CONVERGENCE & DIVERGENCE

I stood behind the piano, watching the choir sitting in neat rows, chatting before the carol service started. There was an unspoken thank you in my heart. The Recipient heard it. It was as though all that we'd been working towards since October was converging on a single moment, timed expertly to combine in a uniquely defined point in time.

I say expertly, not to celebrate myself, but really to celebrate the timing. I love this idea of convergence and divergence. In maths, convergence happens when a particular function is zoning in on an exact value. That value is said to be the 'limit' of the function. In geometry, the same kind of thing happens with two straight lines which aren't parallel. Eventually, like the vanishing point of a picture drawn in perspective, there is a moment when those two lines meet. Light rays shining through a lens also converge on a single point - the focal point, where everything becomes clear.

My life feels a little like that sometimes - as though things are slowly but surely converging on a particular focal point. You can look around you and see the trends, the things that point in a particular direction, the combining, twisting forces which are hastily speeding towards each other. At some point, the lines will meet.

It's better this way round than feeling like the things in your life are diverging. Divergent functions are angled away from each other and fan out forever, never destined to meet or reach a conclusion. They were together at one point, but that point is of course, in the past.

The more astute among you will have worked out where I'm going with this idea. Where, or rather, when - because convergence and divergence are all a matter of time. Don't worry though, we'll get there. There is a third case first, balanced perfectly between convergence and divergence. It happens when things are parallel.

In the parallel world, things don't ever change - like railway tracks, the lines stay equally spaced away from each other and snake around the corner in perfect synchronicity until the end of the line. There is no vanishing point in the past or the future, there are just straight lines, each stretching to infinity and beyond with their congruent tangents and perfectly aligned normals all at an eternal 90 degree angle to each other. How very dull. I don't think any of us could live like that.

The subtle point I was getting to is that convergence or divergence is all about your perspective, where you've come from and where you're going. Live time in reverse and the convergence of events becomes a great divergence away from that final (or first) focal point - the sunday roast becomes uncooked vegetables, a clucking chicken, plates in the cupboard and a handful of grapes in a sun-drenched vineyard. The further back you go, the more spread out the components are.

Conversely, a broken marriage, a hurting family and a life filled with endless arguing in the unanticipated fallout of a single terrible event... well, that's a clear example of things diverging. Trace it backwards though, as though you've pushed a rewind button on the video recorder, and the chain of events snaps carefully back into focus, converging at the single moment of detonation. It should be said though, that in the example I've used, it's much more likely that there have been several detonations, some of them quietly unseen and unheard but long before the flashpoint.

So really, this idea of convergence and divergence has everything to do with how we perceive time, how we measure it and how we calculate what happened, what won't happen, and what will.

I'm actually feeling OK with the way things are converging at the moment. True, the angle of convergence is slight and the vanishing point is quite impossible to spot. I'm alright though, with ploughing along the tapering track, wondering how the great Designer will bring these lines together at just the right time. What excites me even more is that there are other lines, probably all over the place - things I just can't see, which are also converging on focal points of their own, some of them maybe even inside my own future experience and heading inexorably towards my point of convergence. I get a little thrill that there are invisible plans out there, plans which give me a hope, and yes, a future.

I smiled as Paul, my friend and pastor, welcomed everyone and sat down, ready for the first carol. I saw rows of expectant faces in the choir, looking at me, waiting for the signal. I lifted my hands. As one, they stood up, beaming with anticipation. I held up a conducting finger and sounded an A on the piano. We were off and it had all come together, just about perfectly in time.