The preparation of the child for science

Front matter

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Contents

CHAP. PAGE

PllEFACE 7

I. The Scientific Mind .... 15

Preface

The following volume is an attempt to utilize on behalf of little children the life-woi'k of many great men now almost forgotten. Amongst these may be specially mentioned : —

Nicolas Antotnb Boulanger. He left school a reputed dunce, incapable of learningalgebra. He died in 1759, in his fortieth year, a self-taught mathematician and an eminent engineer. He left behind him in MS. two works, L'Antiquite devoilee par ses usages and L'Origine du despotisme oriental, in which he explained the connexion of fixed mental attitude with the enslavement of the masses, and of periodic reversal of attitude with mental emancipation and power. His books were published after his death in several editions, but seem to have mysteriously disappeared soon afterwards.

Thomas Wedgwood. He was assisted in his scientific researches by Erasmus Darwin (grandfather of Charles Darwin), a then famous physician. His life-long dream was to promote happiness on earth, not by the multiplication of

8 PKEPACE

mechanical appliances for comfort and pleasure, but by the evolution of a Race gifted with powers of intellectual enjoyment, larger than those of man as he now exists. He made a special study of the faculty which he called Genius and the conditions of its orderly development. By Genius he evidently meant, chiefly, the power of seeing truth at first hand. The MS. of his work was entrusted to a friend who is said to have lost it. The rough notes for the book in Wedgwood's handwriting, with a fair copy of one or two of the chapters, were found in 1883. Among the papers was a scrap on which was written, in a shaking hand, the sentence : — ' How exhilarating is the thought that if, by the labour of my whole life, I can add one idea to the stock of those concerning education, my life has been well spent.'

Charles Babbage. By comparing European mathematical processes with certain ideas about the development of human faculty derived from Asiatic sages, he was able to realize the nature of some thought-processes so vividly as to conceive, in imagination, what may almost be called an Automatic Thinker of iron and brass. His calculating machine, if completed, would sometimes have rung a warning bell and put up a signal: — 'More data wanted;' and oc-

PEEFACE 9

casionally it would have put up the signal : — ' Data incompatible with each other.' The machine was, however, not completed ; it is kept in the Mathematical Department of the South Kensington Museum. Babbage's book and pamphlets, more valuable than the machine would ever have been, are practically unknown to the majority of the scientific world.

George Boole. My husband carried out Babbage's idea by means, not of a machine, but of a self-acting algebraic notation, which automatically produces the symbol for ' insuflficient data' (q), and that for 'these conditions are incompatible in the sphere of human consciousness ' (J). He also carried out into other automatic notations Babbage's suggestions about the psychological value of certain traditional opinions on metaphysical subjects. The notations adopted by him have been used in the application of mathematics to the Physical Sciences ; the use of them for this purpose would be largely facilitated if mathematical teachers had any clear idea of their meaning and origin. His books are still used in Germany and Austro-Hungary for educational purposes. In England they have been superseded by others in which the same notations are employed, but in a manner which tends to conceal their

10 PKEFACE

history and genesis. George Boole was abundantly rewarded in his lifetime with medals and honorary degrees ; but his books are now out of print.

Ram Chundea. Treatise on Maxima and Minima, with introduction by J. Herschell and A. De Morgan about ancient Asiatic Methods.

Geatry : A French Oratorian. His work on Logic contains a valuable analysis of the psychology of the Infinitesimal Calculus ; which he, as did afterwards Hinton, treated as proof of the importance to intellectual progress of rhythmic alternation between the study of detail and the synthesizing of details. He asserts that Geometric Induction is a process of prayer ; by which he means an appeal from the finite to the Infinite for light upon finite concerns. The mathematical portion of his work is out of print.

Benjamin Betts, formerly of the Government Survey of New Zealand, after much study of Fichte's philosophy, invented a peculiar system of co-ordinates, by means of which he illustrated diagrammatically the expansion of thought under pressure from opposing forces. To his surprise his diagrams turned out to resemble the outlines of many known leaf and flower forms,

PREFACE 11

as well as of some not known on this planet. He came to conclusions on vegetable morphology in some respects similar to those arrived at quite independently by James Hinton and expressed in his ' Life in Nature.'

