Life's Ratchet: How Molecular Machines Extract Order from Chaos (11 page)

The normal distribution had been under mathematician’s noses all along. The French mathematician and gambling theorist Abraham de Moivre (1667–1754), in his 1733 book,
The Doctrine of Chances
, had published a formula that extended Pascal’s triangle to very large numbers of trials, much larger than could be practically obtained by Pascal’s method. In the limit of large numbers, Pascal’s triangle could be approximated by a formula describing a curve that looked like a bell. This bell curve, or normal distribution, is what Gauss found in errors of astronomical data. The French mathematician Laplace picked up where Gauss left off and proved that any measurement that depends on a number of random influences tends to have errors that follow the normal distribution. Today, Laplace’s central limit theorem is a key part of statistics, which can predict distributions as varied as people’s heights or masses of stars.

The use of the normal distribution in statistics was perfected by the Belgian scientist Adolphe Quetelet (1796–1874), who subjected everything he could get his hands on to statistical analysis: chest sizes of sailors, heights
of men and women, murders committed with various weapons, drunkenness, and marriages. Wherever he looked, he found the normal distribution. And when he did not find it, he knew that something had gone awry. When, for example, he found the height of French military conscripts strangely deficient at the low end of the scale, he realized that many short men of military age had lied about their height to get out of serving. The minimum size for military service was 157 centimeters (5 feet 2 inches). If you were 157.5 centimeters, why not buckle your knees a little bit during measurement and escape the dreaded military service?

Quetelet’s work illustrated how the error law, the normal distribution, and the central limit theorem governed almost everything. His books were eagerly read not only by future sociologists, but also by future physicists and biologists. If statistics was useful in economics, medicine, and astronomy, why not in other areas as well? As we will see in
Chapter 3
, nineteenth-century physicists like James Clerk Maxwell and Ludwig Boltzmann used Quetelet’s work to develop the statistics of atoms and molecules.

Mathematician Francis Galton, Charles Darwin’s cousin, was one of the first to apply Quetelet’s ideas to a wide range of biological phenomena. He found that the normal distribution governed almost every measurement of an organism: heights, masses of organs, circumferences of limbs. One of his most important discoveries was
regression toward the mean
: Galton found that any offspring of a parent who was at the outer ranges of a distribution, for example, a very short man or a very tall woman, generally tended to “regress” toward the mean of the distribution. In other words, the son of an exceptionally short man tended to be taller than his father, and the daughter of an extremely tall mother tended to be shorter than her mother. Mozart’s children were not geniuses like their father; neither were Einstein’s. And parents of below-average intelligence often have smarter children. In the long run, we all tend toward the average. In some sense, this is a good thing. Genius is unpredictable—which makes it all the more puzzling that Galton became one of the founders of eugenics, the idea that selective breeding of humans could improve humanity. Beyond the obvious human rights issues with this awful idea, Galton’s own “regression to the mean” suggested that the prospect of success would have been highly questionable. “Breeding” two highly intelligent humans would never guarantee that their offspring would be more intelligent than,
or even as intelligent as, their parents. According to Galton’s own “regression towards the mean,” the best bet may be on “less intelligent.”

Despite his tragically misguided ideas, Galton made other important contributions to statistics, such as the
coefficient of correlation
. This statistic measured how two different variables were statistically linked, or correlated. One of the main statistical tools of modern biology and medicine, the coefficient of correlation is mathematically sound but has to be used with care. Just because stork numbers and baby births may be correlated over a few years does not mean that storks bring babies. A correlation is a hint of a possible connection, not a proof.

With Galton’s and Quetelet’s ideas, statistics flourished in the nineteenth century. It became an integral part of biology, and through his use of statistics, Mendel discovered the laws of heredity. The scene was now set to recognize randomness as an important player in the story of life.

The question of chance versus necessity occupied the human mind for thousands of years. For much of this time, philosophers, theologians, and scientists denied randomness any meaningful role in nature, with atomism being the most obvious victim of randomness phobia. However, with scientific advances in the late nineteenth and early twentieth centuries, this stance became more and more difficult to maintain. Randomness reared its ugly head first in biology, through Quetelet and Galton’s work, and finally in physics. The final battles over randomness played out in debates over the existence of atoms, the emergence of statistical and quantum mechanics, and new insights into molecular evolution and the role of mutations.

The randomness debate involved several famous protagonists. Nineteenth-century Austrian physicist Ludwig Boltzmann, cofounder of statistical physics, fought for the existence of atoms, which were still disbelieved more than two thousand years after Democritus and Epicurus. Twenty years later, Albert Einstein proved the existence of atoms in his famous papers on Brownian motion, but was unhappy with the implication that the new science of quantum mechanics was at heart built on randomness. These debates also continued in biology. Ever since Quetelet and Galton
had shown aspects of physiology to be governed by statistics, and ever since the theory of evolution had introduced randomness as a driver of novelty in the development of life, pitched battles were fought over the role of chance in the history of life. Three of the most prominent combatants included D’Arcy Wentworth Thompson (1860–1948), Pierre Teilhard de Chardin (1881–1955), and Jacques Monod (1910–1976).

