The Common Ancestor?

Wow! Dr Adequate really did blow my mind. His logical proof that there must have been an individual who was an ancestor to modern chimps/bonobos and humans AND had (at least) two children, one ancestral to only humans and the other ancestral to only chimps/bonobos is watertight. If we don't throw away common rules of logic, it must be true.After reading the old discussions how the concept of the common ancestor is vague and hard to define, I thought how this relates to Neanderthals and Modern Humans. Am I correct in assuming that the answer to the question "when did Neanderthals and Modern Humans split?," the correct answer is about 70,000 years ago (which is roughly the time they did interbreed, there is genetic proof in the genomes of modern people) or one could argue that it never happened (they were the same species when Neanderthals went extinct, because they had recently interbreeded and modern humans are part-neanderthals)? BUT... in the hypothetical situation that that interbreeding never occurred, they would have split at least 500,000 years ago?

Okay, maybe "split" is not the correct way to describe what I'm after. Clearly they had split when the Wikipedia estimate says (they were two distinct sets with different qualities and had not been in contact with each other for hundreds of thousands of years.)But if we use "being able to interbreed (gametes are able to do so) and also interbreeding" as a definition of a species, this would make Neanderthals and us the same species when speciation is concerned. In that sense there was no split, yes?

It is certainly very helpful in this type of conversations with creationists. I found it informative and well-written. Personally I knew that my third cousin can't be my grandfather's grandfather.

Yes, speciation and determining when it actually happened is a tricky question and what a species mean don't seem to have one unambigious answer. It's more or less a label we humans need to be able to discuss these things using abstract language. In a funny way it seems something instinctively understood and when you look closer, it's a very complicated question. Thanks for your answer.

Setting aside the point that was made ages ago in the first reply (humans are apes), my response is this:If there is a common ancestor to Tram Law, Desmond tutu and Akira Kurosawa, has it been found? If not, should that call into question the existence of their common ancestor?

Yes, obviously specimens of Homo Sapiens have been found.I was more thinking along lines it's an analogy to asking for a common ancestor species of all apes. Since my examples were single individuals, the common ancestor would also be a single individual. And it's just as clear to me that like we don't (not even creationists) doubt there is a common ancestor for modern humans, there's no reason to doubt there's an ancestral species to modern apes, whether it can be found and identified is irrelevant.