"First, you clearly aren't grasping the actual length of geological time and how much opportunity for change and speciation that presents to an evolutionary process."
No I am pretty sure it is no more than the age of the earth...which is far less than 13.5 billion years (I was being liberal).
Life has been on this planet for at least 3.8 billion years.
Assuming an average generation length of 15 years (which is far too much for an average of all living things that ever existed on this planet, by the way), then we are talking about some
250 million generations. But as that average of 15 years is far too much, the real number of generations would MUCH higher.
"Second, you operate under the assumption of completely "undirected" and "random" process. This is incorrect."
That's odd, I swear I mentioned that they follow physical and chemical laws???
That's not the only thing that directs it.
As explained, the part you seem to be missing, or simply misunderstanding, is the role of natural selection in this process.
Physical and chemical laws are only really limiting things in a physical way - not directing them.
In the sense that, for example, whatever mutations take place, they will be mutations within the scope of what is physically possible.
But evolution isn't "just" a bunch of random mutations mixed together like a dice roll.
The changes are
filtered (directed) through natural selection.
"Evolution is directed simply put, by the environment of the niche a population occupies in the eco-system."
Yes of course in the sense of how variety is formed from allele reinforcement, mutation, and so on...still not enough time and no transmutation.
No. Natural selection.
A few thousand generations is already more then enough to cause speciation events. Geological time gives us millions upon millions upon millions of generations and geographic distribution of species gives us milliosn upon millions of "genetically isolated populations" which causes each of these populations to be on their own evolutionary path - which in turn results in enormous diversity between these populations.
Your high school math simply doesn't add up.
The odds of speciation is another matter...speciation is real but only produces variety not anything new (like fish becoming amphibians or amphibians becoming reptiles or any other such undemonstrated nonsense but go with the sci fi if you want (the problem being not one example of speciation produced anything else but varied forms of the same organism - just like with Darwin's finches...or consider the Horseshoe crab if we need 455,000,000 years as proof)
Obviously, we can't observe processes that take millions of years to unfold.
Why you would even point that out is rather strange.
Nonetheless, the genetic record literally holds the genetic history of any particular bloodline. We can use this record to determine common ancestry between species.
Common ancestry is a genetic fact.
