Turing's Cathedral

by George Dyson

Ulam soon returned to Los Alamos, and five months later the scientific world was transfixed by news of the discovery of the structure of DNA. It was now evident how genetic sequences were being replicated, and how information was being conveyed from strings of nucleic acids to amino acids to proteins, but it remained a mystery as to what the translation rules actually were. This puzzle—how life translates between sequence and structure, and in doing so not only tolerates but takes advantage of ambiguity—would hold Ulam’s interest for the rest of his life.

  The translation puzzle also captured the imagination of Russian-born physicist George Gamow, who sent Ulam a telegram on July 20, 1953:

  DEAR STAN, HAVE PROBLEM FOR YOU USING 20 DIFFERENT LETTERS WRITE A LONG CONTINUOUS WORD CONTAINING FEW THOUSAND LETTERS. HOW LONG THAT WORD SHOULD BE FOR FAIR PROBABILITY OF FINDING IN IT ALL POSSIBLE TEN LETTER WORDS? PLEASE WIRE.80

  Stan immediately answered, from Los Alamos:

  PLEASE WIRE WHETHER ONE IS ALLOWED TO SKIP LETTERS IN THE LONG WORD TO FORM TEN LETTER WORDS. IF SO, ANSWER RATHER SHORT. IF ONLY CONTIGUOUS LETTERS ALLOWED ANSWER MUCH BIGGER THAN TEN TO THE TWENTIETH POWER AND CARSON WILL SEND THIS WORD COLLECT.

  LOVE, STAN.81

  TWELVE

  Barricelli’s Universe

  The Star Maker … could make universes with all kinds of physical and mental attributes. He was limited only by logic. Thus he could ordain the most surprising natural laws, but he could not, for instance, make twice two equal five.

  —Olaf Stapledon, 1937

  “GOD DOES NOT play dice with the Universe,” Albert Einstein advised physicist Max Born (Olivia Newton-John’s grandfather) in 1936. There was no proscription against cards. “Every red card (hearts and diamonds) has been recorded as +1, every black card (spades and clubs) has been recorded as –1,” Nils Barricelli explained, as he seeded the memory registers of the IAS computer with random numbers in March of 1953. “In order to prevent any appreciable correlation between the extracted cards we have never taken out more than 10 cards at a time without mixing again the set of cards.”1

  Nils Aall Barricelli, who “had this most wonderful delicious accent,” according to Gerald Estrin, was born to a Norwegian mother and Italian father in Rome on January 24, 1912. He studied mathematical physics under Enrico Fermi and became a vocal critic of Mussolini, whose rise to power prompted him to move to Norway, with his younger sister and recently divorced mother, upon his graduation from the University of Rome in 1936. He lectured on Einstein’s theory of relativity at the University of Oslo, published a volume of lecture notes on the theory of probability and statistics, and spent the war writing a doctoral thesis on the statistical analysis of climate variation, submitted in 1946. “However, it was 500 pages long, and was found to be too long to print,” says his former student Tor Gulliksen. “He did not agree to cut it to an acceptable size, and chose instead not to obtain the doctoral degree!”2

  Barricelli was an uncompromising nonconformist, questioning accepted dogma not only with regard to Darwinian evolution but on subjects ranging from matter-neutrino transparency to Gödel’s proof. “He believed that every mathematical statement could either be proved or disproved. He insisted that Gödel’s proof was faulty,” says Simen Gaure, an assistant who was hired—“he paid us directly out of his wallet, fairly good pay it was too, at least for students”—after a selection process that required searching for a hidden flaw in a sample proof. “Those who could point out the flaw were accepted as not yet ruined by mathematical education,” adds Gaure, who explains that Barricelli intended “to actually build a machine which could prove or disprove any statement of arithmetic and projective geometry.” He never built the machine, but in preparation he developed a programming language called “B-mathematics,” which is how he discovered what he claimed was a circularity in Gödel’s proof. “I once asked him what the ‘B’ in ‘B-mathematics’ was,” says Gaure. “He answered that he hadn’t decided on that; it could be ‘Boolean,’ or it could be ‘Barricelli,’ or something else.”3

