Again, the world is assuredly _perfect_, as being the sensible image and copy of the Divinity, the outward and multiple development of the Eternal Unity. It must, therefore, when thoroughly known and properly interpreted, answer to all which we can conceive as perfect; that is, it must be regulated by laws, of which we have the highest principles in those first and elementary properties of numbers which stand next to _unity_. "The world is then, through all its departments, _a living arithmetic in its development, a realized geometry in its repose_." It is a κόσμος (for the word is purely Pythagorean)--the expression of _harmony_, the manifestation, to sense, of everlasting _order_. Though Pythagoras found in geometry the fitting initiative for abstract speculation, it is remarkable that he himself preferred to constitute the science of Numbers as the true representative of the laws of the universe. The reason appears to be this: that though geometry speaks indeed of eternal truths, yet when the notion of symmetry and proportion is introduced, it is often necessary to insist, in preference, upon the properties of numbers. Hence, though the universe displays the geometry of its Constructor or Animator, yet nature was eminently defined as the μίμησις τῶν ἀριθμῶν--the imitation of numbers. The key to all the Pythagorean dogmas, then, seems to be the general formula of _unity in multiplicity_:--unity either evolving itself into multiplicity, or unity discovered as pervading multiplicity. The principle of all things, the same principle which in this philosophy, as in others, was customarily called _Deity_, is the primitive unit from which all proceeds in the accordant relations of the universal scheme. Into the sensible world of multitude, the all-pervading Unity has infused his own ineffable nature; he has impressed his own image upon that world which is to represent him in the sphere of sense and man. What, then, is that which is at once single and multiple, identical and diversified--which we perceive as the combination of a thousand elements, yet as the expression of a single spirit--which is a chaos to the sense, a cosmos to the reason? What is it but harmony--proportion--the one governing the many, the many lost in the one? The world is therefore a _harmony_ in innumerable degrees, from the most complicated to the most simple: it is now a Triad, combining the Monad and the Duad, and partaking of the nature of both; now a Tetrad, the form of perfection; now a Decad, which, in combining the four former, involves, in its mystic nature, all the possible accordances of the universe.[442]