Hooptedoodle #350 - Strategy for Catching a Bus

This morning I was half-listening to the radio, and there was a phone-in discussion going on about people's private rituals - things they do every day as part of their lives, in that strange cross-over area where planning and commonsense checks start to shade into superstition and even obsession.

There were a lot of predictable items - one guy plays football in his local Sunday league - he always bends down to touch the grass as he walks on to the pitch - this is because his team once had an unexpected win in some competition or other, and since then he has come to believe that if he fails to touch the grass as he walks on then things might work out badly. In other words:

(1) it's become something he does on a regular basis

(2) it might do some good - OK, maybe unlikely, but it does no harm, so the safe bet might be to carry on doing it.

We probably all have a few of these wrinkles, though we might choose to claim that there is some rather more straightforward explanation. I always carry my penknife and a couple of guitar picks in my left-hand trouser pocket. I know where to find them, I can tell straight away if I've forgotten to pick them up from the tray on the bedroom chest of drawers - it's OK - it's a habit, but it's conscious organisation. You bet.

I knew a fellow years ago who played soccer to a decent amateur standard, and he always used to wear his "lucky" vest under his team jersey. He would claim that he was not superstitious, but panic would arise if he found his mother had this vest in the wash on match-day. The vest, by the way, was a total wreck, he had been wearing it since school. It was a relic.

When I was a kid, my dad, when he closed the front door, would tug the lock 10 times to check it was locked. If anything interrupted this procedure, he would start again. One morning (to my ecstatic, though secret, delight) he broke the lock. He would have maintained that he was checking the lock was secure, to keep his family and his possessions safe. Other opinions did exist.

Anyway, to the point. I was reminded this morning of a little conundrum that bothered me for years - not because it was a problem, but because it seemed there was an obvious need for some sort of simple strategy and - though you would think that such things were capable of numerical analysis, I never really managed to think it through.

Let's go back to the 1980s. At this time I lived in Morningside, a suburban district on the south side of Edinburgh, and I worked for a financial institution, whose offices were bang in the business centre - near St Andrew Square.

Each working day I would set off from home on my walk to the bus stop. It was about a mile to the bus stop - for the last half mile of this walk I had a straight view down to the main road ahead, crossing at right angles, where the buses I needed would pass from right to left.

These days the Edinburgh buses are a different proposition altogether - they have computer displays at each stop, which show you which buses, for which routes, are coming, and when they will be there. Everything is monitored. In the 1980s, the best I could do was to have a copy of the timetable on the notice board in the kitchen - I knew the times by heart, of course.

The problem was this last half-mile, during which I could see the bus route in the distance.  Now - a quick ponder on the nature of bus travel:

Suppose the buses ran every 15 minutes at this time of the day - officially, there might be a bus from my stop at 7:30am, 7:45am etc. Now, the traffic was heavy on working days, and the buses did not run on time - this was not any kind of symmetrical distribution - since the drivers got into trouble if they were early (because passengers would miss the bus), the buses would tend to be late. If I left home at 7:05, say, and it took me 20 minutes to walk to the stop, I would arrive five minutes before the 7:30 was due. Thus I might catch the previous bus, if it were running late, I might even, on rare occasions, be in time for the bus before that one, if it was very late indeed. Failing this, I should be in time for the published 7:30, though it could really turn up at any time after 7:30. The safest approach was to just assume that there was an irregular stream of buses, and that their arrival was pretty much random.

Right. So about 10 minutes after leaving the house I would get to the point on my walk where I could now see the buses passing, in the distance, and I would be able to see them from that point on. If a bus passed, I might be able to hazard a guess what official time that bus was supposed to have arrived, but it was not a particularly useful thing to think about during the final ten minutes' trek to the stop.

When I was still half a mile from the stop, if a bus passed, up ahead, then I would just shrug it off - it wasn't a bus I should have been on, the behaviour of subsequent buses was not affected in any predictable way. As I got nearer and nearer to the bus stop, this started to get more pressing; if a bus passed when I was, say, a hundred yards short of the stop then that would be a bit irritating, since a quick dash would have enabled me to catch that one. So the passage of buses at the end of the road became more important as I got nearer to the stop. Obviously, if a dash of a hundred yards would help, I could do this dash at any point during the walk, but that's not the instinct. What the dash might protect me from was not so much the risk of being late (since I should have plenty of time to get to work, and since getting earlier to the stop would simply put me into an unknown (earlier) bit of the sequence) - what I was protecting myself from was the frustration of having missed a bus when it was within my power to do something about it. This last bit is important.

Of course, I could just leave earlier, but that doesn't really change the unpredictability, or I could run the entire mile, which is not ideal if you are wearing a suit and office shoes, and maybe a top-coat, and maybe carrying a case - especially if you are going to spend a bus-ride jammed onto the lower deck - standing room only.

In practice, every day I would jog the last quarter mile - I felt better that way. Then, if I just missed a bus, I would feel that I had tried. I never jogged any previous quarter mile on the way there, because at that distance it doesn't seem like the correct thing to do.

None of this was ever really a problem - I can't recall ever being late for work. What bugged me was the suspicion that deciding to jog, every day, at the point where panic was beginning to set in felt a bit like dumb behaviour. There is a mathematical problem in which a man cuts diagonally across a square field, and a bull in the field charges at him from one of the other corners - it always heads straight towards him. The problem is to identify an equation for the path of the bull, and identify the limiting conditions, but the important, inescapable truth is that the bull is so damned stupid that it fails to realise it can catch the man by taking a short cut - taking a straight line to head him off rather than always just running directly at him.

I always had a feeling that I should have had an advantage over the bull, but it didn't feel like it.