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April 05, 2005
Hund's Rule and Humans
Hund's Rule of Maximum Multiplicity is a simple rule that explains how atomic structure changes as atomic numbers increase. Blockquoth my chemistry textbook:
"Every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin"
In simple English, it says that if two electrons have two spots to fill up, then they would rather occupy one spot each rather than pair up in one spot. This reduces electron-electron repulsion, resulting in lower net energy and therefore a more stable atom. As a corollary, when two electrons do occupy nearby spots, they have opposite spins, because unidirectional spins repel each other more.
All this is well at microscopic, atomic scales. Each one of us is made up of way more atoms than there are people in the world. Wouldn't it be strange, yet somewhat unsurprising, if we too followed Hund's Rule at our macroscopic, human scales? In this post I am going to try and convince you that we do.
Scenario I:
When boarding a bus, passengers fill up all the window seats first. Only after all window seats have been paired up do incoming passengers sit next to other people. Presumably, unhappiness levels are increased if one has to *gasp* share a seat with someone when an open window seat is available. Therefore, unhappiness/disgust/contempt at sitting next to a stranger seems to be the macroscopic analogue of net energy level.
What about spin? On my trips between Boston and New York, I keep hoping for an attractive young woman to be the other electron in my orbital. If I am sitting at a window seat by myself, my seatmate usually ends up being a man, but only after he has explored all possibilities of sitting with attractive young women with free spots in their orbitals. Needless to say, in this scenario, no eye contact is made for the entire trip as we silently curse our luck for sitting with each other. If I am looking to sit in a second seat, I try to sit, in order, near a young attractive woman, a young woman and then a woman. Only after these options fail do I go sit next to a guy. My net energy level is heightened and sooner or later, this unstable arrangement is broken when the trip ends. (Sadly, even if I were sitting next to an attractive young woman in an apparently stable arrangement, we do get blown apart when the trip ends.) Without it being too much of a stretch, we can argue that if I were gay, I would be looking for an attractive young man to sit next to. Spin here is probably the analogue of gender. I try and sit next to someone who has an opposite spin (*ahem*) to me.
The exception to this, of course, is when a couple is traveling together. When they board the bus, they are generally seen to sit next to each other rather than at two separate window seats. The communication overhead, which would be higher if they sat apart, leads to greater unhappiness during the trip. The analogy of unhappiness level to energy level still stands. The exception has proven the rule.
Scenario II:
If you and one other person are in an elevator lobby, waiting for elevators, it is preferable for both of you to board two different elevators rather than get into the same elevator. This ensures a shorter average ride time for both of you. Ride time here seems to the macroscopic analogue of energy level. There doesn't seem to be a clear analogue to spin. Once again, if you are having a conversation with someone, it is more likely that you'll get into the same elevator with them so as to avoid the unhappiness caused by an interruption in the conversation.
Scenario III:
At a cafeteria or other common eating area, it is rare to find strangers sharing a table. Diners prefer to leave fellow diners alone even if they are sitting by themselves at a table that can seat four. Arguments similar to Scenario I above can be made for those who share tables, Of course, in crowded cities like New York, it is hard to follow this rule all the time. Some New Yorkers actually take this as an opportunity to meet new people, because eating alone is awful. Perhaps it is because eating food is inherently more social than traveling that this difference from Scenario I occurs.
It is really rather strange that people can be alone in massive metropolises like New York. Thinking about it in terms of Hund's Rule makes it clearer why. As is the characteristic of good rules, they find use in domains far removed from those of their original formulation. Dr. Hund, I hope you approve of my appropriation of your rule to explain urban loneliness.
Posted by Vishy at April 5, 2005 09:15 PM