HN user
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).
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
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.
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".
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".
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.
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.
Not as prolific as that Nicolas Bourbaki guy, though!
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!
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).
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.
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.
The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!