9 ms·

Planes, Spheres and Pseudospheres

109 points by sohkamyung 3y ago

namanyayg 3y ago
Greg Egan is the best hard sci-fi writer in my opinion. His works like _Diaspora_, _Permutation City_, and _Schild's Ladder_ are based on very high level physical concepts and are amazing reads. Start with his short story collection _Axiomatic_ if you haven't read it, I can bet that every HN reader will like it. His blog articles often go over my head and I admit that I usually understand only the first ~30-50%, after which I give up.
- Frotag 3y ago
  Anyone have recommendations for similar authors? I love how his stories grow in scope (one discovery plausibly leads to another and eventually interdimensional travel). I know Adrian Tchaikovsky is a popular recommendation around here (especially Children of Time and rightfully so), but I'm looking for something with less drama / less character-driven. The 3 body problem is a good example. Also tangential but I recommend trying Last and First Idol for anyone looking for ridiculous, gory, self-consistent sci-fi.
  - enriquto 3y ago
    Take a look at qntm [0], who writes very disturbing short stories. He is also a coder, notably of the famous hatetris game. [0] http://qntm.org http://qntm.org
    - Frotag 3y ago
      Sadly that's another author I'm already caught up with. His SCP series was really memorable though.
      - RupertEisenhart 3y ago
        You're telling me the antimemetics series was memorable? I guess it was bad then ;)?
  - RupertEisenhart 3y ago
    Accelerando by Charles Stross is a blast, fairly hard scifi, at least the first half. Blindsight by Peter Watts is also fantastic, same grade as Egan IMO.
    - 082349872349872 3y ago
      > "Whenever I find my will to live becoming too strong, I read Peter Watts." — JDN
      - badcppdev 3y ago
        Agree. And whenever I see someone recommend Peter Watts I feel the need to add a note warning that he's got a lot of sexual torture stuff in his work so might not be to everyone's taste.
        TwentyPosts 3y ago
        ...There's sexual torture content in Blindsight? Or in his short stories? Having read several of them, I really don't remember anything like that. Can you note some examples?
        082349872349872 3y ago
        It's off-page in Blindsight, but happens to the protagonist, right?
        badcppdev 3y ago
        I'd rather not. That stuff isn't my cup of tea. Why don't you just google it.
        selimthegrim 3y ago
        I think they are talking about the trilogy with Starfish
        hindsightbias 3y ago
  - xtiansimon 3y ago
    Saturn Run by John Sandford and Ctein (2015) has a appendix where the authors runs down the science behind their space science (and calls out something like Star Treky science explaining). I read this after the Arthur C. Clarke, Stephen Baxter series Time’s Eye series, which also has fantastic science themes.
  - cubefox 3y ago
    I haven't read him, but Vernor Vinge was also a mathematician.
  - carapace 3y ago
    Larry Niven
  - jrussino 3y ago
    You may also like Ted Chaing's work. Some of his stories are available online for free here: https://www.freesfonline.net/authors/Ted_Chiang.html https://www.freesfonline.net/authors/Ted_Chiang.html His short story "The Story of Your Life" was adapted into the 2016 movie "Arrival".
nologic01 3y ago
This looks like its has been made with mathematica? Would be cool to have 1) a javascript differential geometry vizualization lib that would allow interactive learning in the browser and 2) a python / notebook version that would allow some further experimentation and integration with data sources etc.
ghusbands 3y ago
https://web.archive.org/web/20231105115601/https://www.gregegan.net/SCIENCE/PSP/PSP.html https://web.archive.org/web/20231105115601/https://www.grege... (The original page has been taken down due to bandwidth usage.)
- xioxox 3y ago
  https://twitter.com/gregeganSF/status/1721133470880321738 https://twitter.com/gregeganSF/status/1721133470880321738
  - sandworm101 3y ago
    Lol. HN, on sunday morning, just ddosed a website of mostly text and a few static images.
    - artiii 3y ago
      and a few movies in gif. Let's see, och _only_ 270MB (via webarchive)
      - BlueTemplar 3y ago
        Ohgodwhy. Now I won't even click on the IA link because I don't want to be a burden for them.
  - cubefox 3y ago
    I wonder why something like that can still happen in 2023. Shouldn't web traffic be orders of magnitude cheaper now than twenty years ago?
  - dTal 3y ago
    I don't get it. He has a 500 gigabyte monthly quota, and the single page linked here is 270 megabytes (!) according to another comment (I didn't check but it's full of unnecessarily hi-res movies in .gif format). Why does he assume that 2000 hits of a page in 6 hours is so implausible that it must be "a weird malicious bot attack, or some kind of web crawler stuck in a loop"? That's only 5 hits a minute! Hasn't he heard of "going viral"?