An English mathematician and biologist, Thompson was best known for his 1917 masterpiece
On Growth and Form
, a book filled with astonishing insight (and many fascinating diagrams) of how mathematical principles guide the shapes and forces of living organisms. Thompson did not believe in teleological life forces. It seemed frivolous to him to invoke nebulous reasons, when a mathematical or physical explanation would do. He saw a continuity of complexity acting throughout all of nature and therefore no unbridgeable chasm between the living and the dead. “The search for differences . . . between the phenomena of organic and inorganic, of animate and inanimate things, has occupied many men’s minds, while the search for community of principles or essential similitudes has been pursued by few. . . . Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, molded and conformed.”

In all of this, Thompson was humble—he allowed the possibility that not all phenomena of life could be explained through physical laws alone. But he felt that too often, biologists of his time surrendered too early, and that many phenomena of life
could
be explained, if scientists were given sufficient time to gain insight into the involved complexities. In the battle between purpose and mechanism, he understood the usefulness of invoking final causes, but realized that one cannot stop there, but must find the physical reasons for how structures arise. “In Aristotle’s parable, the house is there that men can live in it; but it is also there because the builders have laid one stone upon another.” For Thompson, a full explanation needed to contain an explanation of both why a structure was there and how it was constructed.

On the other hand, Thompson, while fond of mechanistic explanations, did not support the theory of evolution. For him, explanations should be explanations of necessity—chance was to play no role. He also did not favor theological hand-waving: “How easy it is, and how vain,
to survey the operations of Nature and idly refer her wondrous works to chance or accident, or to the immediate interposition of God.” Invoking chance, God, or any extraneous life principle when met with ignorance was a cheap trick, according to Thompson, designed to keep us from doing the hard work of finding the true causes.

Where Thompson had polite disdain for final causes, Chardin, a French Jesuit priest, paleontologist, and anthropologist, celebrated them— envisioning even atoms and molecules as bound to a higher purpose. Chardin made the reconciliation of science and religion his life’s work. As a scientist, he knew that the theory of evolution was the best explanation for the development of the living world, and he became an enthusiastic champion of evolution, although with a twist: In his masterpiece
The Phenomenon of Man
(written in the 1930s, but published in 1955), Chardin envisioned evolution as an upward motion toward more complex and sophisticated forms of life, which would ultimately culminate in a single, universal mind, which he equated with God. According to Chardin, evolution was guided by a mysterious psychic energy, an energy not yet measured or discovered, but nevertheless evident from the progress seen in the evolution of our universe. Mind was primary, pulling matter along in its wake. Chardin’s philosophy was to give “primacy to the psychic and to thought in the stuff of the universe.” Voltaire had made fun of such ideas two hundred years earlier, but now a better understanding of the awe-inspiring history of evolution, and the need to define humanity’s place, made such animistic philosophies fashionable again.

Chardin’s philosophy seemed to offer a way to have your cake and eat it too: You could embrace evolution and all the findings of science, and at the same time, believe in a higher guiding force, although somewhat invisibly. Yet, despite his compromising stance on the big questions of our existence, few were happy with his ideas. The Church felt they were too far removed from traditional theology, and scientists didn’t appreciate the addition of unknown forces just to satisfy a need to place humanity in the center of all being.

One of the scientists who regarded Chardin’s ideas with disdain was the French biochemist and Nobel Prize–winner Jacques Monod. In “Vitalisms and Animisms,” a chapter in his book
Chance and Necessity
, Monod
critiqued Chardin’s logic as “hazy” and his style as “laborious.” But most of all, he was “struck by the intellectual spinelessness of [his] philosophy.” There seemed to be a “willingness to conciliate at any price, to come to any compromise.”

Yet, even for Monod, the problem of how to reconcile the blind motions of atoms and their lifeless laws with the complexity of life was a deep, central mystery. Allergic to any vitalistic or animistic explanations and unable to see how physical laws by themselves could lead to the complexity of life (which was Thompson’s idea), he resolved the dilemma by placing randomness front and center. The origin of life, according to Monod, was an incredibly improbable event. Once it happened, evolution took over, infused with a healthy dose of randomness. While both Thompson and Monod rejected the introduction of guiding principles, such as Chardin’s spiritual energy, they greatly differed on the roles of chance and necessity.

The problems of how life came to be, how life operates (metabolism, growth), and the history of evolution can be answered in many ways. However, we could organize most answers to these questions along two dimensions. There is the dichotomy of “mere physics” versus higher forces (life forces, the soul) along one dimension, and then the question of chance versus necessity along the other.
Figure 2.2
shows schematically how we could visualize these various views. Why are there so many views on the origin and nature of life? Undeniably, it is difficult to see how simple physical laws can lead to life’s complexity, but at the same time, scientists have repeatedly found that yesterday’s ignorance about certain biological phenomena have turned into today’s knowledge—knowledge based on those same simple physical laws. Thus we should heed both Monod’s and Thompson’s warning: When we feel the need to invoke extraneous principles to assuage our ignorance, it is wiser to hold off. Rather, we should continue our search for explanations within known science. So far, this has served us astonishingly well. Chardin knew that the “connection of physics and biology” had to lie in the cell. However, he believed that the cell was “still a closed book” and “an impregnable fortress.” Since Chardin’s time, much of this fortress has been penetrated, the depth of our explanations has greatly increased, and the cell is not quite as enigmatic as it used to be. And in all of this, physics and chemistry have been our guides.