Arrival of the Fittest: Solving Evolution's Greatest Puzzle (27 page)

And with them? If we only step to the text’s neutral neighbors—those with the same hammerhead shape—and determine the shape of all
their
neighbors, we already find 962 new shapes. And if we just walk one step further, to
those
neighbors’ neutral neighbors, we find 1,752 new shapes. Just two steps along this ribozyme’s genotype network, we can access almost forty times more shapes than in its immediate vicinity. The genotype network of the hammerhead shape of course extends much further than just two steps, and it has more than 10
¹⁹
members, too many to count all the new shapes near them with current computers.
²⁸
But we can say with certainty that countless millions and billions of new shapes are near them, all explorable because evolution’s readers can spread out along the genotype network without suffering death.
²⁹

That’s how much genotype networks accelerate innovation. They are like the warp drives of
Star Trek,
science fiction’s solution for faster-than-light interstellar travel. Extrapolate from the hammerhead ribozyme and imagine that evolution had unfolded merely forty times more slowly without genotype networks. Instead of being four billion years along its path, life would have evolved only as far as it did during the planet’s first hundred million years. A few kinds of bacteria would be around, but certainly no multicellular organisms, let alone fish, land plants, dinosaurs, or nonfiction book authors. And genotype networks accelerate evolution much more than fortyfold—so much more we can’t even yet compute it. Without them, life would never have crawled out of the primordial soup.

Science fiction also has another solution to faster-than-light travel: changing the shape of space itself. Inventive science-fiction authors have postulated technologies like “wormhole drives” that allow instantaneous travels between places thousands of light-years apart. It turns out that genotype networks also do something similar. They shrink the distance between texts in the libraries of metabolisms, macromolecules, and regulatory circuits.

Imagine a crowd of evolution’s readers—organisms in a population—congregating near a text describing a circuit with a specific expression code that helps shape some body part, like a bird’s wing. Now imagine that somewhere in the library of regulatory circuits a
new
code exists that modifies the wing to make it slightly more aerodynamic or lighter. The further the readers must travel to find it, the more time they need to find this innovation.

Browsing through such an enormous library seems, at first glance, like hunting for a particular needle in a haystack. You might find the right needle immediately, but chances are you would have to examine most of the haystack—perhaps all of it—before achieving success. Common sense dictates that the same applies to the library, that a new expression code is like a single needle in a haystack many times the size of the universe.

But common sense fails in this library. We had already learned this from our discovery that there are innumerable circuits with the same expression code—the haystack has many needles—but the library is even more bizarre, as we found out by searching for circuits with specific new expression codes. In this search, we created arbitrary expression codes—thousands of them—and for each such code we used our computers to generate a pair of circuits, where the first circuit produced one of these codes, and the second produced the other. The two circuits differed also in most of their wiring pattern, in the who-regulates-whom among the circuit genes. We then changed the first circuit gradually, one wire at a time, requiring that each such gene regulation change preserve the circuit’s expression code. How close could we get to the second circuit? Very close, we found out, for example to within 85 percent of the second circuit’s wiring for circuits of twenty genes. In other words, starting from anywhere in the library—
anywhere
—you need not walk very far, only fifteen steps away from a genotype network, before finding the genotype network of
any
other circuit. It is as if your needle were
always
nearby, no matter where you started to search.
³⁰

If this doesn’t sound strange enough, get ready for something even stranger.

Imagine that the square in figure 19 is the library, and the dot is a single text in it. The circle around this dot has a radius that is 15 percent as long as the sides—this is how far a reader would have to travel from a genotype network, on average, before finding a specific new expression code, as we had found out from exploring the circuit library. A simple calculation shows that a circle with a radius of fifteen centimeters, inside a square that is one hundred centimeters on a side, has an area of 707 square centimeters, a little more than 7 percent of the square’s area.

Actual libraries aren’t two-dimensional, of course. They exist in three dimensions. For simplicity’s sake, let’s say that our library building is housed in a three-dimensional cube, and the area of the library containing circuits with a new expression code is now a sphere. If so, then the sphere inscribed inside the library will now have a radius 15 percent as long as the sides of the cube, just as with the square. The ratio of their volumes, however, becomes very different. The volume of the sphere covers not 7 percent of that of the cube, but only 1.4 percent.

The libraries of regulatory circuits, of course, aren’t three- or even four-dimensional. They occupy higher dimensions, where cubes become hypercubes and balls become hyperspheres. In four dimensions, our hypersphere—still with the same radius—contains 0.2 percent of a hypercube’s volume. In five dimensions, it covers 0.04 percent, and so on.

