The Canon (14 page)

Metric or otherwise, our anthropocentric sense of scale can impede our comprehension of the cosmos, indeed of virtually every science apart from the psychology of our distorted sense of scale. Thus, the scientists I interviewed were unanimous in their conviction that people would benefit enormously from a better grasp of nature's true dimensions: the length and breadth and tenure of the visible universe, the timeline of life on earth, the sublime spaciousness that persists even down to the imperceptible atom. Talk about the size of the cell, they said, and of the cell's citizens, the proteins, the hormones, the compressed coil of genes cloistered away in the nucleus. And what of the pirates that invade the cell: How big is yersinia, bacterial bearer of plague, compared to a white blood cell that yearns to knock it offstage? Remember the viruses: Where might Ebola weigh in? And how many of any could dance on a pin?

Frankly, I can't imagine a happier assignment than to talk about scales, especially because I don't have to step on any of them and then start pushing them around the bathroom floor until I find the best spot. Sometimes just knowing how the things you can't see compare to the things you can't miss is the better part of understanding. Moreover, practicing scales in nonhuman keys can have the salubrious effect of forcing you to question who's normal and who alien. "In my field of particle physics, the notion of time is essential, but we deal with times that are vastly different from everyday human concepts," said Robert
Jaffe of MIT. "We deal with things like the time it takes light to cross a proton, on the order of 10 to the minus 24 seconds." In other words, a trillionth of a trillionth of a second. "People say, that's ridiculous, how can you be dealing with such ephemera," he said. "But the sense of alienation that people bring to the subject is a result of an anthropocentric concept of time that is in fact the real oddball here. Our perception of time is very unusual and hard to find in other systems of physics. It's easy to find extremely short time scales, like those that apply to many subatomic particles, and it's easy to find extremely long time scales, like those that pertain to the universe and to very stable particles, but it's very unusual to find scales like hours, days, and years. Our quirky concept of time has to do with the celestial mechanics of our solar system, and of the fact that we're poised between the energy scale of gravity and the world of nuclear forces."

To play any scales beyond our pedestrian ones, to talk of celestial harmonics or quantum dynamics, you need scientific notation, otherwise known as the powers of ten. The power of this notation has almost but not quite infiltrated popular culture, thanks in good part to Philip and Phylis Morrison's best-selling book
Powers of Ten.
But scientific notation deserves even greater magnitudes of fame, for it is both lovely and useful, like a fine old oak table with claw feet and spare leaves for when company comes. It's called powers of ten because you're asking, How many times do you have to multiply your figure by ten to get to where you're going? Ten times ten, or 10
²
, is 100; ten times ten times ten, or 10
³
, is a thousand. Add another power of ten to that string, and you've got 10
⁴
, or 10,000. Scientific notation allows you to write perversely large numbers in compact form, and to manipulate them with the sort of ease rarely encountered beyond the privacy of your microwave oven. As of late 2006, for example, the U.S. national debt stood at $8.5 trillion. You can write that out in long form, as 8,500,000,000,000, and almost feel the red ink flowing from your veins. Alternatively, you can translate the quantity into scientific notation, by putting a decimal point immediately after your leftmost digit, and counting rightward to find your power of ten, or exponent. With a figure like 8.5 × 10
¹²
, you won't feel nearly so overwhelmed, and may even come to think of such sums as reasonable and rational, at which point you'll be qualified to run the Office of Management and Budget.

To gain a quick grip on things by way of scientific notation, it helps to memorize those superscripts that correspond to numbers you know. A thousand with its three zeros is 10
³
, a hundred thousand 10
⁵
, a million
10
⁶
, a billion 10
⁹
, a trillion 10
¹²
, a googol 10
¹⁰⁰
, a Google a search engine and transitive verb, and Gogol a nineteenth-century Russian novelist. You can see, then, why "exponential growth" is so pushy. The exponent of a billion may be only three more than that for a million, but that cute little three means, I raise you a thousandfold, dear.

Scientific notation works just as well for the furtive as for the discursive, although in this case you're talking about powers of one-tenth rather than powers of ten. One-tenth of one-tenth is one-hundredth, written as 10
^-2
; one-tenth of one-hundredth is one-thousandth, or 10
^-3
. Keep biting the right-handed bit of Alice's toadstool. Down you go, you're a fractionated Italianate family. You're milli—a thousandth, 10
^-3
; or micro—a millionth, 10
^-6
; or nano—a billionth, 10
^-9
; or pico—a trillionth, 10
^-12
; or femto—a millionth of a billionth, 10
^-15
.

