I read somewhere once that the majority of people who have ever lived are alive right now. I don't remember enough of my differential equations to verify this, but the reasoning goes something like this.

For hundreds of thousand of years, the human population of earth was relatively small. As technological advances and our intellect led to increased survival, the population gradually grew, and it took quantum leaps with the invention of agriculture and industry and with advances in medicine and public health. In the last few hundred years, the population has grown exponentially, and since the number of people being born is a function of population, and since the number who survive long enough to have their own children increases, eventually you must reach a point where the number of people living exceeds the number of people who are dead. People live longer today, too; they are being born much faster than they are dying off, and our past demographic history was dominated by tiny populations for most of its history.

According to what I read, the point at which the living outnumbered the dead occurred about ten years ago, at about 5Gd (Gigadudes) and even though the calculation was admittedly basd on many assumptions, it is also relatively insensitive to initial conditions. It matters little whether we started off with 1 or 2 million Cro-Magnons.

So if we each are born with the reincarnated soul of one of our ancestors, we are forced to face one of two conclusions: either we should have run out of souls a long time ago, or there is a reservoir of unused souls out there somewhere which is available to be passed on to newborns. Of course, the latter option is equivalent to saying that reincarnation doesn't happen at all, we all start out with unused souls.

Can someone help me sort out this vital existential question?