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Old 18th February 2011, 06:37 PM   #201
sol invictus
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Originally Posted by Piggy View Post
Quite correct, physics doesn't know or care which side is heads and which side is tails. But that's entirely irrelevant to my argument.
No, it really isn't.

Can you please respond to the rest of that post (quoted here for your convenience)?

Originally Posted by sol invictus View Post
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? Note that if 100 heads is impossible, then whatever sequence you'd get by starting with 100 heads and turning all the Fs into tails is also impossible, since that's what I would have gotten had I not flipped the Fs. But since my table of Fs and NFs was arbitrary, that means all sequences are impossible, which is obvious nonsense.

Therefore, 100 head sequences are possible.
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Old 18th February 2011, 06:37 PM   #202
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Originally Posted by sol invictus View Post
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? Note that if 100 heads is impossible, then whatever sequence you'd get by starting with 100 heads and turning all the Fs into tails is also impossible, since that's what I would have gotten had I not flipped the Fs. But since my table of Fs and NFs was arbitrary, that means all sequences are impossible, which is obvious nonsense.

Therefore, 100 head sequences are possible.
Try that with the example of the cup and stairs and you should see the error you're making.

In any case, let's pursue this on another thread, please, because we're not contributing to the OP here.
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Old 18th February 2011, 06:41 PM   #203
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Originally Posted by blutoski View Post
Essentially: you are arbitrarily lumping them together as a 'type' vs another 'type' which is straight runs.
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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Old 18th February 2011, 06:41 PM   #204
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Originally Posted by Piggy View Post
Try that with the example of the cup and stairs and you should see the error you're making.
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).
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Old 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.

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Old 18th February 2011, 06:46 PM   #206
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Originally Posted by Alan View Post
Or let's say I toss a coin until I am on a streak of heads and 'feel' like the streak has to break soon.

Then, I go up to somebody and bet with them that it's going to come up with tails. Would the tosses beforehand affect the tosses in this bet and give me an unfair advantage?
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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Old 18th February 2011, 06:48 PM   #207
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Originally Posted by sol invictus View Post
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).
I think it's relevant, too, but the OP does not, so I will defer.

Please, let's split this off if you'd like to continue the discussion on this point in particular.
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Old 18th February 2011, 06:51 PM   #208
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Originally Posted by Alan View Post
Do you agree or disagree with the following?

"The chance of getting heads or tails is approximately 50/50".
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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Old 18th February 2011, 06:55 PM   #209
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http://www.internationalskeptics.com....php?p=6893315

Here is a new thread.
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Old 18th February 2011, 07:48 PM   #210
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Originally Posted by sol invictus View Post
Again, there is a difference between the assertion "sequence A is more likely to be produced by cheating than it is by chance" and "producing sequence A by chance is impossible".



But (as we keep pointing out) that's quite obviously a false statement. If that particular sequence is impossible because it is very unlikely, then all sequences of the same length are impossible, because they are all equally unlikely - a patently absurd conclusion that can be trivially falsified.
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).
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Old 18th February 2011, 07:52 PM   #211
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Originally Posted by Piggy View Post
No, the monkey is a real flesh-and-blood monkey.
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.
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Old 18th February 2011, 07:58 PM   #212
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Old 18th February 2011, 08:01 PM   #213
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Originally Posted by tsig View Post
I have never seen anyone claim it refers to actual monkeys who are more likely to pee on the typewriter than type on it.
Are you kidding me?

Are you seriously claiming that the saying originated with the notion of simulated monkeys?

At any rate, my use of this example stands, because my intent was to contrast simulations and idealizations with the real world.
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Old 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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Old 18th February 2011, 08:43 PM   #215
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Originally Posted by Malerin View Post
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.
Jorge Luis Borges's Library of Babel
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Old 18th February 2011, 09:30 PM   #216
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Originally Posted by Alan View Post
In case you missed it.
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Old 18th February 2011, 09:39 PM   #217
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Originally Posted by Alan View Post
In case you missed it.
No, I didn't miss it, but it's late here so I thought I'd wait for another day before diving in. Thanks for starting the new thread.
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Old 19th February 2011, 02:40 AM   #218
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Originally Posted by Malerin View Post
Ahh, now what if the same person wins the same lottery again? We might say it's a fluke. Given how many people play the lottery, there might be some repeat winners. But if they win again? And again? At some point, you become extremely skeptical of chance, and much more open to some rigging of the lottery.
I brought that up way back on page 1!

Originally Posted by OnlyTellsTruths View Post
As far as varying levels of "possible" go, I'm going to steal Modified's great example from the
Impossible or just unlikely
thread:


Someone wins the big weekly one in a billion lotto.

Now compare that to the same person winning it every single week of their life.

The first is nearly impossible. The second is so close to impossible that it basically equals impossible.

Again, this brings to mind the .999... repeating = 1 thread.
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Old 19th February 2011, 03:25 AM   #219
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Originally Posted by Piggy View Post
Jorge Luis Borges's Library of Babel
You are correct.

And I believe the coin tossing experiment itself is played out in Tom Stoppard's "Rosencrantz and Guildenstern are Dead". Since I don't have the text in front of me at the moment, here's a summary from Wikipedia:

Quote:
The play opens with Rosencrantz and Guildenstern betting on coin flips. Rosencrantz, who bets heads each time, wins ninety-two flips in a row. The extreme unlikeliness of this event according to the laws of probability leads Guildenstern to suggest that they may be 'within un-, sub- or supernatural forces'. The reader learns why they are where they are: the King has sent for them. Guildenstern theorizes on the nature of reality, focusing on how an event becomes increasingly real as more people witness it.
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Old 19th February 2011, 05:30 AM   #220
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Originally Posted by Piggy View Post
Are you kidding me?

Are you seriously claiming that the saying originated with the notion of simulated monkeys?

At any rate, my use of this example stands, because my intent was to contrast simulations and idealizations with the real world.
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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Old 20th February 2011, 08:21 AM   #221
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Originally Posted by sol invictus View Post
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?
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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Old 20th February 2011, 08:26 AM   #222
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Originally Posted by tsig View Post
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
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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Old 20th February 2011, 08:32 AM   #223
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Originally Posted by Piggy View Post
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.
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.
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Old 21st February 2011, 08:47 PM   #224
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Originally Posted by Piggy View Post
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.
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:
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.
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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Old 22nd February 2011, 04:48 AM   #225
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Originally Posted by OnlyTellsTruths View Post
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!)
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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Old 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?
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Old 23rd February 2011, 07:21 PM   #227
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Originally Posted by Simon Bridge View Post
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.
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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Old 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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Old 6th March 2011, 02:44 PM   #229
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Originally Posted by OnlyTellsTruths View Post
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.
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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Old 6th March 2011, 02:48 PM   #230
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Originally Posted by Piggy View Post
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.
Thus the reason one should check ones gut reaction with actual numbers.

http://www.schneier.com/essay-162.html
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