Yefet shall dwell in the tents of Shem.
— Genesis 9:27
Beauty is truth, truth beauty.
That is all ye know, and all ye need to know.
— John Keats
What can be more different from truth than beauty? Truth is an objective concept. In mathematics it is always defined with respect to a certain system of axioms. To say that a statement is true means to derive this statement from the first principles – axioms. In empirical sciences, the truth of a hypothesis must be tested experimentally. This objectivity, however, is relative. In mathematics, truth is relative with respect to a given system of axioms. The statement, for example, that given a line and a point, there exist only one line parallel to the given line that can be drawn through the given point is true in Euclidean geometry but is not true in the geometry of Lobachevski. In the empirical sciences, truth is relative to a then current level of empirical knowledge. For example, Newton's law of gravity was considered true until a new astronomical fact – the precession of the perihelion of Mercury – was discovered. This eventually led to the formation of Einstein's General Theory of Relativity, which replaced Newtonian theory as the new "true" theory. New satellite experiments conducted now in space are aimed to subject General Relativity to tests of unprecedented precision, which will determine if it is true after all. Thus, no theory is true in an absolute sense, but only in so far as it does not contradict currently available empirical data.
Beauty, on the other hand, is a purely subjective concept. What seems beautiful to one may be repulsive to another. "Beauty is in the eye of the beholder," as the saying goes.
Beauty is a product of contrast. One color can hardly be beautiful (Kazimir Malevich's "Red Square" notwithstanding). A mixture of contrasting colors, as in paintings by Kandinsky, can be quite beautiful, however. In Kabbalah, beauty is represented by the Sefirah (emanation) of Tiferet (literally translated as "Beauty"). This Sefirah is the merger of two opposite influences – the Sefirah of Chesed (Kindness) and the Sefirah of Gevurah (Strict Judgment). It is a child of the two sexes – male consciousness of Chochmah (Wisdom) and female consciousness of Binah (Understanding). More generally, it is the culmination of a dialectic triad: thesis, antithesis and synthesis; it is in the synthesis of opposites where we find beauty.
At the first glance, truth appears to be different in this regard. Opposites do not bode well for truth. Indeed, the tautology, A = A, is always true. On the other hand, the statement, A = (not A), is never true. Why then, is Truth, in the Kabbalah, represented by the same Sefirah, Tiferet, as Beauty? Perhaps it is because Tiferet represents Divine truth, which can embrace opposites. Indeed, Torah, which is called Toras Emmet, the Torah of Truth, is represented by the Sefirah of Tiferet. Torah embraces opposites: when two Talmudic sages disagree, we do not say that if one of them is right, the other must be wrong. To the contrary, we say, "Eilu v'eilu divrei Elokim Chaim" – both opinions are the words of God. It is noteworthy that the Hebrew word for truth – emmet – is made of three letters: Alef, Mem and Tav. Alef is the first letter of the Hebrew alphabet (Alef Bet), Mem is the middle letter and Tav is the last letter. This signifies that truth must permeate the whole spectrum, from the first letter to the last letter, and ultimately be a synthesis of opposites (as Maimonides rules, the true path is the middle path). Similarly, Kabbalah identifies the attribute of truth with "the middle bolt," which "extends from one end to the other," (Zohar, I:1b, 224a) (as the middle bolt in the Tabernacle, which went through every board, connecting them together) "uniting the lowest and the highest extremmet and making them a single entity, in each level passing through the central point," (Tanya, ch.13). Divine truth, unlike the truth know to us from logic and empirical science, is absolute by definition, because it is revealed to us by the absolute Being – God. Therefore it can contain and unite the opposites.
Emmet, truth, is also associated with the emanation of Yesod ("foundation"). Jacob's son, Josef was a personification of the Divine attribute of Yesod. Josef (as his father Jacob who was the embodiment of the Divine attribute of Tiferet) was beautiful. Both sefiros, Tiferet and Yesod, represent the middle line in the sefirotic tree.
Beauty is subjective. Why, then, is "beauty" the term used by scientists to describe abstract mathematical constructs? What is even more puzzling is that beauty has been described by great physicists as a driving force in the search for a true theory of nature, moreover, as a criterion of truth! The standard answer is that beauty is symmetry. Symmetry plays a fundamental role in science, as every conservation law (such as the law of energy conservation, for example) can be described in terms of a particular mathematical symmetry (called symmetry group). On a spiritual level, however, it seems to me that people created in the image of God, the source of all beauty (recall that Beauty-Tiferet is a Divine emanation), "genetically" inherit the sense of beauty from their Creator, and, therefore, are drawn to beauty. There is also the presumption that the Universe created by God, the source of all beauty, must be conceptually beautiful – hence the search for mathematically beautiful theories of nature.
Two nations contributed most to the Western civilization. The Jews, descendants of Shem, gave the world the truth of monotheism, Toras Emmet. Thus, it is written, "You give truth to Jacob." (Michah 7:20). The Greeks, descendants of Yefet (Japheth), gave us beauty, embodied in its sculptures and architecture. Even the Hebrew word for Greece, Yefet, is etymologically related to the word yafe – beauty. Physical beauty worshiped by Greeks is the antithesis of truth as it is written, "sheker hahein vhevel hayofi…" – charm is deceitful, and beauty is vain… (Proverbs 31:30) This antagonism was the spiritual underpinnings of the war between Jews and the Greeks celebrated during Chanukah. Ultimately, in messianic times, these two opposite concepts, truth and beauty, shall merge, as it is stated in the "Torah of Truth" (Genesis 9:27), "Yefet shall dwell in the tents of Shem."