I'd love to see a video about a sport which has been designed to work in hyperbolic space and how that would look in Euclidean space.

@Contra1828

6 жыл бұрын

Capture the flag would be fun... the flags would be just a few dozen meters away, the hard part would be 1) finding it and 2) finding your way back, so you would need a team of people standing in a line to serve as a breadcrumb trail back to your base.

@user-cn4qb7nr2m

5 жыл бұрын

chess.

"even if you decide to walk around the block, the odds of actually ever getting home again are quite low" that cracked me up a little :D

@GODDAMNLETMEJOIN

3 жыл бұрын

The game hyper rogue has several quests designed around this.

Hyperbolic humans just would invent different sports that actually work

@magicandmagik

9 жыл бұрын

aajjeee good point.

@edancoll3250

9 жыл бұрын

aajjeee Like Guy-wire Bowling, or Missball.

@5nefarious

9 жыл бұрын

aajjeee Hyperbolic _humans_ alone is a bit of a stretch. Hyperbolic slime monsters, perhaps?

@Supermario0727

9 жыл бұрын

Nice job assuming the consequence.

@Ur0pinionDoesntCount

9 жыл бұрын

Edan Coll "missball" hahaha :D

I want to see Hyperbolic chess.

@ZenoRogue

7 жыл бұрын

Play HyperRogue, it is not hyperbolic chess, but close.

@thegoosh6469

3 жыл бұрын

@@ZenoRogue Dude, just put a chess land in for 11.4

@TomtheMagician21

3 жыл бұрын

ZenoTheRogue man you really are all over KZread

@mjwetter9889

3 жыл бұрын

If you play 3 man chess (the hexagonal one made by George R. Dekle Sr.), then it's technically in hyperbolic space. There's also an app which generates n man chess that just fits another distorted square unto the polygonal board.

i didnt know CPG Grey played baseball

@joshuahall7677

9 жыл бұрын

I was about to say

@IsYitzach

9 жыл бұрын

Tom Smith It was on the shirt. That means he owns the team. He doesn't have to do anything physical or show up to the game.

@joshuahall7677

9 жыл бұрын

**facepalm**

@numberphile

9 жыл бұрын

Tom Smith he did --- hear him talk about the satisfaction of "the crack of the bat"... overcast.fm/+BgMVqozpU/44:01

@thesmity31

9 жыл бұрын

Numberphile i need to catch up on Hello Internet, I am missing out on vital trivia! :)

Hyperbolic space is quite a mesmerizing concept. More videos on this topic please, Brady!

Between these videos I learned that hyperbolic sports are, awful, boring, and uninteresting. How about a video on a use of hyperbolic stuff?

@alicewyan

6 жыл бұрын

Just like in Euclidean space, who would've thunk. A bit of a more detailed description of that hyperbolic space would have been nice though.

CGPGrey plays hyperbolic baseball, gets hit in the face. Liverpool plays hyperbolic football/soccer, owns 3 to 0. And you call yourself an unbiased youtuber Brady? :P

@numberphile

9 жыл бұрын

supersmashsam when did I call myself unbiased?

@RedInferno112

9 жыл бұрын

Numberphile Sat down like a boss! :P

@supersmashsam

9 жыл бұрын

Numberphile Don't get me wrong, I didn't want to attack you or anything. It's nice to see elements from the podcast getting referenced in your videos. I was just trying to point out that aspect of the video.

The analogies in this video are kind of ridiculous, like if he said "imagine you play baseball on a sphere -- so, I'll convert my 300 feet to 300 radians, and OH MY GOD MY GOLF SHOT ORBITS THE EARTH 47 TIMES zomg spherical geometry is so amazing". But somehow, we manage to play golf on this sphere we call Earth with no issues. Similarly, the way he took 300 feet and just plugged 300 hyperbolic units into his formula, well, of course you're going to get a completely ridiculous outcome. This video offers no understanding at all for situations with a sensible, subtle degree of hyperbolic curvature, hence all the comments in this video saying "glad I don't live in hyperbolic space" when there are perfectly cogent theories that we do live in hyperbolic space...

