>> No, you're missing Gould's point. The thought experiment involves
>> rewinding history and estimating the "ex ante" probability of getting
>> the same result in alternate timelines 2 through n...
>
>
> But given his complete ignorance of initial conditions for his
> "experiment," his estimates of *ex ante* probability have to be
> completely arbitrary.
Sure, but as I said, according to probability theory, it is almost certain that the outcome of a string of millions of random events will lead to a different outcome if the process is repeated. You don't need to know the exact probabilities to make that claim.
>> ...From the standpoint of probability theory, it is highly unlikely
>> that a long string of random events would occur exactly the same way
>> more than once. Simple example: if you flip 5 heads in a row with a
>> fair coin, next time you flip a coin 5 times you are very, very
>> unlikely to see 5 heads in a row...
>
>
> But if you flip that fair coin long enough, you are certain to get
> virtually half the throws as heads, virtually half as tails. That
> 50/50 outcome is all we know when we look at the final "winnings" of
> our bets. The exact sequence of heads and tails is irrelevant.
No, you're confusing the outcome of a chain of different random events and the expected value of the repetition of independent, identical trials. What has happened in the universe is the former, not the latter. --An example: assume the dinosaur extinction event was due to a huge meteorite hitting the earth (I know that is contested, but play along). If that random event had not occurred in universe timeline 2, that would have had tremendous consequences on the evolution of different species on our planet, and we almost certainly would see a different distribution of animal species and families on the planet today. Thus the "exact sequence" in which random events occur has significant consequences, and the expected value of a combination of identical random events over a period of time is irrelevant.
>> ...Thus it is almost certain that a "rewind" of history would lead to
>> different outcomes, simply because random events would "break" in
>> different ways in each timeline...
>
>
> But, as pointed out, the "differences" in final result would be
> infinitesimal. The outcome is absolutely *lawful*.
This makes no sense to me. The laws of probability are what make it almost certain that the repetition of a long string of different random events will result in significantly different outcomes each time.
>
>>
>> ...I agree that this probability argument is moot if you believe that
>> there is an intelligent deity guiding the development of the
>> universe. (I'm not sure if the last sentence of your post is serious
>> or facetious.)
>
>
>
> No deity need have anything to do with it, and a deity *external* to
> nature cannot conceivably have anything to do with it. All that is
> required is the proposition that the ultimate course of events takes
> form in the determining context of formal natural law. Einstein's
> phrase was an idiomatic expression of this (Platonic) concept.
> Sheldrake's suggestion of a "morphogenetic field" is another
> (nonmathematical) expression of that concept.
Based on my understanding of probability theory, I do not share your faith in the immutability and inevitability of the existing timeline. There is also a ideological trope embedded in this that concerns me: "Things have to be the way there are; there is no alternative". I suspect that you would not apply this trope to human history. Given that human activity is part of the universe and often changes the universe, how can the universe as a whole be due to formal natural law unless our existing political and economic systems are inevitable products of formal natural law?
Miles