I recently read David Berlinski’s A Tour of the Calculus, a wildly imaginative and lyrical look at the intuition and origination of one of math’s most recognizable elements. I was delighted as he described the wondrous experience of seeing mathematical functions in everyday life (an experience I’m prone to myself), and I was lulled into a certain sense of dualistic comfort when he uncovered the natural yet unexpected partnership between differentiation and integration, the two processes wholly defining the calculus.
While I read today’s teaching, I couldn’t help but be reminded of Berlinski’s musical prose, of the unambiguous manner in which he related unassuming but intimately connected ideas–which is, as you’ll soon see, precisely the challenge presented today.
3.21 Rabbi Elazar ben Azariah taught:
No Torah, no worldly occupation;
No worldly occupation, no Torah;
No wisdom, no piety;
No piety, no wisdom;
No knowledge, no understanding;
No understanding, no knowledge;
No sustenance, no Torah;
No Torah, no sustenance.
Much like addition warrants subtraction and multiplication mandates division, it’s expected of most processes that, once committed, they can be undone. What goes in, comes out. What turns on, turns off. What is broken, can be fixed.
The pairs presented here, however, seem less like inverses than a delicate system of affirmative contrapositives asserting not opposites, but equality.
A palpable allegory comes in the form of set theory, the mathematical understanding of placing things into bins, some of which might overlap, and then analyzing them. A subset is then like a bin within a bin; it may contain only some of the items in the larger bin (a proper subset) or it might contain all of them. To show two sets are equal, we must show the first is a subset of the second, and then the second is a subset of the first. (After all, if all the items are in the same bin, does it matter which is nested inside the other?)
A formal proof supposes an element in the first set and shows how it must therefore belong in the second set as well. Likewise, Rabbi Elazar presents numerous claims of this sort: If there is no Torah, then there is no worldly occupation (translated directly as “the way of the land”), which can be restated into its natural contrapositive (sharing the same truth value) that if there is a worldly occupation, there is Torah.
Rabbi Elazar doesn’t stop there, however, and continues to show that if an element belongs to the second set, it must also belong to the first: If there is Torah, there is a worldly occupation. Thus proclaimed, they must be equal.
A proof shows that something is true; it does not tell us what it means. For that, we fall into the realm of theorems, but what are theorems other than midrashim with a new name?
The middle equalities are most easily interpreted. Although I often consider knowledge and understanding separate entities (much like addition and subtraction), without one, you can’t easily have the other. If you lack knowledge, you cannot understand what you do not know; and if you do not understand, do you truly possess knowledge?
Similarly, with wisdom must come a sense of piety, for if you are truly wise, would you not show reverence for what is before you? And if you show reverence for what is there, does that not enable one to gain wisdom as well?
This brings us to the beginning and the end, the claims that Torah is synonymous both with a worldly occupation and sustenance.
To make sense of the first, I think it’s helpful to remember that “Torah” literally means “law” and a “worldly occupation” is actually the “way of the land.” With these translations in hand, it becomes a trivial proof to show the law designates the way of the land–since by definition, it must be so. The converse, however, isn’t easily as justifiable: does the way of the land truly shape the law–can the way of the land change the Torah?
On this I defer to the Conservative movement as a whole, this great branch of Judaism whose motto stands tall and mighty as “Tradition and Change.”
The rabbis have forever allowed practice to influence interpretation: The terms warranting the stoning of a rebellious son were made so narrow the words were practically unwritten if not for the lesson they taught, telling us how cherished parents should be to their youth. Some forty or fifty years ago, rabbis decided it’s acceptable to drive to shul on Shabbat, even though driving is expressly forbidden as work on the Sabbath, since the observation of the law should never supersede the spirit of the law. Most recently, the Conservative movement has opened its arms to the LGBT community in the face of glaring Biblical prohibitions–prohibitions, mind you, that have been analyzed in context and declared invalid compared to modern same-sex relationships.
In a more secular sense, we need only look at our own representative government in the United States to see how the way of the land truly does influence the law, just as much as the law influences the way of the land.
No Torah, no sustenance, Rabbi Elazar tells us next, and for this, a new approach is yet needed. “Kemach“–here translated as “sustenance”–means “flour” in Modern Hebrew, so I can surmise even in Biblical Hebrew it referred to physical sustenance–that is, food. However, the rabbis were much prone to metaphor (as much prone as I am to seeing the mathematical in the mundane), so I can only assume a metaphorical understanding of this passage is not unwarranted but wholly acceptable, possibly even encouraged.
These words make me imagine the Torah scroll unraveling into the distance, its sewn sheets of parchment, inscribed with the words given to us by God, settling lightly upon the ground to form a path before me. It is a journey of enrichment, of righteousness, of holiness, a virtuous path affirming what Aristotle said that “the action is the result”–by acting righteous and holy, we become–indeed, we are–righteous and holy.
As I walk along this path, the subtle black letters floating up around me like autumn leaves blowing in the wind, each catching the light in its own way, its own flavor breathtaking and indescribable, my spirit finds the sustenance it needs to hope, to love, to press ever onwards even in the face of life’s darkest and most austere obstacles.
This fantasy quickly fades when faced with the converse. How does spiritual sustenance belong to the same set as the Torah? Surely, any other spiritual act could bring us that fulfillment, and in many ways in my own life, such other acts had–and in the lives of others, who do not take the Torah as their path toward the divine, this question stands yet taller as a pillar dividing, not uniting, the children of God.
The irony of my own journey is that those elements of spirituality I found necessary to leave Judaism to find were ultimately discovered in other realms of this expansive religion that I hadn’t known before. In this particular case, a proof by example suffices–but as any mathematician knows, a proof by example is proof only of the particular, and it is the general rightness of a claim we’re perpetually seeking.
It is my belief–upon which I shall base this forthcoming proof–that God shows himself to different people in different ways, in the manner in which they must find him. I believe no religion is prescriptive of all people, but that all religions unite us in the face of a common creator–who, I might add, I believe takes different forms (and sometimes multiple and contradictory forms) to multiple people.
If with this understanding in mind, the Torah is seen as a particular path to God, yielding a particular point of spiritual sustenance (much akin to the derivative revealing a single point of instantaneous change, an incredibly local characteristic), the converse asserts that any path of spiritual sustenance must draw one back to God (a decidedly global acquisition, one mirroring the rise of area beneath the definition of the integral).
So at last it comes together, that in drawing closer to God, we are sustained, and in so finding sustenance, we draw closer to God.
It amuses me when I can find the religious among the profane, the mathematical among the mundane, but it brings immeasurable peace to my soul when I discover science and faith are one and the same.