@numberphile

9 жыл бұрын

TheHue's SciTech they are meant to be a little ridiculous (or fun, I would prefer) - it is just a fun way to get people who know less about hyperbolic space to think about it....

@TheHuesSciTech

9 жыл бұрын

Numberphile I understand, but a touch of balance would have been helpful perhaps -- "hyperbolic spaces come in different flavours; in a really, really strongly hyperbolic space, you can't even see your own feet! But in a weakly hyperbolic space, you could play golf just fine and getting a hole-in-one might be twice as hard, not 100000000000000000000000000000 times as hard."

@16m49x3

9 жыл бұрын

Numberphile He's got a point you know

@snsnsnsss

9 жыл бұрын

TheHue's SciTech yeah i agree, this video series is pretty rubbish and doesn't offer any valuable mathematical insight whatsoever sorry numberphile :( (bring back james!!)

@TheHuesSciTech

9 жыл бұрын

piff borealis not sure if trolling but I strongly disagree with you... The quality of content on this channel is outstanding in general, even this video which I'm somewhat criticising got me thinking.

Talks about football for European viewers. Gives the length of the field in feet.

@NewNecro

9 жыл бұрын

Suiseiseki Desu Well he did call it soccer...

@EcceJack

9 жыл бұрын

and for Brits it is (I assume) still measured in feet

@aakksshhaayy

9 жыл бұрын

Suiseiseki Desu The length is still talked about in feet, dunno why.

@xenontesla122

9 жыл бұрын

Suiseiseki Desu Just approximate using 3ft ≈ 1m.

@coopergates9680

9 жыл бұрын

xenontesla122 3.28 feet? haha

One day we won't all freak out when we hear people from different countries call things by different names. One day.. maybe.

@stumbling

9 жыл бұрын

naota3k Nothing beats a good game of pedispheres!

@theboss112358

9 жыл бұрын

CowLunch Pedospheres?

@stumbling

9 жыл бұрын

theboss112358 pedi is Latin for foot (or "the foot" or feet or those feet or their feet, I don't know I didn't study Latin so I don't understand the grammar rules). Pedo is actually relating to soil. Paedo relates to children.

Now on the glorious 26th of May There's laughing reds on Hyperbolic Way We're full of smiles and joy and glee It's Everton 0 and Liverpool 3

I think it would be more interesting to play sports in a hyperbolic space with units of 100 feet or something like that. Low enough curvature to be able to function while still being high enough to be noticable.

Thanks for another interesting video Brady. Always appreciate your work, and how you present new ideas in fun ways.

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.

@frechjo

5 жыл бұрын

+1

The field dimensions are within the range found optimal by FIFA: 110-120 yards (100-110 m) long by 70-80 yards (64-73 m) wide, These soccer field dimensions are wider than the regulation American football field width of 53.3 yards (48.7 m), or the 65 yards (59 m) width of a Canadian football field.

Beautiful Hello Internet references. I look forward to next episode's followup :)

The thing is, these formulas assume unit curvature, that is curvature of -1 in Hyperbolic Space, or curvature of 1 in spherical space. In spherical space, a curvature of 1 means the same curvature as the surface of the unit sphere, or a sphere with a radius of 1. 1 is not a very big number, so you can imagine that the small sphere would have sharp curvature. (Smaller spheres curve faster, larger spheres look flatter) The same is true of hyperbolic space; unit curvature is so sharp that things just warp extremely fast, which is why the beach ball would be too small to see if it's only about 3 meters away, the space is just curved very sharply. A lower curvature setup would have more subtle effects, because it has less curvature and is closer to being euclidean.

How would sound travel in hyperbolic space? Due to the logic of the space it seems as if it would be very quite with short bursts of load noises.

I sometimes wonder if space without any mass in it isn't flat but rather positively curved. 1:15 I'm absolutely certain that someone's mentioned this, but the pitcher's rubber is 60 ft. 6 in. from the plate.

