How would you suspend 500,000 pounds of water in the air
with no visible means of support? (Answer: build a cloud.)
—artist Bob Miller
There is something magically seductive about an invitation to a world where everything measures much bigger or smaller than ourselves. To contemplate the vast expanse of ocean or sky, to look at pond scum under a microscope, to imagine the intimate inner life of atoms, all cast spells that take us far beyond the realm of everyday living into exotic landscapes accessible only through the imagination. What would it be like to grow as big as a giant? As small as a bug? Alice ate a mushroom and puffed up like a Macy’s Thanksgiving Day balloon, bursting out of her house; she ate some more and shrank like the Incredible Shrinking Woman, forever in fear of falling down the drain. From Stuart Little to King Kong, from Honey, 1 Shrunk the Kids to Thumbelina, the notion of changing size seems to have a powerful pull on our psyches.
There are good reasons to think a world that’s different in scale will also be different in kind. More or less of something very often adds up to more than simply more or less; quantitative changes can make huge qualitative differences.
When the size of things changes radically, different laws of nature rule, time ticks according to different clocks, new worlds appear out of nowhere while old ones dissolve into invisibility. Consider the strange situation of a giant, for example. Big and strong to be sure, but size comes with distinct disadvantages. According to J. B. S. Haldane in his classic essay, “On Being the Right Size,” a sixty-foot giant would break his thighbones at every step. The reason is simple geometry. Height increases only in one dimension, area in two, volume in three. If you doubled the height of a man, the cross section, or thickness, of muscle that supports him against gravity would quadruple (two times two) and his volume—and therefore weight—would increase by a factor of eight. If you made him ten times taller, his weight would be a thousand times greater, but the cross section of bones and muscles to support him would only increase by a factor of one hundred. Result: shattered bones.
To bear such weight would require stout, thick legs—think elephant or rhino. Leaping would be out of the question. Superman must have been a flea.
Fleas, of course, perform superhuman feats routinely (which is part of the science behind the now nearly extinct art of the flea circus). These puny critters can pull 160,000 times their own weight, and jump a hundred times their own height. Small creatures have so little mass compared to the area of their muscles that they seem enormously strong. While their muscles are many orders of magnitude weaker than ours, the mass they have to push around is so much smaller that it makes each ant and flea into a superbeing. Leaping over tall buildings does not pose a problem.*
Neither does falling. The old saying is true: The bigger they come, the harder they fall. And the smaller they come, the softer their landings. Again, the reason is geometry. If an elephant falls from a building, gravity pulls strongly on its huge mass while its comparatively small surface area offers little resistance. A mouse, on the other hand, is so small in volume (and therefore mass) that gravity has little to attract; at the same time, its relative surface area is so huge that it serves as a built-in parachute.
A mouse, writes Haldane, could be dropped from a thousand-yard-high cliff and walk away unharmed. A rat would probably suffer enough damage to be killed. A person would certainly be killed. And a horse, he tells us, “splashes.”
The same relationships apply to inanimate falling objects—say, drops of water. The atmosphere is drenched with water vapor, even when we can’t see it in the form of clouds. However, once a tiny particle begins to attract water molecules to its sides, things change rapidly. As the diameter of the growing droplet increases by a hundred, the surface area increases by ten thousand, and its volume a millionfold. The larger surface area reflects far more light—making the cloud visible. The enormously increased volume gives the drops the gravitational pull they need to splash down to the ground as rain.
According to cloud experts, water droplets in the air are simultaneously pulled on by electrical forces of attraction—which keep them herded together in the cloud—and gravity, which pulls them down. When the drops are small, their surface area is huge compared to volume; electrical (molecular) forces rule and the drops stay suspended in midair. Once the drops get big enough, however, gravity always wins.
Pint-size objects barely feel gravity—a force that only makes itself felt on large scales. The electrical forces that hold molecules together are trillions of times stronger. That’s why even the slightest bit of electrical static in the air can make your hair stand on end.
