:)

What I would like to do is give a margin of error, e.g. “there is a 95% change that it will be between spoonful 1000 and spoonful 1300” or something like that. But I don’t have the time to figure that out now, sounds like it would be harder to figure out than the expected value.

Of the answers I’ve seen this is the one that makes most sense.

Of course, the real answer is that the sink is haunted.

I got 1022 as the expected value, see my top level comment.

Edit: oops, made a big mistake. Will fix it!

Edit: after correcting I got 1144, much closer to your result 1132.

The answer is about 1144.

Ok, let’s do the probability math properly. Others have mentioned how it’s a matter of probability how long until the last molecule of soup is taken out.

Suppositions:

There are N molecules in every ml of soup and every ml of water.

All soup molecules are the same.

Every spoonful takes out exactly 25N molecules out of the bowl selected at random, and they are immediately replaced by 25N molecules of water.

At the start, there are 500N molecules of soup in the bowl.

The question is:

How many spoonfuls is it expected to take until all soup molecules are removed?

For every spoonful, each molecule of soup in the bowl has a 25/500 chance of being removed from the bowl.

For ease of calculation, I will assume that each molecule being removed is independent of all others. This is technically wrong, because this implies that there is a very very tiny chance that all soup molecules are replaced in the very first spoonful. However, for the large number of molecules we are going to be working with, this shouldn’t affect the final result in any meaningful way.

Number all soup molecules in the bowl: 1, 2, …, 500N.

Define X_i to be the number of iterations it took until molecule i was removed. All X_i are I.I.D.:

P(X_i = 1) = 25/500 P(X_i = 2) = (475/500) * 25/500 P(X_i = 3) = (475/500)² * 25/500 … P(X_i = n) = (475/500)^(n-1) * 25/500 …

This is a geometric distribution with p = 25/500.

Now what we’re interested in if the maximum value between all X_i

That is: max_i { X_i }

Specifically we want the “Expected Value” (basically the average) of it: E[ max_i { X_i } ]

This is exactly the question asked here: https://math.stackexchange.com/q/26167

According to the answer there, there is no closed-form exact answer but a very good approximation for the solution is:

1/2 + (1/λ) H_500N

Where λ = -log(1-p) and H_n is the nth harmonic number.

Now it’s just a matter of plugging in the numbers.

According to Wolfram Alpha, there are N = 3.333*10^22 molecules in 1mL of water, or 1.666*10^25 in 500mL.

Again using Wolfram Alpha, the Nth harmonic number is H_500N = 58.652

With the formula given we get λ = -log(475/500) = 0.051293

Plugging it all in we get the expected number of spoonfuls:

0.5 + (1/0.051293)(52.438) = 1143.97 spoonfuls on average.

With enough coercion we can also force Wolfram Alpha to do the whole calculation in one go: 1/2 + 1/(-log(1-25/500)) * harmonic number (number of molecules in 500mL of water/molecule) giving 1143.9743.

Edit: initially used N instead of 500N and got the wrong answer of 1022.

If you just want to be a contrarian for the hell of it, you’re doing great.

It’s more nature than what’s there now

Maybe. This was in Israel. There’s a sizable Ethiopian population here but it still might be difficult.

Too accurate 😭

I once went to an Ethiopian restaurant with my family. Never again.

I can’t even describe it, but whatever evil concoction they call their version of bread is easily the worst thing I ever attempted to eat.

I never tried to use it but this tracks with what I’ve heard. This blog post is worth sharing: https://www.andrewt.net/blog/vim/index.html (Vim must die and Emacs must not take its place)

Relevant excerpt:

Emacs is a sort of medium-sized operating system in which an enterprising user could, in theory, build a text editor.

I can’t recommend enough that everyone read this post, it’s great. Funnily enough, it seems that Microsoft of all companies did eventually make the terminal editor he was wishing for: https://github.com/microsoft/edit

He (Andrew T) shared this new development on Mastodon a couple of months ago but I can’t find that post too easily. Maybe I’ll ask him to append a note about MS edit to the post.

I’m guessing (not sure) that AltGr, visible in the picture, switches between the two options like Shift would. Shift still switches case.

I think the main reason they didn’t make an umlaut modifier is that ä is considered a distinct letter from a. It would be like asking why have a key for w (“double u”) when it could have been typed as uu. Not a perfect analogy but the best I can think of right now.

Either that or he’s a follower of Hank Green: https://youtu.be/-C3lR3pczjo (plus a few more of his recent videos)

Interesting, it never occurred to me that that might be the case. What other methods are there (besides the obvious resistive heating), and is there some way to check what method my AC uses?

I still would assume all new AC units here function as heat pumps, isn’t it just the cheapest solution to manufacture? Keep in mind that it never goes below freezing so there’s no need to deal with frost and ice.

Yeah, I also think it might as well be a standard feature these days, but honestly I have no idea how often in-game voice chat is used. Personally, if I’m playing anything online it’s only with my friends and we’d be on a Discord voice call. So the game really isn’t in the loop there. But obviously this isn’t the case described here.

Regarding point 1, QI once mentioned this. I tried to find it on YouTube but couldn’t. Basically they said that even for humans, pulling the pin out with your teeth isn’t really feasible, it requires too much force and your teeth/jaw can’t handle it.

Just to chime in, here in Israel I’ve never seen an air conditioner without a heating mode. “Heat pump” isn’t ever talked about because it’s a bog-standard feature of every air conditioner on the market. It’s just “putting the AC in heat mode”.

Our summers are brutal (especially in recent years, fml with climate change) but winters aren’t nearly as cold as European or American, so we don’t really have much call for a whole dedicated heating system. I’m guessing this is why ACs just add heating since it barely affects manufacturing but is a massive selling point (or glaring omission) for the roughly 100% of houses that don’t have other heating solutions.

It’s pretty ironic that we ended up with the most efficient heating solution being ubiquitous specifically because we barely need heating.

Of course, a ton of people (including my mom) still choose to use electric space heaters in the winter. I prefer AC but I can’t deny that the air feels different so it’s a valid preference, if somewhat wasteful. Not as bad as gas or fire though.

So the game does real time speech to text? Sweet.

You know what, you’re right, framing it as a “scientific discovery” isn’t cool.

All I’ll say is cats meow at humans and they don’t meow at other cats except their own mom. To me this instantly defeats this take.

It’s just a fun post though so I’m not judging.

IIRC this was kind of the dream of either Nikola Tesla or Thomas Edison (I forgot which one). But no, it’s not really possible, as others have said.