As my eye hops back and forth between the two rapidly changing numbers, it looks like they're always *different*... unless I focus on a point between them, so I can't clearly see either, but can roughly tell that they look the same.
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just stop the gif randomly
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It's not as if I actually *doubted* Greg, I was just commenting on a funny problem with perception. But okay - now I've verified that the numbers are equal. Unless of course the gif is set to make the numbers look equal whenever you stop it.
2 replies 0 retweets 7 likes -
Replying to @johncarlosbaez @RogierBrussee and
When I was making my u-sub animation a while ago, i was thinking about something similar.. how even an innocent non-linear u-sub seems to deform the region in a way that’s not obviously equal in area to its ‘parent’ region so i was wondering if there were .. 1/2
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Replying to @InertialObservr @johncarlosbaez and
ways to quantify the notion of ‘intuitive’ equal area .. started by fixing 2 points in the x-axis then started deforming curves connecting them .. it started to smell like topology so i dropped it and went back to research
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Replying to @InertialObservr @johncarlosbaez and
Maybe deform one curve into the other along a geodesic defined by the earth move distance, which preserves the integral
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Replying to @sigfpe @johncarlosbaez and
hmm.. i think I understand .. so if I have a curve γ(t) on some manifold, then moving along a geodesic to some γ’(t) will have equal area?
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Replying to @InertialObservr @johncarlosbaez and
It'll be the path that preserves area but moves the smallest amount of "stuff" over time to do it. I'm sure
@gabrielpeyre tweeted an animation along these lines a while back.2 replies 0 retweets 3 likes -
Replying to @sigfpe @InertialObservr and
D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i Retweeted Gabriel Peyré
Ah...it's this. https://twitter.com/gabrielpeyre/status/1137585164886978562?s=21 … I think it's just saying linearly interpolate the "cumulative" density. I don't know if that's interesting in this case.
D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i added,
0:05Gabriel Peyré @gabrielpeyre1D optimal transport interpolation corresponds to interpolating the inverse cumulative functions (the quantile function). https://en.wikipedia.org/wiki/Cumulative_distribution_function#Inverse_distribution_function_(quantile_function) … pic.twitter.com/UBeO7IyYQ6Show this thread1 reply 0 retweets 3 likes
Interesting.. reminds me of using fractional derivatives to interpolate between functions in an animation, though those aren’t area preserving in general
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Replying to @InertialObservr @johncarlosbaez and
That's sounds close to something I've played with: using fractional "functional" powers of functions to interpolate. Eg. f is "functional" square root of sin if f(f(x))=sin(x)
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Replying to @sigfpe @johncarlosbaez and
that’s really neat .. it never occurred to me to use functional roots to interpolate, since (at least for me) they are difficult to solve analytically i first started playing with them when
@CmonMattTHINK nerd-sniped me with a puzzle a few months ago1 reply 0 retweets 1 like - 2 more replies
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