Vespers (or too late to be writing)

Insomnia breeds blogs.

I should be sleeping; I should’ve been writing but instead I spent some time re-reading Logicomix; as the name suggests, it’s a comic book about logic. It is actually a comic book about Bertrand Russell speaking about his quarrels with logic, the foundations of mathematics, certain knowledge and life in general. But this is not a praise of Logicomix. It’s rather a praise of Rachmaninoff’s Vespers.

The Vespers are the evening prayers in most Christian lithurgies. It is the most “popular” canonical hour because of course it is the end of the labour day. Nevertheless Rachmaninoff’s Vespers (opus 37) is an a-cappella setting of an All-Night Vigil, which is exactly what it sounds like: staying up all night, praying-in this case-to the Virgin Mary.

I’m not a Christian. What I am right now is insomniac, waiting for the approval of my thesis so I can defend it, and a little worried about life in general and my life in particular. My worries are mundane: what to do next? Is an academic carrer worth the shambles it brings about? The usual stuff a finishing Ph.D. student worries about. But I digress. I’m not a religious person but nevertheless I find compositions like Rachmaninoff’s Vespers truly beautiful. You must listen to it in order to understand:

Staying up all night doing something as praying sound to many-a-one like a complete waste of time. Praying-they’d say-is futile and superstitious. I agree, more or less. I don’t pray. But I do other stuff, like staying up late reading and/or writing Mathematics; reading-and trying to write-Philosophy; cleaning my room (yes, I’m most productive at night; I think most grad-students can relate). All this sounds also as a complete waste of time. Those activities-among others-are my prayers.

Prayer is a fundamental part of monastical work-life; for us Ph.D.s-to-be our work is the only part of our monastical life… well, not quite monastical in the strict sense (we’re far from saints); I mean a life dedicated to wasting time. Speaking of which, insomnia is also a waste of time and the reason I started this blog. Hurrah for insomnia (?).

Another thing that keeps me awake lately is G.H. Hardy’s Ramanujan. It’s not a biography of Srinivasa Ramanujan, but rather “twelve lectures on subjects suggested by his life and work” (official subtitle of the book). If you don’t know who Hardy or Ramanujan were, you certainly are not a mathematician (or math-aficionado). Suffice it to say that they were two of the most accomplished mathematicians of the beginning of the 20th century. More precisely, what keeps me awake in that book lately is the following series:

\displaystyle\frac{2}{\pi}\left(\frac{2}{B_2}\frac{\log x}{2\pi}+\frac{4}{3B_{4}}\left(\frac{\log x}{2\pi}\right)^{3}+\ldots\right)

which is a formula for approximating… but it doesn’t matter. I’m a mathematician, I study things like the above… well, not quite; it’s not a book of my area so perhaps that’s one of the reasons it keeps me awake. I find Hardy’s book fascinating precisely because I understand very little of it. And thus I arrive to my point (if there is one): we spend a lot of time doing very useless things because we find them challenging, fun, interesting and, above all, meaningful; perhaps “fulfilling” would be a better term. Mathematics is all of the above, and much more… at least to us mathematicians.

My point is the following: we mathematicians (and most people doing research in academia) find what we do full of meaning; some feel that this meaning resides in the possibility of applying mathematical knowledge to understand reality; some others think it is a “knowledge-for-knowledge-sake” kind of thing; yet others insist that some mathematics is not only useful but that ALL mathematics is eventually useful… there’s an opinion to suit anybody’s need. Disregarding the whys and the hows it is a fact that we all find what we do meaningful, with “meaning” to be specified by each mathematician. My own take is that math is a very effective kind of knowledge, not in its form but in its “method”; for me it came a moment in which the world started to make sense; I don’t claim I can understand anything you put in front of me, but doing a Ph.D. in math has helped me to strive for clarity, to go to sources, to ask whatever I don’t understand, and (perhaps more importantly) to find out whom to ask, where to find, what kind of sources to consult. I wanted to be a philosopher; that didn’t work out, I couldn’t even start (perhaps some day I’ll write about that). Now I am a mathematician, by trade if not by title; as such I can now say what kind of problems in Philosophy interest me (perhaps I’ll also write about that) and I can more securely find my way through the vast web of knowledge that is Philosophy (and yes, also Mathematics). Also now I know I can do other stuff, not only math. But the path to clarity is filled with turmoil and at some point you just want to end it all (see, for instance this excellent article about the turmoil of doing a Ph.D.) So whatever comes next… let’s see what happens.

Bertrand Russell spent decades trying to use logic to set mathematics on a rock-solid footing thereby dissipating all possible doubts about its validity… which were only noticed by people working on the foundations of mathematics. A very good friend of mine (Mark Spivakovsky) offered this analogy:

Logicians (and people who work on foundations of mathematics) are akin to a society of spiders living in the basement of a very old yet very stout castle; these spiders are no ordinary: their cobwebs are quite fantastic in shape and complexity; these spiders are convinced that it is their intrincate cobwebs that keep the castle in place and standing, so everytime a strong wind blows their webs they hurriedly and painstakingly start weaving them again so the castle doesn’t reduce to rubble.

Indeed, at the turn of the 20th century mathematics was perhaps at the peak of its performance so far; very few working mathematicianas bothered to even study the most basic questions of foundations. They thought: “if it ain’t broken, why fix it?”. So why did Russell et al. spent so much time weaving mathematics from the bottom up? Because they found it compelling, meaningful, challenging, fun (maybe)… just like I like reading a book about number theory even when I have near to zero knowledge of it; or just as people are willing to stay awake until late praying to the Virgin Mary. Well, if that vigil includes Rachmaninoff’s Vespers count me in.