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by baddox 3122 days ago
Oh oops, you’re totally correct that geometric growth is a synonym for exponential growth. I don’t know what I was thinking, but I may have been confused by the fact that volume grows polynomially faster than surface area for any fixed n dimensions (I now fear I may also be incorrect about this claim, although I’m confident it’s true for n=3).

Still, geometric growth is exponential in n when n is the number of dimensions, which isn’t really the n we were talking about in this context.
1 comments
SomeStupidPoint 3122 days ago
It's precisely the N that I was talking about:

I discuss how seeing 100 steps of a sequence with regular behavior gives you a better sense of its asymptotics than seeing 3 steps, and then how you can generate some steps of that sequence as a mental model.

The N that is changing is the number of dimensions, both in comparing which model gives better asymptotic intuition and in terms of constructing a phase space by adding a dimension at a time.

I'm actually unsure how you could think there's an N that's not dimension, given that the only values discussed (or changing) were dimensions.

Did I not use fancy enough language when making a point to laymen, so you assumed you knew more than me and took a really uncharitable read so you could "correct" me?

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p1esk 3121 days ago
When you say “volume grows” most people assume an increase in 3D volume. If you meant something else, like growth with number of dimensions, then you should’ve clarified it better. I think that’s why you are being downvoted despite the insightfulness of your comment.
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SomeStupidPoint 3121 days ago
It's actual a real problem with people who are moderately good at math:

They sabotage explanations to laypeople by incorrectly nitpicking technical details because they hear informal language that sounds similar to something they know, and rush to regurgitate that fact as a "correction" without really understanding the conversation -- and will insist on doing so unless you use language too sophisticated for the audience you were trying to reach in the first place.

This actually happens with nearly every field, I just experience it most with math -- it's probably related to Dunning Kreuger or whatever.

C'est la vie.

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