Science consists of facts and theories. Facts and theories are born in different ways and are judged by different standards. Facts are supposed to be true or false. They are discovered by observers or experimenters. A scientist who claims to have discovered a fact that turns out to be wrong is judged harshly. One wrong fact is enough to ruin a career.

Theories have an entirely different status. They are free creations of the human mind, intended to describe our understanding of nature. Since our understanding is incomplete, theories are provisional. Theories are tools of understanding, and a tool does not need to be precisely true in order to be useful. Theories are supposed to be more-or-less true, with plenty of room for disagreement. A scientist who invents a theory that turns out to be wrong is judged leniently. Mistakes are tolerated, so long as the culprit is willing to correct them when nature proves them wrong.

Brilliant Blunders, by Mario Livio, is a lively account of five wrong theories proposed by five great scientists during the last two centuries. These examples give for nonexpert readers a good picture of the way science works. The inventor of a brilliant idea cannot tell whether it is right or wrong. Livio quotes the psychologist Daniel Kahneman describing how theories are born: “We can’t live in a state of perpetual doubt, so we make up the best story possible and we live as if the story were true.” A theory that began as a wild guess ends as a firm belief. Humans need beliefs in order to live, and great scientists are no exception. Great scientists produce right theories and wrong theories, and believe in them with equal conviction.

The essential point of Livio’s book is to show the passionate pursuit of wrong theories as a part of the normal development of science. Science is not concerned only with things that we understand. The most exciting and creative parts of science are concerned with things that we are still struggling to understand. Wrong theories are not an impediment to the progress of science. They are a central part of the struggle.

The five chief characters in Livio’s drama are Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein. Each of them made major contributions to the understanding of nature, and each believed firmly in a theory that turned out to be wrong. Darwin explained the evolution of life with his theory of natural selection of inherited variations, but believed in a theory of blending inheritance that made the propagation of new variations impossible. Kelvin discovered basic laws of energy and heat, and then used these laws to calculate an estimate of the age of the earth that was too short by a factor of fifty. Linus Pauling discovered the chemical structure of protein, the active component of all living tissues, and proposed a completely wrong structure for DNA, the passive component that carries hereditary information from parent to offspring.

Fred Hoyle discovered the process by which the heavier elements essential for life, such as carbon, nitrogen, oxygen, and iron, are created by nuclear reactions in the cores of massive stars. He then proposed a theory of the history of the universe known as steady-state cosmology, which has the universe existing forever without any Big Bang at the beginning, and stubbornly maintained his belief in the steady state long after observations proved that the Big Bang really happened.

Finally, Albert Einstein discovered the great theory of space and time and gravitation known as General Relativity, and then added to the theory an additional component later known as dark energy. Einstein afterward withdrew his proposal of dark energy, believing that it was unnecessary. Long after Einstein’s death, observations have proved that dark energy really exists, so that Einstein’s addition to the theory was right and his withdrawal was wrong.

Each of these examples shows in a different way how wrong ideas can be helpful or unhelpful to the search for truth. No matter whether wrong ideas are helpful or unhelpful, they are in any case unavoidable. Science is a risky enterprise, like other human enterprises such as business and politics and warfare and marriage. The more brilliant the enterprise, the greater the risks. Every scientific revolution requires a shift from one way of thinking to another. The pioneer who leads the shift has an imperfect grasp of the new way of thinking and cannot foresee its consequences. Wrong ideas and false trails are part of the landscape to be explored.

Darwin’s wrong idea was the blending theory of inheritance, which supposed the qualities inherited by offspring to be a blend of the qualities of the parents. This was the theory of inheritance generally accepted by plant breeders and animal breeders in Darwin’s time. Darwin accepted it as a working hypothesis, because it was the only theory available. He accepted it reluctantly because he knew that it was unsatisfactory in two ways. First, it failed to explain the frequent cases of hereditary throwback, when a striking hereditary feature such as red hair or musical talent skips a generation from grandparent to grandchild. Second, it failed to allow a rare advantageous variation to spread from a single individual to an entire population of animals, as required by his theory of the origin of species. With blending inheritance, any rare advantageous variation would be quickly diluted in later generations and would lose its selective advantage. For both these reasons, Darwin knew that the theory of blending inheritance was inadequate, but he did not have any acceptable alternative when he published The Origin of Species in 1859.


Nine years later, when Darwin published another book, The Variation of Animals and Plants under Domestication, he had abandoned the blending inheritance theory as inconsistent with the facts. He replaced it with another theory that he called pangenesis. Pangenesis said that the inheritance of qualities from parent to offspring was not carried in the seeds alone but in all the cells of the parent. Somehow the cells of the parent produced little granules that were collected by the seeds. The granules then instructed the seeds how to grow. For the rest of his life Darwin continued to believe in pangenesis, but it was another brilliant blunder, no better than blending inheritance and equally inconsistent with the facts.

