3077: de Sitter

de Sitter

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Title text: Our anti-de Sitter club is small at the moment, but I've started corresponding with the conformal field theory people.

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Explanation

This comic is a pun on two uses of the term "space":

• in the everyday sense as a place for a person or thing to exist in; and
• as mathematical jargon used in topology (a branch of mathematics usually studied at graduate or postgraduate level).

Willem de Sitter was a notable Dutch mathematician and physicist in the late 19th and early 20th centuries, known for his work using topological models to describe the overall structure of the universe. He is best known for formulating the definition of a de Sitter space, which has constant positive (elliptic) curvature, where the sum of the internal angles of any triangle is more than 180°, and lines that initially appear parallel will always meet; the surface of a sphere is an example of a two-dimensional de Sitter space.

In contrast, an anti-de Sitter space is a space that has constant negative (hyperbolic) spatial curvature, where the sum of the internal angles of any triangle is less than 180°, and two parallel lines will diverge when extended. An anti-de Sitter space is a theoretical space with strange curves and extra dimensions which is used in studying the space-time structure of the universe.

The caption "My house is an anti-de Sitter space" refers instead to being against the actual physicist Willem de Sitter, after whom both spatial geometries are named, because the speaker forbids de Sitter from entering their house. This prohibition is pointless since he died in 1934.

The title text refers to conformal field theory, a set of rules for how tiny particles behave on boundaries. The ideas of conformal field theory and anti-de Sitter space are closely linked: everything in an anti-de Sitter space has a parallel in conformal field theory, a property which is usually called the anti-de Sitter space/conformal field theory correspondence or AdS/CFT correspondence for short. The extra pun here is "correspondence" also meaning "mutual communication or discourse", typically communication by letter or email.

Transcript

[A large note is taped to a closed door, which has a doorknob with a keyhole on it. The note reads:]

20th century Dutch physicist Willem de Sitter is not welcome here

[Caption below the panel:]

My house is an anti-de Sitter space.

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Discussion

the titletext still needs an explanation, but i'm not sure i get the connection to conformal field theory; i suspect it has to do with the explosive rate at which hyperolic space seems to "expand" when travelled through, as a pun on the club expanding at a similar rate? - Vaedez (talk) 07:01, 17 April 2025 (UTC) 162.158.90.137 07:21, 17 April 2025 (UTC) I think it's alluding to AdS/CFT correspondence, which I think is a string theory thing.

In hyperbolic space, parallel lines DON'T meet when extended, and in elliptic space they DO. Also, the rotation thing looks strange. In any of the basic geometries you have 360 degrees in a circle. The sum of angles in triangle will be different (smaller than 180 in hyperbolic space, larger in elliptic space). 172.68.213.151 07:58, 17 April 2025 (UTC)

Agreed. I went and changed it. Though technically, the stuff about parallel lines is still wrong. Parallel lines don't meet by definition, and spherical geometry doesn't have them. Maybe someone can add a better explanation? DanielLC (talk) 09:19, 17 April 2025 (UTC)

The yellow wood is a hyperbolic space.141.101.99.4 08:08, 17 April 2025 (UTC)

maybe a pun on "babysitters are not welcome here" Translated ORK (talk) 09:08, 17 April 2025 (UTC)

Fun Fact: the german version of Anti-de Sitter space in wikipedia refers to a [Randall–Sundrum model|https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model] 172.69.150.119 (talk) 09:20, 17 April 2025 (UTC) (please sign your comments with ~~~~)

"...less than 180° in a full rotation" - Shouldn't this be either "...less than 360° in a full rotation" (or perhaps "...the angles of a triangle add up to less than 180°"). 172.69.186.206 09:53, 17 April 2025 (UTC)

I've started to explain the title-text, but not well. I don't really understand either of these concepts. -- Xnerkcd (talk) 10:01, 17 April 2025 (UTC) (please sign your comments with ~~~~)

