Sunday, 14 May 2006

The Mathematics of Literature

I'd always been very slightly disturbed that I didn't really care that maths has applications; I just enjoyed doing it. I settled it with the thought that I was glad that it is applicable, and that somewhere down the line someone (probably an electrical engineer) would apply it usefully. Therefore working on pure maths is part of the creation mandate for the world.

Yet I felt slightly guilty every time I tried to explain to a person that studying maths meant that I would not become an accountant because mathematics is not really about calculations with numbers at all, but concepts. Mathematics is a glorious ensemble of concepts with which the mathematician plays. Oh, it's work alright, but it's beautiful, much like composing music. What made me feel slightly guilty was the lingering idea that it's all made up (although this doesn't bother students of music too much, somehow it plagues a mathematician a little more, because one is supposed to be, after all, in the science 'half' of the university). Is maths true, in the real world? Or is it merely internally consistent? The mathematical existence of both Euclidean and non-Euclidean geometry really didn't help (it makes maths somewhat relativistic as regards corresponding to the world).

Well, passing from my favourite analogy of music, I propose that maths is like a literary genre. It makes reference to the world, but not necessarily in a one-to-one correspondance. Literature cannot be reduced to propositional facts - that is if one does so, it ceases to be literature and loses much of its value. Each literary genre constrains the presentation of the truth and furthers it - "...every genre works out its own ad hoc arrangement with regard to the word-world relation... Some genres (e.g., history, reporting) add to our stock of propositional knowledge [savoir]; other genres (e.e., poetry, novel) increase our knowledge by deepening or intensifying our awareness of what we already know. [connaître] ... Neither genre is "truer" than the other, each aims for its own kind of engagement with reality and its own kind of precision." (Vanhoozer).

I submit that in this way, the various disciplines are like literary genres. Each genre offers its own language, its own culture, and both author and reader recogise and agree to this. Literature is no less true than mathematics, nor the abstractions of mathematics more or less true than their applications in engineering or chemistry. So what Vanhoozer at one point concludes about literary genre, I propose we may conclude about the various disciplines themselves, insofar as the various academic disciplines act as descriptive frameworks:
In conclusion, genres engage the reader and render reality in different ways. The presence of rules and conventions does not preclude real reference, though the way in which a text 'maps' the world varies from genre to genre. Texts have many kinds of objects and can render them in many different ways. The diversity of genres is yet another confirmation of critical realism. No one form of discourse, no one descriptive framework, exhausts all that can be said about the world, humanity, or God. ...

(See also the post God loves maths. And arts. And science.)

[Quotations of Vanhoozer are from Is there meaning in this text?, IVP 1998]


Jess said...

I don't understand why you feel maths needs to have an application. The whole point of pure maths is that it isn't relevant to anything - that's its beauty.


étrangère said...

Thanks for your comment Jess. Are you a Jess that I know or how did you come by? :)

That maths is intrinsically and internally beautiful does not mean that its beauty lies in irrevelance. I didn't say that it needs to have application in order to be beautiful. However, I suggest that the beauty of maths, much like music or literature, is not that it is only internally consistent but that it makes reference to the world around us in some way. I'm perfectly happy that the mathematician or composer delight in the maths to the glory of our creator God without striving to find application (that is an equally beautiful task for others to do) to give a sense of justification - but that it is relevant means that it is part of the mandate God gave us at creation to have dominion over his creation under him.

marc said...

This doesn't add up.

Okay, sorry about the REALLY bad pun. This is a great meditation. I was recently thinking about posting on fractals for my weekly worship post but was having trouble on clarifying God's hand in the beauty of them. THis is helpful, thank you!

étrangère said...

Glad I helped Marc - you've completely baffled me though how there could possibly be a problem in seeing God's hand in the beauty of fractals. They positively cry out 'God's a glorious creator! Look how he delights in order and makes it so beautiful!' They make a mathmo's aesthetic heart sing - and that's when they're just in equation form ;-) The problem is only when mathmos (or anyone) suppress the fractal-creator-praising song and just praise the fractals.

étrangère said...

Or just praise their own intelligence in discovering fractal-generating equations in immitation. Thinking God's fractals after him and then taking the glory. That would be the only problem I see.

thebluefish said...

and u thought no one would want to read this. let that be a lesson to you.

John Dekker said...

Thanks for the post! (I got here via purgatorio).

You might be interested in Vern Poythress' article, Mathematics as Rhyme.

étrangère said...

John, thanks for that article link - you're right I found it very interesting indeed! I researched the foundations of maths as an undergrad, particularly looking at Russel & Whitehead's logicism and Hilbert's formalist foundationalism, considering intuitionism incidentally, and remained interested because of the obvious limitations of each (straight empiricism never attracted me for some reason!). Always fascinated by logic and philosophy of maths, and interdisciplinary relations. I didn't mean my analogy of literary genre to be exhaustive, but just that - a stimulating analogy. What do you think?

The book he references: Foundations of Christian Scholarship, ed. Gary North. Vallecito, Ca.: Ross House, 1976 could be interesting - I'm interested in a Christian approach to each subject particularly for helping students develop such an approach to their discipline.