Fools ignore complexity. Pragmatists suffer it. Some can avoid it. Geniuses remove it.

The title is a quote from the pioneering computer scientists, Alan Perlis. I confess that until last week I had not heard of either Perlis or this quote, but I like the quote very much. I still don’t know much about Perlis.

I like the quote because I think it tells the truth. We can all probably think of a time when a foolish and arrogant politician has suggested a simple solution to a complex problem; a solution that is unlikely to work because it ignores the complexity.

Most of us have to just deal with complexity, and suffer the consequences. While a genius like Newton takes the complex orbits of the planets and replaces them with a few simple equations, removing the apparent complexity of the problem and replacing it with simplicity.

I am no Newton, but I do work on a complex problem, how crystals start to grow from a liquid, and I try to at least chip away at the complexity. Hopefully, I do this without ignoring aspects of the complexity that are important, and so don’t fall into the trap complexity sets for fools.

In particular, this summer I am thinking about crystallisation from solutions, where the solutions are written onto a solid surface, a bit like you would write on a surface with a pen. The liquid written onto the surface evaporates and leaves behind crystals of whatever was dissolved in the ‘ink’. Now, nucleation, which is the process by which crystals start to form, is complex enough in solutions which aren’t spread over a surface and aren’t evaporating. So we start off with a complex problem and make it worse.

But scientists have found that writing solutions onto surfaces in such a way that there is a narrow strip of ink that then widens out into a much wider strip, gives them what they want: a large single crystal. This is a bit like if you take a marker pen with a tip that is sharp along one direction and broader along the other and then make a line in which you rotate the pen tip halfway through.

So, the question is: Why does making a narrow strip connected to a wider strip give a large single crystal? The system is complex. There is a lot going on: the solvent is evaporating so it is changing with time, there will be flow inside the drying ink as solvent flows towards the edges where there is faster evaporation, nucleation itself is complex and sensitive to impurities in the ink which will be moving around due to the flow, etc etc.

On the face of it, this is a complex mess, out of which, as if by magic a beautiful single crystal appears. But what if the only thing that is important is the geometry, i.e., the narrow bit at first and then the broader bit? This at the moment is my working hypothesis. This would imply we don’t have to calculate flow speeds or evaporation rates or count impurities, or anything else. I am currently trying to test this hypothesis, to try and avoid making any foolish mistakes, but if it is at least partially true then I will have done a bit of simplifying and be happy.

 

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