Double Headed Coins and skepticism

[Simon Bridge]

A False Coin - hopefully the link works - I wrote considering the oft-repeated argument (by theists) that the atheist cannot know there is no God because the atheist has not been everywhere. This questions how one can be certain of a negative result only through a finite amount of negative data. eg. How hard do I look for something, and fail, before I can confidently conclude the thing is not there to find?

The usual replies involve teapots orbiting Jupiter. But I figured it should be possible to quantify the effect.

It's been a while though - so if someone would check the math and maybe suggest how to tidy up the rhetoric?

The idea is that I am tossing a coin and it keeps coming up heads - how many tosses before you conclude, reasonably, I'm cheating? How do your initial prejudices affect the answer to this question?

I used Baye's theorum to work out how suspicious you should be given how trustworthy you think I am at the outset and how many heads I've tossed in a row.

(I could use advice on a different word than "toss" for generating a boolean random event using a coin, "throw"? ... English people seem insistent that I am a "tosser" and, now I've finished, I have "tossed off". <sigh>)

 

[Piggy]

I wrote considering the oft-repeated argument (by theists) that the atheist cannot know there is no God because the atheist has not been everywhere.

There's a much easier debunking of that argument.

We do not need to travel everywhere to know there is no God, because God is not that kind of thing. God is not, say, a rock on a distant planet.

To say we need to travel everywhere in order to say there is no God is like saying we need to look behind the fridge to be sure our house isn't infested with galaxy clusters.

 

[Dancing David]

There's a much easier debunking of that argument.

We do not need to travel everywhere to know there is no God, because God is not that kind of thing. God is not, say, a rock on a distant planet.

To say we need to travel everywhere in order to say there is no God is like saying we need to look behind the fridge to be sure our house isn't infested with galaxy clusters.

Sig material!

 

[Andrew Wiggin]

There's a much easier debunking of that argument.

We do not need to travel everywhere to know there is no God, because God is not that kind of thing. God is not, say, a rock on a distant planet.

To say we need to travel everywhere in order to say there is no God is like saying we need to look behind the fridge to be sure our house isn't infested with galaxy clusters.

I look under the couch to see if jesus is hiding there amongst the dust bunnies. If I ever found the bugger, I could tell folks I'd found jesus, and they'd leave me alone. I might even let the bugger crash in my house for a while, as long as he didn't mooch too much from the fridge. Does that count?

 

[AvalonXQ]

The idea is that I am tossing a coin and it keeps coming up heads - how many tosses before you conclude, reasonably, I'm cheating? How do your initial prejudices affect the answer to this question?

This is basic statistics. It involves a null hypothesis and a confidence interval.
We can set the confidence interval at a rather high level (say, p=.0001). Then we determine what range of responses are possible from a fair coin, where the identified result falls within this range of responses.
Even as few as 15 heads in a row would be outside the p=.0001 confidence interval for a fair coin.
What's less clear to me is how this response relates to proof or disproof of God.

 

[sadhatter]

You know, i wouldn't say it is so much in watching your results , as in actually looking into how you could be cheating.

As a D&D player ( usually the dm.) i have seen some downright miraculous statistical anomalies. And have not questioned any of them, simply due to the fact that i could eliminate all methods of cheating. ( or at the very least, make them noticeable to me.).

Personally , assuming you were tossing the coin in a way i could observe, and there was no method of cheating possible. Then i would not question any number of " heads" ( i mean hell i have seen a 100 sided dice roll 100 10 times in a row. ). Now the second you have the ability to cheat though, the ol red flag goes up pretty quick.

To pertain to religion, well it should be obvious, they have all kinds of ways to cheat. Simply the definition of god allows them to cheat every time evidence is shown contrary to its existence. Really, religion in general, and christianity in specific is pretty much made out of ways to cheat logic. ( You can't see god, god won't ever do anything like parting a sea again, god is loving but allowed to do things that would make Hitler cringe because they are 'his way', as just a few examples). Which is what puts up the red flag as to b.s. to me. It is not so much the claim to always have heads ( or to use a d and d analogy, always roll a 20) , but the fact that their entire structure is set up to make cheating ( in regards to following logic.) very easy to do.

 

[blutoski]

A False Coin - hopefully the link works - I wrote considering the oft-repeated argument (by theists) that the atheist cannot know there is no God because the atheist has not been everywhere.

That argument is really more about burden of proof, and it is one that skeptics confront pretty frequently. How can skeptics say there is no Bigfoot or Loch Ness Monster or UFOs?

I prefer to avoid taking that bait and just point out that they're making the positive claim so it's up to them to make a convincing case. Nonexistence is the default against which claims of existence are compared.

This questions how one can be certain of a negative result only through a finite amount of negative data. eg. How hard do I look for something, and fail, before I can confidently conclude the thing is not there to find?

