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18th February 2011, 06:37 PM | #201 |
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18th February 2011, 06:37 PM | #202 |
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18th February 2011, 06:41 PM | #203 |
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It's absolutely not arbitrary, considering that fair games and rigged games have decidedly different results spaces.
It's like saying that a completely flat plane is not somehow qualitatively different from all of the various configurations of mountains that are possible. Now, I think this point is probably relevant to the OP, but since Simon thinks otherwise, let's move this discussion elsewhere. |
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18th February 2011, 06:41 PM | #204 |
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I read your example, but no, I don't see the "error I'm making". Can you tell me what it is?
While you're at it, can you answer the question I asked you? Is a sequence of 100 heads still impossible if I flip/don't flip the coin after catching it according to a pre-determined plan? As for being on topic, I think this discussion is on the topic of the paper the OP asked for comments on, so I don't see the problem (but I also don't object if a mod wants to split out some posts and start a new thread). |
18th February 2011, 06:44 PM | #205 |
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How about we go through this more simply. Hopefully this will stop us from going around in circles if we are more direct.
Do you agree or disagree with the following? "The chance of getting heads or tails is approximately 50/50". I will ask some similarly simple follow up questions. EDIT: I'll start a new thread as Piggy wanted. Although it is related to the topic of this thread. |
18th February 2011, 06:46 PM | #206 |
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But Simon is not asking about this.
Simon is asking about how we arrive at confidence in a determination of cheating over a large span of events. So the relationship of any two given events is irrelevant. As I said before, there is no combination of any two coin flips that does not conform to experience, or to our expectations of spans of random events in a turbulent world. And if you look at Simon's paper, you'll see that a run of 2 flips is not considered as even potential evidence of cheating. In order to get at what Simon is writing about, as well as what I'm writing about, you have to deal with much larger spans. |
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18th February 2011, 06:48 PM | #207 |
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18th February 2011, 06:51 PM | #208 |
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As long as your focus is on one flip, then yes, certainly.
But keep in mind, if the odds of the wind being in direction X at any given moment during a hurricane are, say, 1/8, this does not in any way imply that a steady directional wind might possibly be sustained for an hour during a hurricane. |
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18th February 2011, 06:55 PM | #209 |
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18th February 2011, 07:48 PM | #210 |
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Right, all sequences are unlikely. I should have stated that "for all intents and purposes, it's impossible for someone to correctly guess* the result of a billion fair coin tosses". A billion heads in a row implies that we're predicting the outcome ahead of time.
* I originally put "predict", but this would preclude psi abilities (or other possible methods of seeing into the future). |
18th February 2011, 07:52 PM | #211 |
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To paragraph I posted came from here:
http://en.wikipedia.org/wiki/Infinite_monkey_theorem And reads in full: The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces a random sequence of letters ad infinitum. I have never seen anyone claim it refers to actual monkeys who are more likely to pee on the typewriter than type on it. |
18th February 2011, 07:58 PM | #212 |
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18th February 2011, 08:01 PM | #213 |
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18th February 2011, 08:10 PM | #214 |
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I remember reading about a library so large that every possible combination of letters was made into an actual book. The library wasn't the problem. Finding the right book was.
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18th February 2011, 08:43 PM | #215 |
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18th February 2011, 09:30 PM | #216 |
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18th February 2011, 09:39 PM | #217 |
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19th February 2011, 02:40 AM | #218 |
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19th February 2011, 03:25 AM | #219 |
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Laugh while you can, monkey boy. |
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19th February 2011, 05:30 AM | #220 |
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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 |
20th February 2011, 08:21 AM | #221 |
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20th February 2011, 08:26 AM | #222 |
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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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20th February 2011, 08:32 AM | #223 |
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Laugh while you can, monkey boy. |
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21st February 2011, 08:47 PM | #224 |
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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.
Quote:
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. |
22nd February 2011, 04:48 AM | #225 | |||
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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.
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23rd February 2011, 06:59 PM | #226 |
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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? |
23rd February 2011, 07:21 PM | #227 |
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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. |
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24th February 2011, 02:56 AM | #228 |
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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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6th March 2011, 02:44 PM | #229 |
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6th March 2011, 02:48 PM | #230 |
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Thus the reason one should check ones gut reaction with actual numbers.
http://www.schneier.com/essay-162.html |
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