Turing's Cathedral: The Origins of the Digital Universe

by George Dyson

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.

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.

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.

In answering the Entscheidungsproblem, Turing proved that there is no systematic way to tell, by looking at a code, what that code will do. That’s what makes the digital universe so interesting,

Early computers were built in many places, leaving fossils that remain well preserved. But what, exactly, once everything else was in place, sparked the chain reaction between address matrix and order codes, spawning the digital universe in which we are all now immersed? C(A) is all it took.

A digital universe—whether 5 kilobytes or the entire Internet—consists of two species of bits: differences in space, and differences in time. Digital computers translate between these two forms of information—structure and sequence—according to definite rules. Bits that are embodied as structure (varying in space, invariant across time) we perceive as memory, and bits that are embodied as sequence (varying in time, invariant across space) we perceive as code. Gates are the intersections where bits span both worlds at the moments of transition from one instant to the next.

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

To a digital computer, the only difference that makes a difference is the difference between a zero and a one.

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.

data (numbers that mean things) but also executable instructions (numbers that do things)—including

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.

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. With the introduction of breech-loading, rifled artillery, accuracy improved to where it became possible to test-fire a gun a fixed number of times, distributing the shots across a range of distances, and then use a mathematical model to fill in a complete firing table (or range table) from there.

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. “The German developments are going bad and worse, the papers today wrote of the expulsion of 36 university professors, ½ of the Göttingen mathematics and physics faculty,” von Neumann reported to Flexner on April 26. “Where will this lead, if not to the ruin of science in Germany?”34

The establishment of the dual Austro-Hungarian monarchy in 1867 had brought an interlude of peace and prosperity, and a lifting of restrictions against Jews, to a country best known, according to Klári von Neumann, “for the gallantry of its men, the beauty of its women, and last, but not least, for its hopelessly unhappy and unlucky history.”1 When the towns of Buda and Pest, on opposite sides of the Danube, were amalgamated in 1873, the new Hungarian capital, now rivaling Vienna as the cultural and economic center of the Austro-Hungarian Empire, became the fastest-growing city in Europe. There were more than six hundred coffeehouses, three of the world’s most rigorous high schools, and the first subway system on the European continent in young Neumann János’s Budapest.

Hungarians had been facing the impossible for eleven hundred years, with few resources except a strategic location that had been occupied by the Roman, Ottoman, Russian, Holy Roman, Habsburg, Napoleonic French, Nazi German, and Soviet empires in turn.

Von Neumann, according to Stan Ulam, credited Hungarian intellectual achievements to “a subconscious feeling of extreme insecurity in individuals, and the necessity of producing the unusual or facing extinction.”13

The Hungarian language, a branch of the Finno-Ugrian family incomprehensible to outsiders and closely related only to Finnish and Estonian, fortified Hungary against encroachment by its neighbors, while prompting Hungarian intellectuals to adopt German as a medium of exchange. To survive in a non-Hungarian-speaking world, Hu...

Budapest, the city of bridges, produced a string of geniuses who bridged artistic and scientific gaps. In both mathematics and cinema it was said, “You ...

“He, more than anyone I know,” adds Klári, “took it as a most personal affront that any nation, group of people, or individuals, could possibly prefer the base and unsophisticated philosophy of Nazism or any other ‘ism’ to such minds as Einstein, Hermann Weyl, Wolfgang Pauli, Schrödinger and many, many others including, last but not least, himself.”

According to Rear Admiral Lewis Strauss, von Neumann was “able to take the most difficult problem, separate it into its components, whereupon everything looked brilliantly simple, and all of us wondered why we had not been able to see through to the answer as clearly as it was possible for him to do.”52

While World War I had been a battle for bigger guns, World War II (and the cold war that followed) became a battle for bigger bombs.

the surprising thing about large explosions being not how much energy was released, but how unpredictable was the damage produced as a result.

On August 6, 1945, a uranium-fueled atomic bomb yielding 13 kilotons was dropped on Hiroshima, followed by a plutonium-fueled bomb yielding 20 kilotons on Nagasaki on August 9. The Japanese surrendered on August 15.

The development of electronics, according to Zworykin, could be divided into three epochs. “In the first, beginning with DeForest’s invention of the audion in 1906 and ending with the First World War, electron currents were controlled in vacuum tubes in much the same manner as a steam valve controls the flow of steam in a pipe,” he explained. “No more attention was paid to the behavior of the individual electrons in the tube than is customarily expended on the motion of the individual steam molecules in the valve.”

“In the second period,” beginning in the 1920s, Zworykin continued, “the directed, rather than random, character of electron motion in vacuum was applied in the cathode-ray tube.” In the third period, beginning in the 1930s, beams of electrons were further subdivided into groups. “This subdivision was either on the basis of time, the electrons being bunched at certain phases of an applied high-frequency field as in the klystron or magnetron, or of space, as in image-forming devices,” Zworykin explained. “The electron microscope and the image tube are typical representatives of this group.”7

“The whole computation is made in the binary system of numeration so that any number is expressed as a sum of powers of two.”

if electronic circuits could count, then they could do arithmetic and hence solve, inter alia, difference equations—at almost incredible speeds!”

The ENIAC was programmed by setting banks of 10-position switches and connecting thousands of cables by hand. Hours, sometimes days, were required to execute a programming change. “Programming steps were very expensive to come by,” says Eckert. “It took boxes and cables and things. Doing something a second time, or reiterating something—we were 100,000 times faster than a human being—was very cheap.”29

He wanted to build a fast, electronic, completely automatic all purpose computing machine which could answer as many questions as there were people who could think of asking them.”