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The importance of being constant: the fundamental things apply … as time goes by

Natural History, Nov, 2004 by Neil deGrasse Tyson

Mention the word "constant," and your listeners may think of matrimonial fidelity or financial stability--or maybe they'll declare that change is the only constant in life. As it happens, the universe has its own constants, in the form of unvarying quantities that endlessly reappear ill 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.

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Some constants are local and limited, applicable in just one context, one object, or one subgroup. Others are fundamental and universal, relevant to space, time, matter, and energy everywhere--thereby granting investigators the power to understand and predict the past, present, and future of the universe. Scientists know of only a few fundamental constants. The top three on most people's lists are the speed of light in a vacuum, Newton's gravitational constant, and Planck's constant, the foundation of quantum mechanics and the key to Heisenberg's infamous uncertainty principle. Other universal constants include the charge and mass of each of the fundamental subatomic particles.

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. In the 1990s the stork population of Germany increased, and the German at-home birth rate rose as well. Shall we credit storks for airlifting the babies? I don't think so.

But once you're certain that the constant exists, and you've measured its value, you can make predictions about places and things and phenomena yet to be discovered or imagined.

Johannes Kepler, a German mathematician and occasional mystic, made the first-ever discovery of an unchanging physical quantity in the universe. In 1618, after a decade of engaging in mystical drivel, 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. Turns out, this amazing relation holds not only for each planet in our solar system, but also for each star in orbit around the center of its galaxy, and for each galaxy in orbit around the center of its galactic cluster. As you might suspect, though, unbeknownst to Kepler, a constant was at work: Newton's gravitational constant lurked within Kepler's formulas, not to be revealed as such for another seventy years.

Probably the first constant you learned in school was pi--a mathematical constant denoted, since the early eighteenth century, by the Greek letter [pi]. Pi is, quite simply, the ratio of the circumference of a circle to its diameter. In other words, pi is the multiplier if you want to go from a circle's diameter to its circumference. Pi also pops up in plenty of other places, including the areas of circles and ellipses, the volumes of certain solids, the motions of pendulums, the vibrations of strings, and electrical circuits.

Not a whole number, pi instead has an unlimited succession of nonrepeating decimal digits; when truncated to include every Arabic numeral, pi looks like 3.14159265358 979323846264338327950. 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.

Because pi is an "irrational" number, you can't represent it as a fraction made up of two whole numbers--2/3 or 18/11, for instance. But the earliest mathematicians, who had no clue about the existence of irrational numbers, didn't get much beyond representing it as 25/8 (the Babylonians, about 2000 B.C.) or 256/81 (the Egyptians, about 1650 B.C.). Then, in about 250 B.C., the Greek mathematician Archimedes--by engaging in a laborious geometric exercise--came up with not one fraction but two, 223/71 and 22/7. Archimedes realized that the exact value of pi, a value he himself did not claim to have found, had to lie somewhere in between.

Given the progress of the day, a rather poor estimate of pi also appears in the Bible, in a passage describing the furnishings of King Solomon's temple: "a molten sea, ten cubits from the one brim to the other: it was round all about ... and a line of thirty cubits did compass it round about" (1 Kings 7:23). That is, the diameter was ten units, and the circumference thirty, which can only be true if pi were equal to 3. Three millennia later, in 1897, the lower house of the Indiana State Legislature passed a bill announcing that, henceforth in the Hoosier state, "the ratio of the diameter and circumference is as five-fourths to four"--in other words, exactly 3.2.

The importance of being constant: the fundamental things apply … as time goes by

Natural History, Nov, 2004 by Neil deGrasse Tyson

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