July 24, 2008 8:45 AM Subscribe

This week in mathematical physics, John Baez looks at the amazing tile patterns in the Alhambra in Granada, dividing the patterns into their characteristic Wallpaper Groups based on their symmetries. And if these patterns aren't good enough for you, try drawing your own with the Escher Web Sketch tool.
posted by kiltedtaco (20 comments total)
23 users marked this as a favorite

Elsewhere, Alfred Einstein sings a moving ballad about the Vietnam War.

posted by not_on_display at 9:24 AM on July 24, 2008 [1 favorite]

posted by not_on_display at 9:24 AM on July 24, 2008 [1 favorite]

EMRJKC94: Physicists, especially string theorists, care a lot about orbifolds, and Baez is making the point that you can classify possible symmetry groups of tilings by classifying certain kinds of orbifolds.

posted by escabeche at 9:26 AM on July 24, 2008

posted by escabeche at 9:26 AM on July 24, 2008

I assume the word "finds", which the poster left out, indicates the math came from mathematical physics.

posted by DU at 9:26 AM on July 24, 2008

posted by DU at 9:26 AM on July 24, 2008

more generally, physical laws and symmetries are deeply connected. if you find that there's some neat symmetrical description in the maths (some value is constant, or changing the sign of something doesn't matter, say) then you can typically trace that through into a "meaning" in physics (if the maths is an equation in physics that describes "something") that corresponds to a law like conservation of energy, or momentum. those are very simple examples, but the whole idea is taken much further in mathematical physics. for example, the "standard model" for particles is based on ideas fairly closely related to the wallpaper patterns here and "string theory" is, perhaps, nothing more than an exercise in taking these ideas to their absurd (and pointless) extremes.

posted by not sure this is a good idea at 9:51 AM on July 24, 2008 [3 favorites]

posted by not sure this is a good idea at 9:51 AM on July 24, 2008 [3 favorites]

I think the field "mathematical physics" is often considered more a branch of math than of physics, anyway; John Baez belongs to the math department at his university.

posted by dixie flatline at 10:07 AM on July 24, 2008

posted by dixie flatline at 10:07 AM on July 24, 2008

Am I the only one who read that as Joan Baez?

posted by Confess, Fletch at 10:28 AM on July 24, 2008 [1 favorite]

posted by Confess, Fletch at 10:28 AM on July 24, 2008 [1 favorite]

No. No, you're not.

I was very confused there for a minute.

posted by EmpressCallipygos at 10:38 AM on July 24, 2008 [1 favorite]

(they're cousins)

i like how he's coauthored with greg egan :P and acknowledges tony smith!

posted by kliuless at 10:44 AM on July 24, 2008 [1 favorite]

i like how he's coauthored with greg egan :P and acknowledges tony smith!

posted by kliuless at 10:44 AM on July 24, 2008 [1 favorite]

Wait, Greg Egan is a mathematician? I thought he was a computer programmer.

posted by DU at 10:51 AM on July 24, 2008

posted by DU at 10:51 AM on July 24, 2008

I read it as Joan Baez too.

I am fascinated by the wallpaper groups. Thanks for posting this.

posted by wittgenstein at 10:51 AM on July 24, 2008

I am fascinated by the wallpaper groups. Thanks for posting this.

posted by wittgenstein at 10:51 AM on July 24, 2008

*Enters thread to make Diamonds and Rust joke; is too late*

posted by Kwine at 11:06 AM on July 24, 2008

posted by Kwine at 11:06 AM on July 24, 2008

they're cousins... no joke.

posted by geos at 11:22 AM on July 24, 2008 [1 favorite]

It would've been better if they'd just left it as Escher Sketch.

posted by StickyCarpet at 11:23 AM on July 24, 2008 [1 favorite]

posted by StickyCarpet at 11:23 AM on July 24, 2008 [1 favorite]

DU: he calls himself a "science fiction author and computer programmer", but he has a BSc in Mathematics. I was pretty surprised to find out he wasn't a physics professor or something; his "Foundations" essays on relativity and quantum mechanics (1 2 3 4) are the most concise and thorough introductions I've ever seen.

posted by teraflop at 11:47 AM on July 24, 2008 [2 favorites]

posted by teraflop at 11:47 AM on July 24, 2008 [2 favorites]

wallpaper groups are so last week...penrose tiling is where it's at...

srsly tho, love the escher tool...

posted by sexyrobot at 12:10 PM on July 24, 2008

srsly tho, love the escher tool...

posted by sexyrobot at 12:10 PM on July 24, 2008

Conway's proof that there are only 17 groups is brilliant (use the Euler characteristic of the resulting orbifold). It's considerably simpler than previous proofs.

Conway also did a nice version for the frieze groups (the symmetry groups along a panel, kind of like a one-dimensional version of the wallpaper groups) and came up with the idea of representing each of the seven types as a type of footprint. I saw him demonstrate these once, which was quite funny (he's a bit chubby and for some of them one has to jump in the air and spin 180 degrees).

posted by twoleftfeet at 12:41 PM on July 24, 2008

Conway also did a nice version for the frieze groups (the symmetry groups along a panel, kind of like a one-dimensional version of the wallpaper groups) and came up with the idea of representing each of the seven types as a type of footprint. I saw him demonstrate these once, which was quite funny (he's a bit chubby and for some of them one has to jump in the air and spin 180 degrees).

posted by twoleftfeet at 12:41 PM on July 24, 2008

I saw "Joan Baez", as well and lo, I was confused.

Anyway, that Escher Web Sketch tool basically means I will not accomplish anything else at the office today. Thanks!

posted by trip and a half at 2:40 PM on July 24, 2008

Anyway, that Escher Web Sketch tool basically means I will not accomplish anything else at the office today. Thanks!

posted by trip and a half at 2:40 PM on July 24, 2008

Just a BSc in Math and he's co-authoring. Now I don't feel a **bit** underachieving!

posted by DU at 4:30 PM on July 24, 2008 [1 favorite]

posted by DU at 4:30 PM on July 24, 2008 [1 favorite]

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posted by East Manitoba Regional Junior Kabaddi Champion '94 at 9:18 AM on July 24, 2008