These electrical forces would present major problems to flea-size Superman. For one thing, he’d have a hard time flying faster than a speeding bullet, because the air would be a thick soup of sticky molecules grasping him from all directions; it would be like swimming through molasses.
Flies have no problem walking on the ceiling because the molecular glue that holds their feet to the moldings is stronger than the puny weight pulling them down. The electrical pull of water, however, attracts the insects like magnets. As Haldane points out, the electrical attraction of water molecules makes going for a drink a dangerous endeavor for an insect. A bug leaning over a puddle to take a sip of water would be in the same position as a person leaning out over a cliff to pluck a berry off a bush.
Water is one of the stickiest substances around. A person coming out of the shower carries about a pound of extra weight, scarcely a burden. But a mouse coming out of the shower would have to lift its weight in water, according to Haldane. For a fly, water is as powerful as flypaper; once it gets wet, it’s stuck for life. That’s one reason, writes Haldane, that most insects have a long proboscis.
In fact, once you get down to bug size, almost everything is different. An ant-size person could never write a book: the keys to an ant-size typewriter would stick together; so would the pages of a manuscript. An ant couldn’t build a fire because the smallest possible flame is larger than its body.
Shrinking down to atom size alters reality beyond recognition, opening doors into new and wholly unexpected vistas. Atom-size things do not behave like molecule-size things or human-size things. Atomic particles are ruled by the probabilistic laws of quantum mechanics. Physicists have to be very clever to lure these quantum mechanical attributes out in the open, because they simply don’t exist on the scales of human instrumentation. We do not perceive that energy comes in precisely defined clumps or that clouds of electrons buzz around atoms in a permanent state of probabilistic uncertainty. These behaviors become perceptible macroscopically only in exotic situations—for example, superconductivity—a superordered state where pairs of loose electrons in a material line up like a row of Rockettes. With electrons moving in lockstep, electricity can flow through superconductors without resistance.
Scale up to molecule-size matter, and electrical forces take over; scale up further and gravity rules. As Philip and Phylis Morrison point out in the classic Powers of Ten, if you stick your hand in a sugar bowl, your fingers will emerge covered with tiny grains that stick to them due to electrical forces. However, if you stick your hand into a bowl of sugar cubes, you would be very surprised if a cube stuck to your fingers—unless you purposely set out to grasp one.
We know that gravity takes over in large-scale matters because everything in the universe larger than an asteroid is round or roundish—the result of gravity pulling matter in toward a common center. Everyday objects like houses and mountains come in every old shape, but mountains can only get so high before gravity pulls them down. They can get larger on Mars because gravity is less. Large things lose their rough edges in the fight against gravity. “No such thing as a teacup the diameter of Jupiter is possible in our world,” say the Morrisons. As a teacup grew to Jupiter size, its handle and sides would be pulled into the center by the planet’s huge gravity until it resembled a sphere.
Add more matter still, and the squeeze of gravity ignites nuclear fires; stars exist in a continual tug-of-war between gravitational collapse and the outward pressure of nuclear fire. Over time, gravity wins again. A giant star eventually collapses into a black hole. It doesn’t matter whether the star had planets orbiting its periphery or what globs of gas and dust went into making the star in the first place. Gravity is very democratic. Anything can grow up to be a black hole.
Even time ticks faster in the universe of the small. Small animals move faster, metabolize food faster (and eat more); their hearts beat faster; their life spans are short. In his book About Time, Paul Davis raises the interesting question: Does the life of a mouse feel shorter to a mouse than our life feels to us?
Biologist Stephen Jay Gould has answered this question in the negative. “Small mammals tick fast, burn rapidly, and live for a short time; large mammals live long at a stately pace. Measured by their own internal clocks, mammals of different sizes tend to live for the same amount of time.”
