Hacker News: tmhn2

New comment by tmhn2 in "The Dark Night of Mathematics"

tmhn2 — Sat, 25 Jul 2026 17:39:55 +0000

It's important to remember that historically many advances have been made without "customer value" in mind. Indeed, freeing oneself from such concerns can open up unexpected avenues for discovery which only later provide "customer value".

New comment by tmhn2 in "The Dark Night of Mathematics"

tmhn2 — Sat, 25 Jul 2026 17:32:45 +0000

That seems OK to me. I'd rather live in a state that funds beauty than one that doesn't. Think grants for artists, etc. A strictly practical world is not a good world to live in.

New comment by tmhn2 in "Shingles Vaccine Linked to Slower Biological Aging in Older Adults"

tmhn2 — Mon, 16 Feb 2026 05:37:47 +0000

I think one reason it's discouraged is that it's not completely clear how long it lasts, and getting it early may result in less protection later in life. Also it's only been tested in that age group. (At least, this is what I heard when I researched getting it early a while ago).

New comment by tmhn2 in "The Case That A.I. Is Thinking"

tmhn2 — Tue, 04 Nov 2025 09:38:16 +0000

Research mathematicians have been finding the tools useful [1][2]. I think those problems are interesting, novel, and hard. The AI might stumble sometimes, but it also produces meaningful, quality results sometimes. For experts working on interesting problems, that is enough to be useful.

[1] https://mathstodon.xyz/@tao/115420236285085121 [2] https://xcancel.com/wtgowers/status/1984340182351634571

New comment by tmhn2 in "Astronomers unveil strong magnetic fields spiraling Milky Way's black hole"

tmhn2 — Thu, 28 Mar 2024 03:45:37 +0000

In that usage the object (football) ends up in the state of spiralling. So the HN title would, strictly speaking, mean that the magnetic fields are causing the black hole to spiral, which isn't right.

It's probably sort of being mixed up with the transitive verb "to circle", which goes the other way, with the subject ending up in a state of circling.

New comment by tmhn2 in "Stephen King on Mass Shootings: We're Out of Things to Say"

tmhn2 — Sat, 28 Oct 2023 08:49:41 +0000

This comment made me curious so I looked up some data (sorry for the formatting, I don't know how to do it better):

Guns per 100 people - Finland 2017: 32.49 (total of 1.79 million) [1] - US 2017: 120.5 (total of 393 million) [2]

All gun deaths - Finland 2017: 138 [1] (~77.09 deaths per million guns) - US 2017: 39773 [2] (~101.2 deaths per million guns) <- A bit higher

Mean death rate per million in mass shootings, 2009-2015 [3] - Finland: 0.132 <- A bit higher - US: 0.089

[1] https://www.gunpolicy.org/firearms/region/finland [2] https://www.gunpolicy.org/firearms/region/united-states [3] https://worldpopulationreview.com/country-rankings/mass-shoo...

The data seems to suggest that the number of deaths and mass shootings sort of tracks with the number of guns, and that Finland isn't particularly better off "per gun".

New comment by tmhn2 in "It's Getting Too Hot for Tropical Trees to Photosynthesize, Scientists Warn"

tmhn2 — Fri, 25 Aug 2023 23:59:33 +0000

Right. What "reduction in biodiversity" means is that some species will adapt fast enough and some won't. Unfortunately, there is no lower limit to "reduction in biodiversity".

New comment by tmhn2 in "It's Getting Too Hot for Tropical Trees to Photosynthesize, Scientists Warn"

tmhn2 — Fri, 25 Aug 2023 23:05:26 +0000

> some tropical trees will still be able to photosynthesize in tropical regions. Those will become the dominant species.

Unless the environmental changes happen too fast for adaptation to keep up with--the tree of life can have dead ends.

New comment by tmhn2 in "Basics of Proofs (2017) [pdf]"

tmhn2 — Sun, 18 Jun 2023 05:30:56 +0000

And another fun and powerful technique is "proof by intimidation" (https://en.wikipedia.org/wiki/Proof_by_intimidation), in which you don't have to know what you're doing, but other people have to think you do.

New comment by tmhn2 in "Bernoulli Family"

tmhn2 — Sun, 18 Jun 2023 05:16:40 +0000

Not as prolific as that Nicolas Bourbaki guy, though!

New comment by tmhn2 in "Terence Tao makes progress on the Collatz conjecture (2019)"

tmhn2 — Thu, 30 Mar 2023 05:06:30 +0000

John Conway showed a generalization of this problem is undecidable. I can't find a PDF but there's a blurb and citation on wikipedia: https://en.wikipedia.org/wiki/Collatz_conjecture#cite_ref-33

I don't know enough to say anything more intelligent about it, but I guess if you are reading through comments on this article you might find it interesting!

New comment by tmhn2 in "Terence Tao makes progress on the Collatz conjecture (2019)"

tmhn2 — Thu, 30 Mar 2023 04:56:17 +0000

I don't think it's correct as stated in the article.

Looking at the paper, it basically says: the orbit starting with N dips to f(N) for "most" N, where f is a function that goes to infinity.

So, you can't pick f(N) = 200, but you can at least pick an f(N) that goes to infinity really slowly--a lot more slowly than previous results (f(N) = ~N^0.7924 is mentioned as a previous result).

New comment by tmhn2 in "Surprise computer science proof in combinatorics"

tmhn2 — Tue, 21 Mar 2023 21:25:42 +0000

The authors of the paper are academics in university CS departments with heavy math backgrounds (one with a B.S. in mathematics, another was a visiting professor at MIT dept of mathematics). I don't understand what you mean or how it relates to the article or surrounding circumstances.

New comment by tmhn2 in "American colleges in crisis with enrollment decline largest on record"

tmhn2 — Sun, 19 Mar 2023 08:26:51 +0000

Feedback is critical, though.

I imagine many folks who have watched a lot of videos on, say, economics or history or physics or whatever else hugely overestimate what they understand since they get no expert feedback to test their understanding.

Programmers tend to like self-teaching since it's very easy to get that feedback--write the code and see if it works! But not every subject is that way.

New comment by tmhn2 in "These Shapes Are Topologically Equivalent"

tmhn2 — Fri, 10 Mar 2023 11:05:53 +0000

The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!