Ready for a premiere? Below you find the first guest post here on Mindcoolness, written by my good friend Vadim, a Russian-blooded mathematician and cognitive scientist from Finland.
On his blog and podcast Bats and Seahorses, he explores the intersection between art and science as well as the human nature of scientific work. Check it out! If you like his stuff, make sure you follow him on Instagram (@batsandseahorses), Facebook (@batsandseahorses), and Twitter (@seabathorse).
In this guest post, Vadim describes his creative obsession with mathematics and how he tricks himself into a flow state. Additionally, he reveals his secret technique to combat cognitive fatigue. Now, without further ado: Enter Vadim.
Have you ever been stuck in solving a puzzle? You couldn’t solve it, but you couldn’t stop trying either? It may have been a Rubik’s cube or a jigsaw puzzle. Being a mathematician means to be in that state almost all the time. It’s addictive. I have never even heard of an academic mathematician who would voluntarily stop working and attending conferences after reaching the maximum retirement age.
Doing mathematics puts me into a state of flow. When I am in this state, I am not aware of anything apart from the problem I am solving. Or at least, I do not want to be aware of anything else. If my attention is forced on something else (typical distractions are getting very hungry and someone talking to me), I get annoyed.
It has happened to me several times that I found myself in a different place without knowing how I got there, because I was thinking in between. My addiction to the state of flow started when I was very young and the reason it was important for me already as a teenager was its therapeutic aspect. I could disappear into it.
Importantly, mathematics is certain. When I was younger and didn’t know whether a girl I had met would ever call me back, I still knew that if the radius of a circle is doubled, then its area is quadrupled. Mathematics brought emotional stability into my life.
On the other hand, you are also certain that you are wrong, when you are wrong. And this can be a very humbling experience. You may be thinking for days, but if the proof is wrong, there is nothing you can do about it.
As every addiction, it has its ups and downs. Life as you know it may go by while you are in that state. So I learned to control it. Below I touch upon two aspects of that: how I get into the state and how it kills cognitive fatigue.
How I enter a state of flow
The most important thing is to have a precise problem to think about (see below for examples). It works best if it is a problem on the verge of my skillset and I have a feeling that I am close to an answer. For example, if I think that a particular technique can be applied to solve the problem, I usually can’t stop before I either solve the problem or get completely convinced that the method doesn’t work as I expected.
The feeling that drives me forward in such situations is a mixture of the anticipation of intellectual pride and a need to resolve an inner conflict. Sometimes, it is only one of these two. The inner conflict in this case is the mathematical problem itself: it gnaws at me when I have the pieces but just can’t put them together.
My last big mathematical project culminated in three months of intensive thinking. In such periods, I don’t have problems concentrating for even 10-12 hours in a row. On the contrary, I may have problems getting out of it. How not to get lost in flow is a topic for a separate post.
That state is in a way similar to meditation, and in other ways completely different. In my state, I am very focused. When other thoughts cross my mind, they get fired.
I may even trick myself into the state. It’s like the psychological finding that a forced smile can elevate one’s mood. Similarly, doing things I usually do when I think helps me to enter a flow state: When I am in the state, I often get up and start walking; so, reversely, walking helps me to get into the state. When I am in the state, I usually frown; so frowning in that particular way helps me to get there. Touching my facial hair in a weird manner and scratching my head may have similar effects.
How I kill cognitive fatigue
I cannot be in a flow state and cognitively fatigued at the same time, so getting into the state kills my fatigue. Here is how I do it.
I have a particular mathematical statement whose proof is difficult enough (for me) so that I don’t see it clearly without having to think through the steps every time. But also, it is easy enough so that I can actually reconstruct the proof in about 10 minutes. Once I do it, the cognitive fatigue is gone (unless it is overwhelming and I fail). Personally, I use the so-called Delta System Lemma, which states that every uncountable set of finite sets has an uncountable subset whose elements’ pairwise intersections are identical.
Now, don’t worry. I have a strategy that you implement without first having to study set theory for years! Every grid can be turned into a knot:
Given a grid, you just need to traverse it with a pen to obtain the knot. It requires some concentration. Learn to do it first on paper and then without—in your head. You may start with a 2×2-grid (i.e. just one square) and move onto larger ones. Doing the above 2×3-grid in my head already gets me out of cognitive fatigue in 80% of cases. (Tip: You can also use this technique to get rid of a boner. Blood goes to the head.)