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Loops Across Space (gregegan.net)
149 points by sohkamyung on June 22, 2023 | hide | past | favorite | 72 comments



Egan is one of my favorite sci-fi writers. It takes a while to understand some of the concepts he writes, but imo he's written some of the best works in hard sci-fi that also deal with a lot of philosophy.

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'll go in to plug the Clockwork Rocket series (Orthogonal and its sequels) and Incandescence, all of which have much more to do with physics and spacetime than Permutation City and short story collections like Instantiation (which I also love).

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.

[1] -https://www.gregegan.net/ORTHOGONAL/00/PM.html


If you liked Clockwork Rocket, you'll also like Dichronauts.

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.)


Unless it is a complete spoiler, could you elaborate on what those universe designations mean?


IANAP, but those +/+/+/+ are the signs in the distance function of your universe. Specifically ++++ is an Euclidean spacetime where the distance of any point in spacetime is the sum of the squares of the distances in each dimension (including time). Our universe is not Euclidean but Minkowski spacetime where the opposite sign is used for the time-like dimension (which gives origin to special relativity).

Egan explores universes with two timelike dimensions (++--) and all spacelike dimensions (++++).


Besides what sibling said-

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.


wouldn't there also be +/-/+/+ for negative space dimention?


Incandescence is my favorite because it makes me cry.


Instantiation does contain a short story (The Gateway) about a space anomaly which, IIRC, had some Didicosm-like properties, like lack of mirroring.


I would also go to bat for Diaspora, single-handedly re-invigorated my interest in science fiction


I loooove diaspora! Egan was inventing neopronouns 25 years ago and it totally works in the context of the story, reader doesn’t even bat an eye seeing ve/ver/vis so consistently and casually after a few pages. Just one of the many forward-thinking aspects of that story.


When this book came out I'd previously seen ze/zir which sounds less jarring in legacy English. I think this was from a few people in the sf world in online discussions rather than in fiction, though I can't really remember anymore.

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.


I went to a small rural school on the east coast and circa 2005 or so I recall getting a mass email from an acquaintance explaining their new pronouns of ze/zir. That was the first I had ever heard about someone preferring different pronouns, and it was probably close to a decade before I heard those particular ones in any other context. All that is to say that it makes sense if it had made its way out to a rural college in 2005 it was probably being used a bit more widely in the SF a few years prior.


Also chalk up Tim Leary for "hir" back in the 1970s (maybe 1960s).


Diaspora is one of the most interesting and captivating things I have ever read. I love it dearly.


I loved Permutation City and his short story collection, Axiomatic and really liked Distress. However, I stopped reading Diaspora 30% in. If it hasn't click yet, should I still keep reading?


> I loved Permutation City and his short story collection, Axiomatic and really liked Distress. However, I stopped reading Diaspora 30% in. If it hasn't click yet, should I still keep reading?

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 am totally fine with dry. What usually pulls me in with Egan and hard scifi in general, is cool technological ideas and seeing how they play out societal (example: floating island state in Distress). Egan sticks out to me that he also will apply or combine existing concepts in mind-warping ways (example would be the infinite cellular automata in Permutation City). So far non of that has really happened for me in Diaspora. AI existing at a faster speed than the physical reality is cool, but feels like table stakes.


I'm not sure how far into Diaspora you made it, but the further you go the more mathematical or physics-based it gets. Computability/complexity theory show up later, there's a large portion of the book dedicated to an alternative physics model, etc


Oh, that sounds wonderful. None of that has really come up yet. Thank you! I'll give it another shot.


Greg Egan is a true genius, and I don't use that word lightly. He's a true polymath. In another era, I suspect he could have been one of the leading scientist/mathematician/philosopher of his time.

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...


Quarantine is my favourite. Permutation City was great, but difficult - I think because whilst I can mentally touch the concept I can't quite hold it.


Permutation City isn't that tough, is it?

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.


I'm of two minds about Quarantine. I loved the overall concept of it and the mystery narrative of gradual discovery, but the end of the story felt rather flat and unsatisfying. Maybe he intended it that way, to contrast it with the grandiose events in that short window before (I could say more, but I don't want to spoil it). But it still felt kind of rushed to me.


> I loved the overall concept of it and the mystery narrative of gradual discovery, but the end of the story felt rather flat and unsatisfying. Maybe he intended it that way, to contrast it with the grandiose events in that short window before (I could say more, but I don't want to spoil it).

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.


Interestingly there are no photos or video of Egan publicly available. All we have over the last 30 years is his/her/its textual output. I'm 50/50 on whether "Greg Egan" is in fact a LLM.


About 20 years ago, there was this individual on Slashdot that was frequently commenting, quite knowledgeably, on many many subjects. I am still wondering if it was a test of an expert engine.


I've seen LLM output. If Greg Egan is an LLM, you can come to my house, choose any hat within it, and I'll eat it.


Would you say his writings are over the head of most readers? If not, what are a couple you would start with? Would Permutation City be understandable to a lot of people? You just make him seem like he's writing about very complex topics haha


He definitely does write about complex topics and is one of the harder sci-fi writers I've read.