In the number of dimensions where our circuit library exists—get ready for this—the sphere contains neither 0.1 percent, 0.01 percent, nor 0.001 percent. It contains less than 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 percent, or one 10
^-100
th, of the library.
³¹
This is the tiny fraction of the circuit library a reader needs to explore, starting from its own genotype network, to find a circuit with any one expression code. That it is so small emerges from a simple geometric principle in spaces of ever-higher dimensions: A ball with constant radius occupies ever-decreasing and ever-tinier fractions of a cube’s volume.
³²
(This volume decreases not just for my example of a 15 percent ratio of volumes, but for any ratio, even one as high as 75 percent, where the volume drops to 49 percent in three dimensions, to 28 percent in four, to 14.7 percent in five, and so on, to ever-smaller fractions.)
³³

The same counterintuitive phenomenon holds in other libraries of innovation: The more dimensions they have—the larger their collection of metabolisms or molecules—the smaller the distance to find specific innovations. A browser who starts with a metabolism that can survive on some foods and then blindly searches for one that can thrive on others needs to change only a few reactions and explore a tiny fraction—too small to imagine—of the metabolic library before stumbling upon the right text. The same holds true for RNA. Starting from an existing RNA molecule, a nearby molecule with a new shape—
any
new shape you choose—will be found after changing only a few of the molecule’s nucleotide building blocks and having explored a tiny fraction of the library.
³⁴

The astonishing fact that evolution needs to explore one 10
^-100
th
of a library to secure the arrival of the fittest goes a long way to explain how blind search produces life’s immense diversity. Evolution does not have to search the entire haystack, because the haystack contains more than one needle. In fact, thanks to robustness, and the genotypic disorder it permits, the haystack contains too many needles to count, and they are organized into sprawling but navigable networks.

And if we remember that the neighborhood of each text is extremely diverse, we have understood one more feature of the library’s organization: Genotype networks not only range far and wide but also are tightly interwoven. They form a dense tissue of networks, each genotype network surrounded by many others, interwoven with them on all sides, a tissue so complex that it looks nowhere the same, consisting of millions, billions, or more of different strands, each one corresponding to a different phenotype. If each strand had a different color, this tissue would be woven in such an intricate way that near any one strand, threads of billions of other colors would pass. Only a high-dimensional space can host such a fabric, whose texture is intricate beyond our grasp. This fabric is different from anything we know. It is hidden behind the visible splendor of each living thing, yet all this splendor emerges from it.

Because genotype networks and their fabric are a consequence of robustness, robustness is immensely valuable to innovation. But valuable things are usually not free, and robustness is no exception. Its price—a high one—is complexity.

It’s almost too easy to criticize complexity. In Lewis Carroll’s
Through the Looking-Glass
, Alice is navigating the tale’s fantastic chessboard when she is attacked by the Red Knight, who mistakes her for a white pawn. In the nick of time, Alice is rescued by his opposite number, the White Knight—tellingly, an inventor—who is eager to show his new friend his latest innovations, including boxes that open on the bottom to keep out the rain, a device for trapping mice when they appear on a horse’s back, and a dessert made of blotting paper, sealing wax, and gunpowder:

“You see,” he went on after a pause, “it’s as well to be provided for
everything
. That’s the reason the horse has all those anklets round his feet.”

“But what are they for?” Alice asked in a tone of great curiosity.

“To guard against the bites of sharks,” the Knight replied. “It’s an invention of my own.”

The White Knight is so handicapped by his complex and fantastic inventions that he is literally unable to ride and to accompany Alice on her journey, and so he quickly departs the story. He lives on, however, as an object lesson in the importance of simplicity.

Long before Carroll wrote his story, the fourteenth-century English friar William of Ockham had already expressed an enthusiasm for simplicity when he coined a now famous principle of parsimony: that phenomena should always be understood using the fewest possible facts, or “entities,” as Ockham called them. This ideal—often called Ockham’s (or Occam’s) razor—is usually held up to scientific explanations that are supposed to be both truthful and beautiful. But it could apply equally to the kinds of machines inventors and engineers build, even though engineers already have their own, more earthy motto: KISS, for Keep It Simple, Stupid.

The ideal of simplicity is not just an aesthetic ideal or a philosophical principle. In engineering it also has an economic angle. It costs money to manufacture the parts of a machine. More parts cost more money, a prospect that any sane manufacturer wants to avoid. In addition, assembling a complex machine is more error-prone. Simplicity is better for building machines that work.
³⁵

Anybody who has struggled to understand living beings, and has despaired at their complexity, will sympathize with this yearning for simplicity. Life seems unnecessarily complex in many ways. The regulation circuit that divides insects into fourteen segments contains dozens of molecules,
³⁶
but scientists have known for many years that just
two
molecules interacting in the right way could achieve the same goal.
³⁷
As if to spite us, thousands of insect species segment their bodies in a way that not only took decades to understand but that no self-respecting human engineer would ever devise. And remember the road networks of metabolisms, full of redundant lanes, alternative routes, and unused back alleys. They all raise the same question: Why? Why doesn’t ruthlessly efficient nature get rid of all this complexity?