Re: Probability, Evolution, and Atheism

On May 30, 7:31 pm, tonysin <a2mg...@xxxxxxxxx> wrote:
Alvin Plantinga is a theology professor at Notre Dame, and he wrote
this essay on why belief in evolution is irrational:

http://www.christianitytoday.com/bc/2008/julaug/11.37.html

PZ Myers is a scientist who writes an excellent blog on science and
atheism called Pharyngula, and he wrote this entry to refute
Plantinga:

http://scienceblogs.com/pharyngula/2009/05/alvin_plantinga_gives_phil...

In his essay, Plantinga uses an example of the extremely low
probability of flipping a coin 1000 times, and having heads come up at
least 75% of the time.

In his refutation, Myers scoffs at Plantinga's innumeracy, wondering
why he had to get help to do the calculation: "He needed help from an
expert to multiply simple probabilities? Does being a philosopher mean
you're incapable of tapping buttons on a calculator?"

Well, I agree with Myers that Plantinga's argument is lame, but I
disagree that the calculation is trivial. I would appreciate it if the
members of this group would help me out.

The problem is to find the probability that out of 1000 tosses of a
fair coin, 750 or more will be heads (I've changed the terminology a
bit, but not the math). My math is rusty, but it seems fairly clear
to me that the probability of getting *exactly* 750 heads out of 1000
tosses is the number of combinations of 1000 taken 750 at a time,
divided by 2 to the 1000th power, i.e.

(1000! / (750! * 250!)) / (2^1000)

I hope I'm right so far. Then the probability of getting exactly 751
heads is the same formula, but with 751 at a time, and so on. And so
the probability of getting AT LEAST 750 heads is the sum of the 250
terms for the probabilities of getting exactly 750, 751, ..., 1000
heads in 1000 tosses.

Am I right so far?

If so, I don't see a non-tedious way to add up the 250 terms, nor do I
know of a calculator that you can just "tap buttons" for numbers that
size. All of my calculators give an error for any factorial much
larger than 70!. Even my Microsoft Math 3.0 won't do combinatorics on
numbers that size. I imagine that a specialized program like Maple or
Mathematica would, but I don't have those.

So my question is, is there an elementary formula for summing those
250 individual terms to get the exact cumulative probability, or do
you have to use some approximation formula (like Stirling's formula
for large factorials) if you don't want to add them one by one?
Thanks for any help.

agreeing to the calculation
is completely the wrong way to go with this question

the appropriate calculation
is simply the rate of accumulation of complexity
which is a number that that is much more reasonable

the error with the "portion of state space" approach is:
most of the state space is never tried during evolution

the dynamics don't feel it out

so the extent of that portion
has little connection to the time necessary for evolution

but when there are ways to estimate the complexity accumulation rates
at various positions in evolutions
then there is a chance of a model with predictive strength

to do this
though
shows immediately that the complexity seen
is easily accessible in the timeframe of history

increase in genetic complexity of things like plants
can be as high as 30% or more
for certain hybridisation events
(like chromosome accumulation events)
and it is clear with variability in single genera
that complexity is accumulated with little regard
for the proportion of possible state space it occupies

it doesn't take a million lifetimes (even in parallel)
to add 20 bits of information to the genes

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
.