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.


Love Greg Egan. Especially loved Schild's Ladder. It was such a cool book, and it's very clear that the author has a serious background to boot, further evidenced by publications like this. Awesome!


Can someone please make a simulator of this! I'd love to see a Geometry Wars style shooter or a puzzle game using these spaces.



That's fascinating but at first glance it's something different?


Can't grant you that wish, but I can give you a few others!

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/


> The first homology group of the didicosm is ℤ4 × ℤ4.

What about the other 5 "orientable platycosms"? I assume 3-Torus is another with ℤ × ℤ × ℤ (?)


Yay, doughnut space! I played with this kinda stuff as a kid back in the QBasic days.

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


You actually want:

    while x > 10 do x -= 10
    while x <  0 do x += 10
    while y > 10 do y -= 10
    while y <  0 do y += 10
What you have will discard some position information every time it wraps. Also, it won't correctly handle changes in position per frame that are larger than 10.


Well, yes, but I also need to take account of velocity and rotation too.

I 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...


Or just

    x = x mod 10  
    y = y mod 10


That depends on how the programming language implements modulo. Some don't wrap around the way you would need here when the dividend is negative. See: https://en.wikipedia.org/wiki/Modulo#Variants_of_the_definit...


Would this work in both flavours of the modulo operator?

    x = ((x mod 10) + 10) mod 10


The issue is that in 3d the mapping is less straightforward if you want avoid stange effects like being mirrored .


How can you have a 3d space with finite volume and no boundary?


In 2D the most intuitive way is the "Asteroids topology": when you exit from one edge you reappear from the opposite one. This space is flat, finite, and without a boundary. In mathematical terms it’s what you get when you take a rectangle and identify the left edge with the right and the top edge with the bottom one. It is also topologically equivalent to the (surface of) a torus, which is also flat and wraps around the same way. (Note that the embedding of a toroidal surface in three dimensions is curved, but the 2D space itself is flat: the angles of every triangle add up to exactly 180°.)

In 3D, just generalize from the 2D case.


> the 2D space itself is flat

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.


Yes, good point, I wanted to include the flatness property (which was the third condition mentioned in the article) but simplified a bit too much in the process.


> It is also topologically equivalent to the (surface of) a torus

Interesting, I thought it would be like the surface of a sphere. What's the difference?


Connectivity. When you go off the top, you come in on the bottom. When you go North on a globe, you come in elsewhere in the North.


Ah, this makes sense. I'm thinking of the Mercator projection of the globe.


When you wrap a rectangle around a sphere, all points at the top edge are identified – thecedge is compressed into a single point, the "north pole", and similarly with the bottom edge. When you go off the top/bottom edge of Mercator at longitude N, you emerge at another point at the same edge, namely at longitude N+180 (mod 360).

(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 poles don't get identified with any point in the plane at all, really - the Mercator projection is infinitely tall, less a rectangle than an infinite strip.

The equirectangular projection does map the top and bottom edges to their respective poles, but Mercator just keeps going up (and down).


> the Mercator projection is infinitely tall

Well dang, I just realized that maybe I've based my homebrew D&D world on a Mercator projection.


Ah, indeed! Got my projections mixed up.


Amusingly this means a lot of old RPGs and such are arguably set on a toroidal world rather than a globe.


When you reach one of the boundaries you re-enter the space at a different boundary. It was one of the very few things I was able to understand.

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 2d: take a square and glue the two pairs of opposite sides together. If you do this with one pair you get a cylinder, and then gluing the other pair gets you a torus. No boundary is left.

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.


Would this allow for Escher type spaces?


Escher's most fantastical spaces would be classified as non-Euclidean, whereas the article here stresses that the spaces it describes are strictly Euclidean.


I think they are rather forms of parallel projection (where farther objects aren't smaller, unlike perspective projection) combined with forced perspective, where things look locally connected from a specific angle:

https://en.wikipedia.org/wiki/3D_projection#Limitations_of_p...


s/Euclidean/locally Euclidean/


Yes, though not with a didicosm. (Unless your standards for Escher-esque spaces are low.)


In the same way a sphere, like the Earth's surface, is a 2d-space with finite area and no boundary.



What does boundary mean in this context then? Because the mobius strip has a boundary on the sides even if it is continuous. I guess boundary means an edge in all directions?


A mobius strip is an example of a space that is finite but unbounded in a single direction. A two dimensional plane that is finite but unbounded in all directions is called a Kline bottle, but you can’t build them for real in 3D space, only distorted approximations.

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.


Not sure why you need a Mobius strip when an untwisted rectangle with two opposite edges joined (outside of a cylinder) has the same property. Unlike a sphere that would be a flat 2d space (but unlike a sphere it would be unbounded only in one direction)


Donuts are another option. That’s what you get when you join a square at each pair of opposite edges.


Indeed the gaussian curvature in a torus is 0.


(in 4d only)


The same way the surface of the earth is a 2D space with finite area and no boundary.


TFA tells you how.




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