  Barricelli operated on the fringes of academia, eventually being awarded a state stipendium by the Norwegian government, which allowed him to remain at the University of Oslo with his own small research group. “He was interested, among other things, in extraterrestrial life,” says Kirke Wolfe, one of his research assistants at the University of Washington, “and in coming up with theories of life and intelligence that would be general enough to accommodate forms that it might take elsewhere.” He believed the question was not whether extraterrestrial life existed, but if we would be able to recognize it. “Our limited experience with the particular type of life which has developed on this planet may prove completely inadequate to form a picture of the possible life forms one may find on foreign planets,” he wrote in 1961, concerning the prospects for finding life on Mars and Venus as the U.S. and USSR space programs were getting off the ground.4

  “The scientific community needs a couple of Barricellis each century,” says Gaure, while acknowledging that Barricelli “balanced on a thin line between being truly original and being a crank.” According to Wolfe, he “was a world unto himself, caught up in whatever work he was doing at the time.” His identity was distributed between Italy, Norway, and the United States. “A sense of origins was not important to him,” says Wolfe. “He picked up and went to wherever he could get the resources he needed to do his work.” Wolfe notes the contrast between Barricelli’s own life as a highly solitary individual and his devotion to the principle of symbiogenesis, where individuality is superseded by cooperation among the members of a group. Barricelli believed that the advantages of mutual cooperation between otherwise competing individuals were a more important driver of evolution than either natural selection or random variation, and he saw his numerical evolution experiments as a way of proving his case. “According to the symbiogenesis theory,” he argued, “the genes gained by symbiosis 1) tremendous developmental possibilities and 2) a very rapid developmental rate.”5

  In his career as a viral geneticist, Barricelli developed mathematical models and avoided laboratory work. “He said the trouble is when you do an experiment and you get a result, there is no way to look back at every step you’ve taken and assure yourself that you took each of those steps correctly, so the result that you get is not verifiable,” says geneticist Frank Stahl. “Who knows but at one step you might have taken a pipette of the wrong size and delivered the wrong amount of something into something else?”6

  Barricelli “insisted on using punched cards, even when everybody had computer screens,” according to Gaure. “He gave two reasons for this: when you sit in front of a screen your ability to think clearly declines because you’re distracted by irrelevancies, and when you store your data on magnetic media you can’t be sure they’re there permanently, you actually don’t know where they are at all.”7

  After publishing the paper “The Hypothesis of the Symbiosis of Genes” in Oslo in 1947, Barricelli executed a series of numerical experiments by hand on graph paper, which resulted in a preliminary report, “Numerical Models of Evolutionary Organisms,” leading to his invitation to the IAS. “He must have contacted von Neumann from Norway and mentioned some of his ideas,” says fellow Norwegian Atle Selberg. “Von Neumann was rather receptive to such things.”8

  “According to the theory of symbiosis of genes, the genes were originally independent, virus-like organisms which by symbiotic association formed more complex units,” he explained. “A similar evolution should be possible with any kind of elements having the necessary fundamental properties.”9 He proposed to test these theories using strings of code able to reproduce, undergo mutations, and associate symbiotically within the 40,960-bit memory of the new machine. In December 1951 he applied for a Fulbright travel grant “to perform numerical experiments by the use of large calculating machines, in order to clarify the first stages in the evolution of species,” but because of a delay in obtaining his Norwegian citizenship the Oslo office reject
ed the request.10

  “Mr. Barricelli’s work on genetics, which struck me as highly original and interesting … will require a great deal of numerical work, which could be most advantageously effected with high-speed digital computers of a very advanced type,” von Neumann wrote in support of the proposal.11 With a research fellowship from the Norwegian government, Barricelli finally arrived in Princeton in January 1953, and, on February 6, was awarded an unpaid membership in the School of Mathematics for the remainder of the academic year, renewed with a stipend of $1,800 for 1954.