Many years ago I enjoyed the privilege of reading Mr. Betts's MS., and had a long correspondence with him. His system of co-ordinates cannot be much used except by those whose hands have been trained in the work of the mechanical draughtsman. It has however been very helpful in suggesting simpler methods. The following quotation from a letter of Mr. Betts will give some idea of the nature of his philosophy. ' Suppose yourself placed at an almost infinite distance on the planetary axis of our solar system, and, focussing (in imagination) aeons of time into a few seconds, and millions of miles into the optical angle, view the condition of our solar system in its passage in the direction of Hercules. What would be visible ? . . . The laws of infinite solar systems throughout the universe are telegraphed to us by the flowers at our feet. . . . These laws of the corollaform we have educed as Laws of Thought, of self- consciousness as revealed in the act of thinking. . . . Some one is thinking there, thinking in potential activity, as you and I are thinking this moment.'

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James Hinton analysed, carefully the Psychology of the processes for the Summation of Series and for solving Quadratic Equations ; as "well as that of the Fluxion method.

Dr. Charles Winslow instituted a series of investigations on Force-lines as co-ordinates for illustration of Laws of Thought. At the same time he corresponded with ladies on Mission Stations and other persons residing in Volcanic districts, who, during many years, sent to him observations on minute points connected with seismic disturbance. After a life of heroic struggle against many difficulties, he published a book, Force and Nature, in which he advanced a psychologic theory connected with Geologic Evolution, which at some points coincided with the theories of J. Hinton ; at some with that of Betts ; at others, again, it reminded me of my husband's system of psychologic co-ordination. He and James Hinton once compared notes in my presence.

The late Dr. Wiltshire was well known as a physician. It was not so well known that he had made a profound study of the effect on the nerves and brain of periodic alternation of mental attitude ; not mere repose, but reversal of attitude as preparation for repose. He believed

PREFACE 13

that the habit of this is conducive, not only to longevity, but to that prolonged youth of the mind which makes old age profitable. He had come to the conclusion that most of the revealing power born into the world is wasted for the service of mankind, by too early precipitating itself in some concrete form, or committing itself to some definite view or opinion. He said : — ' The way to do good work is to live to be old. If you have genius, keep it fresh till you have experience as well.' He expressed to me certain conclusions to which he had come about the bad consequences, to the general morality and health, of the people being educated in habits of slavery to fixed mental attitude.

Gratky held that the Art of Thinking would never flourish during periods of intellectual individualism and competition ; that the essential condition for any marked evolution of it is one of self-effacing communal study. This condition of generous selflessness prevailed in Mathematical Science during the great revival in which A. De Morgan and my husband took part, in the forties and fifties of the last century.

For the last thirty years there has existed an informal group of workers, organized on the communal plan suggested by Gratry, which

14 PEEFACE

has for one of its main objects the study of the Laws of Sequence of Thought-processes. Among its rules are the following : —

Any member is at liberty to communicate to the public any information on psychology or education which he acquires by the assistance of other members.

Any book or article emanating from the group is to be signed by the member who is responsible for the selection and arrangement of the contents. He owes to his colleagues no public recognition, and is expected not to connect their names with any views which he may put forward.

It only remains for me therefore to express my warm thanks to Miss Eleanor Cobham, whose intelligent and devoted assistance has made it possible for me to organize into a form available for publication the mass of material relating to the Psychology of the process of Investigation which has drifted into my hands in the course of a long life.

Maby Everest Boole.

Chapter I

The present volume is specifically concerned with the preparation of the child for science. It ofiers suggestions as to means by which the scientific condition of mind can be induced. Each mother must decide for herself whether, and to what extent, she wishes to induce this condition. The first desideratum is that parents should form a clear idea what is the scientific condition of mind ; the next is that they should know in what consists the preparation for it.

