Is there such a thing as a fair die?
102 thoughts on “A question for ID supporters”
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The Skeptical Zone
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Is there such a thing as a fair die?
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Elizabeth Liddle:
Even wronger. Great.
What does it even mean to say that a probability distribution is “skewed”?
How can a probability distribution be skewed?
Yeah, it’s not like its a statistical term or anything. Oh, wait:
http://en.m.wikipedia.org/wiki/Skewness
This from the same guy who just posted
and
No slums but certainly one hypocritical ass.
LOL! There goes Mung, as brilliant and as informed as always, 😀
Richardthughes:
lol. so? Do tell Richardthughes.
Mung: “Even wronger. Great.
What does it even mean to say that a probability distribution is “skewed”? ”
And now you know. I have enlightened you and you are marginally less ignorant.
Imagine the distribution of the sum of two, non fair dice: [1,2,3,4,6,6] and [1,2,3,5,5,6].
It would have a skew of -0.048ish.
Imagine the distribution of the sum of two, non fair dice: [1,2,3,4,6,6] and [1,2,3,5,5,6].
Why would I imagine such thing on just your say so? You’re a known liar.
What are the probabilities?
[1,2,3,4,6,6] – 1/6, 1/6, 1/6. 1/6, 2/6
how is that skewed?
[1,2,3,5,5,6] – 1/6, 1/6, 1/6. 2/6, 1/6
how is that skewed?
(grabs popcorn, settles in to watch Mung make an even bigger fool out of himself than before) 🙂
oh dear Mung, if you could only understand *very* basic maths and very basic sentences:
“Imagine the distribution of the sum…”
“sum” means adding together. So we’re talking about the distribution of the two dice added together.
You could of course do the math yourself, if you’re smart enough, now I’ve explained a very basic statistical concept.
*Mwah*
Adapa,
i don’t think he’ll be giving play by play highlights of this one over at the pillow fort. 🙁
Sure he will! He’ll just Mung-ize it first and tell everyone how you didn’t understand the concept of skew in probability distributions and how he had to correct you.
Adapa,
Oh good! I look forward to an FYI/FTR, “comments closed”.
Richardthoughes:
Indeed, probabilities sum by addition to equal 1. Assuming the die are independent, and why should that not be the case, the probability of each must equal 1.
Which of your die is skewed?
The sum is skewed, mung. The mean of the sum of two normal dice is 7, the mean of the sum of these two is 7.33. They have more high outcomes than low outcomes.
Do you know what a histogram is? If you do plot one for the outcome of all 36 permutations and compare to that of the sum of two normal dice. Describe to us how they look different and then we can discuss what that means.
This is actually useful stuff that you may get to use in your job which I believe is software related?
Poor Mung.
It reminds me of this:
keiths:
Mung:
Unbelievable, indeed.
And then there was the time that Mung thought the T|H in P(T|H) was a quotient.
Perhaps I should set up a remedial math thread for Mung, the way I did for Joe G.
Indeed. What’s comical about Mung is that he insists that he does know, and then demonstrates the opposite.
Elizabeth attributed at least two claims which I never made here or elsewhere:
1. “Random implies equiprobable.” I never said that, in fact I’ve illustrated binomial distributions where the outcomes of each Bernoulli trial is not equiprobable.
2. “The sum of two dice is equiprobable.” I never said that either. In fact I’ve pointed elsewhere the multicplicity for the outcome of 7 his higher than any other outcome, which means non-equiprobable. I linked to it the multiplicity of the sum of 2 dice being 7 in a thermodynamic discussion:
Talk about knocking down arguments I never made nor intended, sheesh…
Moved a few comments to guano. I may have missed a couple that also slip over the line into rule-breaking.
Thanks Alan.
No, you didn’t, Sal, Apologies, I forgot we were talking about two dice. What you did say was:
And I replied:
In other words, the outcomes were still random – they were just drawn from a skewed probability distribution.
So you are equating “random” with “unbiased” or, not “equiprobable”. I’m saying that that is not a good use of the word “random”. Plenty of random draws are from biased distributions.
I hope I didn’t say that you said that! Anyway, I agree you did not. My error arose when I came back to the thread and forgot you’d been talking about “sliding” two dice. One die gives an equiprobable distribution if fairly thrown. One die “slid” will still give a random result, but from a non-equiprobable distribution.
Anyway, my point is, as I said: when using the word “random” it’s important not to slide between meanings. Lots of things are random, but drawn from non-equiprobable and from non-symmetrical distribution (produced by a Poisson process for instance).
It becomes especially important in arguments about “random mutations”. Mutations are random in the sense of being driven by lots of factors to complex to model, but they are not drawn from an equiprobable or unbiased distribution. They are drawn from a distribution heavily biased in favour of what works.
A follow up question then. Is it possible to determine if a die is fair by only looking at the results generated when it is thrown?
