Double Headed Coins and skepticism

[sol invictus]

That's incorrect. Of course coin flips are "fair" in the common sense of the word -- that is, the flipper is not exerting any control which could reasonably pre-determine the outcome, and over enough flips the heads and tails even out.

It's not incorrect, at least not unless the flipper starts with the coin with heads or tails up completely randomly. But since the whole point of the coin flip is to generate a random heads or tails, that would be rather circular.

It's essentially impossible to flip a coin "fairly", due to conservation of angular momentum and the mechanics of coin flipping.

 

[Alan]

"Fair" in this sense means a coin with an equal chance of landing on heads or tails.
http://en.wikipedia.org/wiki/Fair_coin

I do understand that things in real life are different from things in theory when things like perfection (such as a fair coin) are involved in the theory, but that this does not make it impossible for unlikely things like this to occur..

 

[sol invictus]

"Fair" in this sense means a coin with an equal chance of landing on heads or tails.
http://en.wikipedia.org/wiki/Fair_coin

Right - and that's essentially impossible to achieve in a real flip.

 

[Alan]

Yes, I am aware of that.

 

[Piggy]

Do you recognize the irony in your position? You claim to know that sequences of 100 coin flips never come up all tails in the "real world", and that we're talking about some kind of detached-from-reality theory world.

But how many times have you flipped a coin 100 times in a row? Obviously not enough times to conclude any such thing - and therefore, you're the one using theory. And using it incorrectly, I might add.

As a gambling man, I've dealt cards, rolled dice, and tossed coins enough to know how the patterns go down.

Not only that, but I've observed other games, heard from other gamers.

In this world, runs of 100 heads or tails on a fair coin don't happen. Your numbers on paper don't change that. And I can be content with not understanding precisely why the physics of the world I live in give us those results, while accepting that they do.

Your calculations change nothing.

 

[Piggy]

It's not incorrect, at least not unless the flipper starts with the coin with heads or tails up completely randomly. But since the whole point of the coin flip is to generate a random heads or tails, that would be rather circular.

It's essentially impossible to flip a coin "fairly", due to conservation of angular momentum and the mechanics of coin flipping.

You have a strange definition of "fair" which is every bit as unrealistic as your definition of "impossible".

 

[Roboramma]

I don't live on paper.

I live in the real world of weight and heft and air currents and muscles and neurons.

And viruses, I might add. As sol said, given enough iterations we can be fairly confident that a series of 100 consecutive heads will turn up. And in the real world there are things that do have enough iterations of basically random events that these sorts of things can and in fact do occur.

If, for instance, we were to bet that a bacteria would never evolve along a particular molecular pathway because the chances of the mutation were 1/10³⁰, there's a good chance that we'd turn out to be wrong. And that's the real world.

 

[Roboramma]

As a gambling man, I've dealt cards, rolled dice, and tossed coins enough to know how the patterns go down.

Not only that, but I've observed other games, heard from other gamers.

In this world, runs of 100 heads or tails on a fair coin don't happen. Your numbers on paper don't change that. And I can be content with not understanding precisely why the physics of the world I live in give us those results, while accepting that they do.

Your calculations change nothing.

Sol's calculations predict exactly the same outcome in your games and those of other gamers as you do. He doesn't expect you to have a run of 100 heads either. So clearly you can't distinguish your theory (that it's impossible) from his on that grounds.

On the other hand, his viewpoint predicts that in the case of bacteria that I supplied in my previous post, in a large enough population the mutation would arise. Your viewpoint necessarily predicts that it won't, as something that's impossible in one iteration is necessarily impossible in the second, third and 10³⁰th.

 

[sol invictus]

As a gambling man, I've dealt cards, rolled dice, and tossed coins enough to know how the patterns go down.

Not only that, but I've observed other games, heard from other gamers.

In this world, runs of 100 heads or tails on a fair coin don't happen. Your numbers on paper don't change that. And I can be content with not understanding precisely why the physics of the world I live in give us those results, while accepting that they do.

Except that you do not have enough evidence to conclude (based on your observations) what you are asserting.

You have a strange definition of "fair" which is every bit as unrealistic as your definition of "impossible".

Hmm. Well, the effect I'm talking about is measurable - real coin flips are not fair.

 

[Piggy]

As sol said, given enough iterations we can be fairly confident that a series of 100 consecutive heads will turn up.

Why do you believe that, when experience tells you otherwise?

In the world I live in, the randomness built into our universe restricts such runs to much smaller ranges.

Abstract mathematical worlds that round off all the edges and don't account for the complexity of reality are not, as far as I can see, adequate descriptors, so I do not defer to them.

 

[Piggy]

Except that you do not have enough evidence to conclude (based on your observations) what you are asserting.

