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Ice (johncarlosbaez.wordpress.com)
232 points by robinhouston on Apr 15, 2012 | hide | past | web | favorite | 12 comments

Thanks - a really fascinating article.

Can't help but be reminded of "Cat's Cradle" by Kurt Vonnegut. (If you haven't read it, one of the plot features is "Ice 9", a fictional form of ice that's a solid at room temperature, and causes liquid water to solidify around it. IMHO, one of the coolest plot devices ever).

Edit: Ah, someone beat me to it in the comments section, and included this awesome link: http://unenumerated.blogspot.co.uk/2005/11/patent-goo-self-r...

When I first scanned that article and saw Ice XI, I thought, oh no, is there an Ice IX?

Might be off-topic, but: the mention of E8 reminded me of a story a read a while back, about a physicist who has this theory that all atomic particles(?) could be embedded in E8 . It sounded so beautiful and I wanted to read it but can't find it anymore. Does that ring a bell? If it helps: this physicist was supposed to be a maverick, a surfer dude who was supposed to be brilliant, but was living like a beach bum or something like that. Memory's really fuzzy, so I could be wrong about some of these details...

Edit: found it. I should've searched a bit harder. His name is Garrett Lisi: http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_...

This was a really great article, both using thermodynamics and inorganic chemistry. If you're interested in more theoretical applications of symmetry (or, in its proper mathematical formalism, group theory) to chemical systems, a good starting point is the Wikipedia page: http://en.wikipedia.org/wiki/Molecular_symmetry. Basically, just by using symmetry considerations, you can determine properties about the spectra, etc of various molecules. If you really want to learn about all the nitty-gritty, involving lots of matrix algebra, quantum mechancs, and the whole shebang, you might be interested in the book "Chemical Applications of Group Theory", by F. Albert Cotton.

Pedantic nitpick, but I might as well bring it up first so we can have it out of the way:

“There’s also an uncountable infinity of other patterns that all give you equally dense packings.”

According to the author’s examples using only {a, b, c}, the set of possible packings would be countably infinite.

Unfortunately, the article has kind of a breathless tone because it tries to cover quite a bit of ground all at once. Perhaps it’d’ve been better broken up, but it was still an interesting read. I’d never really considered that there must be different crystal structures to ice, though it seems perfectly obvious once explained.

I think the idea is roughly this: each packing pattern is represented by an infinite string over the alphabet {a,b,c} that has no doubled letters. And there is an uncountable infinity of such strings – continuum many – because these strings are in one-one correspondence with infinite binary strings: there are two possibilities for each letter, because it can’t be the same as its predecessor but it can be either of the other two.

I considered that, then I figured it was reasonable to discount infinitely large pieces of ice.

In that case the number of ice configurations would be finite, not countably infinite.

EDIT: lest someone believe me, this is NOT TRUE, the parent is completely right

There are infinitely many finite strings.

But not infinitely many pieces of ice which will fit within a finite universe [if there is one].

I'm a frigging idiot today.

I appreciate how smoothly the article bridges qualitative clarity and quantitative concreteness.

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