aj7 3y ago
It was I who took the site down playing with his black hole optical simulations in the Tucson airport.
gregfjohnson 3y ago
This brought to mind a cute way to think about the Foucault Pendulum. The idea is to select a given latitude on Earth, and then imagine a cone that "just fits" that latitude, in the sense that it is tangent to the earth all the way around at that latitude. Draw a line all the way around the cone at the given latitude. Then imagine using a pair of scissors to cut the cone vertically up to its apex, and flattening it out to make a circle that is missing a pie slice. A single full rotation of the earth would be equivalent to "driving a car" from one edge of the pie slice all the way around the latitude line to the other edge of the pie slice. At the end of the trip, the car will be pointing in a different direction from the one it started, for every latitude except the poles and the equator. The angular rotation of the car from the start to the end of its trip is the amount a Foucault pendulum would rotate in 24 celestial hours at a given latitude on Earth.
o11c 3y ago
The interesting question for me is: for what geometries is there an efficient mapping to 1-D computer memory without too much stretching? While scaling, keep in mind that cache associativity means you're best off avoiding powers of 2. For rectangles (or rhombuses), many languages already give you 2D arrays with a dense representation; several other mappings are possible and sometimes useful (e.g. the Hilbert Curve [1], but that needs a loop; interleaving might not need a loop in some contexts). For infinite extensions thereof it's not too hard to come up with a mapping, though practically you'll have to switch to block allocation. Wrapping in a single dimension makes a cylinder (without ends), but note that wrapping in both dimensions is topologically a torus but has significant stretching. For triangles, you can just take the triangular number of one coordinate, then add the other, using the sum as the linear index. But in most practical cases where triangles show up, you can use 2 triangles together to make a rectangle (in many use cases, one axis will be a unit longer than the other). For other finite fragments of a plane you're probably best off breaking it into triangles and squares, or even wasting memory. There are no good solutions for a real circle in particular. For a sphere, pick your favorite platonic solid with triangular/square faces. The icosahedron minimizes stretching at the cost of having 20 poles (note that this involves 5 "strips" of 4 triangles each). The tetrahedron minimizes poles at the cost of severe stretching. The cube and octahedron compromise on both. Some non-platonic solids are technically possible but I've never found a reason (particularly, using the truncated icosahedron directly does not decrease stretching compared to the icosahedron). Note that the dodecahedron does not have a reasonable solution; it's not possible to tile its faces so I'm not sure why anyone would care though. For a torus (without stretching; topology isn't sufficient) it's possible to do similarly to the sphere. The easiest way to visualize is 8 cubes forming a hollow square; 2 faces of each cube are not exposed. Approaches using triangles (possibly via hexagons - remember a triangular prism-like can't be properly tiled by regular triangles) are probably possible but that's too much work; this post already took long enough. The triangular pyramid is just the tetrahedron again if including the bottom; you have to use the more-complicated indexing if you have an odd number of triangles. The square pyramid is also possible, with or without the bottom. The pentagonal pyramid without the bottom is possible with the more-complicating indexing. Higher pyramids are likely to imply stretch so aren't worth considering. For hyperbolic geometry, all implementations I'm aware of use per-node allocations, ick. It's probably possible to switch to block allocations (with more-complicated indexing for larger blocks), but that will need to be done separately based on how hyperbolic the geometry is. heptagons are common but would octagons make the mapping easier? [1]: https://en.wikipedia.org/wiki/Hilbert_curve https://en.wikipedia.org/wiki/Hilbert_curve
slowhadoken 3y ago
I see I’m not the only person interested in pseudospheres
- CliffStoll 3y ago
  I've made several pseudospheres from glass ... using a glass lathe and an appropriate jig and 2-D pattern. Much fun!
  - slowhadoken 3y ago
    That sounds awesome. I work almost purely in abstract ideas. I have to get my hands on so art supplies.

