The Romance of Mathematics Part 4

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[6] A Chinese legend relates that a pious hermit, who in his watchings and prayers had often been overtaken by sleep, so that his eyelids closed, in holy wrath against the weakness of the flesh, cut them off, and threw them on the ground. But a G.o.d caused a tea-shrub to spring out of them, the leaves of which exhibit the form of an eyelid bordered with lashes, and possess the gift of hindering sleep.--Dr. Ure.



Most n.o.ble Professors and Students of Girtham,--We have embarked upon a stormy sea of speculation, on a voyage of grand discovery, and the dangerous waves of adverse criticism, and the deceptive under-current of prejudice, often make the steersman's lot by no means an enviable one.

But our vessel is sound and perfectly equipped, and therefore I do not fear to guide her across the great unknown.

It may have occurred to you that the problems which present themselves for solution in social science are far more difficult and complicated than those which arise in ordinary mathematics. That is undoubtedly the case; but this extra degree of difficulty is due to the fact that we make no a.s.sumptions; we take the things as they really are, not as they are a.s.sumed to be. In physical science, if we take into consideration the resistance of the air, the curvature of the earth, the rigid connection which exists between particles in the same body, and a host of other things which are often conveniently neglected in elementary works, how complicated the various problems become! So we must not be surprised at some of the difficulties which occur in social science, as nothing is neglected; the whole problem is before us, and having solved it we need not make allowances for any falsely a.s.sumed _data_.

It is possible that other professors of this science may come to slightly different conclusions to those which I have arrived at. That is only to be expected, because their original observations may have slightly varied. But in physical science allowances are made for different observers. In astronomy, for example, we find the value of the 'Personal Equation.' One observer on looking through the telescope may take the meridian of a star rather differently from another watcher of the heavenly bodies, and the _personal equation_ is used to make allowances for this quickness, or slowness, of observation. So in social science there must be a personal equation too, and our object ought to be, in the ordinary affairs of life as well as in the higher duties of scientific action, to make our personal equation as small as possible.

But until the old proverb, '_Quot homines, tot sententiae_,' has ceased to have any meaning, there will be abundant need of this most useful aid to accuracy.

The close connection which exists between social forces and material forces is plainly shown by the doctrine of the conservation of energy.

'This doctrine,' says Dr. Tyndall, 'recognises in the material universe a constant sum of power made up of items among which the most Protean fluctuations are incessantly going on. It is as if the body of nature were alive, the thrill and interchange of its energies resembling those of an organism. The parts of the stupendous whole shift and change, augment and diminish, appear and disappear; while the total of which they are the parts remains quant.i.tatively immutable, _plus_ accompanies _minus_, gain accompanies loss, no item varying in the slightest degree without an absolutely equal change of some other item in the opposite direction.' So do the forces in the social world ebb and flow, rise and fall, carrying on the same universal law which regulates the energy of material force.

I will now proceed to enumerate some of those forces which exercise such a powerful influence on society.

First, let us take the force of _Public Opinion_, which seems to exercise a relentless sway over the minds and manners of men. This is a very subtle and secret force, which is most difficult to trace, and resembles electricity in the science of physics. We cannot see it, but are only able to judge of its power by its results. Its point of application is not in the individual, but in the collection of individuals who make up the social system; and it is, in reality, the resultant of, or the compromise between, the various elementary forces which make up human society. Yes, compromise is a purely mechanical affair, based on the principle of the parallelogram of forces; and as public opinion is the result of a compromise, we may calculate its force. For example: 'It is required to know the state of public opinion in the matter of politics, when the results of a General Election show that the Conservatives are to the Liberals as 10 : 9.'

Let OC be the direction of the Conservative force.

Let OL be that of the Liberal.

Then by _data_ OC : OL :: 10 : 9.


Complete the parallelogram, and join OP.

Then OP represents the force of public opinion in magnitude and direction.

N.B.--The direction of OL is determined by the amount of deviation of the policy of the Liberals from that of the Conservatives.

