Darwin’s theory received serious opposition on religious grounds. In a popular book, Natural Theology, published in 1802, the theologian William Paley (1743–1805) had compared the complex mechanisms within living beings to the workings of a watch (as the rather less religious La Mettrie had done as well). Clearly, a watch assumed a watchmaker. It did not design and make itself. How could we even suggest that the infinitely more complex designs of living beings had made themselves? Paley’s book was very popular at the time and was one of Darwin’s favorites during his under graduate years. It was only very gradually, and through thousands of painstaking observations, that Darwin came to realize that Paley was wrong.
By removing the last vestiges of purpose, Darwin’s theory of evolution made God unnecessary for explaining the natural world. This, of course, was not the first time God had been made unnecessary. Physics had already banned God from the heavens (“I have no need for that hypothesis” answered the physicist Pierre-Simon Laplace when Napoleon asked him about the role of God in the universe), and Helmholtz had banned vital forces. The last refuge of the supernatural seemed to be the wondrous multiplicity of life forms. Now even that became the result of blind forces.
While much has been made of the religious critics of Darwin’s ideas, his theory was similarly met with initial reservations by his fellow scientists. Here, the reasons were different. Darwin’s theory lacked crucial ingredients: How were variations transmitted to the next generation, and how were new variations generated? Certainly, Darwin made a strong case, based on the breeding of dogs, orchids, and fancy pigeons, that animals can be changed dramatically over relatively short time. But this seemed to require the guiding hand of a breeder. Where did variety in nature come from? How could this variety lead to the changes observed? How were variations inherited? Why was the offspring similar, but not identical, to the parents? Although Darwin hit on the crucial mechanism to explain evolution—variation and natural selection—there were many gaps.
Unbeknownst to Darwin, a Moravian monk, noting curious patterns among generations of pea plants in his garden, had already discovered some of the missing puzzle pieces. The research of this monk, Gregor Mendel (1822–1884), was published in a rather obscure journal, the Proceedings of the Natural History Society of Brünn, and remained virtually unknown until it was rediscovered in the early twentieth century. What Mendel had discovered in his research with his beloved pea plants were the laws of inheritance: the fact that traits are inherited whole, and that traits from each parent can be combined in various ways in the offspring. Before his work, it was not clear how inheritance worked, and blending inheritance could not be discounted. In blending inheritance, the traits of the offspring are a blend of the traits of the parents. Mendel found this to be wrong: If it were true, pea plants would soon assume some average color, the blend of the colors of parents and grandparents. This is not what happened. If, for example a red pea was crossed with a white pea, Mendel got pink peas in the next generation, but surprisingly, the “granddaughter” peas could again be pure white or red. The trait white had not been blended out, but was merely dormant (recessive) and reappeared in a subsequent generation. The observation that the inheritance of traits was not blending, but rather was conservative, was extremely important for Darwin’s theory. Only traits that could be passed on whole to the next generation could spread through a population and explain the emergence of a new species. If traits were blending, any new traits would soon be blended back into mediocrity.
Darwin’s work was well received by the antivitalists of the time. Helmholtz embraced Darwin’s ideas—they provided “the possibility of an entirely new interpretation of organic purposiveness.” Indeed, together with the life force, purpose could now be placed on the ash heap of scientific history. But one problem remained. According to Helmholtz, “the controversy [over Darwin’s theory] now centers mainly on the scope that should be assigned to variations of species.” The problem was that the parts of Darwin’s theory that dealt with necessity were no problem. If a new, useful trait emerged, Darwin’s theory neatly explained how it would spread through a population by natural selection. This was just fine with the physicists—nineteenth-century physics was based on regularity and iron-clad natural laws. But what laws could explain where new traits came from? A life force? God forbid! Randomness? Not much better, and unimaginable to a thoroughgoing mechanist like Helmholtz. Indeed, the role of randomness in science had not much improved since Aristotle had rejected it over two thousand years earlier. Everything had to follow laws. But what was the law of variations?
* Bob Proctor, motivational speaker, in The Secret, directed by Drew Heriot (Prime Time Productions, 2006). Quote from IMDb, “Memorable Quotes for The Secret (2006),” www.imdb.com/title/tt0846789/quotes, accessed July 8, 2010.
* Rhonda Byrne, The Secret (New York: Atria Books, 2006). Certainly, everything is energy. Byrnes’s next sentence, after the claim “human beings manage their own magnetizing energy,” goes even more astray: “You are an energy magnet, so you electrically energize everything to you.” The statement make little sense and would not be found in any physics book. But making scientific sense matters little when it comes to publishing books. After all, The Secret sold millions of copies.
* As I trace the history of beliefs and knowledge about life, I will restrict myself to Western philosophy and science. This is not to diminish the thoughts and achievements of other cultures, but Western thought provides many of the examples of how to think about life. And despite the many important outside influences on Western thought, modern science is mostly an outgrowth of European philosophical history, starting with the ancient Greeks.
