There is a famous paradox from Zeno of Alea, in Ancient Greece, called the Dichotomy Paradox. It ‘proves’ that motion is impossible by pointing out that before you can arrive somewhere you have to get half way there, and then you have to cover half of the remaining distance, and half of the distance then remaining, and so on – thereby never actually reaching your destination. If you are familiar with infinite series you will know that by definition, according to mathematicians, the sum of 1/2 + 1/4 + 1/8 + 1/16 + 1/32… is 1, which means that you will arrive at your destination – although to me there has always been an infinitely small piece missing from that bit of maths. A sort of a priori requirement that we devise a system in which the answer is 1, because if it isn’t, our understanding of our world quickly falls to pieces. Who says there’s no need for faith in maths.
But that isn’t really what I wanted to write about today. I was thinking about the infernal muddle that scientists get themselves in when they try to answer seemingly simple questions, and for some reason it put me in mind of Zeno’s Paradox.
Suppose a scientist asks a question. He breaks the problem down into pieces, as every good scientist does, and sets up an experiment to try to find the answer to his question. But in the process he finds that he can’t answer the question until he has answered two new questions which he hadn’t realised needed answering. Attempting to answer these two new questions, he designs two new experiments. But now he finds himself with four unanswered questions – and the process continues, with 8, 16, 32, 64 and 128 questions to answer, at which point he calls for help. He trains new scientists and shares out the questions, but still, with every attempt to find answers the number of questions increases exponentially, until each of the new scientists is forced to train more scientists to work under them. And so eventually we have an infinite number of scientists, and yet the original question remains unanswered.
This illustration is perhaps just as contrary to our experience as Zeno’s Paradox (although far less elegant in it’s falsity); clearly science has answered quite a few questions over the years. But generation after generation of scientists are trained and set to work on exceptionally specific aspects of science, with very little idea of what is being studied in the lab next door, never mind in other fields – even though they are usually being studied in adjacent buildings on the same university campuses.
The original scientist who asked the original question died long ago. So is it time we started asking today’s scientists to step back from their work, and once again ask that first question?
Science has proclaimed to the world many times over the last few hundred years that “we’ve nearly solved it”, “we know almost all there is to know”, and that soon “nothing will be beyond the understanding of science”. But any scientist who’s being honest with you will say that it’s become apparent that there is no endpoint to scientific enquiry. Even an infinite number of pieces can still be divided by two (and yes, you can double infinity, a rather fascinating idea which I remember being brushed under the carpet in first year calculus at university).
Of course the fact that there is no end to the process of enquiry doesn’t invalidate that process, but surely if you are on a path that has no end it would be wise to remember why you are walking that path – to shift your gaze to the horizon regularly, and see that the fragments of your enquiry are parts of one perfect whole, and that they only make sense in the context of that whole.