I love this series! Soccer, baseball, golf sound really difficult (near impossible) in hyperbolic space. This makes me wonder though, what sports, if any, would be easier in hyperbolic space?

@adiamo0001

9 жыл бұрын

Frisbee - No Skeet shooting - Possibly easier depending on the gauge Racquetball - Potentially easier? Badminton - No Ski Jumping - No idea how travel distance would change? Weightlifting - More difficult since shortest paths are curved paths Curling - No High jump - Potentially easier?

@legendgames128

2 жыл бұрын

@@adiamo0001 "Weightlifting - More difficult since shortest paths are curved paths" No the "curved paths" are straight lines, they just diverge.

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"

@BunniBuu

9 жыл бұрын

fatsquirrel75 You didn't even read the title, did you? These videos were about sports in hyperbolic space. Please, try harder. P.S. "-chan" is an honorific, not a last name. I don't expect you to know that, but it's not as if my name is "Bunni Chan" on here.

@awesometech12384

9 жыл бұрын

Bunni-chan the videos weren't made to display how you could convert it from euclidean space to work in hyperbolic, they were made to use common things to explain what hyperbolic space is like, therefore what you said wouldn't make sense unless it was included in another follow-up video stemming from the subject

@BunniBuu

9 жыл бұрын

NotDragon12384 That's weird considering the video is titled "hyperbolic sports" and the video is 100% about our euclidean sports being used in hyperbolic space. I feel like there are much better ways to explain hyperbolic space than football, if that was the goal (pun unintended)

@Wexexx

9 жыл бұрын

Bunni-chan People are used to euclidean space. That's why they use it as standard, so we can see the difference. If I start to spew out whats different in axioms many wouldn't give a shit nor understand.

@coopergates9680

9 жыл бұрын

Bunni-chan I would agree that they should have used about 1/5 of the negative curvature that they did xD

Really nice Video! loving your channel! Greets from Germany.

wouldn't there be an curvature parameter, and all the video talks about is when the curvature corresponds to 1 foot, but it could be an mile or 300 feet

@SKyrim190

6 жыл бұрын

Charles Wang yes, you're perfectly right and that is why those videos are so confusing (sadly)

@devinward461

4 жыл бұрын

Sorry for the super late reply but thanks for pointing that out, I was getting really confused. If the length unit was much bigger, would things look fairly similar to Euclidean space up close?

@evannibbe9375

4 жыл бұрын

This is due to using sinh and cosh directly rather than using some factor on them to reduce the curvature.

Nice nod to the podcast there with Grey at the plate. He took that shot to the head like a champ!

That was Liverpool's problem this season; they weren't playing in hyperbolic space! Tell Brendan!

Lesson learned, it's very hard to stay straight in hyperbolic space

I love these videos!

Brady seems Liverpool fan as the score suggests...

Grey playing sports is the most mind boggling part of this video.

@Numberphile Could you guys do some videos on the Hilbert problems? Alternatively on logical problems that corned Russel and Gödel. Thank you very much

Brady is testing how many of us listen to hellointernet, And yes that was CGP Grey.

Good to hear I can still play table tennis in hyperbolic space :)

Brady confirmed Liverpool supporter

What's fun about a hyperbolic world is that if you ever get separated from someone, you are never going to see them again.

For soccer in Hyperbolic Space, what would happen if you change the field shape? Say a circular shaped field centered at the origin

This all depends on how curved the hyperbolic space is. If the negative curvature is low, the area around you that feels flat could be large.

Now all we need is a video on hyperbolic sports commentators!

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.

@KnakuanaRka

4 жыл бұрын

Yeah, I was wondering what their scale is or where they mentioned it. The Earth's surface uses spherical geometry, but on levels smaller than countries, Euclidean geometry works just fine. Why can't the same be true of a hyperbolic world?

@GODDAMNLETMEJOIN

3 жыл бұрын

The issue is that negatively curved space rapidly goes from being inconsequential to having an utterly dominating effect without stopping in the middle.

I wonder what an animal evolved to live in hyperbolic space would look like

Could you do something like this for elliptical space?