* Other examples are explanations based on steam engines (thermodynamics) and chemistry or computers (the brain as computer). All of these explanations capture some aspects of life at least metaphorically, but ultimately they fail and should be used only with a giant grain of salt. The heart is not a clock, and the brain is not a computer.
* The term teleomechanism was introduced in Timothy Lenoir, “The Strategy of Life: Teleology and Mechanics in Nineteenth-Century German Biology (Chicago, University of Chicago Press, 1989; 1982).
2
Chance and Necessity
Everything existing in the universe is the fruit of chance and necessity.
—DEMOCRITUS
We believe that God created the world according to his wisdom. It is not the product of any necessity whatever, nor of blind fate or chance. We believe that it proceeds from God’s free will.
—CATECHISM OF THE CATHOLIC CHURCH, ARTICLE 295
FAINT WISPS OF HYDROGEN AND HELIUM ARE SWIRLING through the immensity of space. The cosmos is vast and empty. Suddenly, the visitors glimpse a tiny illuminated island: a galaxy in a sea of nothingness. Looking closer, they notice that the island is made of smaller points of light: little nuclear fireplaces called stars, sprinkled into the cold darkness of space. Around many of the stars, small sand grains and blobs of gas leisurely circle their star’s illumination. On one of the sand-grain planets, heated by its star to a comfortable 293 degrees Kelvin, white water vapor clouds beautifully set off the deep blue of saltwater oceans and the yellow-brown of continents. The tiny two-legged creatures inhabiting this little world, having just begun to glimpse a few feeble answers to the endless mysteries surrounding them, believe themselves to be the center of the universe. Chuckling, the visitors keep their giant spaceship cloaked, and move on.
Meanwhile on Earth, completely ignorant of being observed by powerful beings from outer space, humans seem incapable of shaking their illusions of superiority. As far as they know, this is the only planet with life, and they are the only intelligent life among millions of species. Only a few humans sense that this doesn’t seem right. One of them writes a comic strip Calvin and Hobbes, in which a little boy called Calvin observes: “The best proof that there is intelligent life in the universe is that they have not contacted us.” Maybe it’s because they would di
e laughing.
In our belief that we are the center of the universe, we have assumed much, just to be proven wrong time and again: No, the solar system does not revolve around Earth. No, the universe does not end beyond Pluto, or even beyond our Milky Way galaxy, but it is much bigger than we ever thought, full of stars in some places, but for the most part filled with staggering emptiness. No, there is no special life force—our bodies are part of nature, run by molecules. And no, we are not a separate creation from all the other animals, but are their close cousins—all, including ourselves, historical accidents of evolution. In short, we are lucky to be here.
This last insult to our pride, that we may be here—at least partly—by accident, by chance, may be the toughest nut of all. But what is so bad about chance?
Randomness
You know the story. Traveling to some faraway destination, say, Turkey or Singapore, you run into the neighbor of your cousin, who happens to know about the perfect job opening for you. Fate, right? Many see hidden meanings when the unexpected strikes. Some become superstitious, some believe in karma, others in the will of God. Few people would admit it happened by chance, that it was simply a coincidence. Why do so many people reject the influence of randomness on their lives? Why are we bothered by randomness? Randomness invokes chaos, lack of control. If randomness rules, all bets are off. But is that really true?
Until the end of the nineteenth century, everybody believed that randomness had no place in any explanation of the world. People disagreed, however, how the specter of randomness was to be exorcised. The mechanists believed in mechanical necessity: If we knew the locations and speeds of all the particles in the universe at some point in time, and had a powerful enough computer, we could predict every future event. The religionists instead believed in the unfathomable will of God. If you couldn’t explain why something happened, the explanation was that God wanted it this way. And the philosophers believed in . . . just about everything, except randomness. The consensus was that if something happened by chance, it only seemed that way because of our ignorance of all the circumstances.
Yet, clearly, many events seemed out of reach of our predictions. One way to deal with unpredictability was to accept it as fate, the will of God, or human ignorance. Another way was to find ways to quantify our ignorance, to tame the unpredictable.
A Short History of Gambling
The first time anybody ever thought about quantifying unpredictability was not in the name of science, but in the name of making a quick buck (or whatever currency they had at the time). The goal was to know how much to wager in a game of chance.
Gambling is an ancient pastime: Roman soldiers guarding the body of Jesus on the cross gambled for his meager belongings. Today, gambling is as popular as ever. Las Vegas, an entire city located in a place where there shouldn’t be a city, is dedicated to this sinful activity. The city hosts poker championships, and there are always roulette games, blackjack, slot machines, and numerous other means to help you lose your money.
Poker has become something of a fad in recent years, especially among physicists. Unfortunately, my physics credentials are not much help: I am a lousy poker player. The problem is that I am terrible at bluffing. All good poker players can hide their emotions and are excellent strategists. But why should physicists in general (myself excluded) be any good at this game? The reason is that physicists understand probabilities.
