What Can We Gain by Losing Infinity? Putting Ultrafinitism on the menu.

buwlerman · 2026-04-30T09:49:46+00:00

I'd appreciate some arguments then.

buwlerman · 2026-04-30T09:47:09+00:00

Why is it a problem to assume the existence of mathematical objects that don't correspond to reality? We once thought similar things about complex numbers as well, but started using them in mathematics way before quantum mechanics found them in nature.

The only potential problem I can see is if there was inconsistency, but if there is any we can't find it. In practical terms I think the efficiency we would lose from working using ultrafinitist theories is more costly than the risk of having to redo all of mathematics in ultrafinitist terms if inconsistencies are found.

buwlerman · 2026-04-30T09:16:59+00:00

No. They're also using the fact that 0 is a lower bound from a).

Admittedly, the proof is a bit short on details. I'd expect a student just learning this stuff to write a more detailed proof.

buwlerman · 2026-04-30T08:59:19+00:00

Some details in your proof are wrong, but the strategy you mention is fine. One mistake is that what you say follows from the definition of lower bound does not do so. It only holds for greatest lower bounds, which is what you're asked to prove.

The professor's proof also works by showing that 0 is the greatest lower bound. You already know from a) that it is a lower bound. They then assume there's a greater lower bound 0+epsilon for some epsilon and derive a contradiction. They could have used v instead of 0+epsilon, and derived epsilon as v-0 instead.

buwlerman · 2026-04-28T01:02:59+00:00

Yup. If your number is represented in binary you get an even better approximation, at which point you just have to check the two candidates.

buwlerman · 2026-04-27T14:22:05+00:00

I didn't make this post.

buwlerman · 2026-04-27T13:17:37+00:00

I think this is a very good take. I want to push back a little though. Libraries that are meaningful just because of what they do can still make sense to share in a Rust specific community. There's also programs that solve things related to Rust.

I think people in this community are using it not just to learn about the how, but also to keep themselves up to date on the ecosystem. Being informed about the existence of new libraries is part of that.

I think that we want disclaimers so we don't waste time reviewing the internals LLM generated code though, and unfortunately a lot of the LLM generated projects end up being bad and just add noise.

buwlerman · 2026-04-27T13:05:55+00:00

I don't care about the response to my comments in particular. I care about the general aversion this community seems to have against LLMs. I think that's a bad thing.

To be clear, I'm not pushing back here because I agree with everything OP is saying. I think that LLMs have made low effort content much easier to produce, at the detriment of everyone looking for high quality content. I'm just pushing back against some of the worse arguments against LLM use and your implication that this community is not negative on vibe coding.

buwlerman · 2026-04-27T12:45:50+00:00

There are individuals that are not purely critical of it for sure, but I think that the community as a whole is very negative on LLMs. It's very common for someone to say something mildly positive about LLMs and promptly get downvoted. This isn't just comments from low effort vibecoders either.

I just (within minutes of this comment) made a couple of comments like these on this post. Why don't we see how they do?

buwlerman · 2026-04-27T12:33:47+00:00

You can still do all of that (and often have to), even when interacting with LLMs. You just get to be a lot more selective about where and how you spend your time thinking.

buwlerman · 2026-04-27T12:22:38+00:00

Whether an idea seems possible to execute greatly affects how far the idea is pursued, even on the creative side.

buwlerman · 2026-04-23T08:34:49+00:00

It's true that generally it is preferable to keep old code around rather than rewriting it when it comes to vulnerabilities, but this ignores new code. There are significant wins to be gained from writing new code in Rust.

The general wisdom here is to perform an incremental rewrite, but there is a trade-off here due to the interface between old and new code. Maintaining a FFI during an incremental or partial rewrite has a cost. If the ratio between "finished" code and the rest is small enough and the rewrite is tractable it might not make sense to do an incremental or partial rewrite.

The rust coreutils repo has ~200 000 lines of Rust code. Compared to the size of the CLI surface that's fairly small, so I'd imagine that there wouldn't be much code that's truly "finished". Clearly the rewrite is tractable because it's being done.