Sure I do. My brain is built for this world, and is in fine working shape.

I don't yet know, because nobody knows, precisely why the physics of our world results in the actual behavior we observe. But that's no reason for me to abandon actual experience for abstractions which describe idealized worlds stripped of all the stuff we don't yet have a handle on.

To accept that world as the true world would be insanity.

Hmm. Well, the effect I'm talking about is measurable - real coin flips are not fair.

They are not "fair" according to a description which, as far as I can tell, is not particularly relevant to reality.

 

[Alan]

As a gambling man, I've dealt cards, rolled dice, and tossed coins enough to know how the patterns go down.

Not only that, but I've observed other games, heard from other gamers.

In this world, runs of 100 heads or tails on a fair coin don't happen. Your numbers on paper don't change that. And I can be content with not understanding precisely why the physics of the world I live in give us those results, while accepting that they do.

Your calculations change nothing.

When you said it was impossible, I felt like poking fun of that position by suggesting that you think that it would be against the laws of physics. I didn't do that, because I thought that would not be fair.

But it seems you do think it's against the laws of physics.

"Patterns"? Does that mean you can predict what will happen?

You are arguing against simple matters of mathematics, based on anecdotes.

 

[Roboramma]

Why do you believe that, when experience tells you otherwise?

For much the same reason that I think that if a star has a high enough mass, when it goes supernova a black hole will result: because we have a theory about what is happening, a theory that is increadibly robust and has stood up to all attempts to falsify it, and that is what it predicts.

Similarly our understanding of mathematics and probability, along with the physics of coins, is very well tested and understood, and it predicts that given enough iterations such a string would occur.

But here's the thing, if we could find an event that did have enough iterations that I would expect something with an equally low probability as 100 heads in a row to happen, would you expect that such an event would not happen?

 

[Alan]

There's a very large opaque bag with a billion balls in it. One of those balls is red and the rest are white. I remove some balls without looking until they are removed, see that they are white, and then I insist that there is some mysterious force of physics that is forcing me to pull out only white and that there's no way I could possibly pull out a red one.

I think that is similar to this.

 

[Piggy]

For much the same reason that I think that if a star has a high enough mass, when it goes supernova a black hole will result: because we have a theory about what is happening, a theory that is increadibly robust and has stood up to all attempts to falsify it, and that is what it predicts.

The difference here is that observation confirms the black hole theory, but not the "100 heads on a fair coin is possible" hypothesis.

Our universe behaves in a way consistent with black hole theory. It does not behave, as far as we can tell, in a way consistent with the 100-heads hypothesis.

 

[Piggy]

There's a very large opaque bag with a billion balls in it. One of those balls is red and the rest are white. I remove some white balls without looking until they are removed and then I insist that there is some mysterious force of physics that is forcing me to pull out only white and that there's no way I could possibly pull out a red one.

That's what this is like.

The two situations are in no way comparable.

 

[Roboramma]

The difference here is that observation confirms the black hole theory, but not the "100 heads on a fair coin is possible" hypothesis.

We've never actually observed a black hole forming. So, no, we don't have direct observational evidence that a large enough mass star will form a black hole. We only have the consequences of very well tested theory.

Our universe behaves in a way consistent with black hole theory. It does not behave, as far as we can tell, in a way consistent with the 100-heads hypothesis.

Actually, it does behave in a way consistent with the 100-heads hypothesis. Can you offer anything with which it is inconsistent?

Please note that there is no prediction that "100-heads"* are commonplace, only that they happen when there are enough iterations.

*And also note that I am talking about all events with that probability.

 

[sol invictus]

SBut that's no reason for me to abandon actual experience for abstractions which describe idealized worlds stripped of all the stuff we don't yet have a handle on.

And yet, that's precisely what you are doing.

They are not "fair" according to a description which, as far as I can tell, is not particularly relevant to reality.

I'm not following you. What I'm saying is the following:

1) start with a normal coin on your cocked thumb, heads up.

2) flip it normally

3) catch it, and (say) don't turn it over

4) look at it

You'll find that it's heads measurably more often than it's tails. That's as it should be based on Newtonian physics, and it's been confirmed experimentally.

Not only that, people can learn to control the effect in a way so that the flip looks normal, but the result is much more likely to be heads than tails.

ETA - and the same goes if you exchange "heads" for "tails" everywhere in that post (what matters is which side starts facing up).

 

[Roboramma]

The two situations are in no way comparable.

Actually that seems to sum up your evidence pretty well. Where does the comparison break down?

Or to make myself more clear, you accept that a string of two heads is possible. What number of consecutive heads is the maximum possible number?
After that number has been reached, what do you think stops another head from turning up?

 

[Piggy]

I'll live in my world, y'all live in yours.