Now we can start to examine a world that stretches beyond the realm of ordinary accountability. What happens, for starters, in subsections of seconds? In a tenth of a second, we find the proverbial "blink of an eye," for that's how long the act takes. In a hundredth of a second, a hummingbird can beat its wings once, and it is by the grace of this hyperbolic wing-flinging that these birds can hover like helicopters to sup in midair.

A millisecond, 10
^-3
seconds, is the time it takes a typical camera strobe to flash. Five-thousandths of a second is also the time it takes the
Bolitoglossa rufescens,
a Mexican salamander that resembles a blade of grass and that owns one of the fastest tongues in nature, to extrude its mauve sling and snag its prey.

In one microsecond, 10
^-6
seconds, nerves can send a message from that pain in your neck to your brain. On the same scale, we can illuminate the vast difference between the speed of light and that of sound: in one microsecond, a beam of light can barrel down the length of three of our metric-resistant football fields, while a sound wave can barely traverse the width of a human hair.

Yes, time is fleeting, so make every second and every partitioned second count, including nanoseconds, or billionths of a second, or 10
^-9
seconds. Your ordinary computer certainly does. In a nanosecond, the time it takes you to complete one hundred-millionth of an eye blink, a standard microprocessor can perform a simple operation: adding together two numbers, say, or flagging that questionable travel-and-expenses figure on your tax return.

The fastest computers perform their calculations in picoseconds, or trillionths of a second, that is, 10
^-12
seconds. If you could observe the intimate behavior of the water molecules in your lukewarm bottle of Dasani, you would see that every three picoseconds or so, the weak chemical links that hold adjacent water molecules together dissolve and reform again, a shimmering glimpse of the tentative nature of even the most carefully marketed products.

Ephemera, however, are all relative. When physicists, with the aid of giant particle accelerators, manage to generate traces of a subatomic splinter called a heavy quark, the particle persists for a picosecond before it decays adieu. Granted, a trillionth of a second may not immediately conjure Methuselah or Strom Thurmond to mind, but Dr. Jaffe observed that the quark fully deserves its classification among physicists as a long-lived, "stable" particle. During its picosecond on deck, the quark completes a trillion, or 10
¹²
, extremely tiny orbits. By contrast, said Jaffe, our seemingly indomitable Earth has completed a mere 5 times 10
⁹
orbits around the sun in its 5 billion years of existence, and is expected to tally up maybe another 10 billion laps before the solar system crumples and dies. "That brings us up to 15 times 10
⁹
orbits, considerably fewer than 10
¹²
," said Jaffe. "In a very real sense, then, our solar system is far less stable" than particles like the heavy quark. The shackles of "our personal, anthropocentric conception of time," said Jaffe, "make it hard for us to understand the vastness of the stability that these particles embody."

Scaling down to an even less momentous moment, we greet the attosecond, a billionth of a billionth of a second, or 10
^-18
seconds. The briefest events that scientists can clock, as opposed to calculate, are measured in attoseconds. It takes an electron twenty-four attoseconds to complete a single orbit around a hydrogen atom—a voyage that the electron makes about 40,000 trillion times per second. There are more attoseconds in a single minute than there have been minutes since the birth of the universe.

Still, physicists keep coming back to the nicking of time. In the 1990s, they inducted two new temporal units into the official lexicon, which are worth knowing for their appellations alone: the zeptosecond, or 10
^-21
seconds, and the yoctosecond, or 10
^-24
seconds. The briskest time span recognized to date is the chronon, or Planck time, and it lasts about 5 × 10
^-44
seconds. This is the time it takes light to travel what could be the shortest possible slice of space, the Planck length, the size of one of the hypothetical "strings" that some physicists say lie at the base of all matter and force in the universe. Chronons and strings remain more in the realms of mathematics and philosophy than empirical reality, however; and no one knows what would happen if we shaved our numbers further, and took a long gambol on a really short Planck.

