h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Sorry, but that isn't what frequentism is. Frequentism is the (really rather barmy) claim that a probability literally is the number of times the outcome has occurred divided by the number of tests. This is barmy because if it means 5012316821312767 out of 100000000000000000 coin flips have come out heads then then probability of a coin flip coming up heads is 0.5012316821..... Which is mad...

Actually, scratch that. That *is* what you said it is. But I hope people weren't taught that in school.

Actually it means the probability is 0.050..., but that's neither here nor there.

Okay, okay, so I just looked at the numbers and guessed when they were about the same lengths....

I didn't actually expect such pernicitiness!

Ben has a little counting problem to go with his reading problem...

Just kidding - I've done the same kind of misreading myself - I always feel it lowers my credibility as a Scout, but it still happens. I try and blame tiredness generally...

If you consider the fact that with an actual coin, as opposed to a theoretical coin, there may, in fact, be something other than the theoretical 50/50 split. If for no other reason than that in a real coin tossing situation there is the real but slight chance that the coin will land on edge. If that chance is there then the heads/tails chances cannot be 50/50. Further, it the coin is so made that its center of gravity is closer to one face than the other, there will be a real chance that the flips will favor one side over the other.

All of this, of course, assumes that the method of tossing the coin is unweighted, und so weiter.

In this sense, the probablility cannot be determined theoretically since it is in direct reference to the actual real world events. All theoretical calculations can say is 'IF the coin is a theoretically fair coin AND if the methods of tossing the coin are statitically equal but random in effect AND there is no chance of the coint landing on edge THEN the odds SHOULD be .5 for a particular face to show on any given coin toss.'

Barton

Ah no, this is just the debate. According to Frequentists, probability isn't a model notion such as that 'if you were to flip a coin it would land heads 50 in every 100 time', it's a historical notion - because the probablility of a head is the number of times a head has been flipped, divided by the number of times a coin has been flipped. And that's /all/.

In other words, because there has never been a perfectly fair coin, it's meaningless to talk about the probability that it'd land heads, according to the Frequentist position.

These people need help....

I think that's probably (no pun intended) true, but its not something strange or silly. There is no way, short of measuring all necessary parameters of the coin and the local gravity variations etc to give a completely accurate description of what it will do. And once you know all that you know which way its going to land, so probability is out the window.

So, given a coin, we can't work out the exact probability of it showing heads without throwing the baby out with the bathwater. But the point is that if we assume the probability is 1/2 **it seems to work**. This is exactly the same approach as in physics - we observe things doing stuff, guess some equation with no intrinsic link to the things, and if it works we say 'this is what they do'. Of course they may do something completely different tomorrow, but, as yet, coins have not.

And anyway, probability is just a subjective notion - the coin knows perfectly well which way up its going to land, and so would we if we put a fast enough computer on the job. It's like quantum physics, two slits and all that. It may be that the electrons know which slit they're going through, but we don't, so we say their behaviour is probabilistic. Consider a native of Flatland (a 2D universe) who has managed to toss a coin in a third dimension of which it knows nothing. All it sees is the coin disappearing and then reappearing heads up with probability 1/2, whereas we clever 3D people can see which way it will land.

Although unless you can demonstrate to me that the coin in question is perfectly 'fair' I would contend that saying you know the probability to be something else (say 0.5%) is as ridiculous.

Z

Erm, Swiss, this is just what frequentism disagrees with. According to frequentism, you *CAN* work out exactly the probability of the coin coming up heads - you just need to be able to divide - since past instances are all that define probability. Unfortunately, it has nothing whatsoever to do with what will happen on the next throw, so is pretty much no use.

Please write out 100 times "I will read the entry before making inane comments", and have it on my desk by tomorrow morning...

In Flatland, of course, the coin nearly always on edge. (Unless it lands on edge, which would then be a point, a line, or a very small oval.) Exactly what is a coin in Flatland, anyway?

Barton

I'm imsgining a world contained on, say, a table which exists in a wider 3D world, say, this one. A coin would be a disc (or square, or whatever) which the Flatlanders manage, somehow, to propel out of their world and out of their comprehension. It then returns under gravity and lands on the table, either heads or tails.

It was only an example of a wider point, anyway.

Of course, Flatlanders couldn't see whether such a coin is heads or tails, for the same reason that I can't see my lungs...

so they paint half the boundary black and the other half white and record which colour points north

sheesh!

Well that's more like a roulette wheel than a coin... I mean, why flip it if you can just spin it for the same effect?

j/k - couldn't resist...

because then they could measure the rate of rotation and the friction and predict where it would end up. The point is that if they flip it they can't

Heck! They can't even predict HOW to flip it let alone what will happen if they do.

Of course, i could whisper in the 'ear' of Flatland Einstein that all he has to do is rotate it 90 degrees to everything and then it would either come back just the same or magically reversed, for instance if his coin was a 'b' it might come back a 'd' (not that I wanted to raise any racial issues) Obviously there is no difference between a 'b' and a 'q' or a 'd' and a 'p,' that's just spinning (which is all that you could tell with a symmetrical shape painted half blue and half red, no matter how it was translated. A coin would need to be asymmetrical in order to be percieved as having been 'flipped.'

(Is this off topic? )

Barton

*gasps*

Barton, you are a genius. Nuff said.