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28th February 2011, 04:51 PM | #201 |
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And add just one to that "random-looking" sequence and that 101-long sequence is less likely to occur than 100 heads. Woahhhhhhhhhhhhhh.
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28th February 2011, 05:16 PM | #202 |
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Here's an interesting question: How long a streak would allow us to judge the fairness of the coin-flips?
Theoretically, you could never say it wasn't an honest coin, as long as the string of results is potentially infinite. By the same token, a given Diaconis machine might actually be producing random results, over an extremely long timespan, and we'd just never be able to tell. |
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28th February 2011, 05:44 PM | #203 |
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Are the coin flippers aware of the series?
i.e. it has to be the same coin flipper for all 100 flips right? Or would you accept 10 coin flippers doing a single flip each in order, not aware of the others results (only the score keeper is). I.e. is this a blind test, doble blind test, or not a blind test at all> It seems you'd only accept a single coin flipper, aware of the whole series. How I see the bias would work: the real-life coin flips are non-random, to a small extent. Toss a coin 200 times and see what stats you get. Even if you get close to 50-50, not everyone tosses the coin the same way, so you'd need a 'toin coss' protocol. The 50-50 result, which i think was partially your point with the smooth spaces earlier, is quite unlikely, probabilistically, even though it's the most likely result. Throw 2 d-6 dice. 7 is the most likely result, but it's less likely than ie. '6 or 8' together. How do I place the coin before the toss? Where is it placed, its it always heads-up before the toss? How high do I toss it? Do I catch it or let if fall? do we have a minimum amount of revolutions to qualify for the test? It would be interesting to ask some experienced illusionists how much they can bias a coin toss with a random, not-pre-selected and not wighed coin. If they can acheive a good result (meaning strong bias), then I think it is fair to assume that a flipper aware of the series might subconciously be able to influence the toss to break a long series. How big is his chance to influence it, and if he would influence it reliably enough to break the series reliably is difficult to answer due to the very small probability he would have a chance to break a 99 long series in the first place. |
28th February 2011, 05:45 PM | #204 |
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Just a side note - noting Piggy's error that we would by definition a need a zillion years of coin flips to get the 100 heads. The 100 heads sequence is just as likely to occur on the first 100 flips as on the zillionth zillionth.
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28th February 2011, 06:01 PM | #205 |
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You are correct, but on average we'll only hit our pre-determined sequence in half a zillion years.
A typical scenario, that deals with data more random than your average coin toss - finding encryption keys through a brute force attack. Say you have an encrypted message and you know the plaintext (the message before encryption). Therefore you can test all 2^64 individual key in the following manner. Select a key. Encrypt the message with your key. Check if the encrypted message is equal to the original encrypted text you were given. Repeat till you find the key. It turns out you're very lucky if you get the key in say around the 25% of the tested keyspace (and usually around the 50% mark, and of course, unlucky around 75% mark) even though as you correctly stated, the chances of you selecting the correct key (randomly) for the first attempt are the same as for every other attempt (assuming perfect randomness - and results of encryption are anb extremely good approximation of pure randomness, though we can do even better than that) EDIT: if I remember correctly, we'd be dealing with a normal distribution here, and 68% of results fall within a standard deviation of the mean. The mean here will be 50% of the exhaustive keyspace search. The standard deviation for a series of 100 coin tosses is 5, so if the coin is fair and the toss truly random, 68% of results will be 45-55, a probability of hitting 50, the most likely result, is below 8 percent. |
28th February 2011, 06:11 PM | #206 |
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Yeah, I was thinking about that this morning. You'd have to posit ESP, I suppose, if the flipper couldn't see the results, and I'm not willing to go that far, although I've been on threads with skeptics who will.
Or I don't know, maybe there is some strange-but-not-provably-physically-impossible scenario out there. When you're talking about "no chance" it gets real dicey to say. But for my money, no, I can't see a way around that. |
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28th February 2011, 06:15 PM | #207 |
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I believe the article on the Diaconis machine talked about that, but I believe the illusion was to "flip" the coin so it spun and wobbled while remaining face up or down, and the magician made the choice of heads or tails between grabbing the coin and laying it on his arm.
