Sunday, May 3, 2015

Flow and Grothendieck-like Problem Solving

Flow: a pleasant, efficient, focused state of mind.
Alexander Grothendieck: revered mathematician living between 1928 and 2014 who had an unusual approach to mathematics.

The idea that being in a state of flow is desirable for computer programming is now commonplace; good information on the nature of this mind-state and techniques for inducing it are more sparse. My idea here is that the meditative mind-state and flow are one and the same—which I suspect is uncontroversial. From there, however, I'd like to address a general problem in learning how to flow at will, which I think can be made more clear by analogy to a style of problem solving that Grothendieck was especially known for (not that it was unique to him by any means, but it seems to have been a sort of trademark because he took it to such extremes).


After spending years dealing with a computer-related repetitive strain injury, I found that using computers was not the same even after I’d resolved the physical component of the problem. Eventually, in trying to discover the source of the problem that remained, I came across the notion of ‘flow,’ which instantly connected with certain common occurrences from my pre-injury programming days. Recent occurrences of this state were utterly absent; and, in fact, the more I thought about it, the more sense it made that my current problem in using computers could be clearly characterized as ‘anti-flow.’ If there’s some axis in the space of mental states where a large positive value indicates being in flow, my problem was that I had a large negative value on this axis (such an axis could sensibly be named ‘acceptance of things as they are’—which will make more sense by the end of the essay). So, my interest in flow began.

Reading more, it would’ve been difficult not to connect this concept to the ‘meditative mind-state’: a state in which all experience is accepted as okay, lacking in self-awareness, and characterized by direct interaction with the objects of experience. The opposite involves the heavy presence of meta-thought, analyzing what one is doing as one does it. 

Reading more, I discovered this excessive meta-thinking is basically synonymous with anxiety. This makes intuitive sense: you meta-think about something you’re doing when you think there might be something wrong with it. And, being in a state of flow, characterized as behavior lacking meta-thought, has an intuitive reason for being more efficient: it’s like the difference between running a procedure encoded in software, executed on a general purpose chip—and having the procedure directly represented in hardware. In both cases you have this trade off of efficiency for mutability. Further, it makes sense that flow would be enjoyable and meta-thinking not: anxious experiences are unpleasant ‘by design’—they encourage the experiencer to change something, to get out of that mode; by contrast, the more you’re able to stay in a state that doesn’t require meta-thought, the better things must be going for you, and your mind rewards you.

So, in order to resolve my computer use issues, which I could now more usefully state as, “in order to move toward Flow on the ‘Acceptance Axis’” or “in order to reduce anxiety while using computers”—I could draw from methods in Western psychology, or Eastern philosophy. I have explored both and both have been useful. Ultimately, however, the literature surrounding Eastern meditation practice and, to a surprising extent, life perspective—was the most directly applicable. Isn't it strange, though, that 'life perspective' should concretely affect my ability to engage in some activity? I thought it was, and I spent a lot of time thinking about how that could work. Here's how I think of it now.

‘Life perspective’ is another way of referring to the conceptual framework in which one thinks, their total set of Schemas, the conceptual categories available for organizing experience and the rules relating those categories. Just to give an idea the kind of thing I’m talking about, I’ll give two ridiculously stripped down, simplified examples of personal conceptual frameworks.

(1)I am an autonomous entity with a fixed set of actions and senses. I exist in a universe made up of small objects that follow fixed rules. I am made up of these objects. After a certain duration I will cease to exist. While I exist I will experience some things that are good and some that are bad, and the proportion of good and bad experiences will depend in part on my actions.

(2)I am an eternal soul that can suffer or feel joy. Temporarily I exist in a ‘physical’ universe, and depending on the moral character of my decisions while here, I will suffer or feel joy eternally afterward.

One’s ‘life perspective,’ as a framework, provides a special kind of vocabulary—a set of terms to make statements 'in terms of.' What makes this kind of vocabulary special is that it provides terms that could be ordered based on how general or particular they are, where the more particular terms are arrived at by supplying parameters to the more general terms. For instance, if you say, “the most fundamental things in existence are ‘physical entities’,” then you have the general term ‘physical entity,’ and everything else in your framework must be expressible as some parameterization of that general term (e.g. "that is a physical entity with location X, Y, Z, smelling like W, with color R". So, the more general a term is, the more other terms are potentially impacted by it. This is the same as in any framework, and modifications to these very general terms are what we call 'fundamental' changes. In science, such changes are often called ‘revolutions’; they are how we change ‘paradigms’ (this is Thomas Kuhn’s popular terminology anyway), rather than elaborate the present one. These changes of very general framework terms are also what take place in significant software refactors; they are what determine whether you work with elegant structures, or whether you become an expert in the application of duct tape. 