  The delays over Barricelli’s nationality were matched by the delays in completing the computer, and, as it turned out, he arrived in Princeton at just the right time. The goal, as he explained it, was “to find analogies or, possibly, essential discrepancies between bionumerical and biological phenomena,” and “to observe how the evolution of numeric organisms takes place by hereditary changes and selection and to verify whether some of the organisms are able to speed up their evolution by gene replacements or by acquiring new genes or by any other primitive form of sexual reproduction.” On one level, Barricelli was applying the powers of digital computing to evolution. On another level, he was applying the powers of evolution to digital computing. According to Julian Bigelow, “Barricelli was the only person who really understood the path toward genuine artificial intelligence at that time.”12

  Four weeks after Barricelli began his experiments, James Watson and Francis Crick announced their determination of the structure of DNA. While Barricelli was working to encode evolutionary processes by means of numerical sequences, Watson and Crick were working to decode evolutionary processes by means of chemical sequences. After the Watson-Crick results appeared, Barricelli would refer to strings of DNA as “molecule-shaped numbers,” emphasizing the digital nature of polynucleotide chains. “The distinction between an evolution experiment performed by numbers in a computer or by nucleotides in a chemical laboratory is a rather subtle one,” he observed. Information theorists, including Claude Shannon with his 1940 PhD thesis on “An Algebra for Theoretical Genetics” (which was followed by a year at IAS), had already built a framework into which the double helix neatly fit.13

  “Genes are probably much like viruses and phages, except that all the evidence concerning them is indirect, and that we can neither isolate them nor multiply them at will,” von Neumann had written to Norbert Wiener in November 1946, suggesting that one way to find out how nature makes its copies would simply be to look. In December 1946, after consultation with Vladimir Zworykin and Andrew Booth, von Neumann submitted a proposal to determine biomolecular structures by bombarding centimeter-scale models, made out of small metallic spheres, with radar waves. The resulting diffraction patterns would then be compared with those produced by X rays of biological molecules on a one-hundred-million-fold smaller scale. “The best chance for a real understanding of protein chemistry lies in the x-ray diffraction field,” he wrote to Mina Rees at the Office of Naval Research. “I need not detail what any advance in this field will mean.” He requested emergency funding and appended “a list of certain items that are probably available in Government Surplus equipment, and which would be very helpful for the work.”14 Nothing came of this proposal—an approach that might have accelerated the discoveries of Franklin, Watson, and Crick.

  Instead of focusing upon natural mechanisms that were microscopic and highly complex, Barricelli sought to introduce primitive self-reproducing entities into an empty universe where they could be directly observed. “The Darwinian idea that evolution takes place by random hereditary changes and selection has from the beginning been handicapped by the fact that no proper test had been found to decide whether such evolution was possible and how it would develop under controlled conditions,” he wrote. “A test using living organisms in rapid evolution (viruses or bacteria) would have the serious drawback that the causes of adaptation or evolution would be difficult to state unequivocally, and Lamarckian or other kinds of interpretation would be difficult to exclude.” We now know that lateral gene transfer and other non-neo-Darwinian mechanisms are far more prevalent, especially in microbiology, than was evident in 1953.

  “If, instead of using living organisms, one could experiment with entities which, without any doubt could evolve exclusively by ‘mutations’ and selection,” Barricelli argued, “then and only then would a successful evolution experiment give conclusive evidence; the better if the environmental factors also are under control.”15 To attempt this in 5 kilobytes was wildly ambitious, but this was 1953. Jetliners were carrying their first commercial passengers, the space age was beginning, and tail fins were beginning to appear on cars. New elementary particles were being discovered faster than Oppenheimer’s group of young theoretical physicists was able to keep up. The computer’s initial teething problems were settling down. A second layer of electromagnetic shielding had been added to the Williams tube amplifiers; self-diagnostic routines had been adopted; input/output had been improved by switching to punched cards from paper tape. For the period March 2–6, 1953, the computer was operating 78 percent of the available time. For March 9–13, operational status was 85 percent, and for March 16–20, 99 percent.

