# Turing's Cathedral  ## Metadata - Author: [[George Dyson]] - Full Title: Turing's Cathedral - Category: #books ## Highlights - There are two kinds of creation myths: those where life arises out of the mud, and those where life falls from the sky. In this creation myth, computers arose from the mud, and code fell from the sky. ([Location 38](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=38)) - Tags: [[pink]] - In late 1945, at the Institute for Advanced Study in Princeton, New Jersey, Hungarian American mathematician John von Neumann gathered a small group of engineers to begin designing, building, and programming an electronic digital computer, with five kilobytes of storage, whose attention could be switched in 24 microseconds from one memory location to the next. The entire digital universe can be traced directly to this 32-by-32-by-40-bit nucleus: less memory than is allocated to displaying a single icon on a computer screen today. ([Location 40](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=40)) - Tags: [[pink]] - Von Neumann’s project was the physical realization of Alan Turing’s Universal Machine, a theoretical construct invented in 1936. It was not the first computer. It was not even the second or third computer. It was, however, among the first computers to make full use of a high-speed random-access storage matrix, and became the machine whose coding was most widely replicated and whose logical architecture was most widely reproduced. The stored-program computer, as conceived by Alan Turing and delivered by John von Neumann, broke the distinction between numbers that mean things and numbers that do things. Our universe would never be the same. ([Location 44](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=44)) - Tags: [[pink]] - Numerical simulation of chain reactions within computers initiated a chain reaction among computers, with machines and codes proliferating as explosively as the phenomena they were designed to help us understand. It is no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time. Only the collective intelligence of computers could save us from the destructive powers of the weapons they had allowed us to invent. ([Location 64](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=64)) - Tags: [[pink]] - Turing’s model of universal computation was one-dimensional: a string of symbols encoded on a tape. Von Neumann’s implementation of Turing’s model was two-dimensional: the address matrix underlying all computers in use today. The landscape is now three-dimensional, yet the entire Internet can still be viewed as a common tape shared by a multitude of Turing’s Universal Machines. Where does time fit in? Time in the digital universe and time in our universe are governed by entirely different clocks. In our universe, time is a continuum. In a digital universe, time (T) is a countable number of discrete, sequential steps. A digital universe is bounded at the beginning, when T = 0, and at the end, if T comes to a stop. Even in a perfectly deterministic universe, there is no consistent method to predict the ending in advance. To an observer in our universe, the digital universe appears to be speeding up. To an observer in the digital universe, our universe appears to be slowing down. ([Location 68](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=68)) - Tags: [[pink]] - It is impossible to predict where the digital universe is going, but it is possible to understand how it began. The origin of the first fully electronic random-access storage matrix, and the propagation of the codes that it engendered, is as close to a point source as any approximation can get. ([Location 79](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=79)) - Tags: [[pink]] - There was one notable exception: Julian Bigelow, who arrived at the Institute, in 1946, as John von Neumann’s chief engineer. Bigelow, who was fluent in physics, mathematics, and electronics, was also a mechanic who could explain, even to a three-year-old, how a fan belt works, why it broke, and whether it came from a Ford or a Chevrolet. ([Location 94](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=94)) - Tags: [[pink]] - Orders: Let a word (40bd) be 2 orders, each order = C(A) = Command (1–10, 21–30) • Address (11–20, 31–40) The use of bd for binary digit dates this piece of paper from the beginning of the von Neumann project, before the abbreviation of binary digit to bit. ([Location 129](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=129)) - Tags: [[pink]] - The term bit (the contraction, by 40 bits, of “binary digit”) was coined by statistician John W. Tukey shortly after he joined von Neumann’s project in November of 1945. The existence of a fundamental unit of communicable information, representing a single distinction between two alternatives, was defined rigorously by information theorist Claude Shannon in his then-secret Mathematical Theory of Cryptography of 1945, expanded into his Mathematical Theory of Communication of 1948. “Any difference that makes a difference” is how cybernetician Gregory Bateson translated Shannon’s definition into informal terms.2 To a digital computer, the only difference that makes a difference is the difference between a zero and a one. ([Location 281](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=281)) - Tags: [[pink]] - Turing then demonstrated the existence of a Universal Computing Machine that, given sufficient time, sufficient tape, and a precise description, could emulate the behavior of any other computing machine. The results are independent of whether the instructions are executed by tennis balls or electrons, and whether the memory is stored in semiconductors or on paper tape. ([Location 306](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=306)) - Tags: [[pink]] - Von Neumann set out to build a Universal Turing Machine that would operate at electronic speeds. At its core was a 32-by-32-by-40-bit matrix of high-speed random-access memory—the nucleus of all things digital ever since. “Random access” meant that all individual memory