109 points by sohkamyung 3y ago

Greg Egan is the best hard sci-fi writer in my opinion. His works like _Diaspora_, _Permutation City_, and _Schild's Ladder_ are based on very high level physical concepts and are amazing reads. Start with his short story collection _Axiomatic_ if you haven't read it, I can bet that every HN reader will like it. His blog articles often go over my head and I admit that I usually understand only the first ~30-50%, after which I give up.

Frotag 3y ago
Anyone have recommendations for similar authors? I love how his stories grow in scope (one discovery plausibly leads to another and eventually interdimensional travel). I know Adrian Tchaikovsky is a popular recommendation around here (especially Children of Time and rightfully so), but I'm looking for something with less drama / less character-driven. The 3 body problem is a good example. Also tangential but I recommend trying Last and First Idol for anyone looking for ridiculous, gory, self-consistent sci-fi.
- enriquto 3y ago
  Take a look at qntm [0], who writes very disturbing short stories. He is also a coder, notably of the famous hatetris game. [0] http://qntm.org http://qntm.org
  - Frotag 3y ago
    Sadly that's another author I'm already caught up with. His SCP series was really memorable though.
    - RupertEisenhart 3y ago
      You're telling me the antimemetics series was memorable? I guess it was bad then ;)?
- RupertEisenhart 3y ago
  Accelerando by Charles Stross is a blast, fairly hard scifi, at least the first half. Blindsight by Peter Watts is also fantastic, same grade as Egan IMO.
  - 082349872349872 3y ago
    > "Whenever I find my will to live becoming too strong, I read Peter Watts." — JDN
    - badcppdev 3y ago
      Agree. And whenever I see someone recommend Peter Watts I feel the need to add a note warning that he's got a lot of sexual torture stuff in his work so might not be to everyone's taste.
      - TwentyPosts 3y ago
        ...There's sexual torture content in Blindsight? Or in his short stories? Having read several of them, I really don't remember anything like that. Can you note some examples?
        082349872349872 3y ago
        It's off-page in Blindsight, but happens to the protagonist, right?
        badcppdev 3y ago
        I'd rather not. That stuff isn't my cup of tea. Why don't you just google it.
        selimthegrim 3y ago
        I think they are talking about the trilogy with Starfish
      - hindsightbias 3y ago
- xtiansimon 3y ago
  Saturn Run by John Sandford and Ctein (2015) has a appendix where the authors runs down the science behind their space science (and calls out something like Star Treky science explaining). I read this after the Arthur C. Clarke, Stephen Baxter series Time’s Eye series, which also has fantastic science themes.
- cubefox 3y ago
  I haven't read him, but Vernor Vinge was also a mathematician.
- carapace 3y ago
  Larry Niven
- jrussino 3y ago
  You may also like Ted Chaing's work. Some of his stories are available online for free here: https://www.freesfonline.net/authors/Ted_Chiang.html https://www.freesfonline.net/authors/Ted_Chiang.html His short story "The Story of Your Life" was adapted into the 2016 movie "Arrival".

nologic01 3y ago

This looks like its has been made with mathematica? Would be cool to have 1) a javascript differential geometry vizualization lib that would allow interactive learning in the browser and 2) a python / notebook version that would allow some further experimentation and integration with data sources etc.

ghusbands 3y ago

https://web.archive.org/web/20231105115601/https://www.gregegan.net/SCIENCE/PSP/PSP.html https://web.archive.org/web/20231105115601/https://www.grege... (The original page has been taken down due to bandwidth usage.)

xioxox 3y ago
https://twitter.com/gregeganSF/status/1721133470880321738 https://twitter.com/gregeganSF/status/1721133470880321738
- sandworm101 3y ago
  Lol. HN, on sunday morning, just ddosed a website of mostly text and a few static images.
  - artiii 3y ago
    and a few movies in gif. Let's see, och _only_ 270MB (via webarchive)
    - BlueTemplar 3y ago
      Ohgodwhy. Now I won't even click on the IA link because I don't want to be a burden for them.
- cubefox 3y ago
  I wonder why something like that can still happen in 2023. Shouldn't web traffic be orders of magnitude cheaper now than twenty years ago?
- dTal 3y ago
  I don't get it. He has a 500 gigabyte monthly quota, and the single page linked here is 270 megabytes (!) according to another comment (I didn't check but it's full of unnecessarily hi-res movies in .gif format). Why does he assume that 2000 hits of a page in 6 hours is so implausible that it must be "a weird malicious bot attack, or some kind of web crawler stuck in a loop"? That's only 5 hits a minute! Hasn't he heard of "going viral"?