Like Darwin’s theories of blending heredity and pangenesis, Kelvin’s wrong calculation of the age of the earth and Pauling’s wrong structure for DNA were speculations requiring blindness to obvious facts. Kelvin based his calculation on his belief that the mantle of the earth was solid and could transfer heat from the interior to the surface only by conduction. We now know that the mantle is partially fluid and transfers most of the heat by the far more efficient process of convection, which carries heat by a massive circulation of hot rock moving upward and cooler rock moving downward. Kelvin lacked our modern knowledge of the structure and dynamics of the earth, but he could see with his own eyes the eruptions of volcanoes bringing hot liquid from deep underground to the surface. His skill as a calculator seems to have blinded him to messy processes such as volcanic eruptions that could not be calculated.

Similarly, Pauling guessed a wrong structure for DNA because he assumed that a pattern that worked for protein would also work for DNA. He was blind to the gross chemical differences between protein and DNA. Francis Crick and James Watson, paying attention to the differences, found the correct structure for DNA one year after Pauling missed it.

Fred Hoyle’s wrong theory of the universe had a different status from the other mistakes, because Hoyle was a young rebel when he proposed it. The steady-state universe was from the beginning a minority view. The decisive evidence against it was the discovery in 1964 of the microwave radiation pervading the universe. The microwave radiation had been predicted to exist as a relic of the hot Big Bang. The radiation proved that the hot Big Bang really happened and that the universe had a violent beginning. After that discovery, Hoyle was almost alone, preaching the steady-state gospel to a small band of disciples.

Albert Einstein, the last of Livio’s five blunderers, is an exception to all rules. He is widely quoted as saying that his addition of dark energy to the theory of gravitation was his biggest blunder. Livio has carefully examined the evidence and has come to the conclusion that Einstein never made this statement. The evidence points strongly to George Gamow as the guilty party. Gamow was another brilliant blunderer with a reputation for making up colorful stories. Einstein blundered in the opposite direction when he changed his mind and dropped dark energy from his theory. Nature played a big joke on him fifty years after his death, when she revealed that three quarters of the total mass of the universe is dark energy.

Einstein invented a steady-state model of the universe many years before Hoyle. This steady-state model was discovered recently by a group of Irish scientists in an unpublished Einstein manuscript. Einstein abandoned the idea and never published it, probably because he found that steady-state theories are contrived and artificial. When Hoyle noisily promoted the steady-state cosmology twenty years later, Einstein never mentioned that he had discovered and discarded it long before. Einstein must have recognized it quickly as a brilliant blunder, clever but not likely to be correct. (I am indebted to the Irish scientist Cormac O’Raifeartaigh for information about this discovery.)


After reading Livio’s account, I look on the history of science in a new way. In every century and every science, I see brilliant blunders. Isaac Newton’s biggest blunder was his corpuscular theory of light, which had light consisting of a spray of little particles traveling along straight lines. In the nineteenth century, James Clerk Maxwell discovered the laws of electromagnetism and proposed that light consists of electromagnetic waves. In the twentieth, Einstein proved that Newton and Maxwell were both right and both wrong, because light behaves like particles in one situation and like waves in another.

The chief difference betwen science and other human enterprises such as warfare and politics is that brilliant blunders in science are less costly. Hannibal’s brilliant crossing of the Alps to invade Italy from the north resulted in the ruin and total destruction of his homeland. Two thousand years later, the brilliant attack on Pearl Harbor cost the Japanese emperor his empire. Even the worst scientific blunders do not do so much damage.

The worst political blunder in the history of civilization was probably the decision of the emperor of China in the year 1433 to stop exploring the oceans and to destroy the ships capable of exploration and the written records of their voyages. In no way can this blunder be called brilliant. Before the decision, China had a fleet of ocean-going ships bigger and more capable than any European ships. China was roughly level with Europe in scientific knowledge and far ahead in the technologies of printing, navigation, and rocketry. As a consequence of the decision, China fell disastrously behind in science and technology, and is only catching up now after six hundred years. The decision was the result of powerful people pursuing partisan squabbles and neglecting the long-range interests of the empire. This is a disease to which governments of all kinds, including democracies, are fatally susceptible.