Braddy, what's up with that C.G.P Grey symbol inside the baseball player drawing?

Hi BrDy, lovee the easter egg of the team Cgp Grey baseballer. I wonder if uou chose him just to knock him out. hope to hear about that on the next HI. Congratulations on all your work.

This is so trippy. The area is 2pi, but the goal is 300 feet away, I can only see 7 feet in front of me, and no matter what we do, the ball will go out of bounds.

Can you do an episode about the probability of the penalty kicks in soccer , and how the goalkeeper can manage to interfere depending on the speed and the power and the direction of the ball ?

Dear numberphile, could you create a sport which smoothly fit with hyperbolic space's characteristics, which would be impossible to play in Euclidean conditions ? That'll be very interesting to find out. Regards (Sorry Bad English because it's not native language)

If you are at the center, you could not see much because as stated in the previous episode, things take infinite amount of time to get from the periphery to the center of the circle.

Isn't there a range of hyperbolic spaces? Some less distorted, some more so? How does that affect the equations?

would it be possible to adapt the field size and shape so it would play as if it was normal space?

@JubilantJerry

9 жыл бұрын

samramdebest Perhaps one can make the long edges of the soccer field horocycle arcs (arcs of infinitely large circles in hyperbolic space). Then I think the field would look more normal, since opposite edges would be equidistant I think.

cant wait to do this maths next year. initial thought is i guess euclidean space can be considered to follow the same rules as hyperbolic space at r->∞ from the origin?

Hi Brady. Will there be more videos with James Grime?

@numberphile

9 жыл бұрын

Mathieuj4 yes

but what if you aren't in the middle of that space? i think there's shouldn't be such dramatic change in vision and all

Wouldn't the soccer ball curve or scale along with it? because the soccer field remains a rectangle... only in hyperbolic it looks like it curves?

Dodge Ball would be entertaining in Hyperbolic space. You only have to aim in the general direction of the opposing team and hope for the best. Though being on the receiving end of a face level dodge ball coming in at you wouldn't be fun, there would be no way to avoid that weird smell you get after taking a blow to the nose.

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?

@JezzaWest

Жыл бұрын

Wdym straight lines are the shortest path

I wonder what possibilities a retina and nervous system would have in hyperbolic space to better deal with the challenges of that topology.

Assuming the laws of physics stay the same, the beach ball would look the same in both Euclidean and hyberbolic universes because light always takes the shortest path to your eyes, meaning that it would take the strange curve in hyperbolic space and make everything look the same

Whats about Wintersport to show that. I dont know the english word, but it is (-1) in H. Vor whats about billiard to show that the angelsum in a triangle is smaller than 180°

if anyone ever makes a hyperbolic maze game my brain will explode

@ZenoRogue

7 жыл бұрын

There are several hyperbolic maze games already.

Would love to try hyperbolic bowling.

Well, nothing would work like described, due to the fact that the light will also have a hyperbolic trajectory...

3:10 wait the definition of the unit of length has influences on the hyperbolic space? I would have thought you could just "convert" the space from one to another. And does this mean you can think of an infinite amount of hyperbolic spaces? like the hyperbolic space defined by 1cm, by pi cm, ...

@il2xbox

9 жыл бұрын

samramdebest No, he was being sarcastic. Actually 1 meter is still about 3.3 feet in hyperbolic space.

@happmacdonald

9 жыл бұрын

samramdebest He's done at least one thing wrong in his explanation. Hyperbolic space can be as curved or as nearly flat as you would like. The more curved it is, the shorter distances you'll start to notice things being "off" compared to flat space. What he's done is somehow skipped a step where he tells us how curved his example space is compared to a foot. :( One of the things I don't yet know about hyperbolic space is what is a handy way to describe how curved it is. I know that whatever values you plug into those "sinh" functions have to be expressed in a unit that is somehow tied to the spatial curvature, but I do not yet know how. I know that on a sphere you can talk about the circumference of the sphere as a unit, or "one radian" which is just 1/2π times the circumference. But since hyperbolic space, like flat space is simply-connected you can't just "measure around it" like that so whatever curvature units it is popular to use must work differently than that. :(

But wouldn't they make game fields different shape in the hyperbolic space?

