But this thinking and reading project took some time.
Maggie Koerth-Baker at BoingBoing pointed me at an old essay in Natural History Magazine by Neil deGrasse Tyson, "The Importance of Being Constant." Most of it was written for me. I learned things and I learned to think about things differently. I've been looking for someone to write like this since Stephen Jay Gould died.
What a way to begin a Saturday. I have plenty of things to think about as the temperature falls from the present 34° to an expected low of −5° tonight.
"… the universe has its own constants, in the form of unvarying quantities that endlessly reappear in nature and in mathematics, and whose exact numerical values are of signal importance to the pursuit of science. Some of these constants are physical, grounded in actual measurements. Others, though they illuminate the workings of the universe, are purely numerical, arising from within mathematics itself…"
Okay, I had never thought of the fact that some constants are natural and others are artifacts of measurement ("purely numerical…"). Very interesting. Confusing, but very interesting.
He also wrote:
"Whenever a repeating pattern of cause and effect shows up in the universe, there's probably a constant at work. But to measure cause and effect, you must sift through what is and is not variable, and you must ensure that a simple correlation, however tempting it may be, is not mistaken for a cause… "
Oh, the time I've spent trying to teach those ideas.
Later in the essay, Tyson wrote:
"Kepler figured out that if you square the time it takes a planet to go around the Sun, then that quantity is always proportional to the cube of the planet's average distance from the Sun…"
I will never understand how someone could "realize" that squaring and cubing numbers that measure things create relevant relationships. If somebody wants to square time and cube distance measurements (which are not even measurements of the same things), my response would probably be, "So what?!"
Even though I got lost somewhere in Tyson's description of Newtonian constants (never mind the quantum physics), he was quite clear about some things:
"No matter when or where you live, no matter your nationality or age or aesthetic proclivities, no matter whether you vote Democrat or Republican, if you calculate the value of pi you will get the same answer as everybody else in the universe. Thus constants such as pi enjoy a level of internationality that politics does not, never did, and never will—which is why, if people ever do communicate with aliens, they're likely to talk in mathematics, the lingua franca of the cosmos, and not English."
Another thing I've spent hours trying to teach.
Although, I do wonder if the universality of these constants is a safe assumption. The Chinese spent millennia convinced that their culture was the center of the world (whatever shape it had). Where did that get them? And the author describes at the end of the essay how some physicists are looking for evidence that constants change over time. Why not look for evidence that they change over space as well?