I found Poincare’s discussion of the subconscious, and the metaphor he uses to describe the subconscious to be somewhat insightful, or at least a new / fresh way to consider how instances of scientific or mathematical genius occur. Poincare stresses the importance of periods of conscious effort, “broken up” by intervals of unconscious mental play, during which the mind looks through various combinations of ideas. The subconscious effort, Poincare asserts, is analogous to atoms(which had previously been held to the inner-walls of a container) moving about in space, combining in new and unique ways. The periods of conscious effort simply alter the positions of the atoms on the walls of the container (prior to their random motion) and, later, develop further the useful combinations which the subconscious supplies to the conscious mind.
While I’m sure some instances of mathematical insight do occur in a way similar to this (perhaps so called "ah-ha" moments), I don’t think that this metaphor of the subconscious “throwing ideas at the wall” simply to see what “sticks” is entirely, or universally accurate. I think many times the intervals of so called “subconscious effort” may instead be times of rest, when the brain can escape “intellectual ruts” which may constrain thought to limited avenues during conscious effort. Upon returning to one’s work after a rest, the problem may be more easily solved because one realizes a relationship implicit in the work, previously unrecognized. I don’t deny that rest and subconscious “thinking” play a crucial role in organizing and consolidating data, and in “outside-the-box” thinking; but, I think Poincare’s theory of the subconscious mind as some sort of super-computer, which can work through unlimited combinations before finding one which appeals to the conscious mind’s aesthetic sense is a bit of a distortion, or at least somewhat extreme.
I do, however, agree with Poincare's emphasis on the need for discernment in mathematics. I think discernment is a tool which is invaluable in any discipline, particularly in mathematics and the natural sciences. In mathematics, as Poincare asserts, there are, indeed, so many possible relationships between ideas, theories, and concepts. A computer could, theoretically, list every possible relationship; but, it requires the very human quality of discernment to determine which ideas are useful, and which are most applicable to whatever it is that is being studied. Similarly, in the natural sciences, there are perhaps infinite numbers of different hypothesis or questions which could be posed and a similar quantity (if not more) of data which could be collected. Again, one requires discernment to determine the “right” questions to ask and the types of data which should be collected and analyzed to answer the question(s) at hand. In other words, these sorts of endeavors require a very deliberate effort, which a computer could not accomplish.
Finally, I noticed some commonalities in theme between the two texts, which I think are worth mentioning. Both authors, especially Hilbert, stress the simplicity and elegance often found in mathematical results, as well as the fact that simplicity and rigor need not be mutually exclusive in proof, nor in defining mathematical problems. These ideas, I believe, are widely applicable, particularly in fields dealing with or relating to education. If we can define problems and results in such a way that they are accessible to more, without sacrificing the rigor of definition or depth of contained information, mathematics may become a discipline which appeals to more and which encourages greater pursuit of its problems.
I also agree that the idea of the unconscious mind being a supercomputer is not necessarily the case. I remember my AP Biology teacher in high school saying that the brain can only process two hours of information about a topic before shutting off and not taking up any additional facts. She wasn’t telling the class that during our study break we would magically be able to understand how something like cellular respiration worked. Her emphasis was that, as you said, we need time to unwind some and file everything away in whatever file cabinets we have in our minds. This also somewhat ties in with people saying that they “need to sleep on it.” Essentially, people mean they need time to think it over, but a lot of times people will actually sleep and make a decision in the morning about which they feel more confident than had they made the decision the night before, regardless of if it would have been the same decision. I know the capacity and function of the unconscious is just a small portion of the readings, but the mysteries of what goes on in our unconscious mind are intriguing. It is said that humans only use 10% of their brain capacity at any given time. Do we use more when we are sleeping or involved in other activities that stimulate the unconscious mind? If so, what sort of implications does this have? At some point in the future, will we able to implant thoughts into the mind and have critical thinking processes take place while we sleep? Will it ever become like the world in Inception, where there are a million things going on in a dream within a dream within a dream?
