From the earliest times man has endowed numbers with magical properties. We all know that misfortunes come in threes, that the seventh son of a seventh son has remarkable gifts, and that it is unlucky to sit down thirteen at table. Even in more erudite spheres the tendency is discernible: how else can we explain the interest in perfect numbers, the search for an ever-larger prime, or the desire to add-before computers made it too easy-yet another incontrovertible term to the decimal expansion of x? Few men, in fact, are able to regard numbers as contingent properties of the landscape; to most of us they are entities to be viewed with apprehension or awe. In no field of scientific endeavor is this more evident than in numerical taxonomy. Some taxonomists, placidly remarking that "computers cannot do taxonomy," choose to disregard numerical methods completely, perhaps on the assumption that if one closes one's mind sufficiently tightly, the nasty thing will eventually go away of its own accord. Such an attitude is not harmful; indeed, it may serve the useful function of reminding those of us who work in this field that other, older and well-tried, methods exist, and that large areas of taxonomy can survive without our ministrations. Nor need we fear those who, perhaps from apprehension for their professional future, denounce the methods with Luddite fervor; at least they recognize the problem, and with patience and forbearance on both sides the schism may be healed. But in some numerical writing I think I have detected a hint of authoritarianism a suggestion that the methods are objective and absolute, free from human error, enshrining some form of revealed truth, and that it is only a matter of time before numerical taxonomy supersedes the professional taxonomist. Such an attitude does the greatest possible disservice to the development of numerical taxonomy, for any work of man whether it be a work of art, a tool, or a scientific discovery is diminished in stature if it is made the subject of exaggerated claims. The admirable properties of a hack-saw will be overlooked if one insists on regarding it as a cataract knife. Similarly, the tremendous power of numerical classificatory methods will be dissipated if one insists on claiming for them powers they do not possess and using them for purposes for which they are not intended. But what powers do they possess, and for what purposes are they intended? This article claims to do no more than set down one man's answers to these questions. Nevertheless, any worker in this field will, I think, be led to the conclusion that among many biologists