The triangle holds its place as a symbol in the mathematics of ideal proportions. As a symbol in ethics it at once suggests the idea of mathematical exactness and method in connection with spiritual problems. A true spiritualism is able to demonstrate its position in the exactness of the law of pure mathematics. A spiritualism that fails in this, fails in the only method known to finite comprehension as exact, and leads to the inference, that a law can express more than the law giver. The law of mathematics holds our highest concept of absolute Truth. The law is universal, and in its unfolding gives us the highest possible relation. Music, art, poetry, all that we know of the ennobling and beautifying expressions of the soul, manifest themselves in numbers. The truth of music is in measure; the truth of art is in proportion; the truth of poetry is in ratio. Science has never revealed anything but a broader application of the law of number. Chemistry is combination or addition. Botany is analysis or subtraction. In astronomy we strike the true because the incomprehensible — we deal with the unknown quantity. The true basis of reasoning is from cause to effect. To correctly measure the force of a stream we will go to its source. When the source is unknown, it becomes the unknown quantity of our calculation, and through the application of it as an unknown quantity, we approximate to a true knowledge of it. In dealing with the greatest of all problems — that of existence — mathematical principles have been ignored. I know it is objected that mathematics are too cold for religion. "We want the warmth of sentiment and emotion in spiritual things." The warmth of sentiment and emotion, unsupported by the truth of mathematics, is the song without music, poetry without rhythm, and art without harmony. It abides where music, poetry and art have not yet become the language of the soul. As compared to the warmth derived from a mathematical basis, it is the flash of light reflected from a mirror as distinguished from the direct glow of a sunbeam; one scorches and dazzles, the other warms; one blinds the vision, the other is a "lamp to the feet," revealing the way. A change in the multiplication table to suit the fancy of every one who had a problem to solve, would make a chaos of all calculation — without an exact basis in ethics this is our condition in spiritual things. One man's revelation is not another's; and each holds his opinion, or sentiment, as truth. One man's opinions or any set of men's opinions cannot alter the truth as discovered in mathematics. Here and here only, can we determine the problem of life in the terms of law. Here we reach a solution that brings us to the recognition of brotherhood in spiritual things, as we are a recognized brotherhood in mathematics. The axioms of truth have no more to be changed in dealing with the realities of life, than in dealing with its grosser calculations. A universal brotherhood finds its realization in the universal recognition of a Deity that appeals to all in the harmony of an everywhere manifested law.
Starting with the triangle as the unit of all subjective operations our conception of it is based upon our knowledge of the objective unit: we proceed from a knowledge of the part to a concept of the whole — or unknown unit. To do this we transmute the objective to the subjective and raise the power of the numeral to infinity. When thus raised to the power of the infinite unit the triangle is our symbol for truth. As a symbol for the whole of truth, it holds the key to all science, to all wisdom, and its study leads with certain steps to and through that door wherein the mystery of life ceases to be a problem, and becomes revelation. An understanding of the triangle depends upon the analysis of the objective unit, the arithmetic definition of which is "a single thing." The first idea we get from this single thing is wholeness; nothing can be added to it nor subtracted from it without impairing its unity as a single thing. Second: Its unity involves the idea that it can be separated, that it consists of parts. Third: These parts hold certain unchanging relationship to each other, then as related to its wholeness it has unity, as related to its separableness it has diversity, and as related to its unchangeableness it has identity; unity, diversity and identity, are the essential qualities of every "single thing," or every unit, and the equilateral triangle is the symbol that manifests these three qualities in unity. The figure 3 does not do it as we lose in it the idea of three related parts. Three separate 1's will not do it, as the idea of unity is lost. We combine the three is to express the unity and diversity, and when combined we have the idea of identity, and the triangle is the symbol of the subjective unit, Each side of the triangle is the figure 1, and this manifests unity in its wholeness, diversity in its two ends and identity in its central; point which is changeless for every figure 1. Thus the figure 1 manifests the triangle in the symbol and the first deduction we make is: the unit is a trinity. The triangle is a unit, each part of the triangle is a unit, hence, it follows that every part manifests the whole. Seen in motion the triangle measures the arc of the pendulum, these successive arcs make the circle and the circle marks Infinity — or the pendulum swing that marks eternity in space and time, and so annihilates space and time. This idea of the unit in connection with motion and form gives the idea of motionless and formless as manifested truth. Form and motion involve change, the unit cannot change. The magnetic needle in its perfect poise illustrates what I mean, and shows: the motion of the unit in, positive or centrifugal, in negative or centripetal, and poise. Perfect poise is changeless. The absolute is always the center, a change in the center belongs to finite perception and not to Infinite Truth. The unknown quantity of Infinite Poise will always be the unknown quantity, but as the part manifests the whole we shall always have a measure of understanding proportioned to our discernment. As we do not hold the center, we do not hold both the positive and negative, and so we manifest a minus quantity in all our thinking. The symbol cannot change. Its action in truth is Energy in Poise. Delsarte makes a clear exposition of this principle. Perfect expression in music is vibrating harmony, and then music is soundless. The human form is the prophecy of the principle in limbs — or positive, head — negative and torso — poise, the hand manifests it in fingers, palm and thumb, the thumb indicates the line of physical balance, and falls when the balance is lost.
Blood, bone, and breath, circulation, secretion and respiration: all functional activity shows us the symbol. We have it in the planet as water-centrifugal, earth-centripetal, and air-poise, or manifested as liquid — solid and gas. It expresses the law of chemical affinity and the organic cell. Light, electricity and magnetism are its etherealized exponents. Of the three primary colors, blue is the life or centrifugal ray, yellow is the illuminating or centripetal ray and red is the warm or poised ray. The ideal of these rays is blue for life or will, yellow for wisdom, and red for love, which brings us to the Divine Father principle, the Divine Mother principle, and the Divine Guild as the Divine Trinity of manifested truth, or the circle of manifested Deity. The nearer man approaches a form that manifests Energy in Poise, the nearer he is to taking his place in the line of the triangle. In expression, voice is centrifugal or going out, gesture is poised or within, and the word is concentered or coming back, and this is the order manifested in the child. We reach true expression in proportion as the energy of going out is at one with the energy of coming back: in other words when the impulse of the creature in aspiration is one with the Creator in inspiration, man finds himself a part of the line of the triangle, a part of the word that "in the beginning was God." To express the truth of the triangle, is to manifest the supreme energy of the universe, and that means the bringing of the line of life in ourselves into the line of truth in ourselves. This is the true work of existence. Love measures the poise, and we know when we have attained it. There is no room for finding fault, for recrimination or judgment of our neighbor, the battle is with the self.