ReplyDeleteAlthough I do agree that the subconscious mind is not a supercomputer, sorting through numerous combinations or ideas to find one that appeals to the conscious mind’s aesthetic sense, I think there is a lot to be said for subconscious activity. As suggested by Henri Poincare, subconscious ideas most susceptible to becoming conscious "are those which, directly or indirectly, affect most profoundly our emotional sensibility" (Poincare, 694). For this to be true it would seem a high level of desire to find an answer is necessary. Obviously, taking a break from a problem allows an individual the opportunity to escape the complexities of the problem and the flaw(s) of their solution. When returning to the problem the person may be opened to a new perspective or recognize a mistake. One of my professors once said, “When you are given a hammer, everything looks like a nail.” This suggests we are eager to use what we know at the given moment to solve the problem at hand. So recognizing the problem and having an approach to solving it doesn't equate to a solution if the approach is flawed. Often it is difficult to come up with alternative approaches or ideas in one sitting. In this way I agree that subconscious work, assuming it takes place, is only beneficial if followed by more conscious work.
ReplyDeleteThis then perhaps ties into Hilbert's belief that, clarity and ease of comprehension attract while the complicated repels us. Does the subconscious cater strictly to clear ideas, only presenting the comprehensible to the conscious? I think this goes without saying. I find it irrational to think my subconscious could or would submit a complicated idea to my conscious (seems counter productive and may suggest multiple personalities). I think it is fair to say that, although the subconscious does go to work occasionally during a conscious break, the conscious is the workhorse of the mind and is what allows for subconscious breakthrough in the first place.
Though as mentioned above the subconscious discussion only refers to a portion of the reading, I do find this conversation fascinating. Do we deny the analogy of our mind as a supercomputer because we are uncomfortable with thinking of ourselves as complex machines?
ReplyDeleteSitting here thinking about it, our thought process is very analogous to the binary system of a computer. The turning on and off of synapses at different times correlates with idea connections, resulting in the final product of a user interface in the conscious thought.
Now imagine that we think of mathematics as an innate truth slowly waiting to be uncovered, an idea relevant in several reading thus far including Hilbert's. That means the decisions we use to connect mathematical concepts into a principle or theorem were already decided for us, we just had to put the right puzzle pieces together. So in this view we are using an electrochemical system of synaptic switches to uncover patterns evident through experience that is programmed into our mind via memory. And what is "spit out" is already decided because mathematical truth is native to this world. This seems very mechanical.
Now while I am certainly on the opposing side of this argument due to the complexity of emotions, altruistic behavior, and the irrational acts, I do not dismiss it lightly but do continue to consider its validity.
I have to agree that our minds are similar to super computers. The necessity of having time to mull things over, especially "sleeping on it", reminded me of the studies they have done on REM sleep. It has been found that REM sleep is the most important cycle for the brain to sift through the information of the previous day, and catalog it in our brain so that we may recall it better later. Jason, I really like how you described of the analogy of the brain to the super computer.
ReplyDeleteWe were actually just talking about freewill in my Motivation and Emotion class just now, and how participants in a study were primed (their first task to unscramble neutral or help related sentences) and whether or not this external stimulus led to a helpful behavior after the study was completed. They found that those primed with unscrambling helpful related sentences were significantly more likely to help the experimenter when he dropped his pens than those in the neutral primed group. The idea behind it was that our subconscious was primed to be more helpful after the task, and even if we were asked why we helped, and we might say that it was because it would be a nice thing to do, it was actually the external stimulus (something out of our control) that motivated the behavior. This tied in with Poincaré's idea of the subconscious leading our thoughts, like the super computer, and I was wondering, does this supercomputer/subconscious thought idea lead you to wonder how much freewill we actually have? Are we just led by our subconscious to believe that we have freewill?
Everyone who's worked on hard problems probably experienced the phenomena when they just can't get it no matter how hard they concentrate on a problem. But the next day, while taking a shower, you get an "aha!" moment where the answer seems to just pop up in your head without any effort.
ReplyDeleteI think in psychology, it is called the eureka effect:
http://en.wikipedia.org/wiki/Eureka_effect
I think it is the best when we just let our subconscious work on the hard problems while we go on with our day.
Even the guy who wrote the proof for Fermat's last theorem would routinely go on walks so that his consciousness would work on it.