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.
Showing posts with label CNPS. Show all posts
Showing posts with label CNPS. Show all posts
Friday, November 17, 2006
Friday, October 20, 2006
I'm going to count from 1 to 1000 while I'm driving
Richard Herring's excellent website introduced me to the strange world of CNPS: that is Consecutive Number Plate Spotting. He explains it better and funnier than I can here, but as a pointless longwinded harmelss taks, I felt inspired as I read. He took a year to spot the 1,000 numerical elements of number plates in the right order.
In trying to work out whether that was a good or bad time, I started looking at the probability, assuming at the start that there was a random distribution of numbers. My first approach was to think in terms of the probability that the next car would have the number required (1 in 1000 or 0.1%), or the second (1 in 999 or a tiny bit more than 0.1%), but then I realised that if I ignored duplicates, there was an elegant solution: for a given number (say 123), it could be encountered anywhere between 1st and 1000th, which neatly gives a mean order of 500th. So in order to complete the challenge, you might expect to have to see 500 x 1,000 = 0.5 million cars (about all the cars in Wales).
Thinking about the question of duplicates, it doesn't actually matter that much if there is a peak (say 100 extra cars with 101 in the number): it would mean that searching for 101 will be much quicker, but on the other hand other numbers would take longer to find since there would be extra 101 duplicates to go through. As far as I can, see this cancels out.*Update below
More problematic, and what gives the game its urgency and charm, is that the world has changed. In 2001, the old three-random-digit number elements plus year-denoting letter were replaced by a two-digit number denoting year + letters, which makes 01-06 easy to do, but also means that the pool of larger numbers is restricted to older cars : it may already be the case that there are no longer any cars with some numbers on the road, and there is no way to find out.
There is an odd apsect to the way the statistics work: it doesn't actually matter how long you spend looking on any particular day: fatalistically, if you only see 300 cars you're unlikely to see the number you need, but then, you might see 900 and still not see it.
There is, at a low level, a bit of the thrill of gambling: you sink into a depressed torpor as one wrong number after another flies by, until suddenly you see the one you need: surprise and joy, almost disbelief, lasts for a few seconds, and then it fades, you switch to the new number, hoping this time it'll be quick... in its own way, it's as addictive as nicotine.**Update below
UPDATES
* This is wrong, further thought has shown. The initial assumption is that there are 1000 numbers, equally distributed, and therefore there is 1/1000 = 0.1 % chance that any given number will be that required. If we then inflate the figure by making 5 numbers represented by 200 rather than 1 per thousand, then the likelihood of 995 numbers when being searched for is 1/2000 = 0.05%, and the likelihood of the five numbers is 200/2000 = 10%. Unfortunately, the higher probability only operates when looking for those five numbers; for all the other 995, there are more, twice as many, wrong numbers to go through. So no, it doesn't cancel out, it makes it harder.
** Having gone through this a few times now, and not being a gambler, I can see why they go on about lucky streaks. After initial hope, you fall into a stupor of near-despair- is that number ever going to come up? That's why, when it does, it is as much a surprise as a joy. Now comes the critical point: any logical view would be that having just won, you are almost bound to endure the long period of loss before you win again, and therefore you would think twice about betting again. Except the voice of hope tells you that you are on a roll, that no way will it be so long to the next win, it's worth trying for a bit at least-- and then in no time at all you have lost so much that it would be foolish to give up when you were 'due' a win again. My view on gambling is that you should look carefully at the people who want you to do it: experienced gamblers, gambling companies, the government. Do these often give away money?
In trying to work out whether that was a good or bad time, I started looking at the probability, assuming at the start that there was a random distribution of numbers. My first approach was to think in terms of the probability that the next car would have the number required (1 in 1000 or 0.1%), or the second (1 in 999 or a tiny bit more than 0.1%), but then I realised that if I ignored duplicates, there was an elegant solution: for a given number (say 123), it could be encountered anywhere between 1st and 1000th, which neatly gives a mean order of 500th. So in order to complete the challenge, you might expect to have to see 500 x 1,000 = 0.5 million cars (about all the cars in Wales).
Thinking about the question of duplicates, it doesn't actually matter that much if there is a peak (say 100 extra cars with 101 in the number): it would mean that searching for 101 will be much quicker, but on the other hand other numbers would take longer to find since there would be extra 101 duplicates to go through. As far as I can, see this cancels out.*Update below
More problematic, and what gives the game its urgency and charm, is that the world has changed. In 2001, the old three-random-digit number elements plus year-denoting letter were replaced by a two-digit number denoting year + letters, which makes 01-06 easy to do, but also means that the pool of larger numbers is restricted to older cars : it may already be the case that there are no longer any cars with some numbers on the road, and there is no way to find out.
There is an odd apsect to the way the statistics work: it doesn't actually matter how long you spend looking on any particular day: fatalistically, if you only see 300 cars you're unlikely to see the number you need, but then, you might see 900 and still not see it.
There is, at a low level, a bit of the thrill of gambling: you sink into a depressed torpor as one wrong number after another flies by, until suddenly you see the one you need: surprise and joy, almost disbelief, lasts for a few seconds, and then it fades, you switch to the new number, hoping this time it'll be quick... in its own way, it's as addictive as nicotine.**Update below
UPDATES
* This is wrong, further thought has shown. The initial assumption is that there are 1000 numbers, equally distributed, and therefore there is 1/1000 = 0.1 % chance that any given number will be that required. If we then inflate the figure by making 5 numbers represented by 200 rather than 1 per thousand, then the likelihood of 995 numbers when being searched for is 1/2000 = 0.05%, and the likelihood of the five numbers is 200/2000 = 10%. Unfortunately, the higher probability only operates when looking for those five numbers; for all the other 995, there are more, twice as many, wrong numbers to go through. So no, it doesn't cancel out, it makes it harder.
** Having gone through this a few times now, and not being a gambler, I can see why they go on about lucky streaks. After initial hope, you fall into a stupor of near-despair- is that number ever going to come up? That's why, when it does, it is as much a surprise as a joy. Now comes the critical point: any logical view would be that having just won, you are almost bound to endure the long period of loss before you win again, and therefore you would think twice about betting again. Except the voice of hope tells you that you are on a roll, that no way will it be so long to the next win, it's worth trying for a bit at least-- and then in no time at all you have lost so much that it would be foolish to give up when you were 'due' a win again. My view on gambling is that you should look carefully at the people who want you to do it: experienced gamblers, gambling companies, the government. Do these often give away money?
Subscribe to:
Posts (Atom)