Gurdjieff and Gödel, part I

 

Prout's Neck, Maine

Kurt Gödel’s incompleteness theory was originally conceived of as a mathematical problem; yet in a universe that runs, largely, on the principle of mathematics, it extends itself rather effortlessly into the question of the nature of Being. 

Simply put, the theorem states that no consistent mathematical system is capable, using its axioms, to prove all the truths about its own nature. Every system must, no matter how logical and apparently perfect, contain elements that cannot be explained using its own set of rules.

Extending this principle to the question of natural law and Being, it suggests that no matter how lawful a universe is, it’s not capable of explaining itself from within the context of its own laws. There must always be something contradictory—inexplicable, irrational— at the heart of any system of mathematics; and in this same way, our own system of physics and natural laws must inevitably contain a mystery at the heart of itself. No perfect truth can be obtained. There’s always something missing.

The theorem itself was a shock to the mathematical community when Gödel presented it. The mathematical community of the 1920s in Europe, and most particularly Austria, which was the hotbed of intellectual fermentation during that period, was infused with a romantic optimism that seems to have been the natural outcome of a late peak in the Age of Enlightenment. The hubris of the community, as reported by historians, caused mathematicians and scientists to believe that everything could be known, if only with enough effort; that everything could be proved and that the system of mathematics and the physical, chemical, and biological laws that it revealed were a thing of flawless beauty. 

The aim, in fact, of a primary faction of the mathematical community in Gödel’s time was defined by its stated aim of discovering the proofs that would verify this. In this sense the best mathematicians were not just number crunchers; they were aesthetes, men and women (few enough women, but there were a few) who believed in the beauty and goodness of numbers, the beauty and goodness of the universe and of natural law. They saw mathematics as an expression of a perfection; and whether or not they were religious, the impulse behind the ideas was, because it beheld a world in which everything made sense, everything was put together perfectly. The question of whether or not there was a God behind this was almost unnecessary. It was the perfection itself that attracted them. Mathematics, in its own right, was the religion.

This was the climate, the atmosphere, that the mathematician P. D. Ouspensky found himself in as he began his search for the miraculous; the same impulse infused him, and the same not entirely secret hope for a perfectly rational, consistent, and aesthetically meaningful universe informed his own search in the books he wrote before he met Gurdjieff. For the mathematicians, this was a rational search that took on the nature of a spiritual one.

This was not the birth of mechanistic rationalism, for those who deny the existence of God; mechanistic rationalism itself, the belief that everything was a machine that could run without a God, had roots well back in the age of Enlightenment. But perhaps it was it apotheosis; a belief that the machine could be perfect. Machines, after all, don’t have parts that don’t make any sense and serve no purpose. When we construct a machine, every part in it has an intelligible relationship from one part to another, so that there isn’t, for example, a random gear that does nothing and seems to have no purpose relative to the rest of the machine. In a properly built machine, every part of it can be explained.

Mathematics was believed to be such a machine; and, in the world of mechanistic rationalism, the universe — which was evidently built on the principles of mathematics, since this is what was used to explain everything and apparently could — would also be such a machine. Everything explicable. Everything logical, rational, predictable and understandable, if only mathematics were correctly applied.

You could explain everything.

This is the world in which man is God. We human beings of the 21st century still live in the backwash of this mistaken principal; and despite the fact that the mathematicians itself proved that the idea is, ultimately, a lie, it’s still stubbornly believed, because human beings would rather believe a lie over almost anything that involves the truth.

In any event, there can be no doubt that Ouspensky, in his turn, influenced Gurdjieff, even though the way the historians of the Gurdjieff work usually present the situation, the influence flowed in one direction only. This is of course quite impossible; the whole point of human relationships is that they’re reciprocal, a fundamental fact that Gurdjieff presented within his own system as passed to Ouspensky. Ouspensky’s search for perfection, his devotion to mathematics, must have all made an impression on Gurdjieff and influenced his view of human proclivities and, most particularly, the proclivities of mathematicians. We can’t expunge this influence from Gurdjieff’s future work, Beelzebub’s Tales to his Grandson; some fraction of Ouspensky’s DNA  leaked into his book, by whatever means, just as Jeanne de Salzmann’s influence did. 

with warm regards,

Lee

Lee van Laer is a Senior Editor at Parabola magazine.