Hamilton's Rule

TommyP asks:  How does Hamilton's Rule (Br - C > 0) of altruism relate to human society?  I've heard it said that for me to give my life for a brother, it should actually require 2 brothers (or 8 cousins).  What's different about humans that allows us to cheat and give our own life for a single, unrelated life?

I believe the rule you are referring too is stated as such:  A Hamilton should never battle a Burr when life is on the line.  But I have no idea what that equation you stated has to do with it.  As far as cheating, it is unlikely that either of the contestants cheated.  But they certanly were selfish.  Pfft, getting shot at just for the sake of 'honor.'  What a waste, as you mentioned if it had been for two of his brothers, or 8 cousins, or even 4 nephews, then it may have been justified.  The rules are slightly more difficult when it comes to women folk, because as Grumpy pointed out in Snow White, they have "wiles, wicked wiles."  As a result it typically only takes one mother, or one sister to set the whole thing in motion.  As far as unrelated lifes, this typically requires money.  See, humans  are the only animals that use money, and for enough of it you can get most anyone to do most anything.  But back to the brother cousin thing, yes, it is not very worth while to go for a 1:1 exchange. 

There is quite a bit of theory behind this, and it is typically called Kin Selection.  William Donald Hamilton studied this phenomenon before contracting malaria in Africa while trying to link AIDS to oral polio vaccines, and subsequently dying.  Well, that is all for this time, hope you have a large family, just to make it worth while if you ever need to expire for the greater good. 

Round 2, Fight 1

Kepler vs. Asimov

Kepler's Laws of Planetary Motion:
   1. The orbit of every planet is an ellipse with the sun at one of the foci. An ellipse is characterized by its two focal points. Thus, Kepler rejected the ancient Aristotelean and Ptolemaic and Copernican belief in circular motion.
   2. A line joining a planet and the sun sweeps out equal areas during equal intervals of time as the planet travels along its orbit.  This means that the planet travels faster while close to the sun and slows down when it is farther from the sun. With his law, Kepler destroyed the Aristotelean astronomical theory that planets have uniform velocity.
   3. The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axes (the "half-length" of the ellipse) of their orbits. This means not only that larger orbits have longer periods, but also that the speed of a planet in a larger orbit is lower than in a smaller orbit. His third law is based on the foundation left by Copernicus, because he uses a mathematical expression to show the correlation between T (time for one revolution) and D (distance from the sun).

Asimov's Laws of Robotis
   1. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
   2. A robot must obey orders given to it by human beings except where such orders would conflict with the First Law.
   3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.

Coulomb's Law

Back to explaining the losers; and Coulomb lost big. Coulomb's Law states: The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

Coulomb's law is very important, if you are a point charge, and there is only one other point charge around. Otherwise the math gets difficult.

For example, for a point charge and a fixed dipole is easier than for a free to rotate dipole, which is easier than for two freely rotating dipoles. Those rotating dipoles would be easier without to calculate if it weren't for entropy. Stupid entropy.

Anyway, when it all comes down to it the potential energy of these different two particle systems is inversely proportional to the distance to the sixth power, and no longer the second power. The Hamaker constant is used to sum up all of these forces, charge, dipole and induced dipole.

An important thing to note about the Hamaker constant is that it is always attractive in a vacuum. So even if nature abhors a vacuum, next time you feel like attracting a significant other it may not be a bad idea to pick one up. Just a little tip for all you guys out there.

Well we didn't really cover Coulomb, but after that shut out did he really deserve it? I hope you learned something anyway.