Loops Across Space
gregegan.net
gregegan.net
Great to see him active on his website (though I'll admit I gave up on understanding this around halfway)
Editing to add: of his works, Permutation City is one of my favorites. Multiple mind blowing concepts. I'm sure it'll be up the alley of many other HN readers.
I think at least part of it is just that he was very early in his writing career, and probably wasn't sure how to stick the landing yet. I love the book, but there's no denying that it has its rough spots.
I'm not claiming that I have ever been clever enough to think up the idea myself, but upon reading it was almost intuitive. I'm half-convinced that our own universe works something like in that story.
Either way, it scales better than having everyone publish an individual pronoun policy and every else remember it, O(1) vs. O(N^2).
Diaspora is excellent.
It depends on what doesn't click. If you're waiting for it to get more down to earth, it doesn't (either literally or figuratively). But I do remember it as starting out very dry, and getting, while not less dry, considerably more absorbing as it went along.
I think Incandescence is my favorite book of the physics set, but the Orthogonal books and their corresponding web notes [1] are an absolute tour de force of deriving a whole universe of physics from a tiny modification to the rules we're familiar with. It was wild to read those as a physics undergrad and still very cool to think about today.
Whereas Clockwork is set in a +/+/+/+ universe, Dichronauts is +/+/-/-. Between that and the +/+/+/- of the ones set in our own, he's covered every possibility.
(+/+/+/+ and -/-/-/- being mathematically equivalent.)
Egan explores universes with two timelike dimensions (++--) and all spacelike dimensions (++++).
In a ++-- universe, you have two timelike dimensions but still just one time dimension. This is to say that one of the space dimensions is timelike, which means you get effects like "time" dilation from ordinary rotation.
Our own universe is +++-. Between Dichronauts and Clockwork Rocket, it's possible to get a good intuition for the underlying geometry that causes special relativity; something none of my physics textbooks even tried.
One comparison I really like: Johannes Kepler -- he figured out planetary orbits _and_ wrote one of the fist (if not the first) SciFi novels. Oh and he saved his mother's life when she was accused of witchcraft -- a parallel to Egan's work regarding the indigenous Australian population.
I sometimes wonder though whether people like Egan are properly appreciated in the modern age. So much noise and competition for attention...
The descriptions of those concepts and the increase in complexity is something that is done over many chapters. But, I've noticed that in some particular parts of the book the "acceleration" of complexity becomes so high that I have to reread things and look up references online to be able to understand and continue.
Without giving too many spoilers, Permutation City takes the concept of cellular automata to the next level. It was approachable to me, and perhaps also became my favorite, because I had experience with those in the past.
To answer your question, Axiomatic is his collection of short stories and is definitely the most approachable. If you like the style presented there, you will also find it worthwhile to try his novels.
There is a certain sense of beauty clear in his longer works, where everything is taken to its pinnacle, and all the ideas fit together like a puzzle in the end.
Hyperrogue is a roguelike set in hyperbolic space: https://store.steampowered.com/app/342610/HyperRogue/
And the author has a lot of videos on non-euclidean spaces! https://www.youtube.com/@ZenoRogue
There's also Hyperbolica: https://store.steampowered.com/app/1256230/Hyperbolica/
And that author also has a lot of videos on its development, non-euclidean spaces, and other games that play with space: https://www.youtube.com/@CodeParade
Not quite in the same family, but maybe a distant cousin - a game where the speed of light is so slow, that merely walking around causes you to experience relativistic effects: http://gamelab.mit.edu/games/a-slower-speed-of-light/
What about the other 5 "orientable platycosms"? I assume 3-Torus is another with ℤ × ℤ × ℤ (?)
Like Asteroids style.
Basically:
If X>10 then X=0
If Y>10 then Y=0
And then again
If X<0 then X=10
If Y<0 then Y=10
while x > 10 do x -= 10
while x < 0 do x += 10
while y > 10 do y -= 10
while y < 0 do y += 10
x = x mod 10
y = y mod 10 x = ((x mod 10) + 10) mod 10I don't see that particular flow in the manual, and of course everything should be FULLCAPS.
https://en.wikibooks.org/wiki/QBasic/Full_Book_View#DO_.._LO...
You don’t have to do such geometric contortions though. The surface of a sphere is a two dimensional space that is finite but unbounded.
There's "continuity" between two points that, in the 3D rectangle representation, don't appear to have continuity. This continuity is possible because spacetime may be all warpy like that... You can't exit the space at the boundaries. The door out of the room walks you into the same room from a different door.
eg. exit Face C at some point, and re-enter from Face A, because Faces C and A are aligned at that point.
I'm lost beyond that point though.
In 3d: take a solid cube and glue the three pairs of opposite sides together. Maybe a bit difficult to visualize, but the idea is that if you live in the cube and try to exit it on one side then you re-emerge into the cube from the opposing side.
https://en.wikipedia.org/wiki/3D_projection#Limitations_of_p...
In 3D, just generalize from the 2D case.
It's not that simple. "Flat" is not a topological property, it's a metrical property. The correct statement is not that "the" 2D torus is flat, but that it is possible to put a flat metric on the 2D topological space that is called a "torus". That's what the "Asteroids" space does.
But it is also possible to put a curved metric on the same topological space--for example, just use the obvious metric derived from the embedding in 3D Euclidean space that we're all familiar with. The "torus" topological space in itself has no metric, and both the flat "Asteroids" metric and the curved "doughnut" metric are valid metrics on that topological space.
Interesting, I thought it would be like the surface of a sphere. What's the difference?
(Also, in Mercator it looks like you can approach the top or bottom edge diagonally, but this is an illusion, an artifact caused by the projection. You can only ever approach the north pole directly from the south, and once you cross it, you find yourself having "rotated" exactly 180° and are now facing south, in addition to having jumped to the opposite longitude. And vice versa for the south pole.)
The equirectangular projection does map the top and bottom edges to their respective poles, but Mercator just keeps going up (and down).
Well dang, I just realized that maybe I've based my homebrew D&D world on a Mercator projection.