We all march to our own metronomes. Yet Davis suggests that all life shares the same beat because all life on Earth relies on chemical reactions—and chemical reactions take place in a sharply limited frame of time. In physicist Robert Forward’s science fiction saga Dragon’s Egg, creatures living on a neutron star are fueled by nuclear reactions; on their world, everything takes place millions of times faster. Many generations could be born and die before a minute passes on Earth.
And think how Earth would seem if we could slow our metabolism down. If our time ticked slowly enough, we could watch mountains grow and continental plates shift and come crashing together. The heavens would be bursting with supernovas, and comets would come smashing onto our shores with the regularity of shooting stars. Every day would be the Fourth of July.
An artist friend likes to imagine that if we could stand back far enough from Earth, but still see people, we would see enormous waves sweeping the globe every morning as people stood up from bed, and another huge wave of toothbrushing as people got ready to bed down for the night—one time zone after another, a tide of toothbrushing waxing and waning, following the shadow of the Sun across the land.
We miss a great deal because we perceive only things on our own scale. Exploring the invisible worlds beneath our skin can be a terrifying experience. I know because I tried it with a flexible microscope attached to a video camera on display at the Exploratorium in San Francisco. The skin on your arm reveals a dizzy landscape of nicks, creases, folds, and dewy transparent hairs the size of redwood trees—all embedded with giant boulders of dirt. Whiskers and eyelashes are disgusting—mascara dripping off like mud on a dog’s tail. It is rather overwhelming to look through your own skin at blood cells coursing through capillaries. It’s like looking at yourself without clothes. We forget the extent to which our view of the world is airbrushed, that we see things through a shroud of size, a blissfully out-of-focus blur.
An even more powerful microscope would reveal all the creatures that live on your face, dangling from tiny hairs or hiding out in your eyelashes. Not to mention the billions that share your bed every night and nest in your dish towels. How many bacteria can stand on the pointy end of a pin? You don’t want to know.*
We’re so hung up on our own scale of life that we miss most of life’s diversity, says Berkeley microbiologist Norman Pace. “Who’s in the ocean? People think of whales and seals, but 90 percent of organisms in the ocean are less than two micrometers.”
In their enchanting journey Microcosmos, microbiologist Lynn Margulis and Dorion Sagan point out the fallacy of thinking that large beings are somehow supreme. Billions of years before creatures composed of cells with nuclei (like ourselves) appeared on Earth, simple bacteria transformed the surface of the planet and invented many high-tech processes that humans are still trying to understand—including the transformation of sunlight into energy with close to a 100 percent efficiency (green plants do it all the time). Indeed, they point out that fully 10 percent of our body weight (minus the water) consists of bacteria—most of which we couldn’t live without.
Zoom in smaller than life-size, and solid tables become airy expanses of space, with an occasional nut of an atomic nucleus lost in the center, surrounded by furious clouds of electrons. As you zoom in, or out, the world looks simple, then complex, then simple again. Earth from for enough away would be a small blue dot; come in closer and you see weather patterns and ocean; closer still and humanity comes into view; closer still and it all fades away, and you’re back inside the landscape of matter—mostly empty space.
So complexity, too, changes with scale. Is an egg complex? On the outside, it’s a plain enough oval, like Jupiter’s giant red spot. On the inside, it’s white and yolk and blood vessels and DNA and squawking and pecking order and potential chocolate mousse or crème caramel.
The universe of the extremely small is so strange and rich that we can’t begin to grasp it. No one said it better than Erwin Schrödinger himself;
As our mental eye penetrates into smaller and smaller distances and shorter and shorter times, we find nature behaving so entirety differently from what we observe in visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be “true.” A complete satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think of it, but however we think it, it is wrong; not perhaps quite as meaningless as a “triangular circle,” but more so than a “winged lion.”
And as we shall see in the next section, the alchemy that can occur as we move from less to more or large to small is both unnerving in its unexpectedness and awesome in its explanatory power.