Sheldon Pollock’s magisterial work of scholarship, a winner of The Coomaraswamy Book Prize, has been such an unexpected source of enjoyment.
Before I get to his book, and the stream of thoughts that it triggered, let me mention another book that was an even greater joy to read, Wendy Doniger’s On Hinduism:
There are two forms of immortality, for instance, one through one’s own children and one achieved through renunciation. Thus the renouncer’s holiness and knowledge are fed back into society that supports him, and the Brahmin must remain outside society in order to be useful inside. This is a self-contradictory situation, another Möbius strip that folds back in on itself, a metaphysical martini with a twist.
I purchased these two books at one of my favorite bookstores anywhere in the world, BahriSons Booksellers, in Khan Market, New Delhi.
It has become an annual ritual (during my visits to spend time with my parents) to purchase a book on India written by respected academic scholars — Pollock is Chair Professor of Sanskrit at Columbia University, Doniger a Chair Professor (Emeritus) of Divinity at the University of Chicago – from this shop.
Back to Pollock:
….Sanskrit’s unique communicative functions – interpretative complexity, ambiguity, polysemy, imagination, deep play, enchantment.
What especially caught my attention was this:
In other words, what began when Sanskrit escaped the domain of the sacred was literature.
And this, a few chapters later (italics mine):
Literature, however, was a unique form of discourse in which what is said joins with how it is said in an indissoluble unity.
Why did I so unexpectedly enjoy this book?
First, it crystallized in my mind that this is exactly the way I feel about algebraic geometry: it is the Sanskrit of mathematical sciences!
Second, I realized that I have been unconsciously plotting its escape from the ivory tower into the practical world for over 25 years!
Now, I do so, consciously and with renewed vigor in the context of quantum computing, with co-conspirators Raouf and Hedayat.
Our recently published expository article Minimizing Polynomial Functions on Quantum Computers opens as follows:
The present paper tells the new story of the growing romance between two protagonists: algebraic geometry and adiabatic quantum computations. An algebraic geometer, who has been introduced to the notion of Ising Hamiltonians will quickly recognize the attraction in this relationship. However, for many physicists, this connection could be surprising, primarily because of their pre-conception that algebraic geometry is just a very abstract branch of pure mathematics. Although this is somewhat true–that is, algebraic geometry today studies variety of sophisticated objects such as schemes and stacks–at heart, those are tools for studying the same problem that our ancients grappled with: solving systems of polynomial equations.
Actually, the elegant use of algebraic geometry is not limited to AQC.
It finds itself as an even more natural language for NISQ computing!
Compiling quantum circuits lends itself to an elegant formulation in the language of rewriting systems on non-commutative polynomial algebras Q⟨X⟩. The alphabet X is the set of the allowed hardware 2-qubit gates. The set of gates that we wish to implement from X are elements of a free monoid X* (obtained by concatenating the letters of X). In this setting, compiling an idealized gate is equivalent to computing its unique normal form with respect to the rewriting system R ⊂ Q⟨X⟩ that encodes the hardware constraints and capabilities. This system R is generated using two different mechanisms: 1) using the Knuth-Bendix completion algorithm on the algebra Q⟨X⟩, and 2) using the Buchberger algorithm on the shuffle algebra Q[L] where L is the set of Lyndon words on X.
We aspire to match the sublime art that is Sanskrit poetry (काव्य,kāvyá).
What is solved (compiling quantum circuits on NISQ computers) joins with how it is solved (computing unique normal form with respect to a rewriting system) in an indissoluble unity.
I wonder if various Fields medalists (especially the French) and Sanskritists will join forces and call for my excommunication from the priesthood, for being a traitor to my twice-born class, for committing high treason, sacrilege, heresy even, for sullying the purity that has lasted for millenia, not just for developing practical quantum algorithms, but, for heaven’s sake, to do so with software commercialization as an important objective, when they read the recently published interview:
Raising a physical Vesper martini (of course, with a twist) to Sanskritizing and commercializing quantum computing using algebraic geometry and software entrepreneurship!