So why are the edges of the soccer field straight? wouldn't it end up looking like a big X?

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.

This would've been better with computer graphics, changing points of view etc. Some of his drawings here and in the main video are a bit misleading without moving the point of view. Also, a first-person view in 3d would've been quite useful.

hyperbolic space bends my mind.

I think he may have missed the point of people asking about units of measurement. Different units will give you drastically different answers based on the equations he gave for area and circumference. For example if you have a circle with a radius of 1 kilometer, you can calculate the circumference with the equation 2*pi*sinh(R), which returns a length of 7.384 kilometers. However if you take the same circle and call its radius 1000 meters instead of 1km (which is the same thing, of course) and use the same equation to calculate the circumference, you get 6.189E434 meters, which is 6.189E431 kilometers. Not only are 6.189E431 and 7.384 unequal, they are several hundred orders of magnitude apart. Can we get an explanation of this? I would guess it has something to do with different hyperbolic geometries being able to have different curvatures, but I would really like to hear a more definite explanation.

@hauslerful

9 жыл бұрын

Wyatt Jackson You're looking for the gaussian curvature value of your space. You can't of course just plug kilometres into your hyperbolic sine, you have to weight the parameter with the curvature parameter, which carries an physical size as well. It's a little bit more complicated than that, but basically you will divide your circles radius by a length in meters or kilometres, or whatever unit you are using. Then the circles circumference will of course be invariant under unit change :)

@W4LL37SK83R

9 жыл бұрын

***** I figured it had something to do with curvature. Thanks for the explanation.

Can we get a video on what exactly what hyperbolic space is and what its use is?

I didn't know CGPGrey was a professional baseball player.

I'd like to see an explanation video of hyperbolic space. All of this talk about it and I still don't know what it is!

3:43 In hyperbolic space, you can't make all four angles of a quadrilateral right

The only question that arises for me is: what would a "good sport" look like in hyperbolic space? What kind of sports could hyperbolic humans have come up with?

Sed kio estas la utilo de la hiperbolica spaco?

I'm not really a fan of golf, but isn't golf an intrinsically hyperbolic sport in the sense used here? Does this video offer solace to those players trying to explain why it is difficult (and perhaps more interesting than it first seems)?

This is great! now i just need to figure out what is going on here.

Почему e^R ? Это же безразмерная величина. В чём это измеряется?

What exactly is hyperbolic space?

In so many other cases they discussed, the distances became absurdly large. Why, then, does the area of the soccer field become so small?

@tgwnn

9 жыл бұрын

dorianXsapiens that's kinda the point, isn't it? since the distances for "normal areas" are super large, then the areas for "normal distances" are super small.

@Dorian_sapiens

9 жыл бұрын

tgwnn I don't understand. I have approximately zero intuition about hyperbolic space (which is why I'm asking), but I could see it going exactly the other way: the distances enclosing an area can enclose much larger areas in hyperbolic space.

Yeah! Coming from Michigan! Go Red Wings!

Nice.

Brady, you should get some smart guys to talk about game theory, considering the death of John Nash, it's quite relevant! And it's super fun and interesting as well

Which sports could work in hyperbolic space then?

In both videos all they did was show us that doing anything in hyperbolic space gives you absolutely ludicrous dimensions/results/equation etc. So what can it be used for? It seems like it's not good for anything.

Beings living in a hyperbolic universe would have evolved biology that can deal with hyperbolic physics. They may have extreme sensory organs, superhuman levels of strength and stamina to deal with distance.

I found a mistake in this video. Randy Johnson was left-handed.

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)

I always asked myself How psychology and mathematics connected if you don't mind answering me and if there is a kind of since that connect both them I really need your help

i'd be nice if someone with some fancy 3D rendering software could give us a picture of what 3D hyperbolic space would like to the human eye. maybe as a gif, to visualize motion?

Is the speed of light in a vacuum different in hyperbolic space?