Another cause of catastrophic blunders is religion. A legendary example of a religious blunder is the story of Tsar Lazar, king of Serbia in the year 1389 when his kingdom was invaded by the Turks. He confronted the Turkish army on the fatal battlefield of Kosovo Polje. The story is told in the Serbian national epic The Battle of Kosovo. The Virgin Mary happened to be in Jerusalem at the time when the Turks invaded, and sent a falcon with a message for the tsar. The falcon arrived on the battlefield and told the tsar that he must make a choice between an earthly and a heavenly kingdom. If he chose the earthly kingdom, his army would defeat the Turks and he would continue his reign in Serbia. If he chose the heavenly kingdom, his army would be annihilated and his people would become slaves of the Ottoman Empire. Being a very pious monarch with his mind concentrated on spiritual virtue, the tsar naturally chose the heavenly kingdom, and his people paid for his choice by losing their freedom.

Seven years after Darwin published The Origin of Species, without any satisfactory explanation of hereditary variations, the Austrian monk Gregor Mendel published his paper “Experiments in Plant Hybridization” in the journal of the Brünn Natural History Society. Mendel had solved Darwin’s problem. He proposed that inheritance is carried by discrete units, later known as genes, that do not blend but are carried unchanged from generation to generation. The Mendelian theory of inheritance fits perfectly with Darwin’s theory of natural selection. Mendel had read Darwin’s book, but Darwin never read Mendel’s paper.

The essential insight of Mendel was to see that sexual reproduction is a system for introducing randomness into inheritance. In sweet peas as in humans, each plant is either male or female, and each offspring has one male and one female parent. Inherited characteristics may be specified by one gene or by several genes. Single-gene characteristics are the simplest to calculate, and Mendel chose them to study. For example, he studied the inheritance of pod color, determined by a single gene that has a version specifying green and a version specifying yellow. Each plant has two copies of the gene, one from each parent. There are three kinds of plants, pure green with two green versions of the gene, pure yellow with two yellow versions, and mixed with one green and one yellow. It happens that only one green gene is required to make a pod green, so that the mixed plants look the same as the pure green plants. Mendel describes this state of affairs by saying that green is dominant and yellow is recessive.

Mendel did his classic experiment by observing three generations of plants. The first generation was pure green and pure yellow. He crossed them, pure green with pure yellow, so that the second generation was all mixed. He then crossed the second generation with itself, so that the third generation had all mixed parents. Each third-generation plant had one gene from each parent, with an equal chance that each gene would be green or yellow. On the average, the third generation would be one-quarter pure green, one-quarter pure yellow, and one-half mixed. In outward appearance the third generation would be three-quarters green and one-quarter yellow.

This ratio of 3 between green and yellow in the third generation was the new prediction of Mendel’s theory. Most of his experiments were designed to test this prediction. But Mendel understood very well that the ratio 3 would only hold on the average. Since the offspring chose one gene from each parent and every choice was random, the numbers of green and yellow in the third generation were subject to large statistical fluctuations. To test the theory in a meaningful way, it was essential to understand the statistical fluctuations. Fortunately, Mendel understood statistics.

Mendel understood that to test the ratio 3 with high accuracy he would need huge numbers of plants. It would take about eight thousand plants in the third generation to be reasonably sure that the observed ratio would be between 2.9 and 3.1. He actually used 8,023 plants in the third generation and obtained the ratio 3.01. He also tested other characteristics besides color, and used altogether 17,290 third-generation plants. His experiments required immense patience, continuing for eight years with meticulous attention to detail. Every plant was carefully isolated to prevent any intruding bee from causing an unintended fertilization. A monastery garden was an ideal location for such experiments.

In 1866, the year Mendel’s paper was published, but without any knowledge of Mendel, Darwin did exactly the same experiment. Darwin used snapdragons instead of sweet peas, and tested the inheritance of flower shape instead of pod color. Like Mendel, he bred three generations of plants and observed the ratio of normal-shaped to star-shaped flowers in the third generation. Unlike Mendel, he had no understanding of statistical fluctuations. He used a total of only 125 third-generation plants and obtained a value of 2.4 for the crucial ratio. This value is within the expected statistical uncertainty, either for a true value of 2 or for a true value of 3, with such a small sample of plants. Darwin did not understand that he would need a much larger sample to obtain a meaningful result.

Mendel’s sample was sixty-four times larger than Darwin’s, so that Mendel’s statistical uncertainty was eight times smaller. Darwin failed to repeat his experiment with a larger number of plants, and missed his chance to incorporate Mendel’s laws of heredity into his theory of evolution. He had no inkling that a fundamental discovery was within his grasp if he continued the experiment with larger populations. The basic idea of Mendel was that the laws of inheritance would become simple when inheritance was considered as a random process. This idea never occurred to Darwin. That was why Darwin learned nothing from his snapdragon experiment. It remained a brilliant blunder.

