The Urge

About a year ago I wrote:

I’ve accepted long ago that my mind latches onto ideas with a terrible grip and it’s inevitable that something that I’m currently spending time on will overwhelm my concentration, to the detriment of all other tasks and thoughts.

I’m starting to realise that I can predict when this will happen. It usually happens when there’s a natural lull in my work, such as the time just after completing a paper or finishing off some code. In the quiet time when my brain starts asking and wondering “What’s next?” I’ll queue up a bunch of possibilities and regardless of the order of their priority there’ll sometimes be one that simply overruns my thoughts. I’ll be able to picture in detail the stages of the task and exactly how to get started and an urge to get working on it; generally I find that there’s no point resisting at this stage and I’d better drop everything to focus on this one thing.

If I don’t drop everything (and attempt to work on what is most important rather than what is most motivating) I’ll generally start drifting into the fun work anyway, in and out of work hours, and it’ll slowly take over; in the meantime, I’ll have been attempting to multitask between a motivated task and an unmotivated one and generally not been as useful as if I’d concentrated on the former alone.

(Of course, there’s always the backlog that accrues during a time of blinkered/focussed working and it’s never fun to sort that out after emerging for breathe. Still, it’s often from the backlog that the ideas for what’s next? emerge.)

I think that learning how to transition continually between these focussed tasks is really the goal of productive work. It’s the dead time in between that’s soul-killing, when you finish a week or a month or a season and ask yourself “What have I been doing all this time?”.

Brief comments on: Everything and More (2003) by David Foster Wallace

I don’t really intend to go on for too long about Everything & More, D.F.W.’s book about the history and philosophy behind infinity and maths. Suffice it to say that you’ll either like it or not depending primarily on two factors:

• Like: If you are a D.F.W. fan (which counts me in)
• Dislike: If you know a lot about the subject matter (i.e., you’re a set theorist–mathematician yourself, which counts me out)

This is assuming, also, that you’re the type of person who likes to read either unique works of literature and/or popular science–type things. Without a fairly good working knowledge of maths, be prepared to work hard to follow along with a good proportion of the book that’s dealing with technical content; it’s not impossible, however: the friend who lent the book to me managed to get through without much background knowledge.

Apparently there are a certain number of technical inaccuracies, or elements of the story that are simply wrong. I’m not one to judge these; (the only error I ever saw was a basic oversight-style typing mistake in a big list of examples of the application of differential equations (or something like that) in which was written F = m dx/dt) but it’s easy to find numerous critiques of the book in which the technical content is rather heavily denounced. However: It doesn’t matter. First of all, in some cases I’m sure D.F.W. was aware of some of the technical problems his popular descriptions required. He admits as much quite early on. But secondly, this is not a book to learn set theory in a mathematical sense. Just as you read Gödel, Escher, Bach to get a taste of some rather meaty mathematics in the context of a much broader philosophical discussion, Everything & More does a truly excellent job elucidating how all the things we learnt in school & university about abstract ideas such as irrational numbers and limits tending to infinity really were huge mathematical/philosophical problems back in the day and we should do better than take them for granted.

The best example of this is the way anyone’s who’s done a little university-level maths can reject Zeno’s paradox by their being taught about convergence of infinite series. How can you cross the road if you first have to reach half-way, and before you reach half-way you must reach the quarter-way mark, and before that get to one-eighths of the way, and before that one-sixteenths, … , ad infinitum? Anyone who’s studied the maths “intuitively” knows that this particular infinite sum equals one, q.e.d., but this result requires them to have already abstracted in their head the very idea of an infinite sum itself as something that is actually possible. It’s not exactly easy to explain how this works without using terms like “tends towards infinity” that a priori assume that infinity is an abstract concept that can be used to explain infinite sums. The formulation of a rigorous (explanation of a) proof is sort-of the main goal of the book (plus fleshing out a good amount of material about how this happened historically, and a number of consequences of what effects this had on the mathematics of the time leading into the current era).

This is a book about how some certain results were discovered, with a sufficient explanation of those results to expand your mind a little or a lot. And like all of D.F.W.’s writing, even just going along for the literary ride is well worth the effort.

Dean Allen on philosophy of self

In explaining something he did about something he made, Dean Allen writes:

I’ve spent the past year or so reading and writing and doing my level best to chip away at 40 years of belief in the logical fallacy that one’s identity meaning – self-worth, self-image, whatever you want to call it – can accurately be measured in the thoughts of others. Much as you and I may enjoy being encouraged through recognition and praise and dislike being saddened by rejection or indifference […], deriving personal value from these transactions in the absence of a well-formed internal frame of reference through which you can decide on your own what does and doesn’t work, and subsequently accept the opinions of others as feedback, is just plain faulty thinking, of the sort that makes otherwise capable, centred people all loopy and weird.