As in physical, so in social science, impulsive forces sometimes act, and effectually disturb our system and our calculations. Public opinion is very liable to the action of disturbing forces. Panic is an impulsive force, which defies the power of the most learned professors of social science to determine its magnitude and direction. Some strange unforeseen catastrophe--the fascination caused by a brilliant and unscrupulous orator, a cruel wrong, a blind revenge for real or imaginary injustice--will sometimes rouse one element of pa.s.sion latent in the vast body of public opinion; so that it breaks with all that hitherto restrained and balanced it, and precipitates society into a course of conduct inconsistent with its former behaviour, and bloodshed, revolution, the breaking-up of laws, are the terrible results of panic or revengeful pa.s.sion.

Society is, as it were, split up by the terrible action of such impulsive forces, just as wood is split up by the repeated blows of the hatchet. It is, therefore, the duty of statesmen to increase the power or force of cohesion, to strengthen the fibres of the State, so that the force of such impulsive blows may not be felt, nor disturb the continuity of the framework of the State. If such measures had been adopted in the neighbouring country of France, much misery might have been avoided, and the terrible revolutions which have so frequently convulsed her social system entirely prevented.

_Friction_ is another disturbing element in our calculations, and although it may be made a useful servant, it is a bad master in mathematics, as in polemics. Without the aid of friction, progress would be impossible. For example: Take the case of a man with perfectly smooth skates on perfectly hard, smooth ice; he would be unable to reach the land unless he had provided himself with some stones, by throwing which he would just be able to get to his destination by a backward motion.

The engine would be unable to proceed on its iron road if it were not for friction. The same is true in polemical science: the government of the country would not be able to be carried on under our present conditions if it were not for _party friction_. But suppose it increased indefinitely, party friction becomes party _obstruction_; and the engine of the State would no longer proceed smoothly and evenly along its appointed course at the rate of sixty miles an hour, but would resemble an old-fashioned coach, up to its axle-trees in mud, its motion altogether stopped by the action of party friction.

We have seen that forces have two ways of acting: that of compelling rest and that of producing motion. In statics forces act so as to prevent any change of motion, or disturb the body's original position.

In kinetics, on the contrary, the power is recognised as acting so as to produce or change a body's motion. Now, in polemical science we have these two ways of considering the action of forces. There is the _statical_ or _conservative_ force, which compels rest, which seeks security, stability, and peace, and is not ardently devoted to change.

It reduces the system to equilibrium. There are, of course, two kinds of equilibrium--_stable_ and _unstable_--according as the social and political system is in a healthy or unhealthy state. If a body is in stable equilibrium, and any slight motion takes place, the body will return immediately to its former position; but if in unstable, it will decline further and further away from its original position, and be entirely upset. So a healthy and sound conservative equilibrium is not disturbed by outside forces, and the State will resume its former position of stability and rest when the opposing force is withdrawn. But an unhealthy and insecure conservatism is as easily disturbed as an egg balanced on its narrow end.

The kinetics of society, that is to say the Radical way of estimating force, is the party of motion, generally supposed to be the 'party of progress.' It has therefore many attractions in the eyes of those who delight in motion, speed, and rushing about. To run at full speed, to feel the keen air upon one's face, to experience the delightful sensation of freedom of will, and limb, are joys which cannot be denied.

Such exercise is beneficial to the system, bodily or political. Motion is the life of all things; it is characteristic of nature; it adores nature; because it is an emblem and characteristic of life. The ceaseless rolling of the ocean waves, the swaying of the trees, the bending of the flowers, the waving of the corn, all these fill us with pleasure; whereas a flat uninteresting plain, unrelieved by the motion of terrestrial objects, is depressing to the spirit. So there is much to be said in favour of motion, and Carlyle has defined progress as 'living movement.' And men love this 'living movement,' and take up the Laureate's cry:

'Forward, forward, let us range, Let the great world spin for ever down the ringing Grooves of change.'

But, after all, there is a danger in this everlasting motion. We cannot tell whither this progress may lead. It may be along a safe sure road; but perchance a precipice may open out before us; and rejoicing in the acceleration of our velocity, with eyes intent upon some distant heights of glory and ambition, we may not discover our danger until it is too late to stop, and a terrible plunge into an unknown abyss of turmoil and tumultuous waves is the alarming result of an unguarded policy of unrestrained 'progress.' I recall to my mind the quaint words of Holmes which aptly ill.u.s.trate my contention.