Personal ‘life perspectives’ are this same way. Incidentally, this is why some people are so interested in metaphysics: it’s a field explicitly addressing the most general structures of personal conceptual frameworks or ‘life perspectives.’ But what difference does it make if you personally have one framework or another? Consider the difference in behavior that results when someone really, truly believes that an afterlife with eternal suffering or pleasure exists and they’ll go to one or another based on their actions, or if someone were to believe that people are essentially robots with no real experience of pleasure or pain. Or, if someone were to believe that all of the universe, including all of humanity, was truly one indivisible whole, so that it becomes meaningless to say "this part of the universe is me, that part is not"; is selfish behavior possible if you deeply believe this? Is fear of death or any form of material loss? Those are extreme examples, with extreme consequences for adoption, but: people's beliefs, their conceptual frameworks (the true contents of which are actually quite hidden from us!), have a pervasive influence not only on how we behave, but on how we interpret our experience.

Let's switch to Grothendieck for a minute. I’ll quote from Pierre Cartier’s essay on him:

Grothendieck’s favorite method was similar to Joshua’s for conquering Jericho. One must seize the place by sapping it; at a certain point, it succumbs without a fight. Grothendieck was convinced that if one had a sufficiently unifying vision of mathematics, if one could sufficiently penetrate its conceptual essence, then particular problems would be nothing but tests that no longer need to be solved for their own sake.” -Pierre Cartier, “A country known only by name” (

This sounds like the same wisdom we hear about refactoring in software: you can change the framework so that the problems within it are easy, or you can work hard solving the problems in the framework. Here’s another quote on Grothendieck's approach:

My friend Bob Thomason once told me that the reason Grothendieck succeeded so often where others had failed was that while everyone else was out to prove a theorem, Grothendieck was out to understand geometry. So when Grothendieck set out to attack the notoriously difficult Weil Conjectures, the goal wasn’t so much to solve the problems as to use them as a test for the philosophy that if you generalize sufficiently, all difficult problems become easy.” -Steven Landsberg, “The Generalist” (

Okay, back to meditation for a minute.

If you try to meditate, you are immediately faced with a problem: “how do I go about intentionally doing something which requires that I do nothing?” If you try to get into a state of flow, you will run into the same problem: it’s characterized by effortlessness; you don’t monitor your actions and decide beforehand which to take next; it's often described as a cognitive mode where you act without taking actions (non-paradoxically: acting without consciously choosing your actions). In the terminology of Taoism, this is called ‘wu wei,’ or ‘non-action.’ To be in this state is a normal part of human experience; it 'just happens' under all sorts of circumstances. The intentional cultivation of wu wei, or flow, is important largely because circumstances often act to prevent it—and if your environment is particularly stressful, those circumstances may be ever-present.

Here's the problem in another form: if practice as a general human activity requires monitoring performance and making corrections, how do you practice the skill of non-monitoring, or intentionally avoiding meta-thought? My proposal is that all valid forms of solution use a Grothendieck-like method, restructuring one’s personal conceptual framework, so that there's nothing to do when it comes time to 'practice,' and yet, in time, you do improve. By contrast, normal practice consists in monitoring yourself as you take some action, then revising your way of taking the action and repeating; this is like proving individual theorems within some existing framework. 

As an example of the framework revision approach: one of the first things one learns when studying Eastern frameworks is a formulation of ‘self’ that differs from the typical Western conception: we think of it as what’s often called the ‘ego’ or the ‘will’—that which decides; but if you think that your most essential identity is the part of you that makes decisions, how are you going to take actions without deciding to take them? Interestingly though, it seems that, most often, the ‘insights’ leading to fundamental personal conceptual revisions are derived from direct, personal experience. Regarding one's conception of self: if you consistently experience yourself doing things without consciously deciding to do them, while still feeling that it was yourself doing them, you are collecting data that implies the ‘ego’ or ‘will’ is too narrow a definition of 'self' and you're inductively led to a revision. So, in this way, meditation is a sort of strictly empirical metaphysics. I think the efficacy of the empirical approach is what makes it possible for Eastern philosophy to not philosophize, rather insisting on non-conceptual approaches. 

When starting to learn to meditate, one inevitably imagines the process will be similar to other things they’ve learned before and they generate all sorts of images of what success would look and feel like; they imagine that they’ll one day be able to say, “now I’m going to meditate” and they’ll begin using this skill called ‘meditation’ that they’ve developed. My understanding is that, in actuality, you will have learned no skill whatsoever; you will have just changed your understanding of self and life so that you arrive at ‘nothing needs to be done’ (where 'be done' refers to intentional action) in more and more situations. Alternatively, it could be said that you more often find yourself in a state of mind where “it’s not necessary that I do anything, but it’s okay to do things if I like,” which is probably also a description of being in the mindset for ‘play.’