Q&A: Ethology – Entropy – An Explanation for Ignoramuses Like Me
Ethology – Entropy – An Explanation for Ignoramuses Like Me
Question
I tried, without much success, to read the argument for intelligent design and the challenge to it based on probability.
I don’t understand what is so complicated about seeing that a sequence of thirty 6’s has some added significance relative to a random sequence. Could I get an explanation of what exactly the atheists’ mistake is?
I’ll explain what I mean with a simple analogy.
There are 10 children in a class, each with a shirt of a different color. Only one of them wears glasses. One child went outside.
If you look at shirt color, there is no difference in probability, even if a certain color seems prettier to me.
But if you look at who wears glasses, there is a big difference in probability as to whether the child who left is the one with glasses or not.
That is, while on the level of shirt colors there is no advantage to any color, on the level of glasses there really is an advantage.
When a die comes up 6 thirty times, then from the perspective of a sequence of 30 possible numbers from 1 to 6, the probability of every sequence is identical [the shirt colors].
But from the perspective of a sequence in which all the numbers are equal, there are only 6 possibilities as against the multitude of all the other possibilities, and therefore the probability is much lower [the glasses].
As an aside, it seems to me that there is really a big confusion in the use of probability between calculating forward and calculating backward.
Answer
I’m not sure you mean what I mean when I disagree with this argument, but if you don’t understand, that’s perfectly fine. You should ask the atheists and not me, since I don’t agree with them. This topic has been discussed here at length in several columns and comment threads. See, for example, here; you can see it briefly there:
https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%A0%D7%93%D7%99%D7%A8%D7%95%D7%AA-%D7%9E%D7%95%D7%9C-%D7%9E%D7%99%D7%95%D7%97%D7%93%D7%95%D7%AA
Discussion on Answer
I distinguished there between rare and exceptional. The probability of getting a sequence of thirty 6’s is exactly the same as any other sequence of 30 outcomes. So the rarity is similar, but the exceptionalness is not. I don’t see any connection at all to the question of glasses and colors. With glasses, only one of them has glasses and nine do not. What does that have to do with die results, where all outcomes are equivalent?
Only the sequence of 6’s has the property of continuity that the other sequences do not have [a property that does not exist in other sequences].
The specialness that every sequence has [the definition of its specialness, which the sequence of 6’s also has] also exists for the 6’s.
Let me go back again: the sequence of 6’s has a property/definition like every other sequence — 30 numbers, each of which falls within the range 1–6, and from that perspective the probability of every sequence is equal == like the shirt colors in the analogy.
The sequence of 6’s has a property of equality among the numbers in the sequence that not all sequences have [only 5 other sequences have such a property].
And from that perspective the probability of such a sequence is 6 out of 6^30, as opposed to another sequence, 6^29 == like the glasses in the analogy.
Where is the mistake?
I’m not following you. Are you claiming that the sequence of 6’s has a different probability from any other sequence? Or do you agree with the distinction I made between rarity and exceptionalness? Either way, I didn’t understand your question.
I’m claiming that the sequence of 6’s has two properties [in the analogy: shirt color and glasses].
Every other sequence [except for five more, a sequence of 1’s or of 2’s etc….] has only one property [in the analogy: shirt color].
When I discuss the probabilities statistically from the “shirts” perspective, I get a different answer than from the “glasses” perspective.
That is, the probability of an unordered sequence is much higher than an unordered sequence,
even though the probability of one specific sequence is identical to that of another specific sequence.
In other words, the specific sequence of 6’s does not have a greater probability than any other sequence by virtue of being a number sequence.
But a uniform sequence [which in this case happens to be the sequence of 6’s] has a significantly smaller probability than a non-uniform sequence.
The sequence of 6’s wears two hats: in one hat its probability is equal to all the other sequences, in the other hat its probability is lower.
If so, you’re just repeating my distinction between rarity and exceptionalness. That requires a probabilistic definition; the “hats” analogy you’re putting on those sequences is not enough. But I won’t get into it here. There were several columns that dealt with this in detail, and also in the comment threads there.
Okay,
could you just point me to the appropriate column?
See column 144 and the comments after it (I think 145 also touches on this a bit).
I read there and didn’t find what my soul was seeking,
and it seems to me I still didn’t quite understand how it relates to my question.
And maybe what I wrote there wasn’t understood correctly. If possible, could you read the example again and enlighten me as to whether I’m mistaken?
Is the example of the shirt color and the glasses clear?
Is the analogy to the number sequence correct?
If I’m right, then there’s no need to get to “special” / “aesthetic” / valuable in someone’s eyes….