Deconstructing the mathematical bridge

For music students everywhere, musical analysis is incredibly useful for many purposes. You can pick out different structures from a musical work, pinpointing particular styles and influences. You can learn to recognise and recreate a composer’s sonic signature in orchestration, rhythm, melody and harmony. Identifying and contemplating these features aids and increases the overall appreciation and understanding of musical works by providing information that connects us back through time to historical context, biography and musical purpose. And, importantly, these are aspects of music that you can hear.

When I was studying for a music degree, we were taught Schenkerian analysis, which I and my closest peers found abstract, boring and pointless beyond its performance as an intellectual exercise. I’m not saying it is pointless, I’m saying it felt pointless and reductive. The joke about any Schenkerian analysis is that what you do is take a great classical work (let’s say Beethoven’s 5th) and reduce it down to the kernel structure of Three Blind Mice.

How neat, how elegant, what a charming coherent unity it all has! Gah, I hated it! How can this possibly add to my understanding when I’m left with so much less than the sum of the parts I started with?

A tutor sympathised with my frustrations, recounting the story of the mathematical bridge in Cambridge. The bridge is hundreds of years old, originally designed by Isaac Newton. Very unusual in design it is made entirely of straight timbers arranged into an arch via some very sophisticated engineering. So ingenious was it that it held perfectly in place between two buildings by its unique balance of tension and compression alone. There it remained for many years until some inquisitive mathematicians wished to understand the design better. They dismantled the bridge with the intention of putting it back exactly as it had been. They failed. By taking it apart and not reaching a full understanding of how it worked, they were unable to restore it to its former elegance and today the bridge is held in place by rivets. Too much analysis can indeed spoil things.

As I start again in psychotherapy I find myself thinking of the mathematical bridge often. Will I discover a new and greater understanding of myself allowing for appreciation, healing and positive change? Or will I be reduced to some disparate sum of my parts that perhaps won’t add up to the whole I started with. Nobody wants to be Three Blind Mice after believing that they might be or have the potential to be Beethoven’s 5th.

What comfort then to discover that the story of the bridge is a myth? The original design (which was nothing to do with Newton at all!) always had rivets in it; there was simply a time when they could not be seen. The bridge has been dismantled and rebuilt twice allowing for maintenance.

There’s a bittersweet quality to myth-busting. The magic of the story that resonates so strongly has to be true, no? As Stewart Lee often ends his ridiculous flights of fancy: ‘This story is not true, but what it tells us is true’. The mathematical bridge myth reinforces our deep fears about self-discovery and change, helping us hide, that’s why we like it. It’s less romantic to go in search of the rivets to tighten them up a bit, but perhaps that’s what the bridge really needs to keep it in place.



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