The Romance of Mathematics / Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion.

by P. H. Ditchfield

All this may appear at first sight surprising; but the real philosopher, who knows that all kinds of truth are intimately connected, will receive such revelations of science with satisfaction rather than astonishment; for this new science, which has opened itself out before me, is only an extension of other well-known laws and discoveries which have come down to us from the remote past.

If my investigations should appear to you, most noble professors, somewhat novel and imaginary, remember the maxim of [73] the sage, that in the infancy of science there is no speculation which does not merit careful examination; and the most remote and fanciful explanations of facts have often been found the true ones. Perhaps some ‘self-opinionated particle’ (I speak mathematically) may have been inclined to laugh at our theories and discoveries, as the wise fools of the day laughed at Kepler and his laws; but time has changed the world’s laughter into praise, and a century hence our discoveries may rank among the achievements of modern science. As Cicero says, ‘Time obliterates the fictions of opinions, but confirms the decisions of nature.’

I have not shunned, most noble professors, to enlist Imagination under the banner of Geometry; for I am fully persuaded that it is a powerful organ of knowledge, and is as much needed by the mathematician as by the poet or novelist. It is, I fear, often banished with too much haste from the fields of intellectual research by those who take upon themselves to give laws to philosophy. We need [74] imagination to form an hypothesis; and without hypotheses science would soon become a lifeless and barren study, a horse-in-the-mill affair ever strolling round and round, unconscious of the grinding corn. In my previous investigations my imagination pictured the symmetry of curves and States; the hypothesis followed that the laws which regulated them were identical, and you have observed how the supposition was confirmed by our subsequent calculations.

In this lecture I propose to examine some of the forces which exist in our social system, and shall endeavour to estimate them by methods of mathematical procedure and analogical reasoning. We will begin with the old definition of Force as that which puts matter into motion, or which stops, or changes, a motion once commenced. When a mass is in motion, it has a capacity for doing work, which is called Energy; and when this energy is caused by the motion of a body it is called Kinetic Energy (in mathematical language KE = ½ MV²). [75] Another form of kinetic energy is called Potential Energy, which is in reality the capacity of a body for doing work owing to its position. For example we may take an ordinary eight-day clock. When the weights are wound up, they have a certain amount of potential energy stored up, which will counteract the friction of the wheels and the resistance of the air on the pendulum. Or, again, we have the example of a water-wheel: first the water in the reservoir, being higher than the wheel, has an amount of potential energy. This is converted into kinetic energy in striking against the paddles, and after this we have potential energy again produced by the action of the fly-wheel.

By the principle of conservation of energy, if we consider the whole universe, not our planet alone (for its heat and energy are continually diminished to some slight degree), we find that no energy is lost.

Force is recognised as acting in two ways: in Statics, so as to compel rest, or to prevent change of motion; and in Kinetics, so as to produce or to change [76] motion; and the whole science which investigates the action of force is called Dynamics.

All this is of course pure mathematics, and I have made these elementary observations for the benefit of my younger hearers, the students of this University. My grave and reverend seniors will pardon, I am sure, the repetition of facts well known to them for the sake of those who are less informed than themselves.

Now before I proceed further, I will endeavour to point out that these elementary truths of physical science hold good in our social system. Each individual is a mass, acted on by numerous forces, capable of ‘doing work,’ which work can be measured and his velocity calculated. Some individuals have a vast potential energy; that is to say, from their position and station in the social system, they have a power which is capable of producing work which a less exalted individual has not. Like the weights in an eight-day clock, or the water in a reservoir, they have a capacity for doing work, owing to [77] the position to which they have been raised. How vast the influence of a Primate or a Premier, a General or a King! And yet their power is chiefly potential energy, arising from the position they occupy, not from the individuals themselves. Schiller has described this in poetical language, which, strange to say, is mathematically correct:

‘Yes, there’s a patent of nobility

Above the meanness of our common state;