APPENDIX A: MITOCHONDRIAL EVE Dennett, p. 97.
Definitions of terms:
A = CURRPOP Current population
B = M(CURRPOP) Mothers of current population
C = M(M(CURRPOP)) Mothers of mothers of current population
D = M(M(M(CURRPOP))) Mothers of mothers of mothers...
DISCUSSION: A society in which all females replaced themselves by giving birth to one and only one daughter who becomes a mother herself is in a "steady state" in regard to mothers. In such a society, B would be less than A (in respect of the birth of males), but there would be no backwards convergence of the sets of mothers towards ever-smaller sets. C would equal B, and D would equal C, etc.
It is only if and when mothers start having "extra" daughters who themselves become fecund that the number of mothers of mothers may possibly increase as we go forward in time. If, for example, out of 100 mothers, 10% of these give birth not just to one daughter, but to two daughters, there will be ten (10) extra daughters. If all of the sisters become mothers, the number of mothers of mothers will increase by ten, minus the fraction of the hundred first-born daughters who do not become mothers, whatever that fraction might be. If it is 10%, the society will be in mother-steady-state once again — with the number of fecund extra daughters just making up for the physiologically barren women and the career girls.
What just "turns out to be the case" carries with it no necessity. Either the set of mothers of mothers will increase, or it will decrease. One can easily imagine a wide variety of contingent factors (Ms. magazine, or the abolition of birth control devices) which might make it turn out one way, or the other.
Looking not forwards, but backwards in time, we are in a position to investigate whether or not the number of extra daughters who turned out to be fecund in fact "made up for" the daughters who were to remain barren. I think that the answer is "Yes," that they did, if only reasoning from tabloid coverage of a world-wide population explosion during recent times.2
I do not know about earlier times, but I think the evidence points towards there being fewer people around. And so I think it's safe to say that the very early sets of mothers of mothers of mothers, etc, were in fact smaller than the later ones, and that these sets do "trend downwards" in size as we go further and further back in time.
However, I do not see them becoming smaller with logical rigor, with one Eve under the cross-hairs. Not unless we are first prepared to demonstrate independently that every example of the species Homo sapiens can be traced back to one physical location and to one woman — to show that human speciation did not occur in different places at different times.
Absent that demonstration, we should be prepared to live with the notion that there were a great number of Eves, each living in different places at probably very different times. We cannot look to the regression of probably ever-smaller mother sets, which is itself an empirical matter — not a matter of necessity — and to the bare logical possibility of one stand-alone Eve, as a substitute for that demonstration.
1 Ordinarily so, but not necessarily so. During the course of a partial or mass extermination of the human species, there might come a point in time when the number of mothers of all human beings remaining alive would be greater than the number of these live human beings.
2 Interesting actuarial statistics would include (a) the percentage of recent mothers who gave birth to more than one child-bearing daughter, and, in those cases, (b) the average number of such daughters, and (c) the average age of these daughters when they gave birth to their first child. This would allow us to calculate how fast the Eve engine has been running, at least over the time periods that we are familiar with, and when Eve lived (if she happened to!)
Editor's note: Professor Dennett has come to agree that there is no logical necessity attaching to the notion of one, stand-alone Eve, and has so stated in his Errors memorandum clickable here.
All original material copyright © Gilbert Scott Markle. All rights reserved.