This one’s just for fun, to find joy in some mathematical aspects of the creation. I did a post in September about the principle of plenitude, a term coined by historian of ideas Arthur Lovejoy about a pervading concept of mediaeval and early modern thought in which it seemed that God must create everything possible or short change the world and himself. This was seldom stated overtly, being more part of the warp and weft of thought, comparable to the modern tendency to see absolutely everything in evolutionary (rather than, say, static or cyclical terms). The idea was probably at its peak in the late seventeenth century, summed up in the phrase natura non facit saltus, found in Linnaeus and treated as axiomatic by Newton and Leibniz. Infinities divided up in infinite ways were the big thing in calculus, taxonomy and even astronomy.
I recently found my very own example. Waking absurdly early for a trip to London before Christmas, I heard a BBC radio programme on church bell-ringing, and noted that “ringing the changes” began in the mid seventeenth century too. The peculiarly English idea of change ringing is to play every possible permutation of bells in your belfry by a memorized algorithm dictated by the physical limitations of handling bells weighing up to several tons. The possible combinations increase exponentially with the number of bells, so that a full change of a large peal of twelve bells has never been rung.
How would such a mathematical approach to church music-making ever come about? The man who did most to promote it was one Fabian Stedman, a university-taught clergyman’s son, in his Tintinnalogia of 1671. He has been called the founder of group theory. At the start of the book he writes:
Cambridge Forty-eight, for many years, was the greatest Peal that was Rang or invented; but now, neither Forty-eight, nor a Hundred, nor Seven-hundred and twenty, nor any Number can confine us; for we can Ring Changes, Ad infinitum. Although Philosophers say, No Number is infinite, because it can be numbred; for infinite is a quantity that cannot be taken or assigned, but there is (infinitum quoad hos) as they term it, that is infinite in respect of our apprehension: Therefore a Ringers knowledge may seem infinite to dive so infinitely into such an infinite Subject.
Somewehere lurking amongst his rather secular approach is, I think, an attempt to reflect in church campanology the ways of God’s plenitude in creation:
Ding Dong merrily on high,
In heaven the bells are ringing…
E’en so here below, below,
Let steeple bells be swungen.
But, especially for those unfortunates with no nearby set of village bell-ringers, look at the maths and hear the bells:
But the following video of Coventry Cathedral, perhaps, gives a better sense of the sheer physical and sonic power of these things, which makes it an expression, rather than a mere symbol, of the fullness of creation:
Mesmerising, isn’t it? But, one would think, such an algorithmic approach to music is definitely the product of another age and a lost philosophy. At least so I thought until I received a link to another video from my brother, who is something of an authority on sort algorithms in Applescript as well as being an accomplished player of middle-European ethnic percussion (how many of those do you know?):
My brother says that his own quick-sort is somewhat faster than this, but one has to take into account the rather slow clock speed of the Hungarian processor…