  An extensive thermonuclear hydrodynamics code, supervised by Foster and Cerda Evans, began running in February, alternating with a lesser calculation, supervised by von Neumann, concerning the decay of a spherical blast wave. The meteorologists ran their trial forecasts during the day; Barricelli usually worked late at night. He was one of the few scientists allowed to operate the computer without the supervision of an engineer, and there are long intervals of machine time, under his control, with sparse log entries until the struggle to assign blame when things came to a halt.

  “Dr. Barricelli claims machine is wrong. Code is right,” the operating log records on April 2, 1953. Often he was still at work when the engineers returned the following day. “Machine worked beautifully. Off!” is his last entry in the early morning of May 31, 1953. “Gott im Himmel!” is appended by the arriving engineer. “Something is wrong with the building air conditioner,” he notes while working late at night on June 22, 1956. “One of the compressors seems to be stuck and the smell of burning V-belts is in the air.”16 In November 1954 the machine logs show Barricelli in control of the computer for a total of eighteen shifts between midnight and 6:00 a.m.

  Barricelli’s universe, appearing closed to outside observers, would appear unbounded to any one-dimensional numerical organisms inside. “The universe was cyclic with 512 generations, and each gene required eight binary digits so that five generations of a location could be packed into a single 40-binary-digit storage location,” he explained. “The code was written so that various mutation norms could be employed in selected regions of the universe.… Only five out of each 100 generations were recorded during reconnaissance. Interesting phenomena were then reinvestigated in more detail.”17

  Laws of nature referred to as “norms” governed the propagation of “genes,” a new generation appearing by metamorphosis after the execution of a certain number of cycles by the central arithmetic unit of the machine. These laws were configured “to make possible the reproduction of a gene only when other different genes are present, thus necessitating symbiosis between different genes.”18 Genes depended on each other for survival, and cooperation (or parasitism) was rewarded with success. Another set of norms governed what to do when two or more different genes collided in one location, the character of these rules proving to have a marked effect on the evolution of the universe as a whole.

  Barricelli played God, on a very small scale. He could dictate the laws of nature, but miracles were out of bounds. The aim, as he explained it in 1953, was “to keep one or more species alive for a large number of generations under conditions producing hereditary changes and evolution in the species. But we must avoid producing such conditions by changing the character of the experiment after the experiment has started.” His guidelines are reminiscent of Le
ibniz’s belief in a universe optimized to become as interesting as possible under a minimum of constraints. “Make life difficult but not impossible,” Barricelli recommended. “Let the difficulties be various and serious but not too serious; let the conditions be changing frequently but not too radically and not in the whole universe at the same time.”19

  Self-reproducing numerical coalitions rapidly evolved. “The conditions for an evolution process according to the principle of Darwin’s theory would appear to be present,” Barricelli announced. Over thousands of generations, he observed a succession of “biophenomena,” including successful crossing between parent organisms and cooperative self-repair of damage when digits were removed at random from individual genes. To avoid debate over the definition of organism and life, Barricelli formulated a more general classification of symbioorganism, defined as any “self-reproducing structure constructed by symbiotic association of several self-reproducing entities of any kind.”20 This definition was broad enough to include both biochemical and digital organisms, without becoming bogged down in the questions of whether they were (or ever would be) “alive.”

  The evolution of digital symbioorganisms happened in less time than it took to describe. “Even in the very limited memory of a high speed computer a large number of symbioorganisms can arise by chance in a few seconds,” Barricelli reported. “It is only a matter of minutes before all the biophenomena described can be observed.”21 The primitive numerical organisms soon became stuck in local maxima from which “it is impossible to change only one gene without getting weaker organisms,” bringing evolution to a halt. Since “only replacements of at least two genes can lead from a relative maximum of fitness to another organism with greater vitality,” it was evident that even in the simplest universes, crossing of gene sequences, not random mutations at single locations, was the way to move ahead.22