Copies, mistakes, and partnerships

Why copy?

The first lesson showed how an open system can keep its order. But being open does not save any single individual. A candle burns out, a cell wears out, a body ages and dies, and a machine breaks. Everything made by humans runs down: a car needs servicing, a computer slows, a program crashes. The second law has its way with every individual thing. Living things have found a way around the problem, not by preventing death but by copying themselves first. The individual dies, and the line goes on.

The mathematician John von Neumann, remembered as a founder of the modern computer and of game theory, took up that observation in the 1940s. He asked what it would take for a machine to make a copy of itself, and he saw that this was a question about the logic of life, not only about engineering.

A machine that copies itself

Making a copy of yourself is harder than it sounds. You might think you could scan yourself in every detail and build a duplicate from the scan. But then the scanner would have to scan itself, including the scan it holds, which would have to include a scan of that, and so on forever. A blueprint that contains a complete picture of itself seems to demand an infinite regress.

Self-reference of this kind has a long history in logic, and it is not always paradoxical. In his 1962 essay “Paradox,” the philosopher Willard Van Orman Quine offered a sentence that talks about itself without using the words “this sentence.” Take the phrase “yields a falsehood when appended to its own quotation,” and write it twice, the first time inside quotation marks. The result says of itself that it is false. In computing, a program that prints its own source code is called a quine, a name coined by Douglas Hofstadter in 1979. In any general-purpose programming language, such programs exist. The trick in each case is to use one description twice, once as a recipe to be followed and once as plain data to be copied.

Von Neumann found the same trick for machines. In a lecture at the Hixon Symposium at Caltech in September 1948, and in lectures at the University of Illinois the next year, he described a machine with a few parts. A constructor can build any machine for which it is given a description. A copier can copy a description. And a controller runs the two in order. The description, a long tape of instructions, describes the constructor, the copier, and the controller, but it does not describe itself. In three steps, the machine reads the tape and builds an offspring; it copies the tape, treating it as raw data and not understanding a word of it; and it attaches the copy to the offspring. The offspring has everything its parent had, including a tape, so it can do the same. No infinite regress arises, because the tape describes the machinery and the copy is made afterward.

The logic of the design matches what cells do. DNA plays the role of the tape. It is read as instructions to build proteins and copied, as plain data, when a cell divides. A cell’s protein-making machinery plays the role of the constructor. The design was worked out on paper well before the structure of DNA was published, by James Watson and Francis Crick in Nature on 25 April 1953, and other scientists, among them Sydney Brenner, later remarked on the match. It is fair to say that von Neumann showed, years before DNA was understood, that a self-copying machine must keep its blueprint separate from the machinery that reads and copies it, the division of labor that cells use. It would not be accurate to say that he predicted DNA.

Von Neumann also worked out a self-copying machine in a different setting, a grid of cells that follow simple rules, a cellular automaton with 29 states per cell, an idea that Stanislaw Ulam suggested. It was unfinished when von Neumann died in 1957, and was completed by his colleague Arthur Burks. The first working computer version, by Renato Nobili and Umberto Pesavento, appeared in 1994 and 1995, in a slightly extended rule set. Von Neumann also guessed at a threshold: below some level of complexity, he suggested, machines can only make simpler machines, while above it they can reproduce and even build more complex ones. That is an insight, not a measured number; simpler self-copying patterns exist, such as Christopher Langton’s loops of 1984.

Mistakes that build

Copying is never perfect. Where the copying process makes mistakes, the description can change, and the offspring can differ from its parent. That is what turns a copying machine into an evolving one. Charles Darwin, in On the Origin of Species (24 November 1859), and Alfred Russel Wallace, whose paper was read to the Linnean Society together with extracts from Darwin’s on 1 July 1858, gave the argument its three parts. Offspring vary. Variations are inherited. And some variations help their bearers survive and reproduce more than others, so that over generations those variations spread: natural selection.

Where do the mistakes come from? Some are slips when DNA is copied. A cell’s copying and repair machinery is remarkably accurate, leaving roughly one error in a billion letters or fewer, but not none. Some are damage: chemical changes in the DNA itself, and the effects of radiation and of reactive molecules produced by the cell’s own metabolism. The result is small but not zero. In a 2012 study of Icelandic families, Augustine Kong and colleagues found that each child carries about 60 new single-letter changes in their DNA that neither parent had, out of about six billion letters; later work puts the typical number nearer 70. Most do nothing. A few matter, for better or worse.

The changes are not aimed. In 1943 Salvador Luria and Max Delbrück showed with bacteria that mutations that make cells resistant to a virus arise before the virus is there and regardless of it. The mutation rate is not perfectly uniform across the genome, and which kinds of change are more likely is not random, but nothing in the process knows what would help. Selection supplies the direction. Try both together.

The simulation shows the three things working together. With copying and mistakes but no selection, nothing improves. With selection but no mistakes, the population stops at the best message it started with. With too many mistakes, the good copies cannot keep their gains. Between those extremes, the population climbs. For a real example, there is a long experiment in a laboratory. On 24 February 1988 the biologist Richard Lenski began growing twelve populations of the bacterium E. coli at the University of California, Irvine. The experiment moved with him to Michigan State University in 1991 and has been kept going ever since, by later caretakers too, freezing samples every 500 generations. It passed 80,000 generations in 2024. Around generation 31,500, one population gained a new ability, to eat citrate, a compound in its broth, in the presence of oxygen, through a chain of mutations, each of which depended on earlier ones.