There is no 'rule' about this.
There are only cultural standards for confidence intervals.

And this is a practical problem for testing paranormal claims. Even skeptics will disagree about the threshold confidence interval for accepting a paranormal claim. In particular, since it is not an established mature field and there is no existing standard yet.

 

[This is The End]

<snip>
The idea is that I am tossing a coin and it keeps coming up heads - how many tosses before you conclude, reasonably, I'm cheating? How do your initial prejudices affect the answer to this question?<snip>

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!)

<snip>i have seen a 100 sided dice roll 100 10 times in a row. <snip>

That's...... unbelievable!

 

[Simon Bridge]

I knew I'd regret bringing up the god angle ... I know there are lots of arguments and approaches, thank you. Has anyone got a comment to make on the paper?


Only thing I got here is that I need to explain in some detail why normal statistical hypothesis-testing is not good enough for the sorts of questions you get looking into paranormal claims.

It also doesn't work well to my purpose ... the idea is to lay groundwork for understanding more complex problems rather than produce an optimal solution to a specific problem. I put all this in the paper so I wouldn't have to write so much here.

There was a thing in skeptical inquirer about this I think:
http://www.abelard.org/briefings/bayes.htm#testing_for_rare_conditions

Oh yeah ... and:
http://www.script-o-rama.com/movie_scripts/r/rosencrantz-and-guildenstern-are-dead-script.html

 

[Kevin_Lowe]

This is basic statistics. It involves a null hypothesis and a confidence interval.
We can set the confidence interval at a rather high level (say, p=.0001). Then we determine what range of responses are possible from a fair coin, where the identified result falls within this range of responses.
Even as few as 15 heads in a row would be outside the p=.0001 confidence interval for a fair coin.
What's less clear to me is how this response relates to proof or disproof of God.

This is a bit like saying that a screwdriver is just a fancy hammer, because you have personally found that if you hit screws hard enough with a hammer they go in.

There's a major difference between "The odds of you doing that with a fair coin are X%" and "the odds of you cheating are Y%".

 

[Malerin]

You know, i wouldn't say it is so much in watching your results , as in actually looking into how you could be cheating.

As a D&D player ( usually the dm.) i have seen some downright miraculous statistical anomalies. And have not questioned any of them, simply due to the fact that i could eliminate all methods of cheating. ( or at the very least, make them noticeable to me.).

Personally , assuming you were tossing the coin in a way i could observe, and there was no method of cheating possible. Then i would not question any number of " heads" ( i mean hell i have seen a 100 sided dice roll 100 10 times in a row. ). Now the second you have the ability to cheat though, the ol red flag goes up pretty quick.

To pertain to religion, well it should be obvious, they have all kinds of ways to cheat. Simply the definition of god allows them to cheat every time evidence is shown contrary to its existence. Really, religion in general, and christianity in specific is pretty much made out of ways to cheat logic. ( You can't see god, god won't ever do anything like parting a sea again, god is loving but allowed to do things that would make Hitler cringe because they are 'his way', as just a few examples). Which is what puts up the red flag as to b.s. to me. It is not so much the claim to always have heads ( or to use a d and d analogy, always roll a 20) , but the fact that their entire structure is set up to make cheating ( in regards to following logic.) very easy to do.

No you haven't.

 

[Malerin]

Actually, my above post is a good example of Simon's problem: at what point do we conclude that an internet poster is exaggerating (or misremembering) an incredibly improbable event?

If I claimed to have seen a fair coin land heads 10 times in a row, no one would be that impressed (although some would probably wonder how I knew the coin and tosses were fair). If I claimed to have seen it land heads 20 times, a few (or many of you) would outright not believe it (or be convinced it wasn't a fair coin/toss). Only the biggest sap to ever post on the forums would believe it was a fair coin and toss if I claimed to have seen it land heads 50 times in a row. And that last result is much more likely than getting a 100 on a D100 ten times in a row. Hence, the skepticism of SadHatter's claim.

Of course, given a fair coin and toss
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
is just as likely as
THHHHTHHTHHHTTHHTTTTTTHHHHHHTHHHHHT

 

[Roboramma]

( i mean hell i have seen a 100 sided dice roll 100 10 times in a row. ).

The chances of that happening are 1/100¹⁰.

That's 1 in 100,000,000,000,000,000,000.

You could roll your D100 dice once a second for a million years and you would still be extremely unlikely to have a single sequence of 10 consecutive 100s.

So I'm quite confident that either you are exaggerating, misremembering, or there was some sort of cheating involved.

 

[sadhatter]

The chances of that happening are 1/100¹⁰.

That's 1 in 100,000,000,000,000,000,000.

You could roll your D100 dice once a second for a million years and you would still be extremely unlikely to have a single sequence of 10 consecutive 100s.

So I'm quite confident that either you are exaggerating, misremembering, or there was some sort of cheating involved.

