The Geometry of Judaism

I sit at my desk at home near the end of April, far from the joyous Lag Ba’Omer bonfires crackling in Meron a world away, surrounded by my sefarim and books, engulfed by endless online shiurim and 24/7 news crawls on tv. All of this brings to mind a line from the poem The Waste Land, “ These fragments I have shored against my ruins.” Outside my window on the radio of a passing car, Alicia Keyes is singing, and I ask myself if her recorded voice, suddenly lost to the gunning of the auto engine, was kol isha? Or was it dependent upon my intent? And then I try to reimagine authentic Orthodoxy, try to reconcile what my friend the hazzan calls “a classical Judaism…structuring life by following classical forms and ideals” with the modern. The nineteenth century poet of Paris, Charles Baudelaire, wrote: “By modernity, I mean the transitory, the fugitive, the contingent…” And I wonder who will come sit in my circle, who will break bread, who will, so to speak, make minyan with me.

I try to write here descriptively, never prescriptively. I am neither by nature nor by accomplishment one to prescribe, certainly not beyond what berakha to make, the order of prayers, or customs of the holidays. More serious matters, such as applying halakha in sensitive personal situations, determining religious responsibility in idiosyncratic or severe circumstances, resolving problems in the fulfillment of mitzvoth hamurot --these are the weighty issues; though routine to the Orthodox Jewish condition, they are best left to the best trained and broadest-shouldered, the posekim who tower in Torah and rule from an ingrained and humane Torah perspective.

I dare to write impressionistically, venture to lay before you “an unfinished inquiry” in the hope that, somewhere out there, there may be readers who lie awake at night after keriat shema thinking the same thoughts, reflecting on the same joys, mulling over the same spiritual aspirations, contemplating the same concerns for our religious selves. Surely there are readers out there who suffer, not always but often enough, the same inconclusiveness? After all, why re-magine Orthodoxy if we are wholly fulfilled? Is there a “but,” a conscious or unconscious hesitancy that prompts the re-imagination?

I can think of one: “But why?”  Yes, we obey the Law to the best of our human capabilities, yet understanding often eludes us. The Chofetz Chayim recognized this. In his introduction to the Laws of Shabbat, he offered the rationale that whoever studies his Mishnah Berurah “will come to know each law, together with its reason and underlying thesis, in both theory and practice.” Rabbi Marc D. Angel recognizes this when he redefines the tam, one of the four sons in the Haggadah sequence. The tam is not “simple and naive” but “pure and whole,” and the tam declares, “I’ll do what my religion requires, but I need something more. I need to know the inner spirit of what the religion demands of me.” Yes, understanding eludes us, yet from the very beginning of Creation, verbal reasoning has distinguished humankind, and the interrogative sentence – Why? What if? To be or not to be? –  has distinguished verbal reasoning. Questioning is an essential tool, a hallmark of our approach to the Torah intended by God to guide every moment of our earthly lives. Certainly we are in our religious rights to seek answers, even impatiently, now, today, before Tishbi Yetareitz Kushiot Uba’ayot, that future time when Eliyahu HaNavi will usher in the messianic age and resolve the unresolved. Admittedly it is stretching the point, but might we not invoke Hillel’s injunction in order to underscore the matter? “Do not justify saying something that is not easily understood on the grounds that, eventually, it will be understood”?


I sit at my desk and my mind conjures voices of the Gaon and the Rav, the Netziv, and Rav Hirsch and the Ramban.  They tumble in memory in no specific manner, for, when the soul wrestles with it, the mind seems to know no order, no time or space, no chronology or hierarchy of Rishonim and Aharonim. Ironically, “There is an order to it all,” they say, their words commingling, “a geometry of Judaism.”

They urge me to go find it in the yod gimmel middot , the thirteen consistent principles of biblical interpretation;  in the underpinning logic of the Seder Olam that “Scripture does not come to hide but to explain” and in the sustained Talmudic attitude “that the essence of Scripture is in the information obtained by logical inferences and extra-logical rules of transference.”