The universe, though, doesn't only like to cut things short; it also opts for the sagging saga approach, dictating thick volumes of time that are nearly as unfathomable as
Finnegans Wake.

Consider Earth time, which really is a Joycean "riverrun, past Eve and Adam's." If you had all the time in the world, what would you have? Creationists, scanning the pages of Genesis, Galatians, and other biblical sources, and counting up the "begat"s, bellow, "Six thousand years!" But the creationists' clock is—what's the word for "off by six orders of magnitude"?—cuckoo. There are one or two otherwise productive geologists who believe the biblical story of creation and insist that Earth really is young but that God has given it the illusion of great antiquity—but that's out of more than 100,000 geoscientists working in the United States alone. No, had you world enough and time, you'd have 4.5 billion years, for it was that long ago that Earth, and the other planets of the solar system, condensed from the flattened Frisbee of rock and dust surrounding the newborn sun. Now, on first mull, 4.5 billion years doesn't sound excessive, decrepit, or particularly awe-inspiring. After all, if you added up the birthdays of every human alive today, assuming a median age of twenty-six, you'd have about 170 billion years.

Yet 4.5 billion years stretched end to end, as they have been, lend Earth an extraordinary degree of flexibility, have made it a place where nearly everything is possible, the comical mandatory, the provisional a familiar pest who never misses a party. Over 4.5 billion years, seas and savannas have swapped places; Earth's magnetic poles have flipped and flopped and flipped again; glaciers have gripped nearly the entire globe in a snowman's nelson; and sumptuous tropical forests of towering club mosses and ginkgo trees, millipedes as long as men are tall, and dragonflies with a falcon's wingspan have stretched from Antarctica and Australia up through Europe and the Americas. Oh, yes, it can be almost impossible to think in geologic time, even for geologists.

"I look at time differently now that I am forty-six than I did when I was twenty, and I will look at it differently again when I am seventy-five," said the geologist Kip Hodges. "But none of this is going to put me in a position where I can understand 500 million or 650 million years, let alone 4.5 billion years."

In an effort to convey the great girth of Earth time, geologists who regularly communicate with the laity have conceived a wide assortment
of metaphors and colorful visual aids, often involving long skeins of knotted yarn or multiple rolls of toilet paper. The science writer Nigel Calder tried comparing the passage of a billion years to a stroll down the island of Manhattan. To your right, ladies and gentlemen, you'll see the George Washington Bridge, and the first signs of unicellular life forms! Hiking past Central Park, Times Square, the Empire State Building: and more unicellular life forms! Other chroniclers have condensed the history of Earth into a single year, while still others have compacted it into a single day.

My favorite time-warp device is the one conceived by Kip Hodges, of imagining Earth as a human being with a seventy-five-year life span. "It's a real eye opener to think of the pace of our planet's development and the pace of evolution, in human terms," he said. By this reckoning, where twelve months is the equivalent of 60 million years, Baby Earth fattened up on a very fast track. It had finished condensing from the planetary disk around the sun and accreting added bits of rocks and metals to reach its present dimensions by one year of age. A month or two later, our big burbling bundle had belched up from its bowels a thick atmosphere of carbon dioxide, steam, nitrogen, sulfur, methane, and a smattering of other elements, a miasmic mix that our lungs would find utterly unacceptable but that allowed liquid water to wallow in the craterous basins on its surface rather than boil away into space. Early in its adolescence, Earth did what a human teenager should not do, and, somewhere, somehow, its saturated, still febrile tissue gave birth to the earliest forms of life. Roughly eight to ten weeks postpartum, blue-green strains of bacteria began spitting oxygen into the atmosphere, sparking a biochemical revolution that life eventually would put to spectacular use. Not until age sixty-three, however—about 700 million years ago—would we see the debut of multicellular animals. Mother Earth reached a grandmotherly seventy-two years before dinosaurs appeared, and the first ape didn't arrive until May or June of the final year, age seventy-five, of our handily, anthropocentrically foreshortened Life of Gaia. Modern
Homo sapiens
awaited the chiming in of December 31, agriculture and animal husbandry arose at 10:00
P.M.
that night, the first writing was scrawled and the first wheel turned an hour later, the American Revolution was fought at 11:58
P.M.
, and Neil Armstrong muddied up the moon and muddled his way into Bartlett's at twenty seconds to midnight.