The Romance of Mathematics Part 3

Oscar Villa, South Kensington, June, 18--.

The Secretary of the aesthetic and Dress Improvement a.s.sociation presents his compliments to the Lady Professor of Girtham College, and begs to contradict emphatically her statements with regard to a subject upon which she is evidently in entire and lamentable ignorance, and to protest against her aspersions upon the artistic studies of this and kindred societies. He begs to state that true aesthetes are _not_ eccentric (they leave that to lady professors and her Philistine followers); that to dress becomingly is one of the princ.i.p.al objects of life, and that true greatness is achieved as much by the study of the art of dress as by any other n.o.ble pursuit or graceful accomplishment.

Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vand.y.k.e Smithson ent.i.tled to greatness? And yet their laurels have been won solely by the art of dress. Perhaps the lady professor has never read 'Sartor Resartus'! In conclusion, he would ask the Lady Professor to refrain from casting obloquy upon the work of the a.s.sociation which he has the honour to represent; to prevail upon her pupils to abandon the unfeminine attire which some of them have a.s.sumed, contrary to the first principles of art; to array themselves in flowing robes of sage-green and other choice colours (patterns enclosed), and to study art, instead of absurd mathematics, which no one can understand, and do no one any good.

(Approved by the Committee of the aesthetic and Dress Improvement a.s.sociation.) June, 18--.

[Editorial Note.]--The next letter, written by a pupil of the Lady Professor, requires no explanation, and speaks for itself.

Jesus College, Cambridge, March, 18--.

My dear Tutor,

You will be glad to hear that after superhuman exertions I have at last succeeded in pa.s.sing my Little-go, and I am eternally grateful to you for all you have done for me. I should never have got through if it had not been for you. All the coaches in Cambridge would never have managed it, but you drove me through in a canter. And why? I never could make up my mind to work for them; but when I coached with you, you made me like it. I almost revelled in the Binomial when you wrote it out for me; and then I could not help listening to you; and you looked so grieved when I would not learn, and made me feel such a brute; so somehow or other you drove some mathematics into my head, and I pulled through. By-the-bye, I think you must have tried the 'brain wave' dodge with the examiners, as five out of the six propositions in Euclid, which you told me to get up specially, were set! I wish I could read people's thoughts; can you read mine? If I were a Don, or a Fellow, or something, I would advise the University to have some lady professors like you to teach the men, instead of some of these sleepy old tutors. It would be a great improvement, and I am sure we should get through a great deal more work.

They have given me a place in the Jesus Eight, which I shall take now that I am released from your professorial ban, and have time for rowing.

But I don't half like giving up mathematics. You see, I have grown fond of the study. Do you think you could make a wrangler of me? At any rate, I should like to come to your lectures again. May I?

Your Grateful Pupil.

[4] It is to be regretted that this letter has evidently fallen into the hands of some autograph collector, who has ruthlessly cut off the signature; but the reader will easily determine, after careful perusal of the doc.u.ment, from whose pen it emanated.

[5] Cf. page 36.

PAPER V.

A LECTURE UPON SOCIAL FORCES, WITH SOME ACCOUNT OF POLEMICAL KINEMATICS.

Most n.o.ble Professors and Students of Girtham College,--Since last 'I wandered 'twixt the pole and heavenly hinges, 'mongst encentricals, centres, concentricks, circles, and epicycles,' like the great Alb.u.mazar, and found them full of life and wisdom for the guidance of our States and laws, I have turned my attention to the Applied Mathematics, in order to determine what other truths this shaft may yield.

The strength of all sciences, according to Bacon, consists in their harmony; and it is truly marvellous how perfect this harmony is, if our ears are tuned aright to hear it. We have observed how the beautiful and regular laws of curves and cones correspond to the social laws of States and nations, guiding them as if by word of counsel, admonis.h.i.+ng them on what principle they ought to regulate their governments and inter-relations. We have seen that the laws which govern thought and light and sound are almost identical, and that harmony pervades not merely the ordinary sciences, but extends her benign influence over these newly discovered fields of scientific research, which I claim to have discovered.

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 n.o.ble professors, somewhat novel and imaginary, remember the maxim of 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 n.o.ble 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 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 a.n.a.logical 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 ma.s.s 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 = MV). 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 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 repet.i.tion 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 ma.s.s, 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 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 n.o.bility Above the meanness of our common state; With what they _do_ the vulgar natures buy Their t.i.tles; and with what they _are_, the _great_.'

