No place for common sense

Not that this is especially deserving of a reasoned rebuttal:

Peanut butter disproves evolution

…A (serious) Creationist clip showing how peanut butter disproves the theory of evolution…

The video explains that evolutionists claim that energy plus matter sometimes results in the creation of life. But since no one has ever found spontaneously-generated life in a jar of peanut butter, that means that matter plus energy from the sun couldn’t have caused life on Earth… Link

…but I just happened to have one handy in some old e-mail. An outspoken creationist friend of mine wrote:

there are over 200 million different species on this planet. Since each is (presumably) evolving differently and over time, it seems reasonable to expect that one, only one, just one tiny one, of these 200,000,000 species would have “sprouted wings” in the last 150 years

where I understood “sprouted wings” to mean “underwent a significant, observable evolutionary change.” That may be a common sense outlook, but this is no place for common sense. Common sense breaks down when dealing with fantastically large numbers and fantastically small odds. Here is how I replied:

Let’s say the earth is 4.5 billion years old, and it took all that time to produce 200 million existing species. (We’ll treat the many other species that have come and gone as statistical fluctuations.) That’s 0.044 species per year on average. Over 150 years you should then expect to see the emergence of 6.67 new species on average, which is .00000334% of the total number of species. Easy to miss.

Let’s do it another way: 0.044 species per year is 22.5 years per species — that is, we should expect a new species every 22.5 years. Assuming each of the existing 200 million species is equally likely to spawn that new species, each species must wait an average of 3.12 billion years to have a 50-50 chance of creating a successor.

(That’s

22.5×log_{1-1/200000000}0.5

1-1/200000000 is 0.999999995, which are the odds of a species not spawning a new species in one year. 0.999999995×0.999999995 are the odds of not spawning a new species for two years in a row; 0.999999995×0.999999995×0.999999995 are the odds of not spawning a new species for three years in a row; and so on. How many times must you multiply 0.999999995 by itself to get to odds of 0.5? That’s what log_{1-1/200000000}0.5 tells you.)

That’s by no means a rigorous analysis — it’s full of extremely coarse assumptions, among other things — but it should be at least accurate enough to convey the vastness of the timescales involved, the number of species, and the odds against having any particular evolutionary expectation met.

Or, as Darryl Zero said,

Now a few words on looking for things. When you go looking for something specific, your chances of finding it are very bad, because of all the things in the world, you’re only looking for one of them. When you go looking for anything at all, your chances of finding it are very good, because of all the things in the world, you’re sure to find some of them.