In heaven the bells are ringing

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…

Jon Garvey

About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
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2 Responses to In heaven the bells are ringing

  1. pngarrison says:

    Have you ever read Dorothy Sayer’s The Nine Tailors? It’s a murder mystery centering around change ringing, which I had never heard of before I read it. Sayers was famously scrupulous for accuracy about facts in her stories, so she matter of factly wrote an authoritative treatise on change ringing as the result of her research for the novel (it wasn’t published with it.) I confess that I never figured out what was going on with the bell ringing until your fine post, but I did solve the mystery before Sayers revealed it, which is the object in a good mystery read.

    When you have grasped just how powerful those bells are, you have a clue as to how the death occurs in the story. I haven’t read it for years, but a lot of people think it’s the best of the Lord Peter Wimsey novels. I have the old BBC production of it on my shelf, so I may have to get it out and watch it soon.

    It’s a wonder that anything ever gets done in Hungary. Maybe they should look into parallel processing. I did a little assembly language programming on the old 6502 (Apple II processor,) and it was a good bit faster than the Hungarian variety.

    • Jon Garvey Jon Garvey says:

      Glad you liked it pngarrison – not quite the usual fare, so I was anxious.

      I seem to have missed out on Sayers’ detective stuff, but can imagine her getting immersed in the campanology as research. There was a short story by John Meade Falkner called “The Nebuly Coat” in which the protagonist keeps hearing in the bell-ringing the protests of the tower that the weight is too much to bear (until it eventually collapses).

      But I have to say there’s nothing quite so English as hearing the bells wafting up the hill from the village of a quiet morning. Except maybe a pint of bitter in the pub opposite the church!

      I have to add regarding the quick sort video that the genteel Amstrad 256 stuff isn’t the kind of music that inspires Bro – this is more his style (work out the time signatures!).

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