'If the wild filly, "Progress", thou would'st ride, Have young companions ever at thy side; But wouldst thou stride the staunch old mare, "Success,"

Go with thine elders, though they please thee less.'

Progress and success do not always go together hand in hand; and while motion is essential to life, it is not always safe to urge a country forward at too great a speed; and security and stability are quite as important to the nation's life as actual progress.

There are other impulsive forces which act occasionally in the sphere of politics, and which baffle all our calculations, and exclude scientific considerations of the polemical problems which arise.

_Ambition_ is such an impulsive force, and when the rulers of the people are actuated by it, and struggle for money, place, and power, politics is degraded from its position as a science, and it becomes impossible to estimate the result of forces so generated.

In my next lecture I propose to treat the important subject of the Laws which govern States and Governments, and which regulate, generate, and control the social forces which we have seen at work in the body politic.



Since the last time I had the honour of addressing you on polemical matters, I have met with a pa.s.sage in the writings of M. Auguste Comte which afforded me much pleasure. It seemed to be the one word for which I had been waiting, and confirmed many of my own impressions and speculations. He lays down two propositions: first, that the constructive politics of the future must be based on the history of the past; and second, that political science is a composite study, and presupposes the complete apprehension of every branch of science, beginning with the physical, such as astronomy, and ending with the moral, such as ethics and sociology. M. Comte evidently does not regard as a vain dream and imaginative speculation the theory that it will be possible for statesmen to calculate a policy, and to determine a course of action by purely scientific considerations. May I entertain the hope that in this university, where all branches of physical science have found a home, and are studied by most able and learned professors, the science of politics may be pursued under most favourable circ.u.mstances?

I trust that each professor will bring before me the results of their deliberations, and contribute to the growth of this particular science for which our university has already become deservedly famous.

My present lecture is devoted to the important consideration of _Law_.

At first sight it may appear to you that the wills and pa.s.sions of mankind are so diverse and unknowable, that it would be absurd to suppose that they can be calculated, or rendered amenable to any law.

But Professor Amos has pointed out that in proportion as we examine history, and compare the actions present and past of different nations and states, the more uniform does human nature appear; the more calculable the actions, sentiments, and emotions of large ma.s.ses of people. As we have already stated, the difficulties of the study are not likely to deter the professors of Girtham College from the pursuit of any particular branch of science.

_A priori_ we might suppose from a.n.a.logy that these polemical laws existed, as there is no department of nature which is not governed by law. It is an essential feature in nature, and also in government. What is political economy but the study of certain laws of nature? These were first discovered by Adam Smith, and have since been traced and estimated by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and many others. Moreover, our physical const.i.tutions are governed by laws, which physicians have determined, and which it is perilous to resist.

Our moral const.i.tution is also governed by laws, which evidently exist, although it is difficult to find them out. But the nation is only an a.s.semblage of individuals; and since individuals are so governed, it is only natural to suppose that the nation, composed of individuals, is so const.i.tuted and controlled. And not only is that true, but we shall see that polemical laws are as permanent and universal, as invariable and irreversible, as the laws of nature which regulate the courses of the heavenly bodies, and raise the tides, or depress the sandstone hills.

We may notice first the preponderant impulse observable in a nation's life in favour of supporting existing facts and inst.i.tutions; and every reformer has discovered the difficulty and danger of changing or opposing the customs and habits of the people. As a wheel will travel most smoothly along a well-worn groove, whereby friction is diminished, so there is a natural national tendency always to run along those paths with which the habits and customs of the people have made them familiar.

This law is nothing else than Newton's first law of motion, which is quite as applicable to human ma.s.ses as to lifeless matter. The tendency of matter to remain at rest, if unmoved by any external agency, and of persisting to move after it has once been set in motion, is a conservative tendency; and is as true in political science as in any other.

The special branch of our science, which we may call the _Biology of Politics_, shows how absolute is the domain of law in polemical matters.

