More Hyperbolic Sports - Numberphile
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Date: 2022-04-08
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Comments and reviews: 9
robbie
You should really show more three dimensional models of this. Don't you think it's hard to represent space, even Euclidean space, in a two dimensional format? I just think it would help a lot. As soon as I saw the short examples of hyperbolic curves when you were explaining feet versus meters some things clicked. So yeah, please more examples of hyperbolic space represented in 3D! It would also help to sort of flatten it out and convert between the two, perhaps explain how you determine distances from things if the paths are so far away, you know? Your videos are pretty great though.
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You should really show more three dimensional models of this. Don't you think it's hard to represent space, even Euclidean space, in a two dimensional format? I just think it would help a lot. As soon as I saw the short examples of hyperbolic curves when you were explaining feet versus meters some things clicked. So yeah, please more examples of hyperbolic space represented in 3D! It would also help to sort of flatten it out and convert between the two, perhaps explain how you determine distances from things if the paths are so far away, you know? Your videos are pretty great though.
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BunniBuu
The concepts in these videos kinda bore me. Like. if we were in Hyperbolic space, we wouldn't use the same fields as we use in Euclidean space. We would change the way we play the sport in order to make it work. It's not like we'd just be trying to play it the exact same way we always have. No duh we wouldn't be able to do the same things as we do in Euclidean space. Like just a guy peeing would be different in Hyperbolic space, what do you expect? I was kinda hoping for some ideas as to how we would change the sport to make it work-- not just saying -lol it's impossible-
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The concepts in these videos kinda bore me. Like. if we were in Hyperbolic space, we wouldn't use the same fields as we use in Euclidean space. We would change the way we play the sport in order to make it work. It's not like we'd just be trying to play it the exact same way we always have. No duh we wouldn't be able to do the same things as we do in Euclidean space. Like just a guy peeing would be different in Hyperbolic space, what do you expect? I was kinda hoping for some ideas as to how we would change the sport to make it work-- not just saying -lol it's impossible-
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burk314
As some others have mentioned, it depends on how curved the space is. In hyperbolic space with low (close to zero) curvature, You may not even be able to see a difference from Euclidean space until you looked at really large distance.
Compare to us living on the surface of the Earth. The Earth is (approximately) spherical and hence not a Euclidean geometry. Yet we model these games off of Euclidean space, since the large radius of the Earth means low curvature. Only by examining large distances can we detect the difference.
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As some others have mentioned, it depends on how curved the space is. In hyperbolic space with low (close to zero) curvature, You may not even be able to see a difference from Euclidean space until you looked at really large distance.
Compare to us living on the surface of the Earth. The Earth is (approximately) spherical and hence not a Euclidean geometry. Yet we model these games off of Euclidean space, since the large radius of the Earth means low curvature. Only by examining large distances can we detect the difference.
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Kram1032
If field of vision varies THAT much, surely people would have evolved very differently.
We'd have a much narrower field of vision to begin with and perhaps we'd have more than two eyes to enlarge the total FOV accordingly.
Speaking of. what can be said about 3D vision? Specifically, what happens before and beyond the plane of convergence where you'd see sharply and which both your eyes are aligned to? I expect there to be some weird distortions
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If field of vision varies THAT much, surely people would have evolved very differently.
We'd have a much narrower field of vision to begin with and perhaps we'd have more than two eyes to enlarge the total FOV accordingly.
Speaking of. what can be said about 3D vision? Specifically, what happens before and beyond the plane of convergence where you'd see sharply and which both your eyes are aligned to? I expect there to be some weird distortions
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TaliesinMyrddin
I like how most videos' previews for related videos play sound snapshots to catch the ears of listeners or suggest something exciting, but on Numberphile it's usually a bunch of mathematical formulas being recited =P
Also note that when I imply math isn't exciting I just mean the whole public perception dealie. I know Numberphile viewers find this sort of thing fascinating, I just find the previews amusing because of the scientific angle.
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I like how most videos' previews for related videos play sound snapshots to catch the ears of listeners or suggest something exciting, but on Numberphile it's usually a bunch of mathematical formulas being recited =P
Also note that when I imply math isn't exciting I just mean the whole public perception dealie. I know Numberphile viewers find this sort of thing fascinating, I just find the previews amusing because of the scientific angle.
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Krombopulos
I don't think these two videos really explained this too well. I mean, what's the point of even talking about hyperbolic space in the first place? Is it just something someone made up so they could talk about how crazy lines and distances are in it or does it serve some purpose to help understand something else? It's pretty clear that the real world does not work that way so what's the point in even discussing this imaginary alternate universe?
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I don't think these two videos really explained this too well. I mean, what's the point of even talking about hyperbolic space in the first place? Is it just something someone made up so they could talk about how crazy lines and distances are in it or does it serve some purpose to help understand something else? It's pretty clear that the real world does not work that way so what's the point in even discussing this imaginary alternate universe?
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kasuha
I wonder why are you discussing such extreme case without even mentioning that things don't have to be that way. If you live in hyperbolic space with low enough curvature, you may not even notice anything is out of order on any scales smaller than interstellar distances. There were even hypotheses that our universe might be hyperbolic and there were some very precise measurements carried out to verify if it is not the case.
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I wonder why are you discussing such extreme case without even mentioning that things don't have to be that way. If you live in hyperbolic space with low enough curvature, you may not even notice anything is out of order on any scales smaller than interstellar distances. There were even hypotheses that our universe might be hyperbolic and there were some very precise measurements carried out to verify if it is not the case.
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Thulyblu
3: 00 You say that it's feet instead of meters because it's American hyperbolic space instead of _European_ hyperbolic space. It would have been more accurate if you had said that it was American hyperbolic space rather than 98. 5% of all other countries - hyperbolic space (about 200 countries of which 3 do not use metric. not just Europe)
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3: 00 You say that it's feet instead of meters because it's American hyperbolic space instead of _European_ hyperbolic space. It would have been more accurate if you had said that it was American hyperbolic space rather than 98. 5% of all other countries - hyperbolic space (about 200 countries of which 3 do not use metric. not just Europe)
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numberphile
really cool video, but light doesn't take a straight line to your eyes but the way that takes the least time. So I assume you could see the ball at a lesser distance than 6 feet. Still you wouldn't be able to hit it correctly beause it would be deformed. Or am I completely wrong about that? How does vision work in hyperbolic space?
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really cool video, but light doesn't take a straight line to your eyes but the way that takes the least time. So I assume you could see the ball at a lesser distance than 6 feet. Still you wouldn't be able to hit it correctly beause it would be deformed. Or am I completely wrong about that? How does vision work in hyperbolic space?
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