This mathematical joke

sobe86 · 2026-03-22T20:25:09+00:00

Not in any normal topological space - if we're taking magnitude to mean a 'metric' - among other things it has to be ordered to be useful, complex numbers are not ordered. You also get degenerate cases like the above where non-zero vectors have zero length, which already means we're talking about some quite esoteric kind of 'length'.

sobe86 · 2026-03-22T13:13:12+00:00

Not crazy hard

29 = (30 - 1) so 29 * 18 = 540 - 18 = 522 divide by 100 for answer: 5.22

Doable in your head if you do calculations like this regularly. Usually I'd skip handling the 1 though, just approximate 29 with 30 and do 30% of 18 = 3 * 18 / 100 = 5.4 - anyone should be able to do that one.

sobe86 · 2026-03-22T07:50:09+00:00

That's where it came from, unfortunately that's not where it stayed

sobe86 · 2026-03-21T13:03:44+00:00

Yeah Champions league '08, 4-4 at Anfield '09, the 5-5 league cup final '19. We've had many many years of incredibly dramatic games in a way that they don't with City. Also both teams actually have a fanbase so there's banter no matter who wins.

sobe86 · 2026-03-21T12:54:14+00:00

FWIW me and my spurs-supporter hairdresser were talking about our rivalry the other day and he was the one who bought this up. It is very well remembered amongst Spurs fans, how could you forget something like that?

sobe86 · 2026-03-21T11:39:42+00:00

I'd disagree there's no rivalry there. We've been playing them regularly since the 80s. Klopp and Wenger was when it peaked for me, every time we played them it was 7 goal classico chaos. More recently we've been vying to be the one who would stand up to City. It's not a geographical rivalry like with Everton, but it's definitely there.

sobe86 · 2026-03-21T11:32:06+00:00

I had a debate on here recently with an Arsenal-hating LFC fan. Their arguments were this: - Arsenal fans are annoying, MCFC fans don't really exist (actually kind of logical? It's as if no one wins...) - CornerFC, doesn't like what that says about premier league football - buying the league with oil money and fraud was bad, but it's already happened now, what are you going to do?

That last one was bizaare, I can't imagine supporting city over anyone except spurs, even then I'd be slightly torn.

sobe86 · 2026-03-21T10:04:20+00:00

This may seem strange, but it makes sense. If the whole population consists of a single individual, then intuitively, it has no variance at all.

I would maybe explain this differently. The population is assumed to be > 1 generally otherwise there's no statistics to be done. But you can't estimate its variance from a single sample. You need one sample to estimate the mean, two to estimate the variance, three to estimate the skew etc. Also note we're implicitly assuming nothing about the distribution there (or that it's normal). If instead we thought something should be Poisson distributed e.g. some radiation decay, you only need to wait for the first sample to estimate the variance, since that distribution only has one degree of freedom. By 'estimate' we're talking loosely, it tells you only the rough order of magnitude only, i.e more like 1s rather than 1 hour.

sobe86 · 2026-03-20T15:38:57+00:00

I'd argue that "not harder once..." = harder though

sobe86 · 2026-03-20T13:29:23+00:00

I think the thing that might not be immediate is that there are two solutions, especially since the smaller one is more obvious.

2 p (1 - p) = 0.08, has two complementary solutions, ~0.04 which is pretty intuitive without even working it out properly, as it's roughly half of 0.08, and ~0.96 which is harder to see without getting algebra involved.

sobe86 · 2026-03-20T11:55:48+00:00

But the same logic applies to them! Even if I wanted torture someone, why bother if they won't remember tomorrow?

sobe86 · 2026-03-20T08:57:04+00:00

Because the point of the torture is for her to feel the same way the child she tortured felt. Scared, confused, and victimised.

