Why Math? Flow

One of the greatest mathematicians of the 20th century, Paul Erdȍs, had a favourite response to the age-old question of the meaning of life: “to prove and conjecture.” While this might seem quaint, or naïve, an answer befitting such a unique and colourful character, maybe he wasn’t so far off.

The quest for the meaning of life is closely related to the pursuit of happiness. However, happiness is much more versatile a concept than what our day-to-day use of the word would suggest. One of the many biases that are inherent in our way of seeing the world is called future discounting (though similar concepts go by many other names), which roughly means that we tend to ascribe more importance to our present feelings and state than to our future feelings and state. This is the reason behind procrastination. The ancient Greeks called this concept Akrasia, and Aristotle was one of the firsts to conduct a thorough philosophical analysis of this concept. The human condition is such that even though we all know it would be better for us to exercise regularly, eat healthfully, and perform our tasks promptly, very few of us do any of those things consistently (not to mention all of them). This schism between what we know would be “better for us,” and what we actually do is the reason for separating happiness from pleasure.

Aristotle advocated the eudaimonic life, which roughly translates as “human flourishing.” The purpose of life, the meaning of happiness, is the creation of a good project. A life well lived and full of meaning is a life that has successfully created a good project – one would like to look back at the end of one’s life and judge that it has been a good project, a good life.

Modern thinkers have identified this craving for meaning as a fundamental motivation of human actions. People are willing to disregard pecuniary incentives and choose a lower-paying more meaningful vocation over a higher-paying one that is less meaningful to them. It is also the reason for the taking-up of hobbies, and crucially for our discussion, for the strive to master one’s hobby – to develop expertise and become better.

Many positive psychologists maintain that the drive for mastery and self-actualization is the key to understanding human optimal experience. This optimal experience has been dubbed flow by Mihaly Csikszentmihalyi, a modern pioneer in this subject. In simplistic terms, flow is a state of complete immersion in a task or activity, where the entire world disappears, when even you disappear; there is only the activity – your entire being is completely focused to the exclusion of every other consideration. Many gamers have experienced this or a similar feeling. It is often reported in serious sports activity, and consistently so at the high-levels of strategy games like chess. Some educational research even suggests that it is manifested when you “lose yourself in a good book.”

Flow is an intoxicating and euphoric state. Many professionals and amateurs, in all fields of activity, constantly try to bring it about.  However, Flow is hard to achieve, something to strive for. Only by continually trying to push yourself, go beyond your current limitations and attain new heights, could you hope to experience such a state. Csikszentmihalyi has a famous diagram that illustrates his theory of flow as being a perfect balance between the skill-level of the performer and the challenge-level of the task at hand. Therefore, this intensely pleasurable state could theoretically be experienced by engaging in virtually any challenging activity over extended periods of time, while trying to adaptively develop the appropriate skills to meet the challenge.

Flow is a perfect balance between skill-level and challenge-level. [Image credit: Wikipedia.]

I do not know any other activity that is as flow-conducive as mathematics. Ask practically any mathematician what first drew them into math, and they would probably describe a flow experience – usually in the form of a difficult problem successfully solved (this is often the turning point). Mathematics is an Ali-baba cave of puzzles, teasers, riddles, conundrums, mysteries, paradoxes, and enigmas – there is something for everyone, at all levels. This richness means that it is always possible to find a challenge that would perfectly balance your skill-level, inducing a state of flow.

While flow is supremely enjoyable and may be inherently valuable, it is also extremely significant for its role in improvement. The desire to attain flow is a contributor to the intrinsic motivation to improve. Furthermore, flow is also a sign both that improvement has occurred, and that further improvement is about to take place. Thus, flow is intimately related, on many levels, to our self-actualization mastery-driven projects. Csikszentmihalyi has famously written that “[o]nly through freely chosen discipline can life be enjoyed and still kept within the bounds of reason.”

This freely chosen discipline was also Aristotle’s answer to the Akrasia problem. Only through consistent work (slow and steady) can we overcome our natural future-discounting bias, and work toward building a meaningful life. A meaningful life, therefore, is a life of striving toward a worthwhile goal, thereby constantly improving ourselves.

In many mastery-driven activities, the attainable skill-level is socially bounded. In competitive sports, for example, it is very clear what an ultimate level of achievement is. In the rare event that such a level is attained, it is unclear where to go from there – it would seem that the project is finished, the objective achieved. This may be the reason for the famous post-competition depression among elite athletes. Mathematics is different in this respect. Solving an interesting and difficult problem simply leads to many other interesting and difficult problems. One can always strive higher, always dive deeper, always develop one’s skills further – math is unbounded, an infinite frontier.

In conclusion, the optimal-experience of flow is one of the strong motivations for taking-up mathematics. The drive for mastery and self-actualization then pushes forward and propels one to scale new heights. Eventually comes the realization that mathematics is an unbounded terra incognita, full of treasures. Thereafter, this land of mysteries forever beckons, promising the opportunity to forget oneself in the flow of a new adventure. By that time, one has come to include math as part of one’s life-project and engaging in it enriches and provides more meaning to one’s life. Some are so stricken with it that they even come to make it the central project of their lives, thereby concluding that “the meaning of life is to prove and conjecture.”

Math beckons…

[Imported from my now defunct blog 10,000 Hours of Mathematics.]