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Definitions of Race
Disclaimer: The only reason I am interested in doing this is because of people who say it cannot be done. It may be that the definitions proposed by racists are all incoherent, and if people like Kenan Malik confined themselves to addressing particular definitions I wouldn't waste much time checking his claims about them when I had no respect for what the proponents had done with them (with Nicholas Wade being a recent case in point). And the same even applies if someone claims to be unaware of any useful definition. Since I am not in need of such a definition for any purpose either bad (racism) or good (medical optimisation), I would feel no need to provide one. But when someone claims that there is no possible way of doing something then they are speaking in a way that attracts my attention in its own right. ( I would have saved myself some unpleasantness and effort by confining my claim to Malik to a disbelief that his argument was convincing, but having asserted that it is possible to provide a definition I now find myself obligated to do so in more detail than what I have sketched out earlier.)
So let's start with something trivial and see if it can be made useful.
Any totally inbred population can be called a race. Or more generally any set of individuals who are descended only from a particular set of individuals in an earlier generation. In case this turns out to be too restrictive, I will call such a race a race of strict descent. With this definition, any arbitrarily chosen set of individuals can be used to define a race (of strict descent) which will consist only of all their strictly mutual descendants (i.e. not including any descendants obtained through breeding outside the group), so clearly we can't expect all such races to be interesting – but some may be. Note also that an individual can belong to more than one race but that when an individual in a race breeds with someone outside it then the offspring will by definition not be of that particular race (but may perhaps, possibly in many ways, be considered as of some new ones defined as mixtures).
Trivial extreme cases are the entirety of a species and a set of siblings. Races can differ in the number of generations for which they last – which I will call the 'depth' of the race. In the likely event that there has not been a successful breeding of a human with a non-human within the last thousand generations, the race of all humans has strict descent for a depth of at least a thousand generations, but perhaps not as much as a hundred thousand. Any individual constitutes a race of depth zero, and any set of full siblings together with their parents constitutes a race of depth 1 but barring incest, a race started by two people cannot have a depth of more than 1. Adding grandparents would produce a race of depth 2 which could be extended by including cousins which arise from matings between siblings of parents and so on. If matings between first cousins are allowed then such a race started by four people could continue indefinitely and if first cousins are prohibited but second cousins allowed then it would take an initial cohort of eight (and so on). Of course aside from some exceptional cases of political or medical significance such family races are not very interesting (except perhaps to their own members), and the term is most often used in the context of larger groups.
The population of any unvisited island will constitute a race of strict descent in the above sense for as long as the island is unvisited after any arbitrary starting point, and similarly for any other isolated population. After whatever date is used for the definition of such a race, if the island is subsequently visited then thereafter its population may include non-members of the race of strict descent, but that race will still exist until such time as every member has an ancestor who arrived after the race was established. For example the race consisting of people descended exclusively from those who were in Australia 10000 years ago probably included a large fraction (but by no means all) of those who were there 1000 years ago but of course a very small fraction of those living there now. In fact, even those descended exclusively from the Australians of just 1000 years ago are not only just a tiny fraction of those living there now, but also probably quite a small fraction of that lot who would self-identify as Aboriginal, so the requirement of exclusive descent would probably need to be relaxed in order to come close to matching the more colloquial understanding. One way to do that would be to identify races of partial descent in terms of the percentage of ancestry from the race of strict descent. Any interval between visitors can be used to start the definition of new races of strict and partial descent, but of course such races are unlikely to be particularly interesting until their period of relative isolation has been substantial.
One reason that a substantial period of isolation might lead to a race that is interesting is because of the possibility that occasional mutation, genetic drift, and the effect of a few highly fertile members may result in the population having some different distribution of characteristics from the global average. But having mentioned the word "interesting" perhaps I should go on to say what I mean by it.
One property that we might think of as making an object or property interesting is our ability to identify it (which is probably in some sense the first level of saying that it embodies information). Of course, except in cases involving recent mutations it will almost never be possible to identify an individual with certainty as belonging to a particular race of either strict or partial descent without actually knowing their ancestry, but it may be possible to make an inference which has much better than even odds of being right. Some races will be more easily identifiable than others and the ease of identification will depend on the measurement tools available (eg just superficial observation vs various kinds of genomic analysis) and it might be useful to identify some measure of the ease with which it can be correctly identified via some tool as the "strength" of the race with respect to that tool.
Here's one way of doing that:
A race (of either strict descent or partial descent at some specified percentage from some specified initial population) whose members differ in their mean value of some measure (which may be either directly measurable or defined as a computable combination of more directly measurable characteristics) from the global mean of non-members by more than 2s standard deviations is said to be of strength s with respect to that measure.
With this definition, given a race-measure pair of strength s, if we use the criterion of guessing that a person is of that particular race whenever that person's value of the relevant measure is within s global standard deviations of the racial mean, then for a race-measure pair of strength 2, assuming a normal distribution of the relevant measure in the global population, a randomly chosen non-member has only a 2.5% chance of being misidentified as a member of the race, and similarly for strength 1 the chance of misidentification of a non-member is about 16%.
Of course, many possible distinguishing variables may not be normally distributed. They may be multi-modal or even discrete. So a more suitable definition might be expressed more directly in terms of something like the excess percentage by which the general population meets the criterion over the actual percentage of the general population that is in the target group.
This may not be the only way of organizing things, but clearly, in order to say anything even minimally useful involving the connection between measures of race and other variables, it is necessary to have something of the same spirit which quantifies the uncertainty introduced by using such proxies.
Of course not everyone will have any race of strict descent (or even partial descent at any significant level of admixture – say more than 10%) that is detectable by any measure of significant strength (other than to the extent of mini-races defined by their known ancestry), and with reduced isolation it can be expected that the "strengths" of all races will decline over time, but I am sure that it will take at least several more generations before it is impossible to say with some confidence of at least half of the people we meet either that they have at least ten percent of their ancestors within the past twenty generations who lived in (sub-saharan) Africa, or(non-exclusively) that they have at least that percentage from East Asia, or that they have it from (greater) Europe (including the Middle East and North Africa). And it will be a very long time before we do not have a good chance of identifying, for at least some individuals, much more details of their ancestral histories just on the basis of a quick visual inspection. In the meantime it may be socially harmful to pay much attention to these possibilities but it is foolish to deny that something is possible just because we don't want people to do it.
And although there may be many ways in which even technically correct uses of the race concept can be harmful, there are also benign uses that are worth consideration. One is just to satisfy curiosity about the prehistoric movements of various human populations. And another may be in emergency medicine where it is quite conceivable that a drug whose immediate delivery has a high probability of saving the life of a random human also has a high probability of being fatally allergenic to the members of some particular race. If there is even a low strength identifier of membership in that race (be it visual inspection or self-identification for example) then using it might improve the overall rate of survival.
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