Some insights into mathematicians

Keywords: social awkwardness, handedness, learning modes, conversation, methods of thinking

I’m one of the fortunate people that have always had a direction in my life (as well as to have the ability to pursue that direction). When I set off for college, there was absolutely no doubt that I would major in math. By the time I graduated I was very comfortable with calling myself a mathematician. Over the decades I have realized that being a mathematician isn’t just a hobby or vocation, it is truly a part of who I am.

I’ve been reading a book on the philosophy of mathematics. One part of one of the essays talks about characteristics of mathematicians. There were three specific characteristics that especially rang true for me; things that I’ve known about myself that I never thought about being common, if not universal, characteristics of mathematicians.

First, I have always had a difficult time with telling left from right. An example occurred in driver’s ed. At the time, passing driver’s education allowed me to get my driver’s license at 16 ½ instead of 17. So I signed up right away (unlike younger generations who are not so anxious to get driver’s licenses). At the end of the course, the instructor had the students drive around the neighborhoods where the DMV tests were usually taken. Three times in a row, my instructor told me to take a right and I took a left. He suggested I not do that during the actual test. Here is what A.V. Borovik says in Humanizing Mathematics and Its Philosophy:

“I collected hundreds of mathematicians’ testimonies about difficulties they experienced in their earliest encounters with mathematics. … The most frequent specific difficulty was telling the left from the right – for lack of logical distinction between the two.”

Let me expand on this. It is not possible to define left and right without pointing. It is necessary to define them in their relation to the direction a person is facing. The problem is that left and right are logically interchangeable, the assignment is arbitrary, and they are symmetrical opposites. This is illustrated by the handedness of molecules (their chirality). Life tends to be based on left handed amino acids while plant sugars (our food) tend to be right handed. We can’t metabolize left handed food. So, if all the right handed food became left handed, we’d be in trouble. But, if all left handed molecules became right handed and all right handed molecules became left handed, there would be no difference in the way anything interacted with each other. Everything would be just fine. The handedness is arbitrary. Because of this arbitrariness – that there is no “logical distinction between the two” – to this day I have to very consciously think about left and right.

Second, a few decades ago I was introduced to a theory that espoused seven modes of learning. (My understanding is that the basic concept that people learn differently holds up, but that the modes identified and other aspects of that specific theory do not.) So I asked myself what my mode of learning is. I settled on geometric and graph theoretic (which are not any of the original seven). I think in terms of objects and the relations between them. My doctoral dissertation reflects this in that it can be described as combinatorial geometry. (See the Art Gallery Theorem for a simple introduction.)

Borovik provides a quick summary of an MRI study (emphasizing that it is only a single study): “Our results suggest high level mathematical thinking makes minimal use of language areas and instead recruits circuits initially involved in space and number (Amalric and Dehane 2016).” Again, this is only one study, but this resonated with my personal concept of geometric learning. It is something different than audio, visual, or verbal activities of the mind.

Third, I know that I take longer than average to respond to comments during person-to-person conversations. I remember a study that looked at the length of the pause between when someone stops talking on the telephone and the other person speaks. In other words, how long is an uncomfortable silence in a conversation? What I remember is that the average pause is about 3 seconds. I figure mine is closer to 4 or 6. This was something I had to express to my girlfriend, whose average length of pause is probably closer to 1 or 2 seconds. I need to be given time to respond before the next part of the conversation ensues. Borovik describes the way mathematicians interact with each other face-to-face. Part of that interaction “includes pauses (for a lay observer, very strange and awkwardly timed) for absorption of thought…”

These insights are probably more awesome to me than many other people. But I think most people find knowing they are not alone to be comforting. Further, and more importantly, being consciously aware of personal characteristics, especially ones that create social awkwardness, can be very useful. It can allow for a dialog to help both yourself and other people develop more pleasant interactions.

(Note: the blog featured image of a man thinking about math is from the Job Monkey Blog.)