Binomial nomenclature

“ In selecting this simple method to illustrate the principle of a binomial system of nomenclature, it is scarcely necessary to remind the reader that I do not intend to imply that every man is specifically distinct from his neighbour! ”

“ One feels inclined to apologise for the poverty of language displayed in the heading above; though no one accepts responsibility for it—the fault lies with the Law of Priority. A strong point in the Linnean System of nomenclature was its binomial character—there were two words only in the name of every animal and plant, the first of the two indicating the genus in which it was grouped, and the second peculiar to the species. ”

“ Why not own up honestly and admit that we cannot name such material? We may state that we think it is so and so and where necessary give reasons for the conclusion, but to pass as fact what is only opinion is not the spirit of modern science. The logical solution of the problem is to name subspecifically only such specimens as are humanly demonstrable and use the binomial for the rest. In other words reverse usual practice and instead of using the trinomial regularly and the binomial on occasion use the binomial generally and the trinomial only where necessity or the facts justify its use. ”

“ In the hope of settling it by some system which should be as nearly as possible automatic and should leave the least possible to the inclination or choice of the individual worker, there was formulated what is called the rule of priority. The valid name of a genus or species is that name under which it was first designated, but with the conditions first that the name was published and accompanied by an indication, definition or description, and second that the author applied the principles of binary nomenclature. ”

“ A name is rejected when there is an older valid name based on he same type (typonym) . Examples. — Canon19. A name is rejected when the natural group to which it applies is undetermined (hyponym) . (a) A specific or subspecific name is a hyponym when it has not been connected with a description, identifiable by diagnostic characters or by reference to a type specimen, figure or locality. Examples. — (b) A generic or subgeneric name is a hyponym, when it is not associable, at least by specific citation, with a binomial species previously or simultaneously published ”

“ In recent years the extension of our knowledge of the world's fauna has led to the breaking up of many of the older genera and a regrouping of the species. In some cases the species name has been adopted to denote a new genus, and then the Law of Priority steps in and says the oldest species name must be retained, so that instead of a binomial we get a mere duplication. ”

“ For ourselves, we believe that the surest way out of the nomenclatural difficulties that beset us is to be found in some such simple rule as this, and that to upset every name that can be upset according to any recognized principle is really the shortest road to that fixity of nomenclature for which we now all sigh like furnaces. ”

“ In other sciences the nomenclature is not at present constructed on any system, either because the species to be named are not numerous enough to require one (as in geometry, for example) , or because no one has yet suggested a suitable principle for such a system, as in mineralogy; in which the want of a scientifically constructed nomenclature is now the principal cause which retards the progress of the science. ”

“ Modern progress in biologic science dates from the adoption of the binomial system, and it is not too much to expect that progress in geographic science will similarly be found to be intimately associated with a study of geographic names and the principles which should control in their adoption and use. ”

“ These ideas are further developed in various papers in the Bulletin and in his L'Anthropométrie, ou mesure des différentes facultés de l'homme (1871) , in which he lays great stress on the universal applicability of the binomial law,—according to which the number of cases in which, for instance, a certain height occurs among a large number of individuals is represented by an ordinate of a curve the binomial) symmetrically situated with regard to the ordinate representing the mean result (average height) . ”

“ The author contended therefore that the present exclusive adherence, for all purposes of description, to the Linnean binomial system, which implies classification when classification can only be attained as the end and crown of our work, is philosophically absurd and practically disastrous. The absurdity of starting by assuming what it is the object of all our researches to find out is self-evident ”

“ Genera are not mere phantoms of the brain (as most naturalists will readily admit) ; but they are, likewise, by no means abrupt, or well-marked, on their outer limits (except indeed by accident,—of which hereafter) , but merge into each other by gradations, more or less slow and perceptible. Such being the case, we can easily understand why it is that the followers of the 'Méthode Mononomique' (who, paralysed by the fact that genera are seldom clearly defined at their extremes, would seem to repudiate them in toto) have rashly regarded the binomial system as intolerable. ”

“ We shall see presently that where the classification is made for the express purpose of a special inductive inquiry, it is not optional, but necessary for fulfilling the conditions of a correct Inductive Method, that we should establish a type-species or genus, namely, the one which exhibits in the most eminent degree the particular phenomenon under investigation. But of this hereafter. It remains, for completing the theory of natural groups, that a few words should be said on the principles of the nomenclature adapted to them. ”

“ When a student enters the field of independent research, he is usually but imperfectly acquainted with the principles of nomenclature which should be followed in palaeontological work. After losing himself in a maze of endless synonyms and confused terminology, he recognises the desirability of adopting some definite and consistent plan in his method of naming genera and species. It is extremely probable that whatever system is made use of, it will be called in question by some critics as not being in strict conformity with accepted rules. ”

“ The resolution of the terminology must take into account as a question of convenience that no category higher than the genus may be written into the nomenclature, and as a matter of fact that there are often three or four degrees of phylogenetic affinities which may be recognized below what seems to be best called a genus. ”

“ Some would use only a binomial for every recognizable form, others want to reduce to subspecific status all species bearing close resemblances to one another, and still others champion two kinds of subspecies: Obviously, the adoption of any of these extremes would work much harm, if for no other reason than that the true genetic relationships between most forms would not properly be expressed by the terms employed.
Most conservative ornithologists advocate a middle course and believe that intergradation should be actually proven before reducing any form to subspecific status. ”

