BLTC Press Titles

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The Worm Ouroboros

E. R. Eddison

The Picture of Dorian Gray

Oscar Wilde

The Art of Worldly Wisdom

Baltasar Gracian

Knowledge of Higher Worlds and its Attainment

Rudolf Steiner

Cosmos and diacosmos

by Denton Jaques Snider


Some difficulty has been felt in getting a good title for this third stage of the elemental Cosmos, which stage, as here conceived, is correlative with Motion and Matter. We have before us Magnitude, but it is Magnitude not as real or material, which would properly belong to Matter. It is Magnitude measured, or rather made to measure itself, in its own forms or symbols, which are mathematical, as we see when numbers are applied to themselves, for instance in multiplication. Five times four is one pure Magnitude measuring off another. The algebraic formula a + b is the unity of any two Magnitudes measured and expressed, yet is itself a Magnitude. Now this Magnitude, measuring itself or at least measured by itself in its own pure forms, we shall call Measure.

The standard or unit of Measure as real we have already noticed under Matter. The hand or foot is such a real unit of Measure which is applied to a real object. But measurement as universal must at last be brought to measure itself.. 'If it measures all things it must not fail to include itself in the universal measurement. What we call Measure in the present case has just this peculiarity: it becomes self-measuring, it is forever turning back upon itself with its measurements. When I say: one half of four is two, I am measuring one measurement by another and stating the resultant measurement (there are four halves in two wholes). As we shall see later, this is specially the field of pure Mathematics, which is Measure, or Magnitude measuring itself in its own terms.

It is true that the word Quantity is often used for the preceding word Measure. In that case we would have to say that Quantity now quantifies itself, makes itself its own content—which it does in the mathematical disciplines. Quantity as two numbers being given, they are still quantified by being added, subtracted, multiplied, divided. That is, Quantity is always turning back upon itself and quantifying itself anew, such is just its process. But we have already Used the word Quantity in a different and more fundamental relation: as the third constituent fact of Motion along with Space and Time.

Perhaps it will avoid confusion if we set down in order the three quantitative phases which have already appeared in the present exposition. (1) Motion, we may recall, is the Separating of Nature, and involves the conception of pure Quantity. That is, there arises with. Motion the thought of the How-much, or of the extent of this separation. Such is the primordial idea of Quantity, which must exist before there can be any measurement. Nature must indeed be measurable, must have in it Quantity ere it is measured. (2) In Matter (as well as Motion) we find Quantity, but with certain new properties. Here we come upon a real or material unit of Measure as Quantum, which is applied to other material objects. An illustration is a yardstick measuring a piece of cloth. (3) But now this yardstick must be taken free of its material substrate and made universal; such is the pure unit of Measure, or rather Measure itself in the sense here used, which through its arithmetical numbers, algebraic symbols, and geometric figures has in it the principle of self-measurement. Again we may use an illustration from Geometry. When I enclose a triangle in Space, I limit the same, quantify it, reduce it to a Quantum. But I do not yet measure it. When, however, I find the sum of the three angles to be two right angles, then I have measured it, I have quantified its original simple Quantity. It is no longer a mere Quantum embracing so much Space. Still further, this measured triangle is not merely measured and equated, but becomes itself a measurer, or a principle of measurement, measuring even the area of the circle.

Accordingly we consider Measure to be the third stage of the elemental Cosmos, of which it is an inherent necessary constituent. The Cosmos is always measuring. When it is said that light moves through 193,000 miles in a second, over so much Space in so much Time, this is a cosmical act of measurement, which remains the same. There is no change in the rate when the ray has traveled from a distant star; its stop is just so long and no longer, measured to the unit of Time. Man undoubtedly has to re-measure the Cosmos and formulate such measurement in his own terms; still the cosmical Measure has always gone in advance of him and given him the cue. The mathematician comes to Nature with his Measure, which is Tris science, having the certainty that it is her own also. The unembodied forms of Measure, which are mathematical, become incorporate in the Cosmos, and rule its Motion and Matter. Gravitation is a cosmical Measure (directly as to mass, inversely as to distance) which existed in bodies long before Newton formulated, even before man existed. Indeed this was peculiarly the gift of Newton, the cosmical gift of Measure, which seemed to be stamped upon his soul as upon the soul of the Cosmos.

Motion and Matter must, accordingly, have their thud, which is Measure, in order to form the process of the elemental Cosmos. This process underlies many of the simplest expressions of our daily life. When I say: the train moves forty miles an hour, the conception rests upon Motion, Matter, Measure; or a piece of moving Matter is measured—measured indeed in the science of Measure. But the train must first run at a certain speed, must measure itself in Motion actually, in the special case. Now it is this Measure, inherent in all Nature, which we seek to grasp not merely in the special case, but universally, as it is in itself. It thus becomes the pure form of itself, expressed in its own categories, and measuring itself first of all and not something else.

It is true that when this ideal Measure has unfolded itself in its own pure forms—in numbers, figures, symbols, which represent only its own processes—it is re-applied to the world outside of it; we can say it goes back and organizes Motion and Matter, making their original implicit Measure (or Quantity) explicit, and giving expression to their native but hitherto unuttcred, or at least unordered, harmonies. Mathematics, which we may call the science of universal Measure, is easily cosmical, finding its most open field in the Cosmos. Certainly the Diacosmos is far less mathematical, though it too must have its measurements.

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