Mendel made a brilliant blunder of a different kind. He published his laws of heredity, with a full acount of the experiments on which the laws were based, in 1866, seven years after Darwin had published The Origin of Species. Mendel was familiar with Darwin’s ideas and was well aware that his own discoveries would give powerful support to Darwin’s theory of natural selection as the cause of evolution. Mendelian inheritance by random variation would provide the raw material for Darwinian selection to work on.

Mendel had to make a fateful choice. If he chose to call Darwin’s attention to his work, Darwin would have understood its importance, and Mendel would inevitably have become involved in the acrimonious public disputes that were raging all over Europe about Darwin’s ideas. If Mendel chose to remain silent, he could continue to pursue his true vocation, to serve his God as a monk and later as abbot of his monastery. Like Tsar Lazar five hundred years earlier, he had to choose between worldly fame and divine service. Being the man he was, he chose divine service. Unfortunately, his God played a cruel joke on him, giving him divine gifts as a scientist and mediocre talents as an abbot. He abandoned the chance to be a world-famous scientist and became an unsuccessful religious administrator.

Darwin’s blindness and Mendel’s reticence combined to delay the progress of science by thirty years. But thirty years is a short time in the history of science. In the end, after both men were dead and their personal shortcomings forgotten, their partial visions of the truth came together to create the modern theory of evolution. Thomas Hunt Morgan at Columbia University understood that the fruit fly Drosophila was a far better tool than the sweet pea and the snapdragon for studying heredity. Fruit flies breed much faster and are more easily handled in large numbers. With fruit flies, Morgan could go far beyond Mendel in exploring the world of genetics.

In my own life as a scientist, there was one occasion when I felt that a deep secret of nature had been revealed to me. This was my personal brilliant blunder. I remember it with joy, even though my dreams of glory were shattered. It was a blissful experience. It arose out of work that I did with my colleague Andrew Lenard from Indiana University, investigating the stability of ordinary matter. We proved by a laborious mathematical calculation that ordinary matter is stable. The physical basis of stability is the exclusion principle, a law of nature saying that two electrons can never be in the same state. Matter is stable against collapse because every atom contains electrons and the electrons resist being squeezed together.

My blunder began when I tried to extend the stability argument to other kinds of particles besides electrons. We can divide particles into two types in three different ways. A particle may be electrically charged or neutral. It may be weakly or strongly interacting. And it may belong to one of two types that we call fermions and bosons in honor of the Italian physicist Enrico Fermi and the Indian physicist Satyendra Bose. Fermions obey the exclusion principle and bosons do not. So each particle has eight possible ways to make the three choices. For example, the electron is a charged weak fermion. The light quantum is a neutral weak boson. The famous particle predicted by Peter Higgs, and discovered in 2012 at the European Centre for Nuclear Research (CERN), is a neutral strong boson.

I observed in 1967 that seven of the eight possible combinations were seen in nature. The one combination that had never been seen was a charged weak boson. The missing type of particle would be like an electron without the exclusion principle. Next, I observed that our proof of the stability of matter would fail if electrons without the exclusion principle existed. So I jumped to the conclusion that a charged weak boson could not exist in a stable universe. This was a new law of nature that I had discovered. I published it quietly in a mathematical journal.

I knew that my theory flatly contradicted the prevailing wisdom. The prevailing wisdom was the unified theory of weak and electromagnetic interactions proposed by my friends Steven Weinberg and Abdus Salam. Weinberg and Salam predicted the existence of a new particle as a carrier of weak interactions. They called the new particle W. The W-particle had to be a charged weak boson, precisely the combination that I had declared impossible. Nature, speaking through an experiment at CERN in Geneva, would decide who was right.

The decision did not come quickly. It took the experimenters fifteen years to build a new machine and use it to search for the W-particle. But the decision, when it came, was final. Large numbers of W-particles were seen, with the properties predicted by Weinberg and Salam. With hindsight I could see several reasons why my stability argument would not apply to W-particles. W-particles are too massive and too short-lived to be a constituent of anything that resembles ordinary matter. I quickly forgot my disappointment and shared the joy of Weinberg and Salam in their well-deserved triumph. As my mother taught me long ago, the key to enjoyment of any sport is to be a good loser.

In Livio’s list of brilliant blunderers, Darwin and Einstein were good losers, Kelvin and Pauling were not so good, and Hoyle was the worst. The greatest scientists are the best losers. That is one of the reasons why we love the game. As Einstein said, God is sophisticated but not malicious. Nature never loses, and she plays fair.