So is the mathematical architecture of the world more like a road network or a rail network? If the latter, then it is mathematically impossible to predict the future. It would be a world ruled by discrete events, including black swan events. As a quote attributed to mathematician Benoît Mandelbrot put it, “Even though economics is a very old subject, it has not truly come to grips with the main difficulty, which is the inordinate practical importance of a few extreme events.” God does, in fact, play with dice in the natural world.
COFFEE AND MINUETS
Charles Q. Choi’s reportage of Rouslan Krechetnikov’s study on the physics of keeping coffee from spilling, as reported in “Fluid Dynamics in a Cup” [Advances], is interesting. But Choi should go, at peak dinnertime, to a restaurant known for very good service. Watch the wait staff move quickly across the floor. When they are carrying liquids, the rule is long stride, short stride, long stride, short stride.
You can walk briskly and not spill things if you’re careful to break up your rhythm as you move. I learned that the first day on the job as a waiter in the 1960s.
I believe a solution for spilling coffee was already discovered 35 years ago on the University of California, Berkeley, campus. At the time, the student union lacked lids for coffee, and inevitably some of the precious brew would slosh out before I reached my 8 a.m. class. Realizing the problem was a buildup of vibrations until a large “beat” frequency caused the liquid to spill, I tried breaking them up by randomly moving the cup side to side and fore and aft as I walked. Eureka! No constant motion, no beat frequency and no coffee spilt.
“This Way to Mars,” by Damon Landau and Nathan J. Strange, says that “for a test flight, astronauts steer the vehicle into an orbit that almost always remains above the south pole of the moon.”
As a retired orbit mechanic, I see this statement as impossible unless there is a Lagrangian point above the lunar south pole. A satellite can remain stationary only over the body’s equator.
Landau replies: I appreciate Bobrow’s observation that the stationary points in the earth-moon system are only in the earth-moon plane.
When writing, however, we were sure to put in “weasel words” where we did not want to open up a can of worms. Here “almost always” is meant to be taken as “not all of the time.” We were alluding to a very elliptical orbit with a low perilune “above” the north pole and apolune “above” the south pole. In our orbit in the earth-moon rotating frame, we are within view of the south polar region 96 percent of the time.