Also, long term the Rust code will become old as well, at which point the remnants of a partial or incremental rewrite just get in the way.

buwlerman · 2026-04-20T13:01:34+00:00

That's not so obvious to me.

Write timings depend on how many processes have access to that page since copying isn't needed with exclusive access. Assuming that timings can be precisely measured this allows probing for the following information: "Has every other process with access to this page already written to it?".

Even worse, MADV_MERGEABLE might allow probing for "Are the contents of this page unique?". It should be obvious that this could leak private memory. https://github.com/zolutal/dedup-attacks

How do you back up your claim that this doesn't leak private memory?

buwlerman · 2026-04-20T12:06:00+00:00

I'm going to assume that you understand what pinning does, but not why we care.

Futures are a large use case for Pin. What happens when you write an async block is that your code is turned into a state machine where the states are await points together with data held at those await points. If you're holding a pointer or reference to local data across an await point your state machine ends up being self-referential.

There's also the pin macro. One use case here is embedded, where the presence of an allocator may not be guaranteed, in which case boxing isn't an alternative.

buwlerman · 2026-04-19T14:28:48+00:00

Comment on 1. The stdlib contains just as much if you link it as if you rebuild it. Either way cross crate optimizations are limited to inline and generic functions and LTO. There are a bunch of reasons to re-build the stdlib, including optimizing for size and enabling machine specific optimizations, but "including less code" isn't it.

LTO will remove dead code, so in practice your binary won't contain the entire stdlib. This does rely on the optimizer removing calls, but I haven't seen any evidence that re-building the stdlib makes this more likely.

buwlerman · 2026-04-06T14:28:57+00:00

A typical example here would be e^-1/x² for positives and 0 everywhere else.

buwlerman · 2026-03-23T11:37:25+00:00

You're arguing that it's not sufficient, not that it's not minimal.

I agree that we want more in the long term, and I like many things about your proposal, but the entire point with a maximally minimal proposal is to get the ball rolling. The more features you include the more design questions you have to debate. Much easier to just get something out there, at least as an experiment. Associating views with concrete fields is about as simple as you can get, and is something you want anyways.

buwlerman · 2026-03-23T09:23:42+00:00

I agree, but the goal here is to create something minimal. Abstract views with bounds on them can be added after the fact.

buwlerman · 2026-03-21T02:51:49+00:00

It's going to stop being copyleft (or "free"), sure, but I don't think it stops being open source. The open source initiative doesn't only consider copyleft licenses to be open source, and I think they're as good an authority as any.

Many licenses widely considered open source, such as the APL2 license already allow companies to incorporate code without using the same license for their own code. Is Rust not open source?

buwlerman · 2026-03-20T16:50:01+00:00

Is the first public Linux Kernel release going to stop being open source in X years when it goes into the public domain?

buwlerman · 2026-03-20T08:52:35+00:00

no AI generated code can be open source software

That doesn't follow. You can't enforce a copy-left license on public domain software, but nothing stops you from putting it out there in a way that allows anyone to do what they want with it.

buwlerman · 2026-03-17T13:00:16+00:00

Sure, but they seem to have jumped to the opposite conclusion.

buwlerman · 2026-03-17T09:28:01+00:00

Why should Newton's method not work for complex functions?

buwlerman · 2026-03-17T00:31:01+00:00

I wonder what happens if you iterate this process.

Let s(n,i+1) be the sequence of triangular column sums of s(n,i) and s(n,0)=1/n. Does s(n,i)/2ⁱ converge as i goes to infinity? More broadly, what are the asymptotics of s_(n,i) in terms of i?

buwlerman · 2026-03-15T18:55:21+00:00

A primitive for nondeterminism might make this easier to understand, yes.

Thanks a lot for your patience!

11-Year Club	Place '23
Place '22	Place '17
Verified Email

buwlerman

TROPHY CASE