I don’t really know how to explain it well, but the wikipedia page on these spaces says it’s negative SCALAR curvature. That is a different concept from what is currently being explained here. The intuitive dimension of curvature applies only to 2-dimensional spaces. In higher dimensions you can look at 2D-slices, and the curvature of those is called the sectional curvature. Scalar curvature is then something of an average of those. Notably, if scalar curvature is negative, that does not mean sectional curvature necessarily always is (though perhaps the higher symmetry of these spaces enforces this? I’m really not sure). The main way you can measure scalar curvature is by calculating the volume of a sphere of radius r – if the scalar curvature is 0 it’ll be the usual formula from Euclidean space, but if it’s negative, then for sufficiently small radii the volume will be bigger than expected (intuitively, more space gets crammed around each point). Feel free to incorporate this into the article. 172.69.225.250 (talk) 10:30, 17 April 2025 (please sign your comments with ~~~~)

I thought it might be a play on "housesitter" and the fact that anti and de can denote negatives, but I'm not sure how BeeVee (talk) 14:37, 17 April 2025 (UTC)

This seems too well-timed to not reference Idaho's Everyone is Welcome Here controversy. 172.68.35.117 (talk) 15:57, 17 April 2025 (UTC) (please sign your comments with ~~~~)

Is this the first strip where the title begins with a lower-case letter? Also, I just noticed that the site's strips use small-caps, while this site uses traditional case. Is that something worth examining? 172.71.98.3 15:03, 17 April 2025 (UTC)

1) Nope. 2) What? --FaviFake (talk) 17:55, 17 April 2025 (UTC)

Then which one is the first? Translated ORK (talk) 09:04, 18 April 2025 (UTC)

The first I found was dPain over dt, the (previous) latest was the Wrong Stuff. There were twenty-nine of them, in my quick scan (nine of them in the "xkcd Phone" series). Seven of them had no capital letters at all. (Surprisingly, IPod doesn't start with "i", though two other direct Apple references do. edit: Misread+misremembered it. It's IPoD and isn't even the direct Apple reference itself, at best an allusion to it. ;) )

It happens frequently enough (around 1% of all comics, so far) to not be particularly noteworthy. 172.71.26.106 10:15, 18 April 2025 (UTC)

Parallel lines by definition are lines that do not meet... So if they meet they are not parallel, though yes at close range they might appear parallel... --Trimutius (talk) 03:36, 18 April 2025 (UTC)

Draw them on a sphere (i.e., a space with positive curvature, a.k.a. a de Sitter space) and they do. The canonical example of this is the lines of longitude on the Earth, which really are parallel at the equator and yet definitely meet at the poles. --172.68.205.150 07:50, 18 April 2025 (UTC)

I think the point being that they aren't parallel lines if they do meet, they (just like on hyperbolic planes) have points where a line that crosses both does so at 90° to each. By the parallel postulate, there are no possible parallel lines (geodesics) in spherical geometry, though there are parallel-line surrogates (the parallel curves of lines of latitude, for example) that obey a looser interpretation. 172.71.26.106 10:15, 18 April 2025 (UTC)

Yes on a sphere you can have triangle made out of 3 right angles... Is it made out of three parallel lines? Of course not, at least that is not how mathematicians treat it... The proper replacement of parallel line postulate in de Sitter space is that all lines intersect, so there is no parallel lines... --Trimutius (talk) 14:07, 18 April 2025 (UTC)

I'm a chemist. Mr. Markovnikov shouldn't appear near my house! 162.158.103.102 11:18, 18 April 2025 (UTC)

I understood that reference. Thank you Dextrous Fred (talk) 19:44, 24 April 2025 (UTC)

i think the joke is that his house is a Euclidian space. Because he wants all triangles to add up to 180 degrees and 2 parallel lines to never meet.
Basically he just wants his house to function normally, not fall down, and have regular corners 172.71.151.156 (talk) 01:14, 23 April 2025 (please sign your comments with ~~~~)

I've added a leading paragraph with some background for non-mathematicians, and swapped the order of the definitions for de Sitter space and anti de Sitter space. Hopefully that resolves the incomplete tag; if you agree, please remove the tag.

Kurahaupo (talk) 10:14, 23 April 2025 (UTC)
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