locations—collectively constituting the machine’s internal “state of mind”—were equally accessible at any time. “High speed” meant that the memory was accessible at the speed of light, not the speed of sound. It was the removal of this constraint that unleashed the powers of Turing’s otherwise impractical Universal Machine. ([Location 310](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=310)) - Tags: [[pink]] - Three technological revolutions dawned in 1953: thermonuclear weapons, stored-program computers, and the elucidation of how life stores its own instructions as strings of DNA. ([Location 398](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=398)) - Tags: [[pink]] - The mechanism of translation between sequence and structure in biology and the mechanism of translation between sequence and structure in technology were set on a collision course. Biological organisms had learned to survive in a noisy, analog environment by repeating themselves, once a generation, through a digital, error-correcting phase, the same way repeater stations are used to convey intelligible messages over submarine cables where noise is being introduced. The transition from digital once a generation to digital all the time began in 1953. ([Location 406](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=406)) - Tags: [[pink]] - According to Thorstein Veblen, the United States had entered the war, belatedly, only to ensure that the transnational interests of the industrialists would be protected against any social upheavals that peace in Europe might unleash. ([Location 603](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=603)) - Tags: [[pink]] - New, long-range artillery and shells were being rushed into production and delivered to Aberdeen to be tested before being shipped overseas to the American Expeditionary Force. The first test round was fired, in the midst of the worst winter on record, on January 2, 1918. Veblen arrived on January 4. With the same ease with which Oppenheimer would later assume command at Los Alamos, he rose to the occasion, assuming command of the entire ballistics group at Aberdeen. As the eldest of eight children, he found that leadership came naturally, while his willingness to shoulder his share of physical hardship on the firing ranges won the loyalty of his men. ([Location 611](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=611)) - Tags: [[pink]] - Since the time of Archimedes and his siege engines, military commanders had brought in the mathematicians when they needed help. The problem facing Veblen was as old as gunnery itself: If you aim a gun in a given direction, and load it with a given shell, where will the shell land? Or, if you want to hit a given target with a given shell, where should the gun be aimed? According to Newton and Galileo, the path of a projectile was calculable, but in practice it was difficult to predict the behavior of a shell in flight. ([Location 622](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=622)) - Tags: [[pink]] - Range, speed, and altitude had increased to where the flight of the shell was affected by factors ranging from the changing density of the atmosphere to the rotation of the earth. Preparing the range tables required enormous numbers of calculations, largely performed by hand. The gap between what the models predicted and where the shells landed was narrowed, as far as possible, by the ballistic coefficient, an empirically derived constant that was rarely as constant as it should have been, and “was made to carry a very heavy burden,” in the words of Veblen’s colleague Forest Ray Moulton.5 ([Location 628](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=628)) - Tags: [[pink]] - Wiener was transformed by the Proving Ground. “We lived in a queer sort of environment, where office rank, army rank, and academic rank all played a role, and a lieutenant might address a private under him as ‘Doctor,’ or take orders from a sergeant,” he wrote. “When we were not working on the noisy hand-computing machines which we knew as ‘crashers,’ we were playing bridge together after hours using the same computing machines to record our scores. We went swimming together in the tepid, brackish waters of Chesapeake Bay, or took walks in the woods.” “Whatever we did, we always talked mathematics,” Wiener explained. “Much of our talk led to no immediate research.” Wiener found that the Proving Ground “furnished a certain equivalent to that cloistered but enthusiastic intellectual life which I had previously experienced at the English Cambridge, but at no American university.” Veblen had gathered a community that would redefine American mathematics in the years between World War I and World War II. “For many years after the First World War,” wrote Wiener, “the overwhelming majority of significant American mathematicians was to be found among those who had gone through the discipline of the Proving Ground. Thus the public became aware for the first time that we mathematicians had a function to perform in the world.”6 ([Location 643](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=643)) - Tags: [[pink]] - Note: Agglomeration effects and in-person work. Unexpected benefits arise from putting high-intelligence people together and letting them work on hard problems - Veblen returned to Princeton determined both to replicate the success of the European institutions and to recapture some of the informal mathematical camaraderie of the Proving Ground. He set three immediate goals: to sponsor postdoctoral fellowships for promising young mathematicians, to free existing professors from crushing teaching loads, and to promote cross-fertilization between mathematics and other fields. ([Location 656](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=656)) - Tags: [[pink]] - “The principle upon which Fine Hall was designed,” according to Veblen, “was to make a place so attractive that people would prefer to work in the rooms provided in this building rather than in their own homes.”13 Jones, believing that “nothing is too good for Harry