And there is the rub. I wouldn't expect one to believe because there would be quite a chance of cheating. Specifically on my end, i could easily be exaggerating, or have been cheated myself.

It is not the result, but the situation that determines how valid something is.

As an aside, to rebut claims of cheating, simply for the lulz, and that i have some spare time. It is statistics, if it can happen it is bound to happen to someone. During my almost decade of playing the game i have seen some rather wacky rolls. From the top of my head, some of the better ones have been:

A d4 landing on a point ( this was actually done over the course of a year, in an attempt to show it could happen.)

A d20 from the time of its use that rolled nothing higher than a 3 for over 50 rolls ( was then microwaved and threw out a window.)

two six sided dice landing on top of each other.

You roll enough dice and you see some wacky crap. I am sure other pen and paper rp'ers have seen just as wacky events.

 

[sol invictus]

One has to be very careful with logic that says "I don't believe you saw such and such because the odds are 1/N". You cannot compute odds like that after the fact - it's a misuse of probability.

Suppose sadhatter had seen a die roll 1 ten times in a row rather than 100. S/he'd be telling us about that instead... which means the relevant odds are not those of that specific event, but the cumulative odds of any event of sufficient interest to sadhatter that s/he would tell us about it.

That said, I don't believe it either.

 

[blutoski]

I knew I'd regret bringing up the god angle ... I know there are lots of arguments and approaches, thank you. Has anyone got a comment to make on the paper?

Only thing I got here is that I need to explain in some detail why normal statistical hypothesis-testing is not good enough for the sorts of questions you get looking into paranormal claims.

I probably wrote my response in a rambling way, sorry. I was trying to address the paper.

The main point I was trying to make is that prior probabilities aside, we will still quibble about the confidence interval thresholds. There is no cultural standard that builds common ground between advocates and skeptics.

The second problem that I didn't mention is that there is often a disagreement about what constitutes the null hypothesis. In your paper it looks like 'phenomenon is naturally occurring'? The reason this is important to paranormal investigation is that when the skeptics succesfully expose a cheat, it's very consistently been about good controls rather than good stats.

 

[bokonon]

I wrote considering the oft-repeated argument (by theists) that the atheist cannot know there is no God because the atheist has not been everywhere.

I think "been everywhere" is the wrong argument, because for most people you're likely to encounter, the God they're arguing for is presumed to be ubiquitous. The claim is more likely to be "the atheist does not know everything," which is perhaps more fair. Why would you be more willing to accept that there are billions of neutrinos streaming through you every second (you just can't detect them) than that there is a divine spirit maintaining the distance between electrons and protons (you just can't detect it)?

Certain other values of "God" are more easily dismissed: A god which will override the laws of physics in your favor if you pray, for instance, can be falsified by showing that no such override occurs.

As far as the coin is concerned, the odds of a string of consecutive heads is halved with each fair throw of a fair coin. The odds of throwing 6 heads in a row is one in 64. If we began a string of throws with 6 heads in a row, that would pass my own personal threshold for being confident that either the coin or the process was weighted, though of course I wouldn't be certain. If that was followed with six more heads in a row, I'd claim certainty.

 

[This is The End]

Suppose sadhatter had seen a die roll 1 ten times in a row rather than 100. S/he'd be telling us about that instead... which means the relevant odds are not those of that specific event, but the cumulative odds of any event of sufficient interest to sadhatter that s/he would tell us about it.

I'm fairly certain that the total number of significant interest events would still be a drop in a bucket. At least in this scenario.

Like in your example, changing the number that appears 10 times in a row. That would be any of the 100 numbers.

100 in 100,000,000,000,000,000,000 is, relatively speaking, nearly the same as 1 in 100,000,000,000,000,000,000.

Add in 900 more "significant events" (which you would think would cover them all); like consecutives (rolling a 1 then a 2 then 3.... up to 10), and it would still be 1000 in 100,000,000,000,000,000,000.

What's an extra zero or two amongst friends?

That said, I don't believe it either.

I notice that in sadhatters newest post s/he doesn't deny that this 10, 100s in a row on a 100 sided die happened.

 

[Piggy]

At a certain point, we need to do what our brains are evolved to do, which is to be suspicious of severe statistical anomalies.

If you're asking for a philosophical or mathematical bright line, you can take your ball and go home.

But if a coin lands on heads even 100 times in a row, we all know it's not a fair coin. The real world we live in simply does not work that way.

 

[Alan]

At a certain point, we need to do what our brains are evolved to do, which is to be suspicious of severe statistical anomalies.

If you're asking for a philosophical or mathematical bright line, you can take your ball and go home.

But if a coin lands on heads even 100 times in a row, we all know it's not a fair coin. The real world we live in simply does not work that way.

It can happen. Our brains are not good at calculating statistics.