They urge me to find it in the heated Talmudic debate between Rabbi Eliezer and the Sages, where the majority rules by rebutting a bat kol, Divine Voice, from heaven with the biblical text, Lo BaShamayim Hi.” Torah Law,” argue the Sages, “is not decided in Heaven but by application on earth of such hermeneutical principles as have been passed down by tradition.”

They urge me to find it in RavSoloveitchik’s Brisker-inspired pyrotechnics, in the way he discovers patterns across the landscape of authentic Jewish texts and practices, and in the way he elucidates Halakhic Man by comparing him to a mathematician, in that both “ live in an ideal realm…enjoy the radiance of their own creations,” and both discern an “ideal-geometric space [that finds] its actualization in the real world”; to find it in the Gaon’s appreciation of mathematical knowledge and reasoning as a means of understanding the world and of divining its relationship to the ideal Torah.

They urge me to find it in Rav Hirsch’s recognition, as described by Dayan Grunfeld, of two revelations, Nature and Torah, each with a set of principles applicable to its own realm, and in Rav Hirsch’s “endeavor to explain the Biblical text out of itself…to objectively investigate the sources of Judaism as given phenomena” by means of a divine science, a geometry, so to speak, of Judaism.

They urge me to go find it in the Netziv’s introduction to his Humash commentary, Ha’amek Davar, where he draws a similar analogy to that of Rav Hirsch: just as it is a mitzvah for the nations of the world to glorify God by studying Nature via the different disciplines of science, so is it our profound obligation as the Jewish nation to study the Torah and to discover therein all that is Divine. 

And, finally, they urge me to find it in the Ramban’s symphonic hakdama to Sefer Bereishit, where he depicts the many portals of wisdom that God created and transmitted to Moshe Rabbeinu– the portal of wisdom concerning the mineral world, the portal of wisdom concerning vegetation, the portal of the trees, the birds, the fish, the wild beasts, and so on until the nigh-supreme portal of wisdom concerning human beings, those creatures in God’s image who possess speech and reason and knowledge of right and wrong.

Echoing these Gedolim, in faint reverberation, come words of mathematicians from off my bookshelf. Here is number theorist Abraham Fraenkel: “The mathematician does not invent the objects of his science – he discovers them.” And here is another theorist, Srinivasa Ramanujan: ”An equation for me has no meaning, unless it represents a thought of God.” And now Kurt Gödel, one of the great thinkers of the 20th century: “Mathematics describes a nonsensual reality that exists independently both of the acts and of the dispositions of the human mind.” Floating in like a coda come these words of Michael Tanner, a Cambridge philosopher: “Mathematics is especially fascinating since it both proceeds according to its own laws but also works wonderfully well, for the most part, in application to experience.” 

So too, suggests Tanner, might we describe instrumental music: “ a self-sufficient series of sounds, which succeed one another according to ‘laws’ which bear only tenuous analogies to anything outside music;” so too, the game of chess, “another extremely elaborate activity that seems capable of endless expansion, but one that is autonomous.” So too, then, in this light, might we gain a glimpse of how the Gaon and Rav Hirsch and the Netziv understood the ideal, transcendent Torah.  And so too would the Rav recognize in Tanner’s view his own analogy of mathematics to the halakha, which proceeds according to its own laws and works wonderfully well in affording the practicing Jew “a living experiential feeling that innervates and enlivens hearts,” as Rav Soloveitchik himself expresses it,

But what can we do when reason leads to contradiction?  To confusion? To uncertainty?  That is where conflict appreciation comes in. Not “conflict resolution,” but, if we are reimagining Orthodoxy, conflict appreciation, indeed. Again, like an incantation, words and phrases of the Rav come to the fore –  “fraught with contradictions,” “wrestles,” “struggles with affirmation and negation,” until finally,“out of the contradictions…there emerges a radiant, holy personality whose soul has been purified in the furnace of struggle and opposition.” Why, after all, shouldn’t we experience bouts of uncertainty?  Entertainment of doubt? Possibility of being wrong? RavSoloveitchik dominates yet again, this time in full oratory: “The grandeur of religion lies in its mysterium tremendum, its magnitude, and its ultimate incomprehensibility... The beauty of religion, with its grandiose vistas, reveals itself to man not in solutions but in problems, not in harmony but in constant conflict of diversified forces and trends.”

