Meta-Discontinuities
I've been a bit mentally congested lately. I was making little progress on my research over the past week, I was bogged down by syntactic annoyances in Mathematica, and I had no idea of my next move in my work. Suddenly over the weekend, however, after sitting around reading for a few hours--Carl Schmidt, no less--I became spontaneously inspired to work on my research, and within a day, I had solved my primary problem in Mathematica and figured out a way to increase the speed of my algorithm by a factor of ~1000. This is all well and good, but a natural question arises: why can I go for weeks with no good ideas and feel terrible about everything I do, but suddenly get weeks worth of good ideas in a period of 2 hours? It is possible that these kinds of discontinuities are a symptom of some mental deficiency that I possess. But if anecdotal evidence is any guide, then I would seem to be in good company with my learning disability.
It is natural that good ideas should be discovered in discrete episodes. The structure of an idea or theory often hinges on a few details, and a muddled idea can develop very quickly once one of these key components is discovered. Indeed, this is the basis for Thomas Kuhn's interpretation of scientific progress as a series of paradigms punctuated by "revolutions". Data for a particular theory accumulates until key evidence reveals flaws in the underlying theory, at which point a new theoretical paradigm is proposed. Whether this is an entirely accurate description of scientific progress is a matter of some debate, but it is clear that personal research should go through some periods of fits and starts as key pieces of information are realized.
But what is not clear to me is why progress should be so inconsistent, and especially why a person can make enormous progress on a problem without consciously thinking about it. For example, why did the solution to my Mathematica conundrum become clear while reading Carl Schmidt's analysis of parliamentary democracy? And why is my progress so irregular that I will sometimes go for days without thinking of any useful or interesting ideas? There must be some kind of subconscious thought process occurring... if only I could do all my thinking without actually thinking about anything!
It is natural that good ideas should be discovered in discrete episodes. The structure of an idea or theory often hinges on a few details, and a muddled idea can develop very quickly once one of these key components is discovered. Indeed, this is the basis for Thomas Kuhn's interpretation of scientific progress as a series of paradigms punctuated by "revolutions". Data for a particular theory accumulates until key evidence reveals flaws in the underlying theory, at which point a new theoretical paradigm is proposed. Whether this is an entirely accurate description of scientific progress is a matter of some debate, but it is clear that personal research should go through some periods of fits and starts as key pieces of information are realized.
But what is not clear to me is why progress should be so inconsistent, and especially why a person can make enormous progress on a problem without consciously thinking about it. For example, why did the solution to my Mathematica conundrum become clear while reading Carl Schmidt's analysis of parliamentary democracy? And why is my progress so irregular that I will sometimes go for days without thinking of any useful or interesting ideas? There must be some kind of subconscious thought process occurring... if only I could do all my thinking without actually thinking about anything!
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There has long been strong evidence that subconscious/unconscious thought is often connected to creativity both in the arts and as "leaps of thought/logic" in other disciplines. I always used to refer to it as putting a problem "on the back burner". I was well known for abandoning a conversation of activity when an sudden insight would strike me - it was the only way I finished some problem sets. It has also played a critical role in the computer modeling I've done the last 15 years. We really do not know how are minds work.