Fuddland
The three-body problem is a classic question in mathematics, usually posed in an astronomical setting, with its solution describing the motion of three masses of various size [a star, a planet and a satellite of the planet, for example]. Unfortunately it’s generally not possible to solve the problem precisely, so one needs to use numerical methods [that is, use a big computer] to work out approximate solutions. The fact that there is not a quick and easy solution has profound repercussions on everyday life, as I recently found out.
After failing to produce any dramatic physical results with mental workouts, I took the controversial stance that the only real way to get fit is to do some exercise, so I decided to take up jogging. I’ve never really got on with running, traditionally preferring to stand for an hour in the rain waiting for the next one than run for a bus that’s about to depart, but the need to do something active coupled with the [perhaps greater] need to not spend my rapidly-waning grant money on a monthly gym subscription meant that regular running seemed a viable option.
Thus I’ve taken to the streets most evenings for the past few weeks, doing short runs for now until my body realises that this isn’t some bizarre anomaly in my otherwise sedentary life. I’m usually out sometime between six and eight in the evening, taking advantage of the darkness to hide my wheezing, red-faced form from the general population, but I do still encounter a few pedestrians, and here’s where the three-body problem rears its head.
A lone pedestrian is no bother: they are especially conscious of other people approaching them and there is enough pavement for the both of us, so I can pass them without a problem.
Likewise, a couple walking along present no real issues: there being only two of them means their gait is fairly uniform [they match their strides to one another]; they are usually engrossed in conversation so perhaps not as aware of others as someone on their own, but again, there is enough room for me to bound past them without difficulty.
When three people are out together though, it’s a different matter. With three people, it’s much more difficult for them to match stride with one another, so their pace becomes more variable. There are not enough of them to split into smaller sub-groups, so they walk abreast the whole pavement, and with factors such as personal space involved, they rarely walk along in a straight line — they weave and cross paths with one another. As Poincare’s work demonstrated, it’s tantamount to chaos, and so it makes jogging past without incident a bit of a problem.
In my first example, three teenage lads were walking and chatting, and I saw them from quite far back so you’d think I’d have time to figure out my clear passage through, but as I approached their individual paths seemed to become more and more eccentric, and as I closed in on them they stopped abruptly, standing across the pavement and beside a tree, forcing me to attempt a daring sideways maneouvre through the slim gap between the right-most one of them and the tree, with an added, breathless, “Excuse me!” thrown in for good measure.
The second example was much more complex: I came across the three bodies, three twenty-something men, as I rounded a corner so had no time to even attempt to figure out a path through the group; two of the three were on bikes, but of course since the third member was on foot, the others were neither riding properly nor were they pushing their bikes as they walked — they were using the very unstable riding-at-walking-speed technique, involving much wobbling of the front wheel and falling to one side fairly often. I attempted to give them fair warning of my approach with the classic “heavy footfalls, I’m running up behind you, you’d better watch out I might be coming to hit you” style of running, but of course they had the collective confidence of three young blokes and paid no attention to noises around them that might otherwise be sounds of impending danger. Thus I again resorted to the sideways-body trick, this time sliding between one cyclist and the pedestrian. Unfortunately this caused the cyclist to brake sharply with surprise and almost go over his handlebars. With further, quite unexpected agility, I managed to turn around, give a few apologies and ask if he was okay, then resume my run when he said he was fine, all without breaking my stride or falling backwards.
These situations would be entirely avoided if one could quickly and accurately solve the three-body problem in one’s head — a clear and compelling demonstration of the need for mathematics research to continue unabated.
[This has been a partly political entry on behalf of the Holy Crap Have I Really Only Got Three Months Of My PhD Left Can I Have Another Extension Please? Party.]
Comments
imogen | 2004 / 12 / 11 – 20:30
ah, ha. i think what you need here is a little help from the laws of motion. think about the law of inertia and frictional forces as you approach the problem of the bodies and three and then shout as loudly as you can: on your left! then, if they don’t get out of the way, it’s only proper jogging form to knock them straight over and keep kicking up heels.
David | 2004 / 12 / 11 – 21:30
Re #1: Heh, I might just try that — I used to use a similar technique on the seven-mile bike-ride to work along the shared cycle/joggers’ path on Nantucket Island, but I don’t think it’s a recognised warning in this country.
I could try a variation and shout “I’m left-handed!” — they should jump right out of the way for fear of being pummelled. ;)
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