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The Science of TV's the Big Bang Theory

Explanations Even Penny Would Understand

ECW PRESS

The Naming of Things

Raj: Sheldon, I want you to meet Neil deGrasse Tyson from the Hayden Planetarium in New York.

Sheldon: I'm quite familiar with Dr. Tyson. He's responsible for the demotion of Pluto from planetary status. [To Dr. Tyson:] I liked Pluto. Ergo, I do not like you.

– "The Apology Insufficiency" (Season 4, Episode 7)

Scientists, right up there with lawyers and loan officers, are widely regarded as inveterate hair-splitters. And they are. They have to be. Science is confusing enough without letting sloppy language make it worse. If you're a scientist, you try to call things precisely what they are:

"Good news — we've successfully detected the Higgs boson!"

"Ah, yes: evidence of a key component of the Standard Model of particle physics, don't you know."

If you're a non-scientist, you try to call things precisely what they are, and then typically you provide an alternative nomenclature, starting with the word "or":

"I saw on the news that they've detected this thingamajig called the Higgs boson ... or something."

"Isn't that, like, evidence of a super-important part of the Standard Model of particle physics ... or whatever?"

Whether using the precise terminology or implying that you may not have it quite right, you're acknowledging the importance of calling things what they are. No one on The Big Bang Theory embodies this rigorous adherence to verbal exactitude more than Sheldon does; as Penny points out, he loves correcting anyone who "says 'who' instead of 'whom' or thinks the Moon is a planet." That's what makes his retort about Pluto so uncharacteristically un-scientist-worthy. If a group of people are going to talk meaningfully about planets, they'd better be in agreement about what a planet actually is — especially if they're scientists. It's nobody's fault (certainly not Dr. Tyson's) that when the word planet was officially redefined, it stopped applying to Pluto.

What is a planet, anyway? Is it just "a big thing that goes around the Sun"? Unfortunately, depending on your definition of "big," that description applies to potentially millions of objects.

Humanity has been down this slippery slope before. In the very early days of astronomy, what people meant by "planet" really was "a big thing that goes around the Sun." For thousands of years, only five or six were known. (There was some disagreement about whether Earth revolved, which Copernicus resolved.)

Then the telescope was invented, and many additional big things that went around the Sun were discovered and named. By the mid-1800s, the number of objects that had been classified as planets had grown to nearly two dozen. Curiously, all the new additions to the list occupied a single region of the Solar System: a ring around the Sun that's now called the asteroid belt. It contains not a few but millions upon millions of tumbling, rolling fragments of rocky space debris, the building blocks of planets. Half its mass is concentrated in four large fragments, yet the largest of these, Ceres, has barely 1% the mass of Earth's moon.

If you glued all the components of the asteroid belt together, they'd make a ball only about a thousand miles across. That's a pretty small ball: it could comfortably squat on the entire Middle East (not that we would ever wish that) without overhanging the edges. Or if you could somehow spread it like cream cheese, you could just about fill all the oceans of Earth to the brim. That's a lot of cream cheese, but it's not a lot of planet.

To continue labeling each newfound big thing that goes around the Sun a planet would have rendered the term virtually meaningless. So astronomers restored sanity by tightening the meaning of the word so that it only encompassed the eight most massive ones. They reclassified Ceres and its puny associates under the new term asteroid ("star-like object").

Sensible, right?

The intervening century and a half has brought us back to nearly the identical situation. Out beyond the orbit of Neptune lie a substantial number of objects, many of them tinier than Earth's moon yet bigger than Ceres — big enough to qualify as planets under the new definition. To keep the word from becoming meaningless again, it was necessary to redefine it in a yet more restrictive sense and to introduce a new term: dwarf planet.

The first of these objects to have been discovered was Pluto. Like Ceres and the other asteroids-née-planets of the 1850s, it has played an important role: its misclassification served to demonstrate the inexactitude of the terminology. Tyson and others lobbied hard for a new category of Solar System objects, arguing that it would be in the best interests of science and the public, and a 2006 vote by the International Astronomical Union made it official.

Unfortunately, in the seven decades since Pluto's discovery, the runt of the Solar System had become an oddly beloved part of humanity's mental furniture. Many people strongly resisted its "demotion," with a good portion of their resentment seemingly grounded in reasons that were more emotional than logical. Awkward company for Sheldon to find himself in.

Atto Way!

Sheldon: This table – it's in square centimeters. I read it as square meters. You know what that means?

Amy: That Americans can't handle the metric system?