Fine,” instructed Veblen to construct a building that “any mathematician would be loath to leave.” ([Location 725](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=725)) - Tags: [[pink]] - The book, expanding upon the Rhodes lectures Flexner had delivered at Oxford in 1928, gave a depressing account of higher education in America, concluding with a call for “the outright creation of a school or institute of higher learning” where “mature persons, animated by intellectual purposes, must be left to pursue their own ends in their own way … be they college graduates or not.” Flexner argued that this “free society of scholars” should be governed by scholars and scientists, not administrators, and even “the term ‘organization’ should be banned.” ([Location 777](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=777)) - Tags: [[pink]] - “It is the multiplicity of its purposes that makes an American University such an unhappy place for a scholar,” advised Veblen. “If you can resist all temptations to do the other good things that might be attempted, your adventure will be a success.”25 ([Location 811](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=811)) - Tags: [[pink]] - Note: To make a place appealing to high-achieving individuals, it needs to prioritize hard problems and only a FEW of them. Trying to do everything at once will lead to lack of focus and catch researchers up in the malaise. Better to have a core set of ideas that are interrelated so that idea cross-pollination can occur - Flexner, who had given away some $600 million over the course of his association with the Rockefeller Foundation, believed that most educational funding had too many strings attached. Now was his chance to try something else. “I should think of a circle, called the Institute for Advanced Study,” he envisioned in 1931. “Within this, I should, one by one, as men and funds are available—and only then—create a series of schools or groups—a school of mathematics, a school of economics, a school of history, a school of philosophy, etc. The ‘schools’ may change from time to time; in any event, the designations are so broad that they may readily cover one group of activities today, quite another group, as time goes on.”27 “The Institute is, from the standpoint of organization, the simplest and least formal thing imaginable,” he explained. “Each school is made up of a permanent group of professors and an annually changing group of members. Each school manages its own affairs as it pleases; within each group each individual disposes of his time and energy as he pleases … The results to the individual and to society are left to take care of themselves.”28 Flexner believed that knowledge, not profit, must be the goal of research. “As a matter of history, the scientific discoveries that have ultimately inured to the benefit of society either financially or socially have been made by men like Faraday and Clerk Maxwell who never gave a thought to the possible financial profit of their work,” he wrote to the editors of Science in 1933, protesting against universities that were beginning to file for patents on their research. This did not mean that benefits should not be expected from pure research. In a Harper’s Magazine essay titled “The Usefulness of Useless Knowledge,” Flexner described the thinking behind the Institute for Advanced Study and argued that “the pursuit of these useless satisfactions proves unexpectedly the source from which undreamed-of utility is derived.”29 ([Location 819](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=819)) - Tags: [[pink]] - Flexner decided to start with mathematics. “Mathematics is singularly well suited to our beginning,” he explained to the trustees. “Mathematicians deal with intellectual concepts which they follow out for their own sake, but they stimulate scientists, philosophers, economists, poets, musicians, though without being at all conscious of any need or responsibility to do so.” There were practical advantages to the field as well: “It requires little—a few men, a few students, a few rooms, books, blackboard, chalk, paper, and pencils.”30 ([Location 837](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=837)) - Tags: [[pink]] - The Nazis launched their purge of German universities in April 1933, and the exodus of mathematicians from Europe—with Einstein leading the way to America—began just as the Institute for Advanced Study opened its doors. ([Location 865](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=865)) - Tags: [[pink]] - He started out determined to avoid “dull and increasingly frequent meetings of committees, groups, or the faculty itself. Once started, this tendency toward organization and formal consultation could never be stopped.”44 ([Location 933](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=933)) - Tags: [[pink]] - Two different Institutes have managed to coexist. “One, which was adopted more by the historical school,” according to Deane Montgomery, “is that it’s a group of great scholars who occasionally communicate with the public and who have great thoughts. They tended more to think of it as a lifetime fellowship for themselves.” Veblen, adds Montgomery, “said he and Einstein and Weyl didn’t feel up to that.”49 The other Institute was the annually changing group of mostly young visitors at the beginning of their careers, interspersed with occasional established scholars taking a year off. ([Location 969](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=969)) - Tags: [[pink]] - At the time of the founding of the IAS, mathematics was divided into two kingdoms: pure mathematics, and applied. With the arrival of von Neumann, the distinctions began to fall. “The School of Mathematics has a permanent establishment which is divided into three groups, one consisting of pure mathematics, one consisting of theoretical physicists, and one consisting of Professor von Neumann,” Freeman Dyson explained to a review committee in 1954.52 ([Location 986](https://readwise.io/to_kindle?action=open&asin=B005IEGK5C&location=986)) - Tags: [[pink]]