The following quotation is taken from Personal Knowledge by Michael Polanyi. The book was based on his Gifford Lectures he gave in 1951–52 at the University of Aberdeen. Polanyi is a philosopher of science who is perhaps not widely known. I have only read the book up to Chapter 4, where the following quotation is taken. The book consists of four parts: The art of knowing, The tacit component, The justification of personal knowledge, and Knowing and being. Chapter 4 is the final chapter of the first part. Indeed, the philosophy of science is a huge topic, and works on this area have shown that science is not necessarily as what we used to or would like to understand.
A well-known scientist, who in his youth had to support himself by giving swimming lessons, told me how puzzled he was when he tried to discover what made him swim; whatever he tried to do in the water, he always kept afloat.
Again, from my interrogations of physicists, engineers, and bicycle manufacturers, I have come to the conclusion that the principle by which the cyclist keeps his balance is not generally known. The rule observed by the cyclist is this. When he starts falling to the right he turns the handlebars to the right, so that the course of the bicycle is deflected along a curve towards the right. This results in a centrifugal force pushing the cyclist to the left and offsets the gravitational force dragging him down to the right. This manoeuvre presently throws the cyclist our of balance to the left, which he counteracts by turning the handlebars to the left; and so he continues to keep himself in balance by winding along a series of appropriate curvatures. A simple analysis shows that for a given angle of unbalance the curvature of each winding is inversely proportional to the square of the speed at which the cyclist is proceeding.
But does this tell us exactly how to ride a bicycle? No. You obviously cannot adjust the curvature of your bicycle’s path in proportion to the ratio of your unbalance over the square of your speed; and if you could you would fall off the machine, for there are a number of other factors to be taken into account in practice which are left out in the formulation of this rule. Rules of art can be useful, but they do not determine the practice of art; they are maxims, which can serve as a guide to an art only if they can be integrated into the practical knowledge of the art. They cannot replace this knowledge.