Other forces may have raised these men to their exalted positions; but their influence is due to their height, their potential energy. Placed on a lower level, they would cease to have that power. How calm the dignity of this potential rank! The water in the reservoir is scarcely ruffled or disturbed, as if unconscious of its power; when it has lost its force it rushes along with a sullen murmur and a roar, howling and hissing and boiling in endless torture, until--

'It gains a safer bed, and steals at last Along the mazes of the quiet vale.'

So the vulgar crowd rushes on, with plenty of kinetic force, making noise enough and looking very busy; while those who seem to sleep in calm forgetfulness, exercise their potential energy, and do the real work of turning the great engine of the State.

There are attractive and repulsive forces (more commonly the latter, the cynic will say) in our social system, but each individual is the centre of various forces acting upon him. In nature all matter possesses the force of gravity, and whatever the size of two particles may be, they mutually attract each other. The earth attracts the moon; the moon attracts the earth. A stone thrown up into the air exercises an infinitesimal force upon the earth; so in the social system every individual, however small and insignificant he may be, exercises some attractive force upon his neighbour. There is no one in the world who does not exercise some influence for good or for evil upon his fellows.

The force of _cohesion_ is manifest in society as in nature, that force, I mean, which resists the separation of a body's particles. Different bodies possess different powers of cohesion, _e.g._, the cohesion of chalk is far less than that of flint embedded in it; even the same body possesses different powers of cohesion in different directions, _e.g._, it is easier to split wood in the direction of the fibres than perpendicular to them. If by our old principle of continuity we change the words 'bodies' into 'States' or 'individuals,' we shall see that the same laws hold good in social science as in natural philosophy.

These are a few a.n.a.logous laws which I have taken almost at random; but it must strike the most casual listener to my remarks that it is wondrous strange that men, regarded as social beings, should possess the same qualities, and be governed by the same laws, as the rest of _matter_. As Bishop Butler says, 'the force of a.n.a.logy consists in the frequency of the supposed a.n.a.logous facts, and the real resemblance of the things compared.' It appeals to the reasoning faculty, and may form a solid argument. Hence, if we can prove the similarity of various laws and conditions, we may not be wrong in a.s.suming by a.n.a.logy the ident.i.ty of those laws and conditions.

I have stated my case in this manner in order to convince the gainsayers, if any such there be, and to banish any doubts or questionings which may have arisen in your minds. I will now proceed with some further investigations, full of the most profound interest and importance.

Doubtless many of the lady-students present are in the habit of welcoming peaceful evening in with a potent draught of 'the cup which cheers but not inebriates;' and as men are great flatterers (for imitation is the greatest flattery), I believe the male portion of my audience have been known to follow that excellent example. Some perhaps are in the habit of burning the midnight oil, and keep their eyes open by means of this fruit of the hermit's pious zeal, endowed by high omnipotence with the power of hindering sleep;[6] but that practice I do not advise, as that delicate portion of our system, the nerves, especially of women, often becomes injured by such stimulating doses.

However, you will have observed (if you do not follow the modern pernicious fas.h.i.+on of taking tea without sugar) that numerous bubbles are formed upon the surface of the liquid. After a few moments these unite into one central ma.s.s of bubbles by the force of mutual attraction.

It appears from considerations which are detailed in works on physical astronomy, that two particles of matter placed at any sensible distance apart attract each other with a force directly proportional to the product of their ma.s.ses, and inversely proportional to the square of their distance.

Now, suppose that we have a number of circular ma.s.ses situated upon a plane surface, they will attract each other with a force which may be determined with exact.i.tude; and the greater the ma.s.ses the greater the force. We will now apply this to polemical science. The agricultural settlement is the first stage in the civilization and formation of a State. How did this arise? First, a single family immigrated to some uncultivated parts of the country, perhaps accompanied by others, who formed a little colony. Other settlements were made in other parts of the land; and thus the country became overspread with these detached and separate communities. An eminent writer declares that these settlements can be traced in the beginnings of every race which has made progress; that they were characteristic of those races in Greece and Italy, in Asia and Africa, which grew into the opulent and famous cities in which so much in the early history of civilization was developed. The colonies of England have been formed in the same way, just as in olden time England itself was occupied when the Roman power ceased.

