In his book, Is God A Mathematician?, Mario Livio presents amazing evidence concerning the correlation between mathematics and the world. Not only is it in the sciences such as physics and astronomy where numbers play a crucial role in describing and predicting phenomena, it is also true in the human realm, where economic and social behavior conform astonishingly to mathematical principles. For example, the Gaussian bell-shaped curve. Such disparate subjects of measurement as average height and weight among populations, frequency of marriages, crime and suicides were discovered to display the same probabilities. This mathematical principle was previously known in the exact sciences as the error curve, a predictable frequency of error in a series of measurements. They were shocked to find it in so many other areas. Whereas in former times, mathematics was used to check or prove scientific ideas, by the twentieth century the agreement between abstract numbers and concrete things is so close that scientists began to take mathematics as their starting point and then running experiments to verify them. The fact that virtually everything can be expressed mathematically suggests that numbers underly the very structure of reality. In other words, that God is a mathematician.* What does Judaism have to say about this? The Sages say that God created the world not with numbers but with the 22 letters of the Hebrew alphabet. In the Genesis narrative, God spoke and the heavens and earth came into existence. To be sure, this does not preclude the possibility that the “utterances” were actually mathematical statements.** Tradition notes that there were 10 utterances. These parallel the 10 Commandments, and the classic commentaries find significance both in their pairing and in the number 10 per se. There is no denying the significance of numbers in Judaism. In Hebrew the letters all carry numerical values. Aleph equals one, Beis equals two, and so on. Thus, the tradition of gematria, combining those numerical values contained in the verses of the Torah to reveal hidden meanings. ***
For example: Hateva (Nature) = Elokim (God). The idea being that God created Nature and that it expresses His will. Everything from the rising and setting of the Sun to the particle zoo in the atom are emanations of infinite Divine wisdom. Gematria has ramifications in halacha too. The classic example is that of the Nazir, one vows to abstain from wine. The verse about the Nazir says he will be, yeheyeh, the combined numerical value of whose letters is 30. From this the Talmud derives that one who takes the Nazirite vow without specifiying its duration is automatically forbidden from wine for 30 days. There are countless gematrias in the Torah. These gematrias, discovered (not invented) by the early Torah commentators, such as the fourteenth century great Yaakov ben Asher, were the precursors of the computer-generated codes of recent years. Not that either should be taken as a proof for the divine origin of Torah. Indeed, they are only what the Sages call parparos---not the main course, but merely an appetizer or dessert; something tart or delicious to stimulate the appetite or round off the meal. (Pirkei Avos, end of third chapter.) So, Jewish tradition’s answer to Mario Livio’s question is: No. God is not a mathematician. For even if He is the supreme mathematician, He is much more than that. He is the First and the Last; but He is also the Creator of the universe, the Ruler, the Almighty, the Father of Mercy, the wisest philosopher, the greatest artist. To define God as a mathematician would be not to praise Him but to limit and thereby demean Him.**** * In view of this, Livio poses the question, were theorems and proofs of mathematics discovered, or invented? That is, was the relation of the hypotenuse to the other angles of the triangle always there, like America, waiting for Pythagoras to find it; or did Pythagoras invent a way of interpreting reality which miraculously fits the trigonometry of the real world? If it is the former, how did human beings gain access to this “abstract fairyland”? If the latter, how explain “that many mathematical truths anticipated questions abuot the world not even posed until centuries later?” Mathematicians themselves are divided on the issue. But either way, there exists a relationship between mathematics and the world which is nothing short of astounding.
** On Simchas Torah we sing, and from Tzion the Torah will go forth, and the davar Hashem from Jerusalem. While davar here is commonly understood to mean word, the Hebrew word has other meanings, including thing. Mathematics enthusiasts could still take the thing here to mean number. *** Rav Reuven Margolios cites an ancient Hebrew script called Levonai, in which the letters resemble the familiar numerical shapes that have been used through the generations (Hamikra v’Hamesora, P. 75). I haven’t been able to locate it, and if anyone could do so, I’d be grateful for the information. ****Maimonides went so far as to assert that God can only truly be described by negative attributes, what He is not. We cannot adequately fathom His qualities; but we can suggest them indirectly. God is not corporeal, does not occupy space, does not change (another reason for the falseness of the Nietzschean dictum “God is dead”). Maimonides writes: "All we understand is the fact that [God] exists, that [God] is a being to whom none of His creatures is similar, who has nothing in common with them, who does not include plurality, who is never too feeble to produce other beings and whose relation to the universe is that of a steersman to a boat; and even this is not a real relation, a real simile, but serves only to convey to us the idea that God rules the universe, that it is [God] that gives it duration and preserves its necessary arrangement." BTW: The Nietzschean dictum is widely misunderstood. He did not mean literally that God is dead, but that he had ceased to be a living force in Western culture.
Dear Friends E-geress* is back! A year and a half after the passing of Rabbi Yechezkel Fox z"l, our beloved friend and teacher, the founder of E-geress, and after receiving a number of queries about the project, we have decided to resume publication. The website E-geress.org is under reconstruction, and we hope to have it fully operating in the coming days. Meanwhile, we are launching the first new issue in this newsletter. E-geress.org is now available on mobile devices as well. We hope you will like it enough to forward it to friends, print it out and post it too. *What's E-geress? An essay on topics in the news and personal reflections from a Torah perspective, published every Thursday.