Henry P. Towsner

Associate professor of mathematics @Penn. Logic and related topics. Sometimes distracted by RPGs and Judaism. He/him/his. @[email protected]

[Henry P. Towsner @htowsner]

@ProfKinyon ✋

[Henry P. Towsner @htowsner]

@littmath This tweet of Murray's just seems straightforwardly correct.

[Henry P. Towsner @htowsner]

@ereliuer_eteer No, I’m saying that when the source of confusion is the definition, that’s what an explanation should focus on.

No one who understands the definition needs an explanation of why 0.999…=1; the whole reason it’s a topic is that people don’t know (or don’t like) the definitions.

[Henry P. Towsner @htowsner]

Except the conclusion is avoidable, as evidenced by the existence of formalisms that avoid it.

As always, there is no complete explanation that 0.999…=1 which doesn’t discuss what the definitions are.

[Kareem Carr, Ph.D. @kareem_carr]

No matter how close we get to 1, the difference between 0.999... and 1 is smaller than that. What number is smaller than every possible difference? Zero.

So, the difference between 0.999... and 1 must be zero.

The unavoidable conclusion is 1 and 0.999... are the same number.

[Henry P. Towsner @htowsner]

@mathemensch There are a handful of seminars in math that are known for having much more interactive cultures, where the audience does a lot of interrupting and asking questions and discussing, so it’s definitely possible within math.

[Henry P. Towsner @htowsner]

My preferred version of the Shavuot story is that Moses came down from the mountain and wrote the first recipe blog: "I've learned a great new recipe for cheesecake, but before I tell you how to make it, I'm going to read these tablets to you."

[Henry P. Towsner @htowsner]

@archernikov Yes, but…

[Henry P. Towsner @htowsner]

@jbeardsleymath That sounds like a totally different system than what I'm used to (both here at Penn and at CMU when I got my PhD). I'm used to a system where the content of the exam is agreed to by the PhD student and the committee, based on that particular students' research interests.

[Henry P. Towsner @htowsner]

@jbeardsleymath I'm sort of confused by this. If you don't care whether your PhD student knows Harnack's Lemma, can't you just tell them not to include it in the qual syllabus?

[Henry P. Towsner @htowsner]

It’s surprising to me that there could be someone in anabelian geometry, of all areas, who’s this wrong about bay leaves.

[Daniel Litt @littmath]

Limiting the replies to this tweet to descriptions of what bay leaves taste like.

[Henry P. Towsner @htowsner]

@SC_Griffith In some religions, the practices are what matters, and believing in a specific reason for them is secondary. It’s helpful, perhaps in the long run necessary, to find the practice meaningful, but that’s a lot easier than reaching belief in the sense of a creedal religion.

[Henry P. Towsner @htowsner]

@SC_Griffith The importance of belief varies a lot from religion to religion. It’s very important to Christianity, so the US and Europe, religion and belief get conflated a lot, but Christianity is highly unrepresentative of religions in general in this point.

[Henry P. Towsner @htowsner]

@CihanPostsThms Oh, I remember this result. I think I may have been the skeptic he’s referring to.

[Henry P. Towsner @htowsner]

and the fact that some of its outputs happen to be factual isn't a good indication that it will be easy to engineer it for all its outputs to be factual.

[Henry P. Towsner @htowsner]

This, and a lot of the discussion about ChatGPT's factual accuracy, seem to me like arguing with my son about whether he's a kitty. Why, just the other day he claimed he had a tail! It's wild how much he'll invent to try to justify his obviously false claim.

[Kevin J.S. Zollman @KevinZollman]

This is an incredibly deep-dive into how much ChatGPT will invent in order to keep the conversation going.

[Henry P. Towsner @htowsner]

But the behavior of ChatGPT doesn't seem very informative about how hard that will be: the fact that it doesn't communicate in a genre it wasn't designed to communicate in isn't a very good indication that it will be difficult to make it do that,

[Henry P. Towsner @htowsner]

@TobyMeadows @KevinZollman @nescio13 Spector's functional interpretation of second order arithmetic