Certainly, science knows uncertainty. Werner Heisenberg’s experiments led to a principle of uncertainty in the last century, and multiverse theorists in this century, including famed physicist Stephen Hawking, posit different universes with different systems of physical laws and behavior, one system potentially confounding another, straight lines not certain to be the shortest distance between two points. On the other hand, and despite the challenges of uncertainty and indeterminacy, there are those scientists who, in their particular fields, might be said to parallel the Gaon and Rav Hirsch in seeking a unifying ideal, a scientific analogue, narrowly speaking, of the ideal Torah. In 2007, Physicist A. Garrett Lisi proposed “A Geometric Theory of Everything,” as Scientific American later dubbed it, encapsulating its thesis as, “Deep down, the particles and forces of the universe are a manifestation of exquisite geometry.” A geometry of science, a geometry of mathematics, a geometry of Judaism – clever analogies, perhaps, but what then are we to make of the last, which concerns us the most?  What does Orthodoxy, a prime breeding ground for proof texts, seek to prove?

As an autonomous system of Law and Ethics, Orthodoxy promises integrity, conscience, identity to those who adhere to its principles, but does it promise them certainty? Surely it sustains those who practice it, teaches us how to tame this world, affords us templates like Shabbat, Rosh Hodesh and holidays to sanctify our time; like synagogues and the peah corner of a field set aside for the poor to sanctify our space,; like bikku rholim and bal tash-hit to sanctify our deeds; like fixed prayer and, keneged kulam, equal to all, Torah learning to sanctify our thoughts. As Rabbi Ira Rohde writes, “Participation in classical Jewish forms does not merely mold or perfect Jewish character, it actually constitutes that character out of undifferentiated chaos. Structure gives coherent, intelligible meaning, and meaning gives life substance.”

Orthodox tradition does promise certainty in the world to come, envisioning experiences of eternity meted out on a sliding scale according to our levels of adherence to Torah ideals during our lifetimes. But contemplation of olam ha’ba, except for the most saintly among us, rarely forestalls the anxieties, the fears, the dark moods that might trip us up…at any moment…unforeseen. Still, as the Rav exhorts, why are we seeking certainty and proof when “the grandeur of religion lies in its ultimate incomprehensibility”?

So I look into the essays of Rav Soloveitchik’s talmid and son-in-law, Rav Aharon Lichtenstein, where he explores the possibility of finding a middle ground that is “halakhically and hashkafically defensible” for those who, like the tam, the pure son, need something more, need to know the inner spirit. What, I wonder, would it require?  And Rav Lichtenstein answers: “ a principled and consistent attachment…spiritual commitment” to a relevant posek and his community of followers. And, he continues, it would require, too, a self-awareness and conscious avoidance of arrogance and ignorance in the way we seek understanding of both our Torah and our world, in the way we question, in the way we choose our personal religious mentors.

I seek to personally grasp this view, and my tentative conclusions are in no wise endorsed by Rav Lichtenstein. While we cannot find ultimate comprehensibility in religion, we can, like Rabbi Rohde suggests, find meaning in our classical Jewish forms and formulations, in the geometry of Judaism. And perhaps, if we use sound judgment predicated on a genuine Torah perspective, we might with proper motivation, to paraphrase Rav Lichtenstein, selectively gather hashkafic components from various Torah thinkers in order to fuse these into a coherent worldview. 