aj7 3y ago

It was I who took the site down playing with his black hole optical simulations in the Tucson airport.

gregfjohnson 3y ago

This brought to mind a cute way to think about the Foucault Pendulum. The idea is to select a given latitude on Earth, and then imagine a cone that "just fits" that latitude, in the sense that it is tangent to the earth all the way around at that latitude. Draw a line all the way around the cone at the given latitude. Then imagine using a pair of scissors to cut the cone vertically up to its apex, and flattening it out to make a circle that is missing a pie slice. A single full rotation of the earth would be equivalent to "driving a car" from one edge of the pie slice all the way around the latitude line to the other edge of the pie slice. At the end of the trip, the car will be pointing in a different direction from the one it started, for every latitude except the poles and the equator. The angular rotation of the car from the start to the end of its trip is the amount a Foucault pendulum would rotate in 24 celestial hours at a given latitude on Earth.

o11c 3y ago

The interesting question for me is: for what geometries is there an efficient mapping to 1-D computer memory without too much stretching? While scaling, keep in mind that cache associativity means you're best off avoiding powers of 2. For rectangles (or rhombuses), many languages already give you 2D arrays with a dense representation; several other mappings are possible and sometimes useful (e.g. the Hilbert Curve [1], but that needs a loop; interleaving might not need a loop in some contexts). For infinite extensions thereof it's not too hard to come up with a mapping, though practically you'll have to switch to block allocation. Wrapping in a single dimension makes a cylinder (without ends), but note that wrapping in both dimensions is topologically a torus but has significant stretching. For triangles, you can just take the triangular number of one coordinate, then add the other, using the sum as the linear index. But in most practical cases where triangles show up, you can use 2 triangles together to make a rectangle (in many use cases, one axis will be a unit longer than the other). For other finite fragments of a plane you're probably best off breaking it into triangles and squares, or even wasting memory. There are no good solutions for a real circle in particular. For a sphere, pick your favorite platonic solid with triangular/square faces. The icosahedron minimizes stretching at the cost of having 20 poles (note that this involves 5 "strips" of 4 triangles each). The tetrahedron minimizes poles at the cost of severe stretching. The cube and octahedron compromise on both. Some non-platonic solids are technically possible but I've never found a reason (particularly, using the truncated icosahedron directly does not decrease stretching compared to the icosahedron). Note that the dodecahedron does not have a reasonable solution; it's not possible to tile its faces so I'm not sure why anyone would care though. For a torus (without stretching; topology isn't sufficient) it's possible to do similarly to the sphere. The easiest way to visualize is 8 cubes forming a hollow square; 2 faces of each cube are not exposed. Approaches using triangles (possibly via hexagons - remember a triangular prism-like can't be properly tiled by regular triangles) are probably possible but that's too much work; this post already took long enough. The triangular pyramid is just the tetrahedron again if including the bottom; you have to use the more-complicated indexing if you have an odd number of triangles. The square pyramid is also possible, with or without the bottom. The pentagonal pyramid without the bottom is possible with the more-complicating indexing. Higher pyramids are likely to imply stretch so aren't worth considering. For hyperbolic geometry, all implementations I'm aware of use per-node allocations, ick. It's probably possible to switch to block allocations (with more-complicated indexing for larger blocks), but that will need to be done separately based on how hyperbolic the geometry is. heptagons are common but would octagons make the mapping easier? [1]: https://en.wikipedia.org/wiki/Hilbert_curve https://en.wikipedia.org/wiki/Hilbert_curve

slowhadoken 3y ago

I see I’m not the only person interested in pseudospheres

CliffStoll 3y ago
I've made several pseudospheres from glass ... using a glass lathe and an appropriate jig and 2-D pattern. Much fun!
- slowhadoken 3y ago
  That sounds awesome. I work almost purely in abstract ideas. I have to get my hands on so art supplies.