“ To one who does not specialize in the history of mathematics such expansions may create surprise, for did not Newton invent the binomial theorem after the death of Oughtred? As a matter of fact, the expansions of positive integral powers of a binomial were known long before Newton, not only to seventeenth-century but even to eleventh-century mathematicians. Oughtred’s Clavis of 1631 gave the binomial coefficients for all powers up to and including the tenth. ”

“ The binomial theorem is a celebrated theorem, originally due to Sir Isaac Newton, by which any power of a binomial can be expressed as a series. In its modern form the theorem, which is true for all values of n, is written as
The reader is referred to the article Algebra for the proof and applications of this theorem ”

“ A binary scale could, as it is developed in primitive languages, hardly extend to 20, or even to 10, without becoming exceedingly cumbersome. A binary scale inevitably suggests a wretchedly low degree of mental development, which stands in the way of the formation of any number scale worthy to be dignified by the name of system. Take, for example, one of the dialects found among the western tribes of the Torres Straits, where, in general, but two numerals are found to exist. ”

“ The object of nomenclature is to obtain a stable list of names, and while experience shows that such stability is unattainable while each author clings to what he or she thinks is the "well-known" name, it equally shows that at first a technical, and then a general, uniformity may be obtained by the rigid application of the principle of priority, whatever the temporary inconveniences of such a course may be. ”

“ Thirdly, as, besides the artificial classes which are marked out from neighbouring classes by definite properties to be arrived at by abstraction, there are classes, viz. kinds, distinguished severally by an unknown multitude of independent properties (and about which classes therefore many assertions will be made) , there must be a name for every kind. That is, besides a terminology, there must be a nomenclature, i.e. a collection of the names of all the lowest kinds, or infimæ species. The Linnæan arrangements of plants and animals, and the French of chemistry, are nomenclatures. ”

“ American Journal of Mathematics, Baltimore, Md. 1888–1890; “Memoir on Symmetric Functions of Roots of Systems of Equations,” Phil. Trans. 1890.
III. The Theory of Binary Forms
A binary form of order n is a homogeneous polynomial of the nth degree in two variables. It may be written in the form
axn
1 + bxn−1
1x2 + cn−2
1x2
2 + ...;
or in the form
axn
1 + (n
1) bxn−1
1x2 + (n
2) cn−2
1x2
2 + ...;
which Cayley denotes by
(a, b, c, ...) (x1, x2) n
(n
1) , (n
2) ... being a notation for the successive binomial coefficients n, 1/2n (n − 1) , .... ”

“ If a title has no number, it represents merely a subject-matter to be divided, a genus,—having no representatives except in the species under it. If a subclass having a generic title has a number, it not only represents a subject-matter to be divided into species but also all other species not falling within the titles indented. Although these relative positions might imply that only proximate species are indented one place, yet mechanical difficulties render it impracticable to so arrange that all species shall be indented under their proximate genera. ”

“ In a finely divided classification, printing of titles for all genera is not practicable; hence great care ought to be directed toward grouping species according to the principles of arrangement herein outlined, noting that whenever a change of basis is made, a new genus is implied, and that subclasses for all other species of the same genus under whatever name, must be brought into juxtaposition as if indented under the implied genus. ”

“ Synonymy is the record of the names applied at different times to the same group or species. With characteristic pungency Dr. Coues defines synonymy as 'a burden and a disgrace to science.' It has been found that the only way to prevent utter confusion is to use for each genus or species the first name applied to it and no other. The first name, once properly given is sacred because it is the right name. All other later names, whatever their appropriateness in meaning, are wrong names in taxonomy. In science, of necessity, a name is a name without any necessary signification. ”

“ Except on subjects for which there has been constructed a scientific terminology, with which unscientific persons do not meddle, great difficulty is generally found in bringing a new name into use; and independently of that difficulty, it is natural to prefer giving to a new object a name which at least expresses its resemblance to something already known, since by predicating of it a name entirely new we at first convey no information. In this manner the name of a species often becomes the name of a genus ”

“ A hybrid between species of different genera may be named by attaching the specific name to the generic name of the female parent, or, if the sex of the parents is unknown, to the generic name coming first in alphabetical order. ”

“ No other science offers so singular a system of nomenclature, so far outside of scientific conceptions. In botany, zoölogy, and topography, objects have distinctive names. We are universally accustomed to apply to the things we speak of designations that belong to them; but a system by itself, a figurative nomenclature, is applied to the groups of stars. ”

“ It was unanimously agreed at Vienna to maintain the oldest specific name when a species is transferred from one genus to another, or the oldest subspecific or varietal name when a subspecies or variety is transferred from one species to another; but, when the rank is changed from species to subspecies or variety, or vice versa, the name need not be maintained, although it is desirable that it should be. To meet this agreement the Philadelphia code requires modifications, as shown by the amendments herewith recommended. ”

“ Binning increases in difficulty exponentially as the number of species increases: the populations and species start to merge together, and the populations get more and more polymorphic and variable in relative abundance (such as in the paper about the Global Ocean Sampling expedition in this issue [25] ) . Further complicating binning is the phenomenon of lateral gene transfer, where genes are exchanged between distantly related lineages at rates that are high enough that random sampling of a genome will frequently include genes with multiple histories. ”