The typically scientific mind may be described as one which stands in a definite relation to As- Yet-Unknown Truth, and especially to that portion of the As- Yet-Unknown which is just below the horizon of knowledge. In proportion as a mind is non-scientific, the occurrence of an unfamiliar phenomenon stimulates it to form some immediate classification or judgement. A new statement is hailed at once as ' true ' or ' false ' ; a new fact is classified as ' good ' or ' bad,' ' nice ' or ' nasty ' ; an unfamiliar action as ' right ' or ' wrong,' &c. In proportion as a mind is scientific, the occurrence of a new phenomenon tends to set it vibrating with a consciousness of coming revelation, and to start a certain cycle of mental attitudes, a cycle of the following kind : —

Homage.

Attention.

Observation.

Analysis.

Antithesis.

Synthesis.

Contemplation.

Effacement.

Bepose.

Judgement or Classification.

The cycle varies in duration ; each phase may occupy a few seconds, or many months, or even years ; but the tendency to fall into some such sequence as that above described at the touch of a new fact is what constitutes the essentially scientific condition.

It would, of course, be impossible to direct the studies of a child strictly in accordance with any such sequence as the above, but a good deal may be done towards inducing scientific elasticity by setting up the habit of rhythmic alternation of attitude. And, if the child is to be prepared for science, something of reverence should always accompany the impact of the As- Yet-Unknown.

That delicate sensitiveness to the touch of the illogical, to the limits of knowledge, and to the Presence of the As-Yet-Unknown, which it was the object of great mathematicians to confer on automatic mechanism, is too often destroyed in the human brain by rough and ready processes, adopted, sometimes for the purpose of fixing the opinions of young people, sometimes for that of enabling them to pass examinations successfully in subjects which they do not really understand. To cultivate it in the young child is the object of some of the precautions recommended in the following pages. None of them, however, are intended to be slavishly carried out.

Many thoughtful parents are beginning to wish that their children, while learning the elements of sciences, could also gain an early initiation into those methods of study by following which the Newton, or Darwin, or Faraday of the future trains himself after his teachers have done with him. The methods in use in schools ought, they think, to differ from the Newton, Darwin, Faraday methods of private study only as the little sapling, which still needs support and shelter, differs from the tree.

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18 PEEPARATION FOR SCIENCE

It seems a not unreasonable desire that the saphng of early method should have some natural tendency towards growing into that particular tree, true science-method. Whereas, so far as I can learn, most of the recognized school methods differ from the essential sciencemjethod rather as the little rose bush or cabbage differs from the oak : the cabbages and rose bushes may bring forth results admirable, charming, and vigorous, which will be good to eat or pleasant to the eye, and productive of prizes at shows ; but they have no sort of tendency to grow into an oak ; and if we happen to want to plant an oak-tree in the place where they have been set, we shall have to grub up some of the roses and cabbages. The youth who means to make scientific philosophy his career usually has to begin by grubbing out of himself what he learned at school ; not of course all the statements about fact, and still less the good habits of order and industry, but all that he learned at school in the way of method of study. There are schools to which this sweeping criticism does not apply ; here and there a teacher of elementary science evolves unconsciously, by some accident of organization or instinct, the true secret of the Newtons and Darwins. The pupils of such teachers are not always particularly successful in their early studies, for a reason which I will explain further on ; the sapling does not grow fast, owing to uncongenial surroundings ,' but it is of the true breed, and, though a starveling, sound at the core. But scientific method is something more definite than the occasional and unconscious action of a heaven-born teacher ; it might be, and ought to be, explained by lecturers on pedagogy to audiences of intelligent pupilteachers.

There is a principle whieh has been formulated in scientific treatises on the Art of Study, such as that of Gratry, and which is so recognized in the circles where science is; being evolved as to be held a matter of course not needing to be stated at all, unless when some science leader is roused to protest by the proceedings of those around him. An instance of such protest may as well be given now. Forty years ago a lady asked me to lend her for her children some good introduction to the study of nature. I lent her a work which had been the delight of my own childhood ; but she promptly returned it with a note to the effect that she could not allow her children to read it, for it was antiquated and not up to modern requirements ; it stated that herring shoals approach Europe from the North, whereas it had lately been discovered that they come from the South (or vice versa — I do not at

B 2 this moment remember which theory was held forty years ago and which twenty years before that) ; and, she added, there is so much that children must learn nowadays that they must not waste their time in learning theories already exploded. A scientific man to whom I showed the letter remarked impatiently that the writer evidently had no idea what she was about ; for, he said, what is most necessary for the children to learn is not what is the last new theory about where herrings are hatched, but how to extract the truth from a series of impressions and statements, each of which is only partially true. In this utterance we have, I think, the key to the most essential element in a truly scientific method of study ; and the case is worth analysing, for it illustrates the grave error, the hidden pitfall, into which the advanced section of the educational profession feU in passing from the ancient ideal of an education based on classics to the modern ideal of an education based on science.

