How many total ancestors do you have?

From the Daily Kos:

Genealogists identify ancestors by following paper trails preserved in archives, €”traditional and digital. Although the goals of genealogists vary, a large pedigree chart is one measure of success. Yet even the most fruitful family trees are unlikely to yield more than a few thousand ancestors.... Yet, as the mathematically-inclined will be quick to point out, one can never find the names of more than a tiny fraction.

So, is an answer possible? I think the beginning of an answer is possible, within certain limits. This is a question for what might be called theoretical genealogy. Like any question of this magnitude, no matter what the discipline, it requires some agreement on definitions. An ancestor is someone who could theoretically been the source of some of your DNA. I say "theoretically," because most of your ancestors could not actually have passed DNA on to you. The probability is too low, since your number of ancestors greatly exceeds your number of genes. So we are counting parents, plus grandparents, plus great-grandparents, etc., until we reach an arbitrary beginning. 10,000 BCE should do nicely, as it puts us at the very beginning of the Anthropocene, the planet's first geologic era caused by us.