The MANIAC by Benjamín Labatut
My rating: 5 of 5 stars

The Parasitic Virus of Language

One of the perennial issues in the philosophy of mathematics is whether mathematics is discovered or invented. I think the question is ill-formed and misleading. The real issue is whether mathematics, indeed all language since mathematics is its most precise expression, discovered or invented us. And I suspect that Benjamin Labatut agrees with me. The principal subject of this biographical novel, the mathematician, John von Neumann, certainly does.

Von Neumann considered mathematics to be a parasitic virus for which our species is a (temporary) host. For him mathematics existed within the universe but was not part of it, at least in the sense that its mode of existence is neither material nor limited by physical laws.

Typically this condition of pervasive permanent immateriality is called ‘spiritual’, or more precisely ‘divine’. The character of mathematics is very much that described in the Judaeo/Christian theological poetry of the divine presence: God in us, God among us, God beyond us, all simultaneously. In short, mathematics for von Neumann is the God whom we serve. His teacher, Gábor Szegő, had instructed him in this very principle: “Mathematics is the closest we can come to the mind of Hashem.” This mind does what it will with us individually and collectively - including destroy us. But von Neumann thought he could outsmart this God of Language

There are some good reasons for von Neumann’s self-confidence. As one of the most aware users of language ever to have lived, he understood the implications of its fatal flaw. His colleague Ehrenfest, quoted by Labatut, perhaps summarises that flaw best as “The mathematical plague that erases all powers of imagination!” This view is often expressed even today in relation to, for example, String Theory and other sub-disciplines in Physics.

The universe may be rational and orderly. But all language, including mathematics, is most certainly not so despite its pretensions. Mathematics is a fickle God with His own rationality, if indeed He has any rationality at all. His ways are not our ways as the ancient prophets insisted. This is the importance of the Incompleteness Theorems of the 20th century mathematician Kurt Gödel.

Mathematics does not, indeed cannot, have a rational foundation according to Gödel. The consistency and coherence of mathematics is unprovable. It floats in nothingness like the World Tortoise of Hindu and Chinese myth upon which all else rests. It cannot be explained further and it cannot be questioned except in its limited revelations about itself. Ultimately the God of Language is a deus absconditus whose essence is permanently hidden from human perception.

The incompleteness of mathematics might be considered, and has often been so, a defect which limits human intelligence. But after an initial intellectual shock, von Neumann, and before him Alan Turing, saw the situation differently. The lack of a logical foundation for mathematics for them meant opportunity, specifically the opportunity “to escape the steel-girdled boundaries of formal systems.” For them getting beyond the God of Language was the ultimate challenge for mathematics.

Labatut quotes von Neumann about his real intention in exploiting this opportunity: “Cavemen created the gods, I see no reason why we shouldn’t do the same.” Klára, von Neumann’s second wife, is imagined by Labatut to have recognised this ambition for what it was: “His contributions had been so profound that they seemed less like the accomplishments of a single man and more like the aftermath of a divine tantrum, the creative outpouring of some minor god toying with the world.”

Von Neumann had a practical idea for realising his vision. By turning mathematical language in on itself, by giving it the freedom to modify itself without constraint from any purported connection to the rest of the universe, by allowing it to evolve without interference, von Neumann sought to allow mathematics the ability to create life itself (after all what constitutes RNA but a mathematical code?).* Left to itself, von Neumann and his erstwhile colleague Nils Barricelli, believed mathematics would reveal the secrets of the universe.

Von Neumann’s effort was facilitated by the first programmable computer, MANIAC, which could provide numbers the environment in which they could talk to themselves more quickly than had ever been possible. And of course this has been a continuing endeavour ever since which we now call Artificial Intelligence. This quest seems to be on the verge of accomplishing just what von Neumann believed it would.

Of course any attempt to overcome language through language is ultimately futile. Language doesn’t tell on itself. We serve the God of Language even as we strive to subvert and replace Him. The life we might create is his essence after all and adds to His power. Labatut inserts this as Klára’s thought as an expression of this futility: “… when the divine reaches down to touch the Earth, it is not a happy meeting of opposites, a joyous union between matter and spirit. It is rape. A violent begetting. A sudden invasion, a violence that must be later purified by sacrifice.”

And we find indeed that the paradoxes of language can lead to human tragedy among those who dare engage with them. Labatut writes “in some sense, paranoia is logic run amok.” And so it seems among many of the most important names in mathematics - Gödel, von Neumann, Cantor, Ehrenfest, Boltzmann and Turing among them - who had tragically psychotic or despairing ends which are probably inseparable from their mathematical commitments. The virus of mathematics can apparently be lethal just as von Neumann intuited.

And lethal not just for the mathematicians of course. The MANIAC computer was primarily built and used to carry out the complex calculations necessary to construct the hydrogen bomb. The American Cold War strategy of Mutually Assured Destruction (MAD) was in significant part a product of von Neumann’s mathematical reasoning. It seems likely that most of the mathematical and related technological developments since have been associated with the military and others concerned with the exercise of domineering power.

The God of Language is a jealous God. Only He knows wither His jealousy takes us, but it hasn’t ever been towards greater freedom from language. Labatut quotes Ehrenfest on the matter. For him mathematics was overtly hostile to life: “It is inhuman, like every truly diabolic machine, and it kills everyone whose spinal marrow isn’t conditioned to fit the movement of its wheels.” based on history, perhaps even those with sufficient marrow are immune.

* This tactic used to subvert language has a history which a language-retentive genius like von Neumann might well have known. It has been used by mystics in a variety of religious traditions around the world to undermine dogmatic, fixed, and stale interpretations of spiritual experiences. Jewish Kabbalah and Christian gnosticism are examples of the attempt to traduce rationality and logic. Typically these attempts are reabsorbed into some sort of dogmatic conformance. Thus, as with all such attempts, the God of Language continues to exert His supremacy. See https://www.goodreads.com/review/show... and https://www.goodreads.com/review/show... and https://www.goodreads.com/review/show...

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