This does not mean evolution has a built-in direction toward complexity. Some lineages became more complex, many stayed simple, and many lost parts: tapeworms have shed genes on a large scale, and in the bacterium that causes leprosy less than half of the genome still works. The apparent rise in complexity may partly be a spreading away from a simple starting point.

Swallowed and kept

A third idea concerns how things get built in layers. Your cells contain little structures called organelles. Among them are the mitochondria, which supply most of a cell’s usable energy, and, in plants and algae, the chloroplasts that capture sunlight. Both are strange. Each has its own DNA, a small ring of genes: human mitochondrial DNA is 16,569 letters long and holds 37 genes. Each has its own ribosomes, the machines that make proteins, which resemble those of bacteria. Each is wrapped in two membranes, and each divides by splitting, like a bacterium.

In 1967, Lynn Margulis, then writing as Lynn Sagan and working at Boston University, published a long paper arguing that these organelles were once free-living bacteria that had taken up residence inside a larger cell. She later recalled that the paper was turned down by about fifteen journals, although that is her own memory of events. She was not the first to propose the idea: the Russian botanist Konstantin Mereschkowsky suggested in 1905 that plant cells arose by such mergers, and others, such as the American Ivan Wallin in the 1920s, argued the case for mitochondria. But she assembled it with enough evidence to make it testable. The gene sequencing that followed bore out the main idea: mitochondria descend from a group of bacteria called alpha-proteobacteria, and chloroplasts from cyanobacteria. The merger of mitochondria is estimated to have happened between about 1.2 and 2 billion years ago.

A common mistake in popular accounts is to describe the host as a multicellular organism. The host was a single cell. Modern evidence suggests that it was an archaeon, a member of the second great domain of single-celled life, related to a group called Asgard archaea. In 2020 a Japanese team led by Hiroyuki Imachi reported growing one such organism, Prometheoarchaeum, after more than a decade of effort. How the bacterium came to live inside the host is not settled: it may have been swallowed as prey and survived, or it may have been a partnership that gradually enclosed it. What is clear is that two kinds of cell became one new kind, and neither partner could easily live without the other.

Why did this matter so much? One influential hypothesis, from Nick Lane and William Martin in 2010, is that mitochondria gave complex cells a vast increase in energy for each gene, which paid for large genomes. It is a hypothesis, and other researchers have argued against it. Still, the partnership paid off. Mitochondria now supply the energy for almost every cell of an animal or plant. A human cell contains hundreds to thousands of them, and a body turns over, by one estimate, tens of kilograms of ATP, the cell’s energy currency, every day, about its own weight.

Levels, and the cycle

Life is built in layers. Genes gather into chromosomes, chromosomes and organelles into cells, cells into tissues and bodies, bodies into colonies and societies. John Maynard Smith and Eörs Szathmáry called the great joinings in this history the major transitions in evolution and listed eight, from molecules inside compartments to human societies with language. Each time, groups of simple units became a single new kind of unit, and the new unit could in turn join with others. That is the cycle: the whole of one level becomes the part of the next. It happened only a handful of times, and nothing guarantees it will continue. Evolution also simplifies, and parts of a complex whole can lose complexity as the whole gains it.

Joining raises a question about cooperation. In a group, competition among the members can tear it apart, and cooperation can hold it together. In 1980 the political scientist Robert Axelrod invited experts to submit strategies for a repeated game, the prisoner’s dilemma, in which each of two players can cooperate or defect and the best outcome for both comes from cooperating, though each is tempted to betray. Fourteen entries and one random strategy competed in a round-robin tournament, and the winner, submitted by the psychologist Anatol Rapoport, was the simplest: tit for tat, which cooperates on the first move and afterward copies the other player’s last move. Axelrod and the biologist William Hamilton described the result in a 1981 paper in Science. Later work showed that tit for tat is not best in every setting, for instance when mistakes are common, but the lesson stands that cooperation can arise among self-interested players who meet again and remember.

The real world has examples. In his 1980 book on the trenches of the First World War, the sociologist Tony Ashworth documented what he called the “live and let live” system. Along quiet stretches of the Western Front, units that faced one another day after day developed unspoken truces: ration parties were left alone, shelling came at the same hour each day, and in one sector a particular hour of the morning was left for private business. The system ended when commanders ordered raids that made restraint impossible. (This is different from the famous Christmas truce of 1914, a one-time event.) Where competition inside a group is held in check, the members can only get ahead by helping the group, and this is one way new levels of cooperation have been built.

The whole picture

This course has followed one thread. Order can appear and last when a system stays open, as in the honeycomb and the body, but it lasts only while energy flows through. Living things and cities follow rules of scale, and the same mathematics that makes animals slow as they grow makes cities faster, with a warning about growth that outruns its limits. Individuals die, so life copies itself, and copying with mistakes, plus selection, produces evolution. And cooperation can turn groups into wholes, which then join with others in turn. Each level takes in, builds, copies, and joins, and the world we see, in all its complexity, is made of such levels.