Greatness

Some are born great, some achieve greatness and some have greatness thrust upon them. I missed out on all three opportunities, damnit. But on at least two occasions I came ever so close…

Algebra was a great revelation to me. Arithmetic had always seemed so limiting in that it solved only specific problems. I didn’t want specificity (I realise now) I wanted generality.

I vaguely knew that when I left my village primary school and went to the big school I’d be learning about more complex things. But I couldn’t imagine how "sums" could ever be significantly different from what we were doing. The best I could come up with was that we’d be using larger and larger numbers, a prospect that failed to thrill me. I had trouble with my 9 times table. I wasn’t looking forward to struggling with my 999 times table or greater. But my speculations all proved to be a failure of the imagination.

The magic age of eleven came and went and there I was at the big school and my timetable had weird words in it that I’d never come across before. Chemistry, biology and physics (I’d only heard of "science" before; I didn’t realise it divided up). Latin, French and German. They were languages; I was happy with that concept. Arithmetic, geometry and algebra. Gosh. Sums really were different!

Arithmetic remained as specific and as boring as it had ever been though we learned some new ideas. Roots and powers were thrilling for a moment but the magic quickly died in the tedium of (pre-calculator) calculation. Geometry was difficult for though it was undoubtedly elegant it also seemed somewhat arbitrary (it would be many, many years before I found out just how insightful and profound that vague feeling really was).

But algebra was the queen of studies. It was a breath of fresh air and revelation upon magical revelation poured into my awakening mind. It was arithmetic without numbers, it solved the general case. It was everything I’d been looking for all my intellectual life. The drudgery of calculation vanished and there was only the pure, white light of the idea.

Little did I know what pitfalls awaited me. Little did I know how much remained to be learned. About ten years later the intellectual shutters came down with a mighty crash and I ran headlong into them and severely injured both my pride and my nose for knowledge. Tensors were my stumbling block. To this day I don’t understand them. But at age twelve, that was a long way in my future. I was in love with algebra.

I tried to explain it all to my grandmother; a long-suffering lady who put up with an awful lot from her only grandchild. She was completely bewildered (they hadn’t had algebra when she was a girl, she explained to me. It hadn’t been invented yet. You didn’t need algebra to sneak up on a dinosaur). She listened patiently as I raved on about quadratic equations. I wrote one down with arbitrary coefficients and then explained to her how to solve it. I went through all the steps and much to my surprise I got completely stuck. The results I was deriving made no sense to me.

And that was the first time I hovered on the brink of greatness, but I turned away from it and the opportunity vanished like smoke in the wind.

There were two very big and very important ideas buried in my failure to solve the equation I’d written down. The first was that there existed a class of problem that the techniques I was learning couldn’t cope with. The second, and much more important, was that there existed a class of numbers of which I was previously unaware. I couldn’t solve my equation because solving it involved deriving the square root of a negative number. Negative numbers didn’t bother me, but the roots of negative numbers did.

In order to solve my problem, it was necessary for me to deduce the rules of complex numbers. The equation was solvable in those terms. But rather than attempting to explore the territory opening up beneath my feet, I simply assumed I’d made a mistake somewhere and took it no further. The door to greatness slammed shut.

My grandmother was very understanding and distracted my disappointment with a treat of some kind.

There was nothing new in the idea of complex numbers of course. Mathematicians had known of them for centuries and the field had been thoroughly explored. But that’s not the point. The point is that I’d never heard of them. If I could have deduced their existence and their properties for myself (repeating, albeit unknowingly, the work of the great mathematicians of the past) then I truly would have exhibited genius. I came so close.

Twenty years after I had shown off my inability to solve quadratic equations to my grandmother, the opportunity for greatness knocked again. This time I was working with the United Nations Environment Programme (UNEP). Our task was to build a database of environmentally significant chemicals. (As an aside, a few years after all this, a dioxin manufacturing plant at Seveso in Italy exploded and caused enormous environmental damage. Information from the UNEP database helped enormously with the clean up effort. I remain quite proud of my association with UNEP).

In order to build the database, we accepted input from all the member states, encouraging them to ransack their archives for potentially useful data. Soon the information was flowing in from a wide variety of sources. This was in the very early days of computers (they were still rare and expensive beasts that occupied large air conditioned rooms) and not all the data we received was in computer readable form. Transcribing the "manual" data was relatively straightforward (though it remained a semi-skilled and labour-intensive intellectual exercise). However the thing that really caused us problems was the computer readable data we received for it arrived in a wide variety of (often mutually incompatible) formats. Reconciling all this and getting it into a shape that made it adequate for OUR database format (obviously greatly superior to theirs) was an enormously complex and difficult task.

I suspect that our efforts represented one of the very first large scale exercises in processing enormous quantities of incompatible data from multiple heterogeneous sources. Certainly there were no generally accepted solutions to this problem and we were forced to invent our own. We succeeded – and I wrote a paper about the solution, for it seemed to me that others might have similar problems and maybe a similar solution might help. The paper was published in a computer research journal of enormous obscurity and as far as I know, nobody read it (it’s the only paper I published for which I received no requests for reprints).

Today, with the proliferation of computers and the ever-increasing necessity for those computers to exchange and share data with one another, the problem has reappeared and all the difficulties that we had to address back in the 1970s have again come to the fore. Two or three years ago, a general solution was found, a solution that can easily be applied to any and every such problem of data exchange (and a lot of other related problems as well). This solution is called XML.

Don’t worry if you haven’t heard about it (though I promise you, if you are involved in the computer field, XML is in your future). The point is that XML is a beautifully elegant and, as is so often the case with breakthrough ideas, beautifully simple solution to the problem.

And I didn’t invent it.

You may have noticed that I haven’t given you a reference to the paper I wrote about my problems with the UNEP database. There’s a reason for that. Reading it today is an embarrassing exercise (for me at least). Time and again I can see my younger self flirting with the ideas that eventually formed the backbone of XML and completely failing to spot their significance. It was a failure of imagination exactly akin to the one I exhibited with my quadratic equation only this time there really was a genuinely original idea waiting to be discovered. And I had absolutely no idea at all that it was there.

I wonder if there’s anything else I’ve missed in the intervening years?