Double Headed Coins and skepticism

[sol invictus]

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)?

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.

 

[Piggy]

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.

 

[Piggy]

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.

 

[sol invictus]

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).

 

[Alan]

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.

 

[Piggy]

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.

 

[Piggy]

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.

 

[Piggy]

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.

 

[Alan]

http://www.internationalskeptics.com/forums/showthread.php?p=6893315

Here is a new thread.

 

[Malerin]

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).

 

[tsig]

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.

 

[Malerin]

 

[Piggy]

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.

 

[Malerin]

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.

 

[Piggy]

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

 

[Alan]

http://www.internationalskeptics.com/forums/showthread.php?p=6893315

Here is a new thread.

In case you missed it.

 

[Piggy]

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.

 

[This is The End]

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!

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.

 

[bokonon]

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:

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.

 

[tsig]

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