Dead languages are fixed for ever, at least as to those parts of the study with which young people are concerned. The dative of such a noun is so-and-so ; this particular word is a dactyl and that a spondee ; and the duty of the schoolmaster was to see that the boys spelled and scanned the words accordingly.

My friend had been trained in the fundamental conception that there is a right way of speUing a word, and other ways are wrong ; and that children should be taught the right way. She had so far outgrown the old classic traditions as to think that it is not enough to know how Virgil scanned Latin, and Aeschylus wrote Greek ; that a citizen of the nineteenth century should know how God makes the world and whence comes humanity's food ; she had read enough science, too, to be aware that it is a growing, not a fixed and limited form of knowledge. She was not foolish enough to imagine she could get hold of any absolute and final opinions about science, to substitute for the absolute and final right ways of writing Latin ; so she enshrined instead, on her domestic altar, the last new up-to-date opinion, having no conception of the true nature of eternal scientific method. What this lady did in detail the advanced section of educationalists have done as a whole ; when they discovered that fixed rules of grammar are not, as used to be thought, sufficient mind-food, they substituted, not the eternal truth of mental pulsation, but up-todateness. The newest textbooks, the latest opinion about evolution, the most newlyinvented and costliest apparatus, the latest method of showing electric or galvanic action — these were supposed to be the characteristics of the best science school ! Yet it is well known that many of our great scientific leaders learned at first from books old even in their childhood, and used simple apparatus of their own contriving for lack of means to purchase any other.

In classical learning it is eminently desirable to secure that the right impression shall be made from the first ; that wrong impressions shall have as little time as possible to deepen themselves. We wish the child's eye and ear to become accustomed from the first to welcome the right and reject the wrong ; we do not wish him to gain any habit of tolerating wrong impressions. If the child uses the nominative where he should use the accusative, and is not at once corrected, that is so much to the bad for his future progress ; if he can be got not to be able to remember a time when he used the word wrongly, that is so much to the good. But in science there are, there can be, no absolutely right impressions ; our minds are not big enough to grasp any natural fact as a whole ; everything depends upon drawing right conclusions from combinations of impressions, each of which is in itself inadequate and partially misleading ; and if the pupil is to be got into scientific methods, that is what he must be trained to do. And in order that he may learn to do it, it is sometimes necessary that each of a succession of ' wrong ' impressions should have time to register itself on the brain and become part of its available stock. Such a statement may naturally convey to the scholastic mind trained in classic traditions an impression of disorderliness, but it does not imply disorder. Up-to-dateness is the cause of disorder ; the haste, the greed, to efface rapidly each partial impression, when we have nothing to substitute for it but some other impression equally partial, is not only unscientific but eminently disorderly.

Some readers may be tempted to think that in mathematics there are no tolerated and mutually corrective errors. The space at my disposal does not admit of entering fully into that question : it is enough to say here that mathematical method is the typical and perfect scientific method, in which the warp and woof oi polar partial apprehensions are so fine and so perfectly woven that the texture is, so to speak, hardly visible to the naked eye ; but it reveals itself on close analysis of mathematical procedure ; and, indeed, it was by means of mathematical investigation that the principle underlying all true scientific mental action was brought to formulation.