These settlements correspond to the circular ma.s.ses situated on the plane surface; they were quite separate from each other, each having its own laws, its own headman or ruler, its own a.s.sembly or parish council.

But as time elapsed, the force of mutual attraction set in; by degrees these separate settlements were drawn together by force which increased in proportion as the settlements increased; until at last one united kingdom was formed under one king, governed by uniform laws and regulations. The bubbles have blended, the circles have come together, and one large circle or other curve is the result. This may be called the _Law of Social Attraction_. In accordance with the results of one of my previous lectures, I have taken the circle as representing the simplest form of government, which figure, in the case of the elementary settlements, must have been small.

Many of you, most n.o.ble professors, are doubtless accustomed to make experiments with the microscope. I will suggest a simple one, which ill.u.s.trates very forcibly what I am endeavouring to show you. Take some particles of copper, and scatter them at intervals over the surface of an object-gla.s.s, and pour some sulphuric acid upon the gla.s.s. Now, what is the result? A beautiful network of apparently golden texture spreads itself gradually over the whole area of the gla.s.s. Steadily it pursues its way, and the result is beautiful to behold. The minute particles of copper were the original settlements scattered over the land; the sulphuric acid the civilizing agent; and the final picture of a united civilized h.o.m.ogeneous nation is well represented by the progressive and finally glorious network of gold. This example is of course outside our present subject, but it serves as a beautiful ill.u.s.tration.

As an instance of the attractive force exercised by small communities upon each other, I may mention the united kingdom of Germany, which is composed of numerous small States and nations, which have been drawn together by the power of mutual attraction. Until recently they were each self-contained, separate const.i.tutions, with their own kings and forms of government; but the attracting force, a.s.sisted by forces from without, has proved too much for them, and the great and powerful united kingdom of Germany is the result.

But why, you may ask, have not the people in Hindustan united in the same way? There the agricultural settlements remain as they did ages ago; separate petty chieftains rule under the all-governing power of England. Why have they not united?

To this objection I reply that there is in social science, as in Nature, a _vis inertia_; that is to say, there is a tendency in matter to remain at rest if unmoved by any external agency, and also of persisting to move, after it has once been set in motion. The _vis inertia_ of some bodies is greater than that of others, and depends upon their weight and density. Now it so happens that the moral _vis inertia_ of the Hindustani is very great, hence their tendency to amalgamation is small. They remain in the state in which they happen to be.

On the other hand the inertia of Englishmen is small, of Englishwomen smaller, and therefore their power of combining is greater. Here let me observe that the quality of inertia is one which ought to be removed as far as possible from each social system. Inertia was regarded as a capital crime by the Egyptians. Solon ordained that inert persons should be put to death, and not contaminate the community. As savages bury living men, so does inertia practise the same barbarous custom upon States and individuals. Observe the putrid state of inert water, the clear and sparkling beauty of the moving stream, bearing away by the force of its own motion aught that might contaminate it. Men more often resemble the stagnant water than the rivulet. A healthy social state enforces labour by natural laws, and banishes inertia as much as possible from the system. If the principles of some noisy English politicians were fully carried out, and all things made '_free_,'

inertia would be increased, and listless indolence pervade the ma.s.ses of our countrymen. I may say that inertia is not entirely unknown in our sister University of Cambridge.

The existence of social forces is supported by the testimony of Dr.

Tyndall, who plainly recognises their power, though he does not attempt to expound their origin. 'Thoughtful minds are driven to seek, in the interaction of social forces, the genesis and development of man's moral nature. If they succeed in their search--and I think they are sure to succeed--social duty would be raised to a higher level of significance, and the deepening sense of social duty would, it is to be hoped, lessen, if not obliterate, the strife and heart-burnings which now beset and disguise our social life.' I accept with gratification Dr. Tyndall's conclusions: to determine, examine, trace, calculate these social forces which exercise such a powerful influence on our characters, our lives, our customs, which produce the greatness of the State, or drag it down with irresistible strength from its pinnacle of glory to an abyss of degradation; to estimate such forces is the great and n.o.ble object of our lectures and researches in this University. Prosecute, most n.o.ble professors, your studies in this direction with all the energy of your enlightened intellects, and there is yet hope that this new science, which I have endeavoured to sketch out, however feebly, may be the means of saving our beloved nation from degradation and ruin, and raising her to a higher level of glory and honour. I hope to continue the subject of social forces in my next lecture.