Thank you.
Now that we have a definition, we can have a discussion. To use my philosophy minor for some use, your argument appears to be the following:
1 - Systems which have identical initial inputs can have different outputs. (In other words, non-determanistic).
2 - Evolution is such a system.
C- Therefore, evolution is random.
I wouldn't call that my argument. For one I talk about two major components of evolution, mutation, and selection. I also go briefly into some of the characteristics of the system would lead to random outputs with random inputs, (the fact the each random input isn't independent of the last, the interdepedency of various species, the non-static environment ...)
1 is just a definition of random, 2 is the conclusion of my argument and C is basically a repeatition of 2.
Your argument is sound, but I disagree with your premises. Specifically, 2. You are including all of evolutionary history as your "system", but only setting the first set of inputs as the same.
I have said, I beleive twice, that even with all non-bioligical inputs the same (meteors, continental drift etc.)
So lets simplify your example into three scenarios:
1) A point mutation occurs. Assuming equal ratios of nucleotide mutation frequiencies, and assuming identical initial conditions, do you think the same mutation would occur a second time?
Not necessarily, specifically because population don't always have all the time in the world to adapt. We are looking at a fairly steady time for humans, but what about populations that are vulnerable. A small breeding population that has a few generations to establish itself either out competes its neighbours or perishes. It doesn't get to roll the dice a thousand times, so mutations don't become inevitable. If a mutation has a one in a million chance it will happend about 6000 times in the next human generation, the same can't be said of smaller breeding populations that occur during history.
Rolling a six on a six-sided die is easy. Just set there and keep rerolling. But if you have to roll it on the next six tries, well now you have a 33% chance of failure.
So while I expect a system of many die-rolls to be predictable, lesser numbers are not.
2) A defined level of variation exists in a population. Selection changes the frequencies of alleles in the population over time (i.e. evolution). Assuming identical initial conditions (i.e. the same defined variation), do you think we would see the same change in allele frequencies occur a second time?
This doesn't invoke the random element of mutation. For the purposes of this argument I am stipulating it is a deterministic process.
3) A population of E. coli exists in which all the members contain a plasmid which encodes a Kanamycin resistance gene. In this gene is a transposon (transposable element), thus switching this gene off. Growing colonies of this E. coli strain on growth medium which contains Kanamycin leads to the arisal of Kanamycin resistant colonies, as a result of the transposon 'jumping' out of the gene, thus switching it back on. When this happens is unpredicable. Given identical initial conditions, do you think the same ratio of Kanamycin resistant colonies would arise?
The number of E. coli around makes me expect that variation in number would be pretty minimal. Again your dealing with a vary large population.