Learning by Inhibition
WLC: Universal Turing Machine with von Neuman’s Architecture
“There have been within the experience of people now living at least three serious crises... There have been two such crises in physics - namely, the conceptual soul-searching connected with the discovery of relativity and the conceptual difficulties connected with discoveries in quantum theory... The third crisis was in mathematics. It was a very serious conceptual crisis, dealing with rigor and the proper way to carry out a correct mathematical proof. In view of the earlier notions of the absolute rigor of mathematics, it is surprising that such a thing could have happened, and even more surprising that it could have happened in these latter days when miracles are not supposed to take place. Yet it did happen.”
John von Neumann (cited from)
The crisis of foundations of mathematics mentioned above by von Neumann was a miracle (unexpected uncertainty) indeed. It forced many mathematicians to direct their interests to fields which they considered relatively “safe” and to experience the constant drain of their enthusiasm. At the same time it challenged and ignited with curiosity the most brilliant mathematical minds of the first half of the twentieth century. Kurt Godel, John von Neumann and Alan Turing were among them.
Yet the true miracle happened when that crisis helped to create one of the most fruitful scientific relationships of all times - the winnerless competition of two geniuses which learned from each other by periodically inhibiting each other’s thoughts instead of reinforcing them.
Neither Von Neumann nor Turing was satisfied with Godel’s proof of his incompleteness theorem that stated that any mathematical formal logic based system couldn’t be consistent and complete at the same time. They tried to disprove Godel but both failed. Instead they developed other proofs of Godel’s theorem. Yet their mutual passion to solving a purely theoretical problem resulted in the invention of the computer, one of the greatest inventions of all times.
Along with creating the first ever artificial intelligence the two also demonstrated the power of clustering of human minds in a particular way that critically enhances the productivity of natural intelligence.
The winnerless competition of Alan Turing and John von Neumann began in 1933 when Turing, then a student, read von Neumann’s book “The Mathematical Foundations of Quantum Mechanics”. Von Neumann was 25 years old when he wrote this book.
They met for the first time in 1935 when von Neumann spent a year as a visiting professor at Cambridge where Turing was working at that time.
When Turing turned 25 in 1936, he wrote the article “On computable numbers for Entscheidungsproblem.” Von Neumann read it and invited Turing to do his PhD at Princeton. By that time, Turing had already managed to attract von Neumann’s attention. He proved the equivalence of left and right periodicity proposed by von Neumann as separate.
Von Neumann offered Turing to remain at Princeton, but Turing was in a hurry to return to his homeland: war was approaching.
Von Neumann was not the last, but the third from the four Great Encyclopedic Mathematicians. Henri Poincare and David Hilbert were the first two. Andrei Kolmogorov was the last. The contribution of von Neumann in all the sciences with which he came into contact distinguishes him even from this cohort of geniuses.
Why? It seems to me that winnerless competition with Turing was one of the reasons for this. And yet, he and Turing were vivid representatives of a rare type of science, the primary science of concrete as the founder of modern Anthropology Claude Levy-Strauss named it, that enabled them to crack as nuts concrete technical problems with the same ease with which they solved the most abstract unresolved challenges of higher mathematics.
It was precisely the deep, perhaps intuitive understanding of the inextricable link between abstract theory and empiricism that helped von Neumann to see in Turing’s solution of a formal logical problem the programming language of a universal computing machine Von Neumann was the first to write such a language. Remember Fortran?
Von Neumann wrote to Norbert Wiener in the second half of the 1950s that he was enraged by the technical limitations which prevented him from seeing the microscopic mechanism of the nervous system. He created a computer as a metaphor for the brain, but ran into the obstacle of insufficient technological development when making a working model of intelligence.
Perhaps there was yet another obstacle. In 1954, Turing committed suicide. The most powerful stable heteroclinic information channel that was connecting the two fastest brains on the planet broke up. Or was it that winnerless competition channel that was accelerating their brains to such a fantastic speed?
Was it one way or another, but in 1957, von Neumann also died. He and Turing formed a “two dimensional non-smooth invariant torus” of two mind systems in a shared phase space. They solved many puzzles, but left to us even more. It is only necessary to be curious about the reality given to us in observations, only taking into account the accumulated experience, and not vice versa. Intrinsic motivation to attain results requires inhibition, not reinforcement.
“Winnerless competition (WLC): A general dynamical phenomenon that denotes sequential switching of prevalence among participants. For example, if in a head-to-head competition, boxer A beats boxer B, boxer B beats boxer C, and finally boxer C beats boxer A, all participants are “winners” for a finite time, but there is no overall winner such as in “winner takes all.”
Rabinovich MI and Varona P (2018) Discrete Sequential Information Coding: Heteroclinic Cognitive Dynamics. Front. Comput. Neurosci. 12:73. doi: 10.3389/fncom.2018.00073
