot of open-source people use, like gitster.

EDIT: Looks like https://improvmx.com do the same thing, but for free.

With this? http://duriansoftware.com/joe/Optimizing-is-multiple-checks-...

I'm a bit confused, how did you implement let, if, else etc.? I don't really know much about the lambda calculus except for what I learned from a short youtube video.

Ah, that explains it. The link actually works, though.

How does the url http://redacted/ work? I've never seen a url without a tld on the end.

Could I register the domain http://foo ?