Fencing and Geometry

Last night I decided to give a lesson around the simple shape of the circle and how it is used in fencing. We discussed it in terms of the engagement, disengagement, counter-disengagement and circular parries. (I even demonstrated the envelopement - although not particularly well I have to say). When discussing the engagement I tried to put across the fact that the circular movement should always be neat and keep the point in line with the target. I reckon the optimum size of a good circular movement should be no wider than a cricket ball, or at most a bowling ball. Beach balls are definitely out! The point I was trying to get across was that the same movement can be used in a number of different ways, both offensively and defensively and that if it can be mastered it can be applied in a number of different ways. When we got into discussing the parry we also started talking about the 'triangle of control' that occurs when the blade is correctly parried into the guard of your foil, giving you the right level of control of your opponent. So there we had a circle and a triangle; if I'd started talking about the defensive square we would have had the full set of Euclidean geometry!
Thinking about this it's easy to see why some of the 17th and 18th century schools of fencing got so into secret geometries and techniques based on mathematics etc. At that point in European history the Renaissance had captured the imagination of the western world and there was a new-found belief that science, mathematics and order were the way to success and a better life. It is no surprise then that arcane theories such as Thibault's mysterious circle started to grip the imagination; surely the new mathematics of universal order would gain the upper hand if applied correctly? In truth the reality of fencing is slightly more chaotic and based upon the ultimate unpredictable system, the human mind. The real mathematical basis of fencing is the time it takes for the brain to interpret, react and trigger the appropriate muscular response. However there are a huge amount of variables in this act. The level of training, age, fitness, experience all play a part in a fencing bout, as does the fencer's personality. Are they aggressive? Are they passive? Do they have a plan? All these factors play a part in the intricate ballet that is a fencing match. So whilst geometry in techniques is fine, there's more too it than that. Is fencing a science or an art? You be the judge!