Double Headed Coins and skepticism

sol invictus said:
Look - suppose we play the following game. I make a table with 100 entries. Each entry is either F or NF. Let's say there are 50 Fs and 50 NFs in some more or less random order. Now, here's the game - I flip a coin 100 times. Before each flip I consult the corresponding entry in my table. If it says F, I flip the coin over after catching it, before uncovering it and reading it. If it says NF, I don't flip it before uncovering it.

Do you stil believe that a sequence of 100 heads is impossible, given that setup?
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This question has turned out to be more difficult than I thought, at first, because it's tricky to figure out, or describe, exactly what's being measured here, since the outcome space describes the interaction of 2 systems.

Will have to ponder this one a bit more.
 
tsig said:
History
] Statistical mechanics

In one of the forms in which probabilists now know this theorem, with its "dactylographic" [i.e., typewriting] monkeys (French: singes dactylographes; the French word singe covers both the monkeys and the apes), appeared in Émile Borel's 1913 article "Mécanique Statistique et Irréversibilité" (Statistical mechanics and irreversibility),[3] and in his book "Le Hasard" in 1914. His "monkeys" are not actual monkeys; rather, they are a metaphor for an imaginary way to produce a large, random sequence of letters.

http://en.wikipedia.org/wiki/Infinite_monkey_theorem
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I'm not suggesting that there actually were monkeys, btw.

But if you note, Borel is not proposing a thought experiment involving simulated monkeys (in 1913 that would have been quite startling) but rather a thought experiment involving monkeys.

The reason I brought up the monkeys was precisely to demonstrate the difference between how our world works in practice, on the one hand, and how idealized systems work, on the other.

Subsequent experiment shows that, as "an imaginary way to produce a large, random sequence of letters" the monkeys fail, because that's not what they actually produce.

ETA: Oops, sorry, I thought I was on the new thread... sorry, Simon!
 
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Piggy said:
This question has turned out to be more difficult than I thought, at first, because it's tricky to figure out, or describe, exactly what's being measured here, since the outcome space describes the interaction of 2 systems.

Will have to ponder this one a bit more.
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I don't think it's tricky at all.

Sol's list does precisely one thing -- transforms one unique sequence of 100 flips into another unique sequence of 100 flips.

Each of those unique sequences still has exactly the same 1 in ~1030 chance of actually occurring.
 
Piggy said:
That's fine. I won't continue to discuss that topic here.

It's not the kind of thing I'd start a thread on, myself, so I'll just drop it unless someone else wants to begin a new thread.
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Well, that didn't work well did it ... I see a whole extra page of writing.

I understand a thread has started on this subject - please everyone: take the discussion there. Thank you.

Btw, are you familiar w/ biological research on the subject? Our brains appear to go through a process very similar to what you are describing. Our "gut feelings" as well as decisions such as what we want to order off a menu are based on non-conscious processes that give us a sense of how certain we are (or aren't) that a particular choice is the right one.
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Biology is mostly outside my field (physics) so I am not actually "familiar with" the literature in the strict sense ... however, I am aware of research and the general structure of models in this area.

What I was trying to do was provide a way of comparing gut-reactions and experienced guesses with something less subjective. One of the outcomes of Bayesian statistics is that you don't have to be very good at guessing the prior for most things ... provided you are open to the possibility of being wrong and will be guided by the evidence.
 
OnlyTellsTruths said:
That is discussed (and is a plot point) during the first 10 minutes of Rosencrantz & Guildenstern Are Dead. (A spin-off of Shakespeare's Hamlet, and a very good movie in it's own right....... if you like Hamlet, of course!)
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Found it on YouTube. You only need to watch from 3:00 to 10:30 (to the end of part 1).

I admit, there isn't that much discussion involved (especially during the first 3 minutes, :)); yet it is fairly funny, especially in light of the these threads.



 
Hmmmm ... a real-life example has shown up in Christchurch NZ just yesterday ... how long to you go over a crumbled building, finding nobody, before you can say for sure there are no survivors in there?

... mind you, it seems someone may have got themselves stuck in there since :/

OT: I noted that the first person to, publicly, mention God in relation to this thing was Barak Obama ... even the befrocked guy in charge of the Cathedral didn't bother to put in a plug for the Allmighty, instead choosing to push general human values. The only people mentioning religion seem to be American tourists.

Oh, there was supposed to have been a psychic prediction ... maybe I'll start another thread?
 
Simon Bridge said:
Biology is mostly outside my field (physics) so I am not actually "familiar with" the literature in the strict sense ... however, I am aware of research and the general structure of models in this area.

What I was trying to do was provide a way of comparing gut-reactions and experienced guesses with something less subjective. One of the outcomes of Bayesian statistics is that you don't have to be very good at guessing the prior for most things ... provided you are open to the possibility of being wrong and will be guided by the evidence.
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Well, what's interesting is that the body/brain might do its own sort of Bayesian analysis, based on its "understanding" of the world, and the conscious brain might have to apply a great bit of force to make a veto, based on its rather different sort of analysis, which may be of many different types.

Our non-conscious brains might turn out to be very good statisticians, when confronted with the kinds of problems they were most likely to encounter during their evolution.
 
Simon,

I'm still not sure if you are saying there could be a way to get beyond the "I'm fairly certain that X, but I can't say for sure" completely, or if you are just trying to find the best way to get to a point where no further information changes the situation.
 
OnlyTellsTruths said:
Simon,

I'm still not sure if you are saying there could be a way to get beyond the "I'm fairly certain that X, but I can't say for sure" completely, or if you are just trying to find the best way to get to a point where no further information changes the situation.
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Both - the second part is the way past the first.

The main point is about how quantifying the "fairly certain" part helps us understand what is going on and to ask meaningful questions.
 
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