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I think anyone who has experience playing old video games can intuit the first 1/3 of the article from this experience. Think of one of those spaceship games pl

I think anyone who has experience playing old video games can intuit the first 1/3 of the article from this experience. Think of one of those spaceship games played on a 2D screen, where you can exit out the right side and re-enter through the left, at the same vertical coordinate. That's a 2D torus, or R^2/Z^2. And one can easily extend this by one dimension to generate a possible physical universe. The generalization is that now you are in a 3D room shaped like a cube, where you can fly into the ceiling and come out the floor (same with the left/right, front/back walls). This is R^3/Z^3, the simplest space like ours that isn't "infinite" (while finite, it might still be very big, and that's why we shouldn't expect to be able to detect this situation by simply shining a light and waiting to see it from behind).

earenndil 7y ago
Hyperrogue[1] takes place in hyperbolic space. Definitely a good way to gain an intuition for it. It offers several different projections, so you can try them out. It's also open source[2]. 1: https://roguetemple.com/z/hyper/ https://roguetemple.com/z/hyper/ 2: https://github.com/zenorogue/hyperrogue https://github.com/zenorogue/hyperrogue
- abnry 7y ago
  Another game to check out in this vein is hypernom, developed by henry segerman, vi hart, and some other people that I don't remember: http://hypernom.com/ http://hypernom.com/
  - eru 7y ago
    In a less principled way, there's also 'Antichamber' and 'Tea for God'. Both use Escher-like spaces that are locally Euclidean but don't connect in proper ways. Eg if you go 360 degrees around a column, you might arrive at a different place in the level from where you started. In Antichamber it's an interesting gimmick. In 'Tea For God' the mechanic is actually useful, because it's a way to fold a big level into the small boundaries of the VR space you defined on the Oculus Quest in your living room.
    - zenorogue 7y ago
      Here is my blogpost on various weird geometries used in games: https://medium.com/@ZenoRogue/non-euclidean-geometry-and-games-fb46989320d4 https://medium.com/@ZenoRogue/non-euclidean-geometry-and-gam...
abiogenesis 7y ago
https://en.wikipedia.org/wiki/Asteroids_(video_game) https://en.wikipedia.org/wiki/Asteroids_(video_game)
lainga 7y ago
We'd expect the size of the universe to to be, at minimum, (oldest visible star's age * c * 2 * star's distance from us) - right - unless we just haven't looked in the other direction and seen the image of the other side of that star.
- simonh 7y ago
  That doesn’t take into account cosmic inflation in the very early universe. This is believed to have smeared out the universe into a mind bogglingly huge expanse, such that our observable universe is a mere speck in the grand scheme of things.
  - lainga 7y ago
    But if the star's visible on one side, it's close enough that it hasn't been redshifted into oblivion, right? The effects of cosmic inflation would only raise that minimum.
    - eru 7y ago
      Yes. The scientific consensus is that the observable universe is vastly bigger than (oldest visible object's age * c * 2 * star's distance from us). See eg "We know that the Universe has been around for 13.8 billion years, but we also know we can see for 46 billion light-years. How is this possible?" at https://medium.com/starts-with-a-bang/how-is-the-universe-bigger-than-its-age-7a95cd59c605 https://medium.com/starts-with-a-bang/how-is-the-universe-bi... (And plenty of similar article when you Google 'size vs age of universe.) Inflation isn't even necessary for this effect, but might amplify it. Inflation is not necessary, because the cosmic background radiation is the furthest thing we can 'see'. And that background radiation stems from when the universe was 379,000 years old. Wikipedia says that inflation lasted at most until 10^−32 seconds after the big bang. Yet, the background radiation seems to come from much further away than your simple calculation would suggest. See https://en.wikipedia.org/wiki/Cosmic_microwave_background https://en.wikipedia.org/wiki/Cosmic_microwave_background Size of observable universe is 93.016 billion light years. The age of the universe is estimated at 13.8 billion years. Observing gravitational waves might let us peek behind the curtain of the cosmic background radiation. Very exciting.
mirimir 7y ago
I probably spent more on Asteroids than on cocaine ;)

earenndil 7y ago

Hyperrogue[1] takes place in hyperbolic space. Definitely a good way to gain an intuition for it. It offers several different projections, so you can try them out. It's also open source[2]. 1: https://roguetemple.com/z/hyper/ https://roguetemple.com/z/hyper/ 2: https://github.com/zenorogue/hyperrogue https://github.com/zenorogue/hyperrogue

abnry 7y ago
Another game to check out in this vein is hypernom, developed by henry segerman, vi hart, and some other people that I don't remember: http://hypernom.com/ http://hypernom.com/
- eru 7y ago
  In a less principled way, there's also 'Antichamber' and 'Tea for God'. Both use Escher-like spaces that are locally Euclidean but don't connect in proper ways. Eg if you go 360 degrees around a column, you might arrive at a different place in the level from where you started. In Antichamber it's an interesting gimmick. In 'Tea For God' the mechanic is actually useful, because it's a way to fold a big level into the small boundaries of the VR space you defined on the Oculus Quest in your living room.
  - zenorogue 7y ago
    Here is my blogpost on various weird geometries used in games: https://medium.com/@ZenoRogue/non-euclidean-geometry-and-games-fb46989320d4 https://medium.com/@ZenoRogue/non-euclidean-geometry-and-gam...

abiogenesis 7y ago

https://en.wikipedia.org/wiki/Asteroids_(video_game) https://en.wikipedia.org/wiki/Asteroids_(video_game)

lainga 7y ago

We'd expect the size of the universe to to be, at minimum, (oldest visible star's age * c * 2 * star's distance from us) - right - unless we just haven't looked in the other direction and seen the image of the other side of that star.

simonh 7y ago
That doesn’t take into account cosmic inflation in the very early universe. This is believed to have smeared out the universe into a mind bogglingly huge expanse, such that our observable universe is a mere speck in the grand scheme of things.
- lainga 7y ago
  But if the star's visible on one side, it's close enough that it hasn't been redshifted into oblivion, right? The effects of cosmic inflation would only raise that minimum.
  - eru 7y ago
    Yes. The scientific consensus is that the observable universe is vastly bigger than (oldest visible object's age * c * 2 * star's distance from us). See eg "We know that the Universe has been around for 13.8 billion years, but we also know we can see for 46 billion light-years. How is this possible?" at https://medium.com/starts-with-a-bang/how-is-the-universe-bigger-than-its-age-7a95cd59c605 https://medium.com/starts-with-a-bang/how-is-the-universe-bi... (And plenty of similar article when you Google 'size vs age of universe.) Inflation isn't even necessary for this effect, but might amplify it. Inflation is not necessary, because the cosmic background radiation is the furthest thing we can 'see'. And that background radiation stems from when the universe was 379,000 years old. Wikipedia says that inflation lasted at most until 10^−32 seconds after the big bang. Yet, the background radiation seems to come from much further away than your simple calculation would suggest. See https://en.wikipedia.org/wiki/Cosmic_microwave_background https://en.wikipedia.org/wiki/Cosmic_microwave_background Size of observable universe is 93.016 billion light years. The age of the universe is estimated at 13.8 billion years. Observing gravitational waves might let us peek behind the curtain of the cosmic background radiation. Very exciting.

mirimir 7y ago

I probably spent more on Asteroids than on cocaine ;)