The law of human life is that men are born, grow, become strong and vigorous, and then decay and die. This is the law of life, to which we must all yield an enforced obedience. This same law is observed to be at work in the heavenly bodies; and astronomy shows us that planets are born, flourish, and at length die, just as our human bodies do. The moon is, as you may have observed, a dead planet, such as our earth may be some day. The same growth and decay are also manifest in national life.

First, there is the birth of the nation, which sometimes lies a long time in a dormant state, and then wakes up to life and energy. China and Russia are examples of dormant States, just waking from a long sleep of childishness and ignorance. The next stage is the strong an healthy period of its existence, which England is at present enjoying; and then, after various stages of gradual decline, we come to the senile period of national life, when every energy and faculty, every national feeling and power of invention, are completely exhausted. As an example of this depressing condition, we may mention Turkey and several of the effete States of South America. Sometimes, when life is nearly extinct in the human body, physicians have made use of the power of galvanism, in order to revive the dying energies. This process of galvanizing a State into life was tried by Lord Palmerston and others on the worn-out frame of Turkey. But such attempts can only meet with partial and transitory success; and where the loss of national power and faculty betokens the senile period of the nation's existence, it is vain to attempt to restore its former life and energy. The study of the biology of politics presents many interesting and important details in this special branch of knowledge; and I commend this part of our subject to the special attention of the professor of physiology. The law of development is observable in nations as in nature. Recent scientific discoveries have tended to take away all ideas of _chance_ in the workings of nature, and have subst.i.tuted _law_ instead of it. It would be unscientific and incorrect to speak of the world being formed by the 'fortuitous concourse of atoms.' So we cannot speak of a State being generated in this manner. Laws--economical, geographical, natural--preside over the formation of States and nations, and produce their further development.

The laws of political motion occupy the same prominent place in our new science as Newton's laws do in ordinary dynamics. These are very important in calculating the positions which various States will occupy in the future. First, we have the _doctrine of nationality_, which prevented the progress of Austria into Italy, and of the Bourbons in Naples, and produced the amalgamation of the small German States in the great empire of Germany. The second law of political motion is the doctrine of the _independence_ of all true States, and the equality of all States to each other. This had its growth in feudalism; and all the chief wars of modern times have been the result of the efforts of nature to establish this law of independence. The doctrine of intervention is a modification of the preceding law, and is applicable when the law of necessity demands its use, such as the restoration of order after protracted anarchy, the abolition of slave trade, etc. The third law is the _law of morality_. Just as for each man there exists a _right_ and a _wrong_; just as _duty_ and _conscience_ are certain elements in his daily motion, which dictate his course of action, although he may chose to neglect them; so a nation is bound by the same moral laws which govern the individual; and a nation errs if it transgresses them.

Christianity is the agent which has produced so powerful an influence in making men obey the dictates of conscience and walk in the path of duty; and I read with thankfulness the conclusion of Mr. Amos, that Christianity has triumphed quite as much in moralizing secular politics as it has in the sphere of individual life.

These are some of the princ.i.p.al laws of motion which I have observed at work in various States and nations. Inasmuch as political science embraces, in addition to the physical sciences, all those branches which are contained in ethics, economics, jurisprudence, sociology and others, the laws of each are generally applicable to the whole grand subject of which my lectures treat. Other general laws may be deduced, and have been enumerated in my previous lectures, from the social properties of curves and conics; and when our researches are complete we may hope to produce a code of laws for the guidance of our statesmen which maybe of immense use in determining the policies of the future. Already there is strong evidence that the affairs of this country are being conducted on sound scientific principles, rather than by any species of guess-work or haphazard contrivances. The use of history is recognised as extremely important in determining a future line of conduct; and statesmen are in the habit of endeavouring to find from their study of the past what is the logical sequence of events. Just as mathematicians endeavour to determine the law of a series of figures, and having found the law, can write down the next, and the next, _ad infinitum_; so scientific politicians may be able soon to establish the various laws of a series of events, and calculate their course of actions. That there is considerable progress in this direction is manifest by the value which they place upon statistics, and their continued use of this important information.

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The Romance of Mathematics Part 4 summary

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