 by Preston MacDougall March 06, 2006
You would think that the fastest way down a ski hill is "straight down". That would be true if mountains were shaped like cones, but they're not. They do have peaks, but they also have cornices, ridges and valleys. And, after many people have been skiing on them, they develop moguls.
You will, however, maximize your speed at any point on the hill if you follow the path of steepest descent, which in mathematical terms is called the negative gradient. This still won't guarantee the shortest time down the hill - there is an art to downhill skiing, not to mention those pesky gates. You may not even make it all the way down. (Swiss lugers didn't leave those sleds with red crosses near the top of the chair lift. They are for getting injured skiers to the lodge, and orthopedic care.) Those who prefer to ski at a leisurely pace schuss down the hill, and will leave serpentine tracks in freshly fallen snow. SCHUSS is also the name of a computer program that was conceived and developed in Richard Bader's research group at McMaster University. The purpose of this program is to trace out gradient paths in the density of the cloud of electronic charge that give atoms and molecules their chemical properties. Almost all of the mass of atoms and molecules is in their nuclei, which are point-like in comparison to the size of atoms themselves, which are already too small to see (in the usual sense). The toxicity of carbon monoxide, which has the formula CO,, does not result from the different mass of the nucleus in the carbon atom that fatally replaces one oxygen atom in the oxygen molecules that we need to breathe. Chemistry is all about electrons - how they are distributed and how this distribution responds to external stimuli. Richard Bader, the great Canadian mogul of theoretical chemistry, has made this truth the cornerstone of his school of chemical philosophy. If you Google the phrase "atoms in molecules" you can schuss straight to his website. In the interest of full disclosure, you should know that I was a student in Bader's group for several years. But don't let that stop you from exploring this school's answers to fundamental questions such as "What is a chemical bond?" or "What is an atom in a molecule?" You will discover that the lines traced out by SCHUSS partition a molecule into its constituent atoms in a manner that is reminiscent of how the drainage of rainfall partitions terrain into catchment basins. For this reason it was originally referred to as "natural partitioning". As improbable as it may sound, this chemical insight may inform a current case before the U.S. Supreme Court: League of United Latin American Citizens et al. v. Perry et al. Otherwise known as the Texas redistricting case, the Supreme Court justices are considering the constitutionality of the mid-decade redrawing of the lines delimiting the 23 congressional districts in Texas. When Chris Martin, the lead singer of the band Coldplay, tags the chorus of their hit song "God put a smile upon your face", he takes the de jure approach with "when you work out where to draw the line, your guess is as good as mine." The song refers to personal matters, but when it comes to drainage basins, or atoms in molecules, de facto dividing lines can be drawn. I am not suggesting that we should partition states into congressional districts that are drawn by computer programs based on chemical or geological phenomena. But it seems to me that with the current system, where a majority of incumbent politicians have total control, their guess is always better than ours. Is it possible that this gerrymandering is slowly poisoning the democratic philosophy that our constitution needs to breathe?
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