I don't know how good a person could get at real flips, but I'd bet it could be mastered with sufficient practice. |
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28th February 2011, 06:20 PM | #208 |
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That's true, but it's not just as likely to occur on the first 100 flips as it is somewhere between the zillionth and the zillion zillionth.
Anyway, no, that's not what I'm saying -- in fact, if the system is potentially infinite, then if you look at it theoretically there's literally no limit (as long as you have a finite number of flips) to the streak from flip 1 forward that would be allowed in a random results space which, at some scale, evenly balanced heads and tails without forming regular patterns. No matter how large your "blob" got, you could just say it's a tiny detail in a much larger arrangement. |
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28th February 2011, 07:15 PM | #209 |
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Let's imagine flipping a coin some extremely high number of times. A number that no one is likely to ever do, but this thread seems hypothetical anyway.
If a coin were flipped a billion times, what's the largest consecutive run of heads you'd statistically expect? And how would you make that calculation? Alternately, if I wanted to know how likely a run of consecutive heads was in certain numbers of throws, I'd divide the number of possible sequences with that many heads by the total number of possible sequences. Let's say a coin is flipped a billion times. There should be 2^billion possible sequences. How many would have 100 consecutive heads? Or am I missing the entire point of the thread? I'm new here, and all. |
28th February 2011, 09:11 PM | #210 |
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Some of the discussion in this topic reminded me of this Dilbert strip.
http://www.dilbert.com/dyn/str_strip...2318.strip.gif |
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28th February 2011, 09:42 PM | #211 |
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Why do you think the real human being flipping a real coin would somehow unconsciously kill or sabotage a streak (that would have gotten heads) rather than continue or perpetuate a streak (that would have gotten tails)?
If someone can influence the coin flip somehow unconsciously, and they have a long sting of heads going, what makes you think they would somehow unconsciously influence the flip to come up tails and end the streak rather than somehow unconsciously influence the flip to come up heads and continue the streak? |
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1st March 2011, 03:10 AM | #212 |
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Of course you could say that. You couldn't say that with zero chance of being wrong, but you could say that with arbitrarily low chance of being wrong.
Which happens to be the very best degree of confidence available. If people only said things with zero chance of being wrong, it would be a silent world. |
1st March 2011, 03:01 PM | #213 |
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I'm sorry, but this really is just silly.
Even if, even if there was some unconscious kill switch in our brains that implores us to sabotage the streak -- even in that case, we've still got a non-zero probability of getting a hundred heads. Because at each step of the way the coin still needs to be flipped. The psychological state of the person is, for all intents and purposes, irrelevant as it pertains to the question of possibility. The system we are dealing with in reality is much larger than just the person; despite the best of intentions, the person can still succeed. Of course, it's possible that the person might start to cheat...but provided they're still actually flipping the coin (as is required) they have a non-zero probability that their cheat will fail (I.e. the coin will keep landing heads). So no: not even in this bizarre fantasy world of yours is there ever zero probability of getting a run of a hundred heads. |
2nd March 2011, 05:20 PM | #214 |
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2nd March 2011, 05:21 PM | #215 |
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2nd March 2011, 05:33 PM | #216 |
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There's a paper linked on the parent thread, btw, that discusses the number of flips needed to make certain streaks likely. I believe it's somewhere between 2,000 and 3,000 flips to make a streak of 10 likely.