@bigglessy

9 жыл бұрын

d3rrial No.

@JMcMillen

9 жыл бұрын

bigglessy how about the speed of dark?

@Alaska1925

9 жыл бұрын

John McMillen Speed of dark is infinite. Which means that it is non existant, since darkness doesn't carry information whatsoever.

@wesselbindt

9 жыл бұрын

The usual way to arrive at the constancy of the speed of light in vacuum is to solve Maxwell's equations in vacuum. The solution will be plane waves travelling at a speed given entirely in terms of two fundamental constants, so it is independent of the frame of reference. The leap Einstein made is to inrerpret these waves as light, arriving at the speed of light in terms of these constants. Therefore, two problems pop up. First is to determine Maxwell's equations in hyperbolic space (this has been done), and solve them in vacuum. If you're lucky, the answer will be something that has a constant speed, which can then be interpreted as the speed of light. The second, more fundamental problem, is that we don't know the values of the fundamental constants in hyperbolic space, and since we can't perform experiments there, we probably never will. TLDR: idk lol

4:23, watch out... there will be angry Everton fans swarming all over the place in minutes :P

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

@TheHuesSciTech

9 жыл бұрын

Kram1032 3D vision wouldn't be much of a problem -- if you move sideways a certain distance, your view of the far distant remains identical, but closer things would change in perspective. In the absurd examples in this video, the baseball that's only 7 feet away would appear to be a point at nearly infinite distance (in terms of focussing cameras, eye lens adjustment, and more to the point, steroscopic vision).

So this is a major theory about how gravity works, right? That we live in some form of 4-dimensional space that has a curve so pathways tend toward larger objects? Hm. I need to look up some more videos.

@coopergates9680

9 жыл бұрын

EGarrett01 Hyperbolic three-space would still be a 3D manifold. If we do live in H^3, the negative curvature is negligible except over astronomical distances.

I'm doing hyperbolic stuff next year, thanks for making me absolutely shit myself.

Radius 1 diameter 2 hence its 2/pi*r

What exactly is the purpose of hyperbolic geometry? I somewhat understand that it is interesting to think about, but I really don't know what the applications of it are in the real world. Can you possibly make a video explaining why hyperbolic geometry exists?

@TheHuesSciTech

9 жыл бұрын

Ben Marquardt Elliptic geometry is an everyday reality for us here on our elliptic Earth: people walking North from the equator (i.e. they're walking parallel) will eventually meet at the North pole (how can parallel lines meet?? only in elliptic space). Hyperbolic space is just the exact opposite, parallel lines diverge apart, angles inside triangles add up to less than 180 degrees, etc, etc. So it's a natural counterpoint to the very very real and practical elliptic geometry of our Earth. It's also believed that perhaps the early universe itself was hyperbolic in nature, so it's worthy of study for that reason alone.

@ronnies07

9 жыл бұрын

Ben Marquardt Naval radio compasses were based on this principle. Until the advent of GPS the good ol LORAN system was used along with a set of hyperbolic maps in order to help ships navigate the high seas.

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.

Liverpool fan I see Brady

Liverpool? Winning? HAHAHAHAHAHAHAHAHAHAHAHA 20 TIMES, 20 TIMES, MAN UNITED

@shugaroony

4 жыл бұрын

4 years on and you haven't added to that pal and don't look any closer of doing so soon - while we are back again European Champions! Lets talk about 6 baby! ;)

Instead of talking about how obviously impossible traditional sports are in hyperbolic space, why not make up hyperbolic sports instead? I'm thinking something similar to skee ball maybe?

@paulfoss5385

5 жыл бұрын

Marko Oppa Sports like trying to stay close by the only people you've come across in a thousand years for as long as possible because if you are ever separated by a few feet you will never see them again and you could be alone in the what looks like a cloudy sphere that you can never move closer or farther away from, but from which unknown horrors could attack you at any moment from unfathomably vast stretchs of land just beyond your reach and you have no idea how you got there or what you even are? I would love to see people play that game in Euclidean space.