Literally meaning “not falling together,” an asymptote is the term given for when a curve approaches a line more and more closely but never actually ever touches it. It’s the name given to the phenomenon of striving continuously for something but never being able to attain it fully. It’s when you’re one millimeter away from something and to the eye’s view, it seems like you’re touching something, but you’re tantalizingly not.
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וַיִּגַּשׁ אֵלָיו יְהוּדָה, “And Judah came close to him’”(Gen. 18.4). The scene is one of tenterhooks and apprehension. Judah is about to plead for his brother Benjamin’s security and so dispenses with the interpreter to speak, at his own peril, directly with Joseph, viceroy of Egypt.
This coming close predicates Judah’s success. And yet it is a strange choreographing.
Of the 20 times this action of “n-g-sh,” “coming close” appears in Genesis, the first instance occurs with Abraham coming forward to God to intercede on behalf of the inhabitants of Sodom (Gen. 18.23). It is a coming close that dispenses with other forms of connection and which strives for ultimate closeness to achieve the suppliant’s aims. It contains an imbalance of power and something unexpected. Critically, it is also a coming close which axiomatically can never be fully achieved, an irrational pairing of two items.
Akin to Michaelangelo’s “Creation of Adam” fresco in the Sistine Chapel, the biblical Abraham can come as close as possible to God but never be in full contact. That’s just not a possibility for man with God. Accordingly, Judah can never fully meet the viceroy of Egypt, dispenser of life-saving food and imprisoner of his brother, face to face on Judah’s terms. This coming close without accomplishing full connection follows through for the other times that this verb appears. This meeting is indeed, the ultimate asymptote.
The Terror of the Asymptote
The asymptote is, at heart, an unsettling concept. As a young child, I felt somewhat shaken and also amazed by the fact that the world works on such precision and that if everything were moved an infinitesimal distance one way or another, everything would crumble. This formative theological moment is witnessed in Judah’s access of Joseph and repeated in the parsha with Joseph beckoning his brothers to come close to him (Gen. 45.4) — and in Parshat Vayechi, at Jacob’s deathbed (Gen. 48.9; 48.13).
The asymptotic relationship whispers to you that you can think you are coming close to your goal, but you’re never going to attain it. It also tells you that when you are trying to break free of a relationship, your being will never be able to fully puncture the axis of this asymptote. You won’t be able to traverse the exit as the pull of the curve holds you infinitely close to breaking through, never allowing closure. You will always be living the myth of Tantalus, seeing the goods of life within your reach but never being able to grasp them. However, foul is fair and as with most things terrifying, there is beauty paired with this movement.
The Beauty of the Asymptote
Even though Judah couldn’t touch Joseph where he actually was, with the recognition of who he was, still his pleas succeeded. Even when you think you’re not there, at your destination, you can still have an impact. Even though nothing will be real — because you always maintain a threadbare distance — you can still make contact. This is our life.
This relationship with the world is the converse of Zeno’s paradox in its popular form. Zeno’s paradox states that an arrow in flight is, at any single point of its flight, at rest for that moment. Therefore, if you were to stick in pin in the chart of the arrow’s flight, you would see that it was not moving at that point. So the arrow cannot ever approximate its end point — because it’s never moving! However, reality is victorious and arrows do indeed reach their targets, even if, as in the fractured plotting of points, they should not.
When Joseph brings his family up to Egypt, Jacob sends Judah as a vanguard to prepare their arrangements for them in Goshen, their allotted living space. Joseph places them at arms-reach from his reality of Egypt but not too close. Goshen is the place which abuts Egypt, but never quite blends into Egypt: it provides its inhabitants with an asymptotic relationship with the land. They will be able to take from Egyptian goodness without becoming one with Egypt. In this sense, the asymptotic relationship can seemingly be a protective one for national identity and it is intentionally crafted thus.
Indeed, on the verse,
וְאֶת-יְהוּדָה שָׁלַח לְפָנָיו אֶל-יוֹסֵף לְהוֹרֹת לְפָנָיו גֹּשְׁנָה וַיָּבֹאוּ אַרְצָה גֹּשֶׁן:
He sent Judah before him to Joseph, to guide the way before him in Goshen, and they came to the land of Goshen (Gen. 46.28),
Rashi quotes Bereishit Rabbah, 95.3, that Jacob was sending ahead Judah to establish a house of learning which would occupy the Jews there. The midrash understands the words, “to guide the way before him in Goshen” as meaning “teaching how to be close” but not too close.
As hundreds of thousands of Jews worldwide now come to the end of a Daf Yomi cycle (a program of studying a folio of Talmud every day), at the start of another large measurable time block, I am encouraged by the beauty of Judah’s asymptotic plea. Even if the task seems mammoth and it seems like you’re only skimming the surface of what’s there, you might still be achieving something. For Joseph’s dreams were figments of his mind, yet they too turned into reality.
It’s worth asking what the Goshen is that we create for ourselves in our own individual circles and in our wider society. When we are the majority power, to what extent do we put others in a Goshen-like place, only coming slightly close to us, but never touching? Do we ride the asymptote because there is no other option or because it is safe for us? Where should we be aligning ourselves?
It is only on trying to break out from Egypt that we are granted the leader of Moses, who can see God face to face. The rest of us fall short of that face to face meeting, a few asymptotically perhaps, most more obviously so.
I hope that, having left the lights of Hanukkah behind us, and as we are faced with other darknesses, we remember the path Judah paved — to use the asymptotic move to find the protection we need, the courage to attain our dreams and the ability to see face to face with what we need when we break out from our previous path.