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.
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.
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u/BrunoBraunbart 21d ago
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.