– "The Romance Resonance" (Season 7, Episode 6)

Amy's not the first to be baffled by Americans' refusal to embrace what the rest of the planet has long found to be a remarkably straightforward system. It's not because the math is tricky. The entire system is based on multiplying and dividing by ten and by various powers of ten (100, 1,000, 10,000, and so on).

And it's not for lack of exposure. Thanks to a concerted push by industry and lawmakers over the past fifty years, it's now easy to find metric measurements everywhere: on soda cans, scales, speedometers — everywhere but in Americans' heads. Yet the public remains devotedly and inexplicably resistant to the system.

Perhaps it's just an entire nation's way of showing solidarity with the many other countries that have also resisted adopting the metric system (namely, Liberia and Myanmar). Or perhaps this is how the public expresses its disdain for the non-English origins of the system or for the many non-English languages represented in it, mostly in the prefixes it uses to imply multiplication and division by powers of ten.

Some of the exponents in the table below are negative numbers. We know that 103 means "three tens multiplied together," but what does 10-3 mean? It's hard to imagine how you could multiply "negative three" tens together. And what do you do if the exponent is zero? What do you get when you multiply no tens together? Zero? An undefined value? Negative infinity? A month of Sundays?

Long ago, mathematicians agreed to extend the concept of powers to cover exponents less than one. It turns out that the zero-th power of any nonzero number is 1. This may seem completely arbitrary, but it's not; it continues a mathematical pattern. Since 102 is one-tenth of 103 (that is, 100 = 1,000 ÷ 10) and 101 is one-tenth of 102, it makes sense for 100 to be one-tenth of 101 — in other words, 1.

Continuing the pattern, 10-1 should be one-tenth of 100 (or []), 10-2 should be 1/100, and in general all negative exponents should indicate fractions smaller than 1. (You may have noticed that a negative power is the same as 1 divided by the corresponding positive power; e.g., 10-210–2 = 1 ÷ 102 = 1/100. Weird, perhaps, but the math supports it.)

Note that all the prefixes ending in -a indicate positive exponents and that all the prefixes ending in -i or -o (except hecto- and kilo-) indicate negative exponents. It's as though an -i or -o ending is the equivalent of the English -th (as in micro- = one millionth). The prefix's first vowel is usually short in English, with the exceptions of micro- (long I sound) and pico- (long E sound). That first vowel also nearly always takes the stress. (The most common exception is kilometer: many people say kilometer. But you can say kilometer if you want to.) Still, none of these prefixes has any real-world meaning unless it's attached to the name of a unit of measure, and therein lies the real power of the system.

Metric Prefixes

(There's no need to memorize or even understand this entire table. Scientists and engineers are just about the only people who ever need to go beyond the first two columns of the first six rows.)

One of the more radical aspects of post-revolutionary France (besides post-revolutionary France itself), the metric system was intentionally designed to be simple and elegant: simple because it uses a single unit for each type of quantity (no more inch/foot/yard/mile confusion); elegant because units that are seemingly unrelated (what does length have to do with mass?) are defined in terms of one another. For instance, a cubic centimeter is the volume of a one-centimeter-by-one-centimeter-by-one-centimeter cube (half the volume of your little toe, perhaps). Under specific conditions, a very precise amount of water will fit into one cubic centimeter, and the mass of that amount of water (roughly equal to the mass of a paper clip) was defined to be one gram. The liter (or litre in countries with British-derived spellings) was defined to be the volume taken up by a thousand of those grams of water, so a cubic centimeter is also called a milliliter.

Prefixes and units of measure mix and match freely. From their names, it's easy to see that a centimeter is 1/100 of a meter and a centiliter is 1/100 of a liter, just as one cent (which is short for centidollar, or it would be if centidollar weren't completely made up) is 1/100 of a dollar and one French centime is 1/100 of a franc. Since a meter is a little over three feet and a liter is a little over a quart, a centimeter must be a little over 3/100 of a foot (about a third of an inch) and a centiliter must be a little over 1/100 of a quart (about two teaspoons).

In the Big Bang Theory sendup that appeared on Family Guy, the "Sheldon" character brags, "I'll have you know that I can bench press over 690 billion nanograms." Impressive — until you convert 690 billion nanograms (690 × 109 × 10-9 grams) to 690 grams, which (at about 454 grams per pound) makes a pound and a half.

These prefixes show up in all sorts of contexts. The measure of sound loudness called the decibel is one tenth of a bel (a far less common but equally valid unit). Your home's electric meter measures by the kilowatt-hour, which is 1,000 watt-hours, or 1,000 times the energy needed to keep a one-watt flashlight bulb lit for one hour.

