
Ice - robinhouston
http://johncarlosbaez.wordpress.com/2012/04/15/ice/
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strags
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...](http://unenumerated.blogspot.co.uk/2005/11/patent-goo-self-
replicating-paxil.html)

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

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ajays
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_...](http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything)

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anusinha
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.

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evincarofautumn
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.

~~~
robinhouston
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.

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

~~~
leif
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

~~~
panic
There are infinitely many finite strings.

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

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

