What experiences well known to me involve an altered perception of time?
One of them is improving a piece of my own prose. After laboring to bring ideas into being as words and then to cantilever those words themselves until everything balances like a Calder mobile, I may raise my head - feeling that a very long time has passed - to find that not even an hour has gone by on the clock. There follows the relief of realizing that less time has elapsed in the material world than in my experience of it — relief since so often it is the other way around, and when it is the other way around I feel a little cheated and frustrated.
Another case is the enlivening of words by music. Sometimes the result is what known as "opera time", in which the events of a musical drama are out of step with the tempo of the same events in real life. I mentioned this effect in passing in recent posts about Donna Elvira and the cantus firmus in some of the Bach choruses. Because altered perception of narrative time is related to the visceral appreciation of music, I think of this effect as having something in common with kinesthesia, the subjective sensation of body movement and position, an idea and feeling of keen interest to me in my daily life and study habits. Of course, not all music produces this effect to the same extent and I know different listeners react differently, too.
Since taking the first steps toward making my peace with mathematics almost two years ago, I have struggled with a third form of altered time-perception: a special feeling that comes about in trying to read and understand a mathematical idea, to fully follow or compose a proof, to formulate and solve a problem. There has been nothing in my life up to now as a humanist — linguistic fieldworker and student of the Chinese script and medieval prosody — that has prepared me for this experience. Part of the sensation is that my mind is being forced into a lower gear-ratio: suddenly, my engine has to make many more revolutions to get the wheels to turn just once.
The low-gear feeling reminds me of a half-hour spent some years ago in a tiny café in Longyan 龍巖, a small Chinese city where a market for coffee developed around 2004. In order to serve my companion and me two cups of coffee, perhaps 8 ounces in all, the café owner ground beans in a hand-operated burr mill for ten minutes, cranking rapidly the whole time. Long before he was done I felt embarrassed at the exertion he had taken on himself to make a good impression on me. He had few customers but I was the first foreigner his shop had ever had, so it was a matter of some moment for him. He had paid a lot of money to have an expert come up from Xiamen 廈門 to teach him how to make and serve coffee the "right way", exactly the right way. His coffee was thin — but after all it was pretty good, better than you would get today in one of the big-name coffee chains here in New York.
In studying Classical Chinese, or reading collections of philological notes on an ancient dictionary manuscript, or collating piles of handwritten dialect data, you learn not to crave instantaneous satisfaction and even to distrust any result arrived at quickly. But by comparison with mathematics, all of those feel like short-term activities whose conceptual finiteness is easy to demonstrate. The reason for the difference must be that the kind of thinking we do in solving humanistic problems does not require such continual recasting of hypothesis and mindset, or for most of us (I hope I am not shocking anyone) as much rigor, either.
Unlike the other two examples I have cited — polishing my own writing, listening to thoughtfully constructed vocal music — the bending of time by mathematics is unpleasant, except in retrospect after I have succeeded in reaching a solution of some sort. I hope more practice will bring me more facility — that is a prescription that certainly works in studying Chinese, and it is what divides the good students from the mediochre ones. Sometimes mediochre students are vastly more brilliant than good ones, but Chinese requires more than brilliance for its mastery; it also requires the investment of time in what may appear to be drudgery. It requires, in short, commitment to some partial vision of the future along with a willingness to ignore the clock. As for math, impatience is certainly my chief obstacle, and impatience is one of what Epictetus calls "things that are up to us". I have tried techniques to increase my stamina and concentration, and to recover more quickly from periodic cognitive exhaustion. And to suppress the arrogant expectation that I can cut through the difficulties quickly. Nothing I have tried helps in a way that I could call striking — I mean that nothing lives up to my arrogant expectation that I can continue to indulge in arrogant expectation — and most of it does not help at all, except to distract me and waste enough time to make me feel a little cheated and frustrated again.
In the end, I think what will really matter is my own willingness to suspend impatience and all expectation of achieving finality, to refuse to feel them. I do not find it hard to attain this suspension on some occasions — when I listen to Beethoven's late music — but in doing math you are not listening; it is as though you are actually composing the music, yourself.