Drunkard's Walk - Leonard Mlodinow [85]
Today chi-square tests are widely employed. Suppose, for instance, that instead of testing dice, you wish to test three cereal boxes for their consumer appeal. If consumers have no preference, you would expect about 1 in 3 of those polled to vote for each box. As we’ve seen, the actual results will rarely be distributed so evenly. Employing the chi-square test, you can determine how likely it is that the winning box received more votes due to consumer preference rather than to chance. Similarly, suppose researchers at a pharmaceutical company perform an experiment in which they test two treatments used in preventing acute transplant rejection. They can use a chi-square test to determine whether there is a statistically significant difference between the results. Or suppose that before opening a new outlet, the CFO of a rental car company expects that 25 percent of the company’s customers will request subcompact cars, 50 percent will want compacts, and 12.5 percent each will ask for cars in the midsize and “other” categories. When the data begin to come in, a chi-square test can help the CFO quickly decide whether his assumption was correct or the new site is atypical and the company would do well to alter the mix.
Through Galton, Quételet’s work infused the biological sciences. But Quételet also helped spur a revolution in the physical sciences: both James Clerk Maxwell and Ludwig Boltzmann, two of the founders of statistical physics, drew inspiration from Quételet’s theories. (Like Darwin and Dostoyevsky, they read of them in Buckle’s book.) After all, if the chests of 5,738 Scottish soldiers distribute themselves nicely along the curve of the normal distribution and the average yearly mileage of 200 million drivers can vary by as little as 100 miles from year to year, it doesn’t take an Einstein to guess that the 10 septillion or so molecules in a liter of gas might exhibit some interesting regularities. But actually it did take an Einstein to finally convince the scientific world of the need for that new approach to physics. Albert Einstein did it in 1905, the same year in which he published his first work on relativity. And though hardly known in popular culture, Einstein’s 1905 paper on statistical physics proved equally revolutionary. In the scientific literature, in fact, it would become his most cited work.32
EINSTEIN’S 1905 WORK on statistical physics was aimed at explaining a phenomenon called Brownian motion. The process was named for Robert Brown, botanist, world expert in microscopy, and the person credited with writing the first clear description of the cell nucleus. Brown’s goal in life, pursued with relentless energy, was to discover through his observations the source of the life force, a mysterious influence believed in his day to endow something with the property of being alive. In that quest, Brown was doomed to failure, but one day in June 1827, he thought he had succeeded.
Peering through his lens, Brown noted that the granules inside the pollen grains he was observing seemed to be moving.33 Though a source of life, pollen is not itself a living being. Yet as long as Brown stared, the movement never ceased, as if the granules possessed some mysterious energy. This was not intentioned movement; it seemed, in fact, to be completely random. With great excitement, Brown concluded at first that he had bagged his quarry, for what could this energy be but the energy that powers life itself?
In a string of experiments he performed assiduously over the next month, Brown observed the same kind of movement when suspending in water, and sometimes in gin, as wide a variety of organic particles as he could get his hands on: decomposing fibers of veal, spider’s web “blackened with London dust,” even his own mucus. Then, in a deathblow to his wishful interpretation of the discovery, Brown also observed the motion when looking at inorganic particles—of asbestos, copper,