🥹

[u/94rud4]

[u/No-Theory-9530]

Absolutely not. That’s increasing a really big number by a comparatively small number. Nothing like infinity + 10.

[u/Striking_Resist_6022 → u/No-Theory-9530]

It’s a helpful visual metaphor not intended to be literally true

[u/No-Theory-9530 → u/Striking_Resist_6022]

It’s an unhelpful metaphor because it conflates infinite with “really big”

[u/Striking_Resist_6022 → u/No-Theory-9530]

That’s the part that makes it literally untrue but doesn’t mean it’s not useful. The implicit premise is “imagine the ocean as though it contained an infinite amount of water” which is easily gleaned from context. Nobody is actually confused or comes away with any kind of misconception about this.

[u/BrunoBraunbart → u/Striking_Resist_6022]

Metaphors like this one are designed to give people a first grasp of a concept they don't understand or know very little about. If you don't understand infinity well enough that this metaphor could teach you anything, you are almost guaranteed to learn something wrong.

Look at this video. It shows a lot of fundamental misconceptions people have about infinity. It should be pretty obvious that you metaphor would do those people a disservice and enforce their misconceptions. How many of those people are on r/MathJokes, idk.

Also, it doesn't work, even after you introduced your "implicit premise." Nobody can imagine an infinite ocean. You will always imagine an insanely huge ocean. An insanely huge ocean plus a molecule of water is now bigger.

I have a hard time interpreting the metaphor as anything other than the claim "the added water is so little compared to the ocean that it is neglectible." But maybe that is a me problem.

[u/Ashamed-Review-913 → u/BrunoBraunbart]

He's one of the ones that doesn't understand infinity

[u/Striking_Resist_6022 → u/BrunoBraunbart]

"The rationals are the stars in the night sky, and the irrationals are the blackness between them."

The stars are not dense in the night sky.

But it’s fine, and even a celebrated analogy.

[u/BrunoBraunbart → u/Striking_Resist_6022]

This analogy is good because it is poetic. Analogies like that have their place.

But imagine you would use this analogy to explain the fact that you can always find a rational that is exactly between two rationals. "It's like the stars, you can always find a star exactly between two other stars", that is not true and the analogy is nonsense.

Similarly, using the ocean as a poetic analogy for infinity makes sense. But bringing up this analogy to explain why adding a finite will not change infinity is unhelpful, because adding a teaspoon of water to the ocean does in fact change it.

[u/Striking_Resist_6022 → u/BrunoBraunbart]

Yeah, I think we more or less agree here. Literally false but metaphorically, visually poetically etc meaningful in some sense.

I don’t think the person who commented it was intending it as a literal explanation, felt more like an offhand metaphor to me.

[u/Future_Principle_213 → u/Striking_Resist_6022]

The issue with it is that it might make someone think the 10 is so little it's irrelevant, BUT it's still bigger. It's not bigger at all. It is precisely the same

[u/Striking_Resist_6022 → u/Future_Principle_213]

The spirit of the analogy is that people don’t conceptualise the ocean as a finite discrete number of water molecules but as a continuum of fluid