Is making a decision the same thing as making a choice? I don’t really know for sure. However, I DO know that if you were to rank my skills in order, relative to the manifestation of those skills in the general population, decisions and choice making would be pretty low down the list. Probably even lower than, say, keepy-uppy. I mean, I can usually manage two or, possibly three, keepy-uppys. And some people can’t manage more than one. What I am trying to say, perhaps with more verbosity this is strictly necessary, is that I am rubbish at making decisions.
For example, yesterday I was in Tesco’s attempting to choose between an aerial booster and an aerial extension lead. These seemed to be the natural options when it came to linking my TV to a too-distant aerial socket. I dithered so much that in the end the security guard, when convinced that I wasn’t loitering with intent to shoplift, said ‘Buy the cable; that’s what I’d choose’. I accepted his decision with gratitude, to his obvious amusement, and the purchase was made. The amazing thing to me was that his decision was made instantly; whereas mine was plagued with what-ifs, withertos, wherefores and other slightly obscure English terms.
I have a couple of things in common with one of my intellectual heroes: the great Ed Witten. First, we both were theoretical physicists between 1994 and 1999; second, I am told, that we are both unskilled in the art of mundane decision making. I remember with pleasure reading the story, according to his wife, that the great Witten was unable to choose between models of exercise bike, whereas he was able to be the most brilliant mathematical physicist ever to have lived. (For point of clarity I wouldn’t even consider comparing myself mathematically against people such as Witten, although I do wonder if I might hold my own against any of the greats in an indecision contest).
The problem with mundane decisions is that they are so complicated. Taking my recent trial in hand, the factors coming into a cable/aerial purchase are almost overwhelmingly complex – there are so many ramifications of any particular choice. If you try to track any of the decisions to its causal conclusion then either: checkmate occurs, and one of the decisions is ruled out (this one rarely occurs,it seems to me) OR: stalemate occurs and the problem becomes similar to a dog trying to pick up a large ball with his jaw: there is no obvious way in.
Anyway: decision-making, a problem many mathematicians have trouble with.
Some are extraordinarily good at making decisions because they have algorithms for making them: For example “Which socks?” “I never wear socks.” or “Which route will you take” “The shortest route according to road distance” or “Are you coming for tea?” “No – I will go for tea at 3:45, as usual”
Some, like me, are extraordinarily bad at decision-making. Such people usually attempt to analyse any decision carefully before choosing. For example: “Tea or coffee” [hmm, not sure. What time is it? How many coffees have I had? Is the tea better than the coffee? Who is making it? Are they likely to make it well? Which cups are available? What sort of milk is there? Do I fancy some sugar? Who is having what? Is there anything to accompany the drink, such as chocolate or a biscuit? Do I, in fact, fancy either a tea or a coffee?] ” Erm. Yes.”
Both of these decision making systems have their strengths and flaws. The first is good for Rapid Decision Making, the second is good for Very Important Decision Making. However, the first system fails when a situation arises for which the decision-maker’s collection of algorithms do not apply. Something novel has arisen, such as: “Do you think that the sunburnt-orange or the burnished-mocha brings out the colour in my eyes better?”. The second system, unfortunately for me, fails almost all the time: “What do you want for tea” “Erm”; “What time do you want to leave” “Erm”; “Which shoes do you like” “Erm”; “What film shall we choose” “Erm”. “What shall we call our child” “Erm”.
Actually, thinking about it, mathematical activity as a whole is a bit like this. Some problems are algorithmic, clearly defined, and linear; others are broad, ill-defined and non-linear. I like the second. I love taking a really hard, ill-formed problem and hacking away at it until the essence of it remains. I don’t like anything systematic; for others the converse is true.
It seems to me that it is possible to take a philosophical stance on decisions: Is a non-random, rational decision always possible? Mathematically we can model a decision as making a choice in a particular situation: for any given situation we could craft a set of possible choices; the decision is to pick one of these choices. More generally we could consider a humongous set S of all possible situations, along with all possible choices for each member of S. If it is possible to make a decision then we must be able to determine some method of assigning a choice to each member of S. The size of S and the sets of associated choices is somewhat mind-boggling. Could we always choose in principle? This is not a trivial matter, even if the sets are cleanly and mathematically defined.
Fortunately, mathematicians have thought about this in great detail and, it turns out, there are in fact two versions of mathematics: the first in which choice is always possible and the second in which choice is not always possible. As a mathematician you need to choose between ‘Maths with the axiom of choice‘ and ‘Maths without the axiom of choice‘
I prefer the second. It makes me feel better when failing to decide between tea and coffee. Oh, go on. Will you choose for me?