Originally, the metric system included prefixes for only the first three powers of ten, using variations on the ancient Greek and Roman words for ten, hundred, and thousand. But since the ancient Greeks and Romans rarely needed to count beyond a few hundred thousand, even when counting ancient Greeks and Romans (it was a smaller world back then), they didn't leave us any suitable root words for higher powers of ten. And that's unfortunate, because following World War II, many governments realized that science and commerce needed standard prefixes for million(th), billion(th), and trillion(th).

Beyond a thousand, it's more convenient to think not in powers of ten but in powers of a thousand; hence the use of commas (or, in some countries, periods or spaces) to break up large numbers into three-digit groups. Our word million is an artificial construction that translates loosely as "big thousand," while billion is meant to evoke the concept of "twice-big thousand," i.e., "big, big thousand."

The conversion from a power of 1,000 to a power of 10 is easy; you just multiply the exponent by three:

1,0001 = 103 = 1,000
1,0002 = 106 = 1,000,000
1,0003 = 109 = 1,000,000,000
etc.

The hard part is agreeing on what to call them.

For the International System of Units, adopted in 1960, the scientists flipped through their dictionaries and came up with a set of prefixes based on six visually arresting words: five Greek, one Spanish. (Spanish! Was there really no way of saying "pinprick" in Greek?)

Within four years, two more powers of a thousand were needed, to bring the prefixes up to a billion billion (and down to a billionth of a billionth). This time, however, the wordsmiths turned away from visual imagery and went back to numbers: two of them from Greek and two from Danish. (Danish! How quickly they gave up on Spanish!) Yes, Danish. And why not? For such a small country, Denmark's contribution to the sciences is remarkable. Anyway, any language that could give the world such a marvelous tongue-twister as rødgrød med fløde, which every Dane's child can say effortlessly (and no one else's child can), deserves a place on the tongues of the world's scientists and engineers.

The prefixes peta- and exa- were formed by dropping one consonant from their respective powers of 1,000: the n from penta ("five") and the h from hexa ("six"). This was an intentional word game, adopted after someone noticed that by coincidence tera- ("monster"), meaning 1,0004, is tetra ("four") with a consonant removed.

The latest additions to the list of prefixes, still with their roots in the Greek counting system, play a combined game of "drop the consonant" and "add a one-letter prefix." And how were those prefixes-on-prefixes chosen? Evidently by starting at the end of the English alphabet (English! Like we earned it!) and working toward the front. So as long as you can recite the alphabet backward while counting in Greek and Danish, you should have no problem with numbers between 10-24 and 1024.

And that's all she wrote. There are no official prefixes to signify 10-27 (= 1,000-9) and 1027 (= 1,0009). But it's only a matter of time, because although economists don't have a need for numbers that extreme (yet), scientists might. After all, 1027 cubic yards is roughly half the volume of the Sun, while |1027 pounds is about the weight of a single molecule of hydrogen on the Moon.

Unfortunately, the next English letter is X, with all of the pronunciation ambiguities that that entails. Worse, the Greek for nine is ennea, and dropping its one and only consonant sound doesn't leave much more than a donkey's hee-haw (and all that that en-tails).

Evidently it's time to abandon the "drop a consonant" scheme, which is why the prefixes xenia- and xenio- have been proposed. (These are unrelated to the Greek xenos, meaning "stranger," as in xenophobia, the fear of Danish children.) However, other candidates are also up for consideration: xenna-/xenno-, xenta-/xento-, and even the brazenly English-centric nina-/ninto- (with a long I sound).

Alternatively, the caretakers of the International System of Units could take the suggestion of a group of students at the University of California, Davis. Reverting to the descriptive-names theme of |mega-,giga-, and tera-,they proposed that 1027 simply be given the evocative prefix hella-.

While all of that is being sorted out, if you're an American (or you know one) looking to help further the spread of metric know-how in the States, why not reprogram the GPS in your car to speak in kilometers instead of miles? (Of course you would want to download the British voice pack for that — which, let's face it, probably has a much more soothing cadence than the American one anyway.) You could also learn to give your height in centimeters, your weight in kilos, and your favorite drink recipes in milliliters.

Work on it. Keep it up. You'll be sounding like a citizen of the world in no time.

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Excerpted from The Science of TV's the Big Bang Theory by Dave H. Zobel. Copyright © 2015 Dave Zobel. Excerpted by permission of ECW PRESS.
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