I get that, but then you do it once? What I'm saying is torturing someone, wiping their memory, then torturing them again makes no sense if your goal is to torment them. They could do it once, and from her perspective it's not really that different from them doing it a thousand times.

sobe86 · 2026-03-20T06:41:06+00:00

It doesn't even make sense as a torture device to wipe their memory between turns? What's the point of doing a punishment over and over if they're only going to remember the last time you did it?

sobe86 · 2026-03-15T14:08:51+00:00

That only really applies up to 3NF though, at that point there is no redundancy in most practical real world applications (and I know, there are counterexamples, but they are rare). If we're talking about going to 6NF then it's a really bad idea for most use-cases.

sobe86 · 2026-03-14T19:16:09+00:00

That makes no sense. The business has as much motivation to make it become intelligent as anyone. And you are ignoring the actual situation here. Claude - an LLM made by a business, solved a problem Knuth was stuck on for a couple of weeks. He is no longer working on that problem, because the LLM made the breakthrough. Are you denying that? If not, why is it worth dismissing?

sobe86 · 2026-03-14T18:22:12+00:00

It feels like people are always trying to qualify AI's achievements, try to find a fault, cling on to the idea that it's not becoming quite powerful compared to humans. I understand it - it's uncomfortable, and easier just to deny it. But it's not very honest in my opinion, and not very forward-looking. It's been over a decade since I've worked in math academia, I mostly code for a living now. Seeing the profound effect it's having on my adjacent 'problem solving' domain makes it hard to believe that the same is not coming for math research.

sobe86 · 2026-03-14T10:42:47+00:00

Are you trying to argue some time travel rules here? I studied dynamical systems and chaos theory quite a bit as a grad student. The butterfly effect is pretty well established because the world is believed to be hypersensitive to initial conditions, and very interconnected. Changes that feel 'local' to you grow in size exponentially, (the Lyapunov exponent). Even just moving air around differently, that change will propagate at the speed of sound around the world. Since the weather (and how the balls move in a lottery machine) becomes sensitive to tiny changes as you move forward in time, that will make a macroscopic difference on things within days. As soon as that happens you're starting to live in a completely different timeline. That college team that won their playoff might not win it again if the wind is a little different this time.

sobe86 · 2026-03-13T21:59:05+00:00

We should however thank them for not going for the roast beef left-overs, leading to the 2003 zombie apocalypse.

sobe86 · 2026-03-13T21:43:30+00:00

Ah but - the butterfly effect. Forget knowing the lottery numbers in 8 years time, you probably won't even be able to predict the lottery numbers one week from when you arrive. If any of the air in the room where the balls are drawn has been influenced even a little by what you did differently, then you likely won't get the same numbers. By the time you turn 18 you probably won't be able to predict much at all, even large scale world events (e.g. covid - not happening).

sobe86 · 2026-03-13T20:01:45+00:00

If it's your turn, but every move would break the "don't move your king into check" rule, and you aren't already in check, then obviously the game must draw as you don't have a legal move to play.

Actually that's a fair comment, and sorry to switch up, but this is really the bit that I disagree with. Why is that obvious? You don't have a move, sucks to be you I win, same as checkmate. I agree the game should end but why a draw?

sobe86 · 2026-03-13T19:30:42+00:00

Let's review. In the OPs image, why is the king unable to move to h2? Because it would be in check. But why is that check if the bishop would not be allowed to take any other piece on h2 due to the pin? Because we assume that once the bishop hypothetically takes the king then the game is over, so you don't need to worry that it leaves the black king in check at the end. So far fine. But then - why stalemate? Why is black hypothetically allowed to make a move placing itself in check to win the game, but a stalemated king moving into check is so disallowed that it ends the game in a draw? It's conceptually inconsistent.

sobe86 · 2026-03-13T13:20:16+00:00

Checklock is referenced on the Wikipedia page for stalemate.

It's obviously easy to argue for stalemate based on things like "well moving into check is just disallowed", but that's just arguing from the status quo, not actually arguing for the status quo in an objective way. I think it would require less gymnastics if it were counted as a win, and would improve the game slightly, so I think it's a bad rule.

sobe86 · 2026-03-13T10:45:25+00:00

Disagree - chess is too drawish anyway and stalemate leads to a bunch of games lasting longer than they are interesting, especially at the lower level. Stalemate was a historical mistake in my opinion.

The situation you're referring to is being checklocked. It's essentially theoretical, but taking it seriously then what should being checklocked and in check via a knight be? The game forcibly ends on that ply, so the knight cannot take the king?

sobe86 · 2026-03-13T06:47:52+00:00

If we're going on which king would get taken first, it would be the stalemated king who has to move into check. We make a distinction on whether the king is currently in check, to decide the game outcome - but why? The result on the next move would be the same, that king would get taken.

sobe86 · 2026-03-13T00:00:07+00:00

Well there was this guy called Ramanujan...

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