A lot of Brillouin Zones

In condensed matter physics we deal a lot with crystals, which is a repeating structure of atoms.  Every crystal is associated with a lattice,* which is an infinitely repeating set of points.

For example, if the points shown above were to repeat infinitely over the plane, they would make a lattice.

A useful concept is the first Brillouin Zone, which is the set of all points which are closer to the center point of the lattice than to any other point of the lattice.  In the above example, the first Brillouin Zone would simply be a square around the center.

Interestingly (but less usefully) there is also a definition for the Nth Brillouin Zone.  The Nth Brillouin Zone is the set of all points such that the center point of the lattice is the Nth closest point in the lattice.  I thought it might be pretty to draw the first few Brillouin Zones, and then I went totally overboard.

The first 27 Brillouin Zones.  The first Brillouin Zone is the red square in the center, and successive Brillouin Zones are each in a different color, moving outwards.  Click to enlarge.

The Brillouin Zones have the interesting property that each one has equal area.  And for any given Brillouin Zone, you can translate the different pieces by integer distances and form a square out of them.

I think one thing that attracted me to condensed matter physics is that there's all this geometry in it... and it's actually useful for describing reality.  Not this Nth Brillouin Zone stuff though, that's useless.  Hardly anyone thinks about the second Brillouin Zone, much less the third or twenty-seventh.

You can get Brillouin Zones of different shapes if you have different kinds of lattices!  And you can even have 3D lattices, producing 3D Brillouin Zones.  Note that even though real crystals exist in 3-dimensional space, they can be layered in 2D structures and thus be associated with 2D lattices.  For example, the 2D lattice I showed is the correct lattice to use for the cuprate superconductors that I study.

*The locations of the atomic nuclei in a crystal often make a lattice, but for complicated reasons, this is not the one I'm talking about.  Every crystal is also associated with a completely different "reciprocal lattice", which is the one relevant to Brillouin Zones.

Arguments: offline or online?

I saw a talk by JT Eberhard, and he said that whenever someone invites him to discuss the fate of his immortal soul over a cup of coffee, he agrees on the condition that the discussion can be put online.  This put on my mind the question of whether it is best to argue in public or private.  "Maybe I should blog about that," I said to my notepad.  And then Greta Christina blogged about it instead.

In a private debate, you only have a chance at persuading one person. In a public one, you have a chance at persuading dozens, or hundreds, or thousands, depending on how big a forum you have.
...
People may be ashamed to express stupid ideas in public — but once they’ve done so, they’re likely to get even more entrenched in them. Once we’ve made an assertion in public, it’s harder to walk it back. It shouldn’t be, but it is.

Noooooo!  Now that everyone on the atheowebs is talking about it, how can I possibly hope to contribute anything worthwhile?  It is the curse of blogs everywhere.

I don't like the way the choices are presented:  Either have a private argument over coffee, or have a public argument over coffee.  I simply don't have arguments over coffee.  I don't like one-on-one arguments, or coffee.  And opportunities for arguments over coffee never appear.  In my circumstances, this is the more realistic set of choices:

1. Talk about atheism without any provocation.
2. Talk about atheism with the slightest provocation.
3. Talk about atheism online.
4. A combination of some, all, or none of the above.

When I talk online, the fact that it's public is not the biggest difference.   The biggest difference is that I produce my own opportunities instead of waiting for them.  The second biggest difference is that it's in writing, not spoken word (where I am far less articulate).  The third biggest difference is that, since my preferred medium is blogging, I decide the focus, and argue with no one in particular.

Is arguing publicly more effective?  Among my choices, in my circumstances, it is definitely the most effective at, well, everything.  It's more satisfying to you, more satisfying to me, more likely to persuade people, and has a more positive effect on my relationships. But it's so tangled up in other inseparable issues, it's hard to say that it has much to do with the public/private aspect.