Major League Baseball pitcher is not. Not every natural process is or can be described algorithmically: the human genome is revealed increasingly as being within the algorithmic realm; along with many other complex and chaotic processes, global weather patterns still lie well outside it.
The algorithmic realm can be thought of as comprising all phenomena that can be satisfactorily governed or analyzed by some system of logic, from the somewhat stilted but still recognizably human language of much modern computer programming to the highest abstractions of mathematics.
The progress of science and technology into the algorithmic realm has depended on progress into the quantum realm. It was von Neumann, more than any other man of his era, who joined the two. We can delve deep into the atom only by rising up to a level of mathematical abstraction just glimpsed in the previous experimental science of the visible world.
But we do not, as von Neumann supremely understood, rise infinitely. As Kurt Godel demonstrated in the early twentieth century, and von Neumann, as Godel’s first interpreter and greatest proponent, repeatedly showed, the symbolic logic driving both math and science — the computer and the quantum — is ultimately axiomatic. It cannot prove itself in its own terms but must rely on a set of assumptions outside the system.
Though it frustrated many, von Neumann found this result both liberating and exhilarating. It would all be up to him. The limits of logic — the futility of the German titanic mathematician David Hilbert’s quest for a hermetically sealed universal theory — would liberate human beings as creators. Godel’s incompleteness theorem emancipates man from determinism and makes logic a more powerful tool of human choice and creation. Reify-ing theory into practice, science into technology, becomes the role of human entrepreneurs and engineers.
Not only could humans discover algorithms, they also could compose them. This loophole in the mathematical logic of the universe would make von Neumann the most influential of all the great scientists of the twentieth century in the practical sphere.
Not only was a new science created, but also a new economy that, more than any other previous human achievement, affirmed the core of all capitalist morality and the basis of all sound political economy: wealth springs from the minds of human beings, and, above all, from the minds of the relatively few human beings who operate at the nexus of word and world — on the borders of math and manufacture — in the realm of the algorithm. The struggle against Marx and Hitler, as between the West and the jihad today, is best understood as a war between the denizens of the new realm and the rage of its enemies who cannot contribute to its genius. Hitler’s claim in
Despite the enormous and indispensable role of non-Jews in the new realm, Hitler’s jibe was on target. The most valorous feats of Jews and the vilest slanders against them arise from this recognition: as the level of abstraction rises in any arena of competition so does relative Jewish achievement. It is easier to observe (and attack) this anomaly than to explain it. Surely IQ, which mostly gauges the ability to perform abstract thought, is part of the explanation. But just as surely figuring in the causes is the diaspora’s long history of exclusion from the “real” economy (as the materialists have always seen it), shunting Jews to the manipulative realms of trade, bookkeeping, shopkeeping, philosophy and finance. In any economy operating at its highest realm of abstraction, the allocation of capital can be among the most valuable kinds of work.
And it did not hurt that Jews have believed from before the fatherhood of Abraham that it was the word that made the world — the ultimate assertion of algorithmic power.
Norman Macrae’s intense and inspirational biography of von Neumann tells the tortured story of the Budapest from which he emerged early in the century. As Macrae describes it: “In the three and a half decades before Johnny’s birth in 1903, Budapest had been the fastest-growing big city in Europe — next to New York and Chicago, possibly the fastest in the world…. [in just eight years] freight traffic on Hungary’s railroads rose from 3 million tons in 1886 to 275 million in 1894 and passenger traffic multiplied nearly seventeenfold.” At the time of von Neumann’s youth, industry was flourishing, with the number of industrial workers surging from 63,000 in 1896 to 177,000 by 1910. Between 1867 and 1903, the population of Budapest rose from 280,000 to more than 800,000, surpassing such cities as Rome, Madrid, Brussels, and Amsterdam.
Vienna’s twin in the Hapsburg Empire, Budapest achieved these feats chiefly through the expedient of welcoming Jewish immigration. With virtually no Jews as late as 1867, Hungary accepted hundreds of thousands by the time of von Neumann’s birth. At the time von Neumann entered the elite Lutheran High School in Budapest, 52 percent of the students were listed as Jewish. Perhaps two-thirds of the leading citizens of Budapest, outside the government — bankers, lawyers, industrialists, musicians, scientists, artists — were Jewish. Although they made up only five percent of the Hungarian population, they became the vanguard of Hungarian economy and culture.
Steve J. Heims’ fascinating joint biography of von Neumann and his MIT rival, Norbert Wiener,
Nonetheless, for most of von Neumann’s youth, Budapest thrived. To eminent business families like the von Neumanns and Kanns, his forebears, the city must have seemed even more secure and idyllic than Beirut seemed to Christians before the eruption of its fifteen-year civil war, triggered by Arafat’s choice of Lebanon as the new operating base and refuge for his PLO.
The idyll came to an end after Hungary engaged on the losing side in World War I and lost two-thirds of its territory. Capitalist progress depends on the long time horizons of stability and peace. In early 1918, inspired in part by the Leninist Russian Revolution, Hungarian leftists launched two general strikes, followed by the rise of a feckless Socialist government amid much carnage. In 1919, a brutal Communist regime took over. Its ruthless poet leader, Bela Kun, a secular Hungarian Jew, cherished a letter of advice from Lenin: “Make these promises to the peasants… Make these pledges to the proletariat… Give these assurances to the bourgeoisie… Do not feel in any way bound by these promises, pledges and assurances.”
With Jewish Communist henchmen numbering some 161 out of the top 2 0 2 officials in his government, Kun murdered 6,000 “class enemies,” focusing on bankers and financiers, many of them Jews, but missed von Neumann’s family, which rushed off to a vacation in their summer home and then proceeded to Vienna. Kun’s Leninist-certified methods, for all their violence, failed to establish his regime. Within months, a new Fascist leader, Admiral Miklos Horthy, took over and perpetrated mass murders of his own, punishing Communist Jews while inviting useful bankers such as Max [von] Neumann back to Budapest to revive the economy. But conditions in Hungary had taken an irretrievable dive.
A new law, then unique to Europe, barred all but five percent of the slots in universities to Jews. The general turmoil, together with the flight of much of the professional and business class of Hungary, plunged the country into chaos, poverty, and crime. As many tyrants before and after, Horthy attempted to take over the means of production and discovered that they were merely so much iron and dirt without the men of production who made them work. As unemployment soared to more than 30 percent, the chief victims of the Jewish flight were the poor and peasants of these countries.
Von Neumann, though, learned a redemptive lesson about the world. Never would he imagine that wealth and security were stable and predictable. Never would he drop his guard before the evil and treachery of humankind. As he told his friend and colleague Eugene Wigner many years later: “It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.”
Accompanying his tragic sense of history, however, was von Neumann’s vision of the hierarchies of knowledge and aspiration. He could climb up from the morass of mittel European politics on the abstract ladders of mathematics and philosophy. As epitomized by von Neumann and Einstein, European Jewish scientists of the time possessed a passionate faith in the coherence of the cosmos. Underlying, suffusing, informing, and structuring the