For example, I claim a given die is not fair. You claim that it is. Can your claim be supported? How?
Simply saying a die is a fair die if it is fair does not get us anywhere. It certainly is non-responsive to the original question asked – is there such a thing as a fair die?
All you have said is that if it is a fair die, it is a fair die. You might have as well said nothing for all that adds. You’ve not said if such a thing as a fair die is possible under your worldview. Is it?
Reminds me of Jorge at TWeb… “complex specified information is specified and complex”.
Mung’s sure puttin’ on a demonstration of ID!
Mung
Hee hee!
Thanks Elizabeth. Apologies for getting snippy. Sorry we can’t have tea. 🙂
OMagain,
Chi Squared test, probably?
The mutations themselves are biased towards what works?
So like some mutations were tried in the past, and they were not useful to the organisms survival, so the mutations started happening less?
How do mutations know what works and what doesn’t? Mutations give a fuck about what works?
Like at one time the mutations were random, and happened because of imperfections in the ability of genes to copy perfectly. Then eventually they stopped because the imperfections just weren’t very satisfying to the organism, it preferred having perfect copies of some genes, so it decided to stop them from being imperfect.
This theory becomes more amazing all the time.
No. Read what she actually wrote. Again.
What I said is that they are randomly drawn from a distribution that is biased towards what works.
This is because new genotypes are generated from a parent genotype that worked – if it hadn’t, it wouldn’t have generated an offspring genotype.
So all the variant genotypes are much more likely to be quite similar to a working genotype than totally unlike a working genotype.
This is, in fact, why fitness landscapes are smooth – because the offspring of parents are more likely to be very like their parents than totally different. And something very like something that works is much more likely to work than something totally different.
There’s actually another sense in which mutations are drawn from a biased distribution. Instead of thinking of entire genotypes, let’s take a specific sequence, say one that affects the size of finch-beaks..
In a very well adapted population, there will be more less-good variants thant better-than-this variants. So mutations will be drawn from a distribution with a bias towards “less-good”.
However, if the environment changes, e.g. a different size of seed becomes the dominant food source, there will now be a larger proportion of possible variants that are better than the current version than before.
Another way of saying this is that there are more ways of being worse than a goood thing than of being better, but more ways of being better than a bad thing than of being worse.
Elizabeth,
But you are totally misrepresenting what the “they” are. The “they” are the random mutations!
So you can’t say, what they are not really random mutations because they are taken from a pool of random mutations that worked. What the heck does the fact that earlier mutations worked have to do with what mutations would occur and where, in future generations for crying out loud?
The mutations are derived from a pool of mutations which were random, but because the pool was more successful, the next round should be less random??
That is just totally bungled nonsense.
Over at JoeG’s playpen he wrote with regard to the OP:
So that’s one aspect of it – it’s construction, and you mention the other now, expected vs actual outcomes.
I wonder if JoeG or any other ID supporter would care to comment on that specifically? Would they accept such a determination of fairness made solely on the outcome of trials rather than the construction of the die?
OMagain,
A sufficiently skilled and aware entity could throw a fair die in a way that got a specific outcome…
phoodoo,
I don’t believe you’ve answered the question posed in the OP.
In your world, can there be such a thing as a fair die?
Please answer before continuing. I ask politely as thread owner.
OMagain,
I believe I was one of the first to answer your question. Although I still don’t know what it has to do with anything.
I think it becomes a bit like Randi’s challenge. We can all agree on a protocol that would toss a fair die fairly I think.
But once we pare away all the objections, as we will no doubt do over time, what will be left I wonder?
No, you said
Which, while vastly amusing (to you) did not answer the question.
So, yes or no?
You mean its a con?
Answer the question.
Try re-reading what I wrote.
If I roll a die, and you get to roll the same die, the die is fair.
keiths:
Please do. It would be a nice change of pace to come to TSZ and actually learn something.
Well, a thread on probability wouldn’t come amiss. Good idea.
That’s simply not true. There are cheaters die where I can roll any number I like then hand it to you and it’ll “become” fair.
If you don’t want to give a straight answer, that’s fine. I understand the reluctance to not want to put your name against anything you might later have to stand by.
Is there such a thing as a fair die?
“There are cheaters die where I can roll any number I like then hand it to you and it’ll “become” fair.”
lol
It’s true, Mung. The fairness of a die is not simply a function of the die itself, but of the technique for rolling it.
As Sal points out, a skilled cheater can produce a biased result with a perfectly normal die.
There is no such thing as a normal die.
OK. Can you say more?
Normal and Fair are subjective.
DEM don’t define normal or fair, only how to measure bias.
Critics of DEM complain that under their analysis normal is subjective.
go figure.
They needn’t be. There are perfectly good objective definitions for both. But in any discussion, of course, they need to be explicit.
Could you cite specifically where they define how to measure bias? I’m not doubting you, I’m just seeking clarity as to precisely what you mean.