Now, however, in my mind’s eye Rav Lichtenstein lifts a finger of warning, concludes with a caveat: “Let the selector beware.”  Though he endorses gathering elements “thoroughly grounded in indigenous tradition,” he nonetheless cautions against incorporating “accretions appended to the tradition.” Might we try to argue that one man or woman’s accretion is another one’s Torah U’Mada or Torah im Derekh Eretz? That there may be responsible ways to cast a net into the sea of wider culture in order to find objects, activities, ideas that support and enrich our careers as humans on this planet and potentially even afford us insight into the Torah? Would we be wrong to call upon Rav Hirsch to defend us? These are not rhetorical questions, but sincere stumblings. Do I read Rav Hirsch correctly? Listen with me as he relates how Noah’s son Yaphet produced “nations which characterize themselves in nurturing art, aesthetic beauty…conscious of some higher ideal up to which [humankind] is to work itself out of its crudeness…Through grace and beauty they foster a taste for more spiritual activities, music, poetry, art.” These “spiritual activities” are, admittedly, mere way stations on the road to the ultimate goal on earth, for that is entrusted to Noah’s son Shem, from whom the Jewish people descend. This goal, modeled by the Jewish nation but intended ultimately for all humankind, is “to build their homes on earth in such a manner that God dwells with them.” But, then again, Rav Lichtenstein expresses reservation about Rav Hirsch’s approach…

…And so, my reimagining Orthodoxy comes full circle to un cri de coeur, an appeal not a protest, a heartfelt inquiry not a confirmation bias.  An aggada in the Talmud comes to mind: “A child in its mother’s womb is taught the Torah, beginning to end, but as soon as it sees the light of day, the child is approached by an angel who taps its lips, and suddenly, entirely the Torah is forgotten.” If all Torah learning is a forgetting and remembering, then perhaps that is why our yearning for understanding is so great, since what we once possessed wholly as our own we must now go through life searching for like a lost jewel. Perhaps that is why some of us seek it even in the oddest of places, for who really knows where they might be hiding, those holy recollections of yore? Surely Shem and Yaphet played together as sibling youths, and who really knows what thoughts transcendent Shem and his more earthbound brother shared? As Midrash Eik ha Rabbah confirms: “If someone tells you there is wisdom among the nations of the world, believe him, Torah among the nations of the world, do not believe him.” So who then can say with certainty that knowledge and experience of the wisdom of nations cannot on occasion yield understanding of our experience as Jews and bear fruit in the garden of Torah?

Rising from my desk, I put my iMac to sleep and turn toward my sefarim and books. I am torn between my Rebbe’s Rebbe, HaRav Elchanan Wasserman, who saw up to the Heavens by looking to the ground in order to keep the gashmiyut of the street at bay, and between my heart’s Rebbe, HaRav Avraham Yitzhak HaKohen Kook, who looked into people’s eyes and declared that he could not help but love all humankind; who fervently embraced the Jewish people and their homeland of Zion; who advised that, rather than immediately refute an idea which seems to contradict the Torah, we instead build the palace of Torah above it.  I am torn between Rav Shimshon Raphael Hirsch, whose commentary seems to me to bestride the Humash like a colossus and whose essays bespeak a modern sensibility and a traditional soul, the very model of Torah im Derekh Eretz, and between Rav Aharon Lichtenstein, who analyzes with clarity and brilliance the Torah’s most complex issues, who lives the Torah’s highest ethic, who at times articulates his original Torah thoughts by reference to world literature and classical humanism, and yet who struggles to consider Rav Hirsch’s humanism as something more than an accretion.

So I turn from the bookcase to the window. The street is quiet, few cars pass by in the evening. The lunar month is half gone and the waning moon is reflected in the glass storm door of my neighbor, a jazz musician; for a moment, I fill the evening’s silence with melody by imagining him nestled against the pillows of his living room couch listening intently to Miles Davis’ album Kind of Blue. It is far easier, I tell myself, than reimagining Orthodoxy. Suddenly, my cell phone vibrates, reminding me that it is time for ma’ariv. As I walk out into the night, I find myself both anticipating the ancient invocation of Barekhu in the beit midrash and wondering, still, who might be out there to make minyan with me.