I have read that it is still inconcievable that a robot can be designed to catch a thrown ball. The casual sophistication of human perception is enormous: to work out from limited sense data not only what is going on in terms of movement, but then to predict and act on it, moving the hand so it is in just the right place. Usually (insert joke about cricketers here). This is achieved by some very clever under-the-bonnet stuff to do with mental spatial models. The human mind is very good at discerning patterns in high-noise data. Sometimes this is meaningful, as when the Greeks observed the planets and calculated their orbits (wrongly, but still); and sometimes it isn't, as when they played joined-the-dots to create the constellations. But being good at making patterns means that we spot 'coincidences' very easily, and are poor at judging probability. That's what keeps astrologers in business: they don't have to be right very often to seem to be on to something. This can be queried: when you look at the people spread-betting on a football match, if 40% bet on each team to win, and 20% bet on a draw, then at least 20% are going to be 'strangely prescient' (this time). And there was also that triumphant moment on the National Lottery when Mystic Meg predicted that those wearing red would be in for a chance tonight etc, but her pyschic powers totally failed to infrom her that that week's draw would be cancelled because of techncial problems.
The reason I raise this is because of the continuing saga of CNPS : Consecutive Number Plate Spotting [up to 48 now- exciting, isn't it?]. And I have borne out Richard Herring's observations on the Gods of CNPS: they are fickle, and they are cruel.
That's the emotional reality of it. Some days, some numbers, they smile, and offer up the numbers like ducks in a row; other days, other numbers, they hide, they cheat, they lurk in shadows, they dive into sidestreets as I approach. And sometimes, to rub in the lack of progress, they arrange parades of the last number, or the one after next, time after time, before getting a glimpse of the right one.
So what's going on, if we start on the basis that the Gods of CNPS (whisper it) don't exist?
Fickleness is easy to explain. As I calculated before, the number of other numbers seen before the right one will vary between 1 and 1000. So some will be long, some short. The long ones of course (duh) last longer, so one's "hours of waiting a long time" seem worse, and so a more memorable. Beyond that, though, I wonder whether the nature of the distribution is disorientating. Most phenomena we experience are bell-curves, where most values occur near the mean (so that rainfall goes up a little, down a little, except this year). But the number-plate probability 'curve' is flat: the extremes are as likely as the mid-range values. This makes it seem even more aribtrary than it is.
The cruelty, the taunting, is even simpler. We are focused on looking for one number, y, but keep seeing the x's we no longer need, or the z's, that we will need next but don't need now. How the Halls of Valhalla must ring with laughter. But, looking at just those three numbers, the likelihood that we see y before z or x is only 1/3. We are more likely to see one of the others. We are just as likely (1/3) to see both of the others before y. No wonder it happens so often. And for repeated numbers: after we have seen an x, there is (again) a 1/3 chance of a y, a 1/3 chance of another x, and 1/3 chance of a z. So building up a conspiracy against me is simple.
I'm not sure how far this gets us, apart from explaining why people are so easily convinced of the workings of fate or luck, and the strength of their convictions, however misplaced.