The ‘Brain Cell Spectrum’
Consider a range of cases along a continuum. On the near end there is an uncontroversial example of a non-person, let us say, a human being that is irrevocably and completely brain- dead, kept alive only by an artificial ventilation machine. On the far end is a clear case of a person, let us say a mature, normally functioning human being. Suppose that scientists have developed the capability to replace every cell of a brain-dead human’s brain, one by one, with exact replicas of the brain cells as they were when they were alive. In the case on the nearest end of the continuum, they replace only 1 per cent of the dead cells with functioning, living ones. In each subsequent case the doctors continue to replace more cells at a time—40 per cent, 60 per cent, 70 per cent—until in the case at the far end there are none of the original dead cells left and the human being has the normal brain functioning of a living, adult human being.
Suppose we are convinced that what started out at the near end of the spectrum as a non-person is, at the far end of the spectrum, clearly a person. What are we to say in all the intermediate variations, where the scientists replace 10 per cent, 40 per cent, or 90 per cent of brain cells cloned from the human? If we accept the punctualist thesis, we must believe that one particular variation marks the point when a human body has become a person. And we would have to say that, for any given variation along the continuum, the individual has either completely acquired the property of personhood, or he has not. Yet it is hard to believe that there exists any sharp point—any critical percentage of brain cell substitution—which is responsible for such a dramatic change. If one simply cannot entertain the idea that personhood is gained instantaneously and entirely with a single percentage variation, there will be ground for serious scepticism about punctualism.
It is irrelevant to the point being made here that the brain experiment is technically impossible. The mere fact that we could not justify identifying the beginning of personhood with a single variation in the abstract hypothetical still reveals something 
about the plausibility of the punctualist thesis. If we were committed to that thesis, we should be able to say quite confidently that one of the variations marks the attainment of personhood, however impossible such an experiment might be. But one could also posit a less fantastical version of a ‘Brain Cell Spectrum’ by inverting the example. In the inverted version, the near end is the case of a human being with a fully functioning brain, whose brain cells die off rapidly one at a time until, at the far end, we are left with an irrevocably brain-dead human being. Again it does not seem plausible to identify the end of the person with the death of any particular cell, although it is evident that the organism at the far end is not a person and that the organism at the near end is one. Our reactions to these cases show that we struggle to accept the ‘existential pop’ idea, particularly because it does not seem reasonable to identify that existential pop with any one of the minute brain variations.
A defender of the conception threshold might object here that brain functioning is not, on her view, the criterion of personhood; genetic humanity is. Being a creature with a set of human DNA, she might argue, is not a question of degree. Thus, the person-making feature, the human genome, does have a sharp borderline. Firstly, however, it must be understood that endorsing a species membership criterion of personhood cannot evade the problems of vagueness showing up on the 'Brain Cell Spectrum'. The human being in question has a full set of human genes both at the near and far ends of the continuum. Unless the proponent of punctualism is going to say that that the subject is a person at the near end, even when irreversibly brain- dead, he will have to say that somewhere along the continuum the human being transforms suddenly into a person (or vice versa, in the case of someone dying one brain cell at a time). And this is the very thing which it seems unreasonable to say.
Secondly, even if we grant that species membership itself is not a question of degree, the coming into existence of a new individual human life form is still clearly gradual. As we have seen, conception is a process like everything else. New, genetically complete human beings come into existence through a succession of infinitesimal events that are non-arbitrarily distinguishable from immediately adjacent events. The advocate of punctualism would still be forced to make the improbable claim that one of these tiny microphysical developments is the sharp borderline between persons and non-persons. Yet the choice between fractional developments here seems just as unintelligible, if not more so, than the choice between brain cell percentages.
However, vagueness can surround the very criterion of species membership as well, at least in theory. To illustrate this, let me introduce another spectrum thought-experiment, formulated by Jeff McMahan:
-  Derek Parfit, Reasons and Persons (Oxford University Press 1984).