I suppose that would mean figuring out the point where more than half of all such runs would contain a streak of that length. But then you get back to the point someone made just upthread, that if you were to do a sufficient number of very long series of coin flips, some of them would show streaks at the beginning, others at the middle, others at the end. There was a Radio Lab episode very recently that discussed coin tosses. As part of their experiment, the RL guys flipped a streak of 7 very early in (or perhaps at the start of, it's hard to tell) a run of 100. Later, they talked to a statistician and said they flipped 7 heads, and he gave them the very long odds. But when they mentioned they'd made a total of 100 flips, he said, oh, that means it's only about 1 in 6. So it goes from a long shot to about like throwing a dart at a calendar and hitting a Tuesday, based on what they did after making the streak. Which makes me think of a scenario like, suppose me and my brother-in-law forgot who owed who 20 bucks, so we agree to flip a coin 10 times and bet $2 on each flip. Well, we decide that he flips, he takes heads, and he gets 10 out of 10 heads. I say, "Dude, that's gotta be a rigged coin", and he says, "No, you see, I always intended to flip this coin another 2,990 times, which is what I'm about to do, so this isn't unusual at all." So I say, well, ok, and take off, but then I realize I left my smokes inside and I go back in and the guy's popped open a beer and is sitting with his feet up watching TV. I say, "You lying SOB, you never intended to make those 2,900 flips... you were cheating me, after all!" |
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2nd March 2011, 05:36 PM | #217 |
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2nd March 2011, 06:57 PM | #218 |
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2nd March 2011, 09:22 PM | #219 |
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3rd March 2011, 01:24 AM | #220 |
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3rd March 2011, 07:56 AM | #221 |
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3rd March 2011, 10:59 AM | #222 |
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I'm not sure it's a derail. I think everyone here, including Piggy, now accepts the fact that there are no "impossible" coin sequences. But how does that fact relate to the way we view the world? For example, if someone wins the JREF Challenge in a tightly-controlled test by, say, correctly naming the first five cards drawn from a deck of cards lying face down, will the prevailing attitude here be that the paranormal has been demonstrated? If not, how about if s/he correctly names the first ten cards? If not, how about if s/he correctly names the entire deck?
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3rd March 2011, 06:07 PM | #223 |
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3rd March 2011, 06:18 PM | #224 |
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It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ |
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3rd March 2011, 06:20 PM | #225 |
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3rd March 2011, 08:10 PM | #226 |
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What does it mean to say that the paranormal exists?
Paranormal is used to describe a wide variety of stuff like tree spirits, mind reading, angels, witches and gods. What do you mean? If an unlikely occurrence happens, what paranormal entity is responsible? The probability fairy? |
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4th March 2011, 01:35 AM | #227 |
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I would say that we've got a demonstration that it's likely that something is going on, and worth further study. Of course it's possible that he or she got lucky, but it's also possible that the world behaves differently than our current understanding suggests. A good place to begin scientific exploration of the phenomenon.
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4th March 2011, 04:52 AM | #228 |
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4th March 2011, 05:29 AM | #229 |
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Yeah that sure is interesting... it's the OP of the month old thread that started this discussion... that you took part in!
Double Headed Coins and skepticism From that thread's OP: Sound familiar?? |
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4th March 2011, 05:32 AM | #230 |
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A human flipping 100 heads in a row = possible.
Piggy's theory that, at some arbitrary point in a human flipping streak, the odds of heads becomes zero = impossible. Post all you want, this will still be true. |
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4th March 2011, 07:29 AM | #231 |
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One or more phenomena exist that science does not currently explain.
In the example that I gave, it would be an apparent case of clairvoyance; i.e., perception outside the five senses. That's not the issue -- the issue is whether you would accept the paranormal as an explanation if the odds were sufficiently high against an event happening. |
4th March 2011, 09:14 AM | #232 |
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If science cannot currently explain something, why would it be paranormal? Was the sun "paranormal" before science could explain its energy source? Was genetics "paranormal" before the discovery of DNA?
Quote:
Quote:
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4th March 2011, 10:29 AM | #233 |
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5th March 2011, 08:31 AM | #234 |
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The probability of such a thing happening are about 1/8*1067. Guessing 52 consecutive cards correctly would have a probability not unlike that of my atoms suddenly appearing on Mars (within the context of quantum theory).
The controls were not adequate. It was a trick! If one were to claim some other explanation, one would have to demonstrate a mechanism and a causality. |
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5th March 2011, 01:03 PM | #235 |
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Okay, so even though it is theoretically possible for someone to correctly guess the order of a deck of cards, you wouldn't take seriously the idea that could happen by chance. We agree there, which I think may distinguish us from some others here, but why would you think it would have to be a trick? Don't you think a mechanism and a causality could ultimately be demonstrated, even though they are currently unknown?
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5th March 2011, 01:21 PM | #236 |
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5th March 2011, 01:23 PM | #237 |
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5th March 2011, 02:31 PM | #238 |
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It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ |
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5th March 2011, 04:11 PM | #239 |
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5th March 2011, 04:24 PM | #240 |
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