As I understand poker, there are two ways of winning: getting a better hand than the other players, or making the other players believe you have a better hand. What makes a poker hand better? A poker hand is better if it is rarer, that is, if getting such a hand happens on average less often than getting a less valued hand. How often, on average, certain hands appear in a set of five cards selected at random is described by the probability of the hand. The probability of getting a royal flush—an ordered sequence (or straight) of cards of the same suit, starting with an ace—is 1 in 649,740. The probability of getting a pair (two cards of the same value) is much higher: 1 in 2.36. What does that mean? It means that in a very large number of randomly dealt five-card hands, a pair will occur about once every 2.36 deals, while a royal flush can only be expected every 649,740 deals. Of course, this does not mean that if you play 650,000 times, you can be guaranteed to be dealt a royal flush. Rather, it means that if you play billions or trillions of times, the number of royal flushes you are dealt divided by the number of total games would approach 1/649,740. But nobody has ever played poker a billion times. So how can we know?
The idea that different outcomes in games of chance, such as poker or dice, have different likelihoods, seems to be as old as gambling itself. How else would you determine how much to wager? Yet, for a long time, the probability of different outcomes was based on experience or feelings, rather than on quantifiable science.
In the movie 21, Kevin Spacey portrays a morally impaired MIT mathematics professor, who teaches his students how to break the bank playing blackjack. Using card counting and secret signs, the students descend on Las Vegas casinos and clean them out. Certainly an interesting way to pay for college and a great idea for a movie (based on a true story), but it is hardly original: the idea to pay for college by gambling precedes 21 by five hundred years.
The person who first conceived of this ingenious use of gambling was born in 1501, an unwanted son to an unmarried couple in Milan, Italy. His mother, Chiara, already had several children and didn’t want another one. When an herbal concoction failed to produce the desired abortion, she was gratified to give birth to a baby so ill that he was not expected to survive. Much to his mother’s chagrin, the baby pulled through after taking a bath in red wine. So began the low-probability life of the first person to develop a theory of probability.
As our hero grew up, his lawyer father, Fazio, used him as a book carrier and mobile reading desk, weighing down the five-year-old with piles of heavy books and kicking him through the streets. Only when the boy became seriously ill at age eight did his father repent and have him baptized, giving him the name Gerolamo Cardano. Cardano was a curious Renaissance genius: physician, mathematician, gambler, mechanical engineer, and founder of probability theory. As Gerolamo grew up, he accompanied his father on visits to many of the lawyer’s clients, whom Fazio consulted in geometry and law. When Gerolamo was thirteen, his father took him to meet the great Leonardo da Vinci. The boy had a voracious appetite for knowledge, learning Latin and geometry, and there was nothing that did not interest him, from witchcraft and horoscopes to the construction of spider webs and the circulation of the blood. He was well on his way to becoming a scholar and making a name for himself. Unfortunately, despite his great promise, his father refused to send him away for further education.
One day, when Fazio struck his wife in a fit of rage, she hit her head on a table. Fazio regretted his violent act immediately, but Chiara, having grown fond of her unwanted son, Gerolamo, milked the incident for all it was worth. Fainting repeatedly and crying out to her sister who had witnessed the event, she made Fazio promise to let her son attend college. Reluctantly agreeing to this blackmail, Fazio suggested law as it was a lucrative field of study. There was a stipend to be had, and Gerolamo’s father, like many fathers, was eager to get his son an education without having to pay the tuition. Gerolamo, however, did not care about law. He wanted to be a medical doctor, but his father refused to pay for such an expensive course of study. Gerolamo had to find the money somewhere else.
He found it in gambling. Gerolamo preferred playing dice, because he had a natural sense for its probabilities. He did not cheat (a practice not recommended in a time when cheaters often found themselves hanging from the rafters), but he knew how to place bets. Before long, he had saved enough money to pursue medical studies at the renowned University of Padua. After some difficult years, including his annoying his fellow physicians by writing a dissertation about their poor practices, Cardano became a successful physician and chairman of the medical faculty in
Padua. He wrote numerous books about medicine and mathematics, especially algebra. And he never forgot his gambling days. Wanting to share his experiences, he wrote the first theory of gambling, Liber De Ludo Aleae (“The book on games of chance”).
Although Cardano’s book was not published until a hundred years after it was written, it was a landmark work, introducing the fundamental idea of calculating probabilities: If you wanted to know the probability of a certain event out of all possible events, count the number of ways the event could occur, and divide it by the number of all possible events. This method of calculating assumed that all events were equally likely. Here is an example: What is the probability that you will roll a sum of 5 with two dice? There are 6 × 6, or 36, ways you can roll two dice: (1, 1), (1, 2), . . . (6, 5), (6, 6). How many ways are there to get a sum of 5? Count them up: (1, 4), (2, 3), (3, 2), (4, 1). That’s four ways. Thus, the probability to get a sum of 5 with two rolls of a die is With some work, you can even work out the probability of a royal flush. Choosing five cards at random out of fifty-two cards provides 2,598,960 different possible hands. Only 4 of these will be royal flushes (one for each suit). Divide 4 by 2,598,960, and you get 1/649,740. You don’t even have to play poker to figure this out.
Life's Ratchet: How Molecular Machines Extract Order from Chaos Page 6
