Peter Cochrane's Hard Drive 1997
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Reality simply doesn't add up
As a student I was besotted by the power of mathematics and physical modelling. My enthusiasm was fuelled by the fact that, barring a few generalising assumptions, and simplifications of real world situations, most of the problems I was presented with could be solved by one technique or another. For me the power of the mathematical process, the training, clear thinking and ability it invokes cannot be understated, and is in stark contrast to the less quantifiable sciences and humanities.

Like everyone else I was in an education system that lulled me into a false sense of security, as I was fed a continual diet of problems that had solutions. This convinced me that our universe was largely well-behaved, with a few non-linear areas that were difficult, but could mostly be avoided.

When I moved into industry it came as a shock to find the converse was true. We can solve almost nothing - relatively speaking. Our universe is principally non-linear, and we mostly get by with approximations to reality, or even gross misrepresentations. I am still surprised that we have been able to engineer and achieve as much as we have, given the frequent crudeness of our models and understanding of reality.

Reflecting upon this recently, I pondered the way we teach mathematics. Given the critical dependence of our civilisation on the subject, it seems paradoxical that it lacks any general acclaim or popularity. While it is often perceived as a nightmare topic, the truth is that with good teaching, most people can become reasonably competent.

When ancient man first attached a sharp stone to a stick to create a spear, he did not seek out a target and then apply a mathematical formula for the force and trajectory. He got by with trial and error, eventually leading to some exceptional encephalisation of his brain over millennia. Not until Newton were the physical and mathematical detail attended to in a rigorous manner. Now we teach our students from formula towards action and projectile. Worse, we divorce them from the reality through computers producing numbers to such accuracy as to obscure the uncertainties of the physical process.

Performing real experiments and making observations prior to mathematical modelling, measuring the outcome of trials against predictions is powerful stuff. But combining this with on-screen modelling introduces a further level of clarity. Plotting a trajectory is only the first stage; introducing the influence of air turbulence and variations in throwing action deepens understanding and insight.

Highly complex systems such as airflow over an aircraft wing, gas flow in a turbine, fluid motion and neural networks, defy mathematical analysis for all but the most stable situations. Non-linearity and chaos dominate the real world and may always fall outside our established routes to solution and understanding. But it is in this realm that we are likely to make the most exciting discoveries. What we require is that intuitive feel for the final outcome. Perhaps the computer can be our stone on a stick, the means by which we move on to understand. Only this time, it will be computers that enjoy the encephalisation - not us.

Peter Cochrane holds the Collier Chair for the Public Understanding of Science & Technology at the University of Bristol. His home page is:
http://cochrane.org.uk