The musings of a previously unemployed Jewish Freemason. I write about the job search, about Judaism, and about Freemasonry.
Friday, August 17, 2012
Deep Consciousness and Waking Consciousness
My background is in mathematics, where there are axioms (which are as few as possible) and there are proofs based on rigorous definitions. And nothing else. You don't really get to even make a conjecture without overwhelming evidence, and that conjecture is worthless compared to a proof. I try very hard to liberally interject conditionals into factual statements: "it appears that", "you might want to consider that", "conceivably", etc.
But I also realize that I can use different epistemologies for different purposes. It has become useful to me to distinguish between truth and fact, making a distinction between the epistemological aims of my spiritual journey from the epistemological aims of my scientific journey, which are not always congruent. When I was working on my math Ph.D., I would work on very difficult math proofs, the kind of problems that took weeks to solve. I would sit down for four-hours stretches, and sometimes make a breakthrough, but often not. I would have to live with the problem for long stretches of time.
In solving a difficult problem, one's mental hygiene needs to be immaculate. I would have every definition and theorem that might be useful to its solution memorized, not merely by rote, but so that I could take those theorems and definitions apart and put them back together again in my mind. Even still, often I would run through scenario after scenario, speculation after speculation, and test them over hours and even days. After much exertion, rest, exertion and rest, I would sometimes suddenly have an insight, and the whole solution would be revealed to me in its entirety, in a flash. It was orgasmic. Sometimes it would take me hours to unpack what I had received and put it in a form that was intelligible to other mathematicians (i.e. writing up the solution), but when I got one of those flashes, the problem was solved in my mind.
I talked to my advisor about this (who, incidentally was a staunch atheist), and he told me that, in his observation, humans in their waking consciousness are just not very smart. We can be disciplined and rigorous, and we can work hard at something. When we work hard on a problem, some deeper consciousness within notices that we are struggling with an idea, and decides that maybe that idea is interesting, and begins to pay attention to that idea. That deeper intelligence is very smart, and it can solve these kind of problems almost instantly. It transmits a solution to the waking consciousness in a very concentrated burst, and then is gone, leaving the waking consciousness to shape that burst into something that works for it.
That is an astonishing description of a mental process, and it should be rightly met with deep skepticism. Had I not experienced it directly over and over again, I would probably dismiss it out of hand. When I was a grad student, I discovered a book by Jacques Hadamard called "The Psychology of Invention in the Mathematical Field." Hadamard was a student of Einstein and Poincaré. He interviewed them and other mathematicians about how they create proofs, and their answers are quite similar to the above. Almost an oracular relationship takes place, where the mathematician courts a muse, who provides answers after sufficient supplication. That's very strange, but the testimony of some of the most brilliant minds of the twentieth century attest to this peculiar mental phenomenon.
When I was studying for my comprehensive exams, I would study by reading old exams going back twenty years, and try to solve those problems in preparation for my exam. These problems were so hard that if I spotted them for the first time while sitting for the exam, I might not be able to solve them. So I studied by solving as many of these problems as I could, and hoping that by memorizing their solutions, I could solve something similar if it appeared on the exam. I was studying for an algebra exam, and I worked on one problem for four hours straight, and got nowhere with finding a solution. It was 1:30 AM, and I was exhausted, so I dragged myself away from my desk and put myself to bed. Asleep, I dreamed the solution to the problem. I felt a blissful glow in the dream, and in the midst of that feeling, a voice said, "That's the real answer to the problem. Wake up, schmuck, and right it down."
I did, and went back to sleep. When I woke up the next morning, I looked at what I had written, and it was a concise and elegant solution to the problem, a six-line proof. Astonishingly, that problem, nearly verbatim, showed up on my exam, and I gave the dream solution. My professor later told me that I gave the most elegant solution to the problem he'd seen in twenty-five years of grading.
That's very strange, and it has bothered me for a long time. Poincaré describes something very similar in his anecdote about creating the Theory of Automorphic Forms. Recall that the word "genius" originally referred to a spirit creature that a person could communicate with who would give him knowledge. Socrates, in Plato's "Trial of Socrates", refers to a "daimonion" who always gave him advice and had never failed him. I think Socrates was playfully exteriorizing a mental process that he relied on, but a mental process that transcended the ego-driven consciousness that is the waking state for most people. The direct experience of such mental phenomena has convinced me that there is more to consciousness than the waking state, and made me eager to explore these different states of consciousness.
But it is unsatisfactory to describe these mental workings as either "belief" or "knowledge". Something else is going on. The flashes I received could have been mental garbage, and indeed, they were worthless before I was able to shape them back into mathematical proofs, which shaping was the result of my training as a mathematician. The speculative burst of insight that caused Picasso to paint Guernica, or caused Miles Davis to record Bitches Brew would have been worthless if bestowed upon someone with no particular talents.
Going back to my split between "fact" and "truth", I would say that the proof I discovered is a fact. The description of these mental processes is a truth for me. Truth is somewhat subjective, and fact is objective. That does not make truth inferior to fact; in this story, the fact comes out of the truth, but the truth was only useful for me, whereas the fact anyone could use. Everyone understands (or should understand) that it takes rigor to come up with facts. I would assert that it takes similar rigor to handle truths, and that most people fall upon their truths almost haphazardly, without scrutiny, mental discipline, or circumspection.