The difference between teaching sciences and training in scientific method is well illustrated in the teaching of botany and biology by dissecting flowers and animals. In the first place, as Professor Geddes constantly reminds his hearers, confusion of mind is induced by using the word ' biology ' to anything which involves destroying the life of the object under investigation. For purposes of scientific investigation, destruction is often necessary (though there need not be nearly as much of it as there is). But, however necessary, it is in itself not biology but necrology, for it shows the pupil not how the thing lives, but how it looks when dying or dead. And this is more than a mere quibble about words ; the whole question of scientific method is involved. Children inherit from their monkey-ancestors an abundant supply of inquisitive destructiveness ; the quality which needs educating, i. e. educing, is reverent patience to stand still and watch other creatures living their lives. Science has been evolved by the balanced action of these two faculties or powers — the natural monkeyinquisitiveness and the educated spiritual reverence. To over-cultivate destructive curiosity is a cheap way of enabling children to make a show in science examinations ; but that sort of thing has no tendency to induce the habit of true scientific method, which depends on alternation of opposites. If a child is to be initiated into scientific method, its early studies must go in the direction of balancing its natural destructiveness by learning to foster life and to study patiently the development of living things. Of course, this ideal is very difficult to carry on in town ; it is, for instance, difficult to study botany in town except by means of cut flowers ; but a good deal might be done by teaching children, when they see a flower, either growing or in water, not to touch it till they have learned all they can of its poise and mode of growth, so as to be able, after dissecting it, to reconstruct in their minds an accurate picture of how it looked before they disturbed it.

The tendency in science classes to an overcultivation of mere monkey-destructiveness has been largely fostered by the claim of certain faddists that children shall be told nothing, but shall ' find out everything for themselves.' What science really does claim in this matter is that a clear line of demarcation shall be preserved between what the individual has observed and what he has learned at second hand. The claim that children shall find out everything and be told nothing is palpably absurd.

As a matter of fact, most science leaders read eagerly and omnivorously on their own subject, being anxious to get all the help they can from previous and contemporary investigators. No man can find out for himself all he needs to know. How could any individual find out by himself the earth's movement round the sun ? What science does claim is, that no child shall be told anything about the motion of the earth tiU he has observed many sunrises and sunsets ; till a clear sense-impression of the earth standing still and the sun moving has become organic within him. This registering of a 'wrong' impression is what in science we have to secure ; while in classics we should try to prevent it.

Now let us see how a true science teacher deals in detaU with this scientific necessity for registering, separately, successive partial and misleading impressions. Her subject is, we wUl say, the buttercup. First, she gets the children to look carefully at the plant as a whole ; if possible, to watch it growing. If they can have a specimen in their garden, and watch the gradual unfolding of leaf and flower-buds, so much the better. If she can draw, she wUl teach them to register with the paint-brush their impressions of it at various stages. She will lead them to observe, among other facts, that it difiers from such flowers as the larkspur by having apparently no nectary. When they have carefully noticed all she can get them to see of the living plant, she proceeds to a

THE SCIEKTIFIC MIND • 27

dissection of the flower. ' What is this ? ' she says, pointing to the scale at the base of a petal. ' A bit of petal turned up,' says one child. ' A stamen with the anther knocked off,' says another. 'I think it looks like a little petal, like the inside petals of a double anemone,' says some specially observant little person. If the teacher is a mere crammer, she will immediately explain the function of the scale ; but if she is a real science teacher, she makes no comment ; she only asks questions to draw out further observations.

Some other day she will explain that the scale is believed to secrete some substance, and, therefore, to partake of the nature of a nectary. But, if she is wise, she will not do this till the conception of an anomalous organ, as to which one could not be sure whether it is a petal or a stamen, has had time to soak itself well in. Then, when the children learn that it is, after all, a sort of nectary, though it is not the shape of one, only that it is not called nectary because the substance it secretes is not honey, this will be a real introduction for them to the conception of metamorphism. It will not enable them to answer questions at an examination on Goethe's theory of metamorphism, still less on any later one ; but it will prepare them to understand metamorphism as Goethe understood it, by

28 PKEPAKATION FOE SCIENCE

leading them to see nature as Goethe saw it. Meantime, if the up-to-date mother or head mistress has been present at the former part of the lesson, this is the kind of comment she will probably make: — 'Miss Dash came to us with the character of a high-class science teacher ; but I am disappointed in her ; she is so dull and behindhand; she constantly lets mistakes pass. Only to-day I heard Bessie caU the little scale of the buttercup a bit of petal ; and Miss Dash seemed not to know any better; at any rate she said nothing. I am sure I read in the Botanists' Magazine that the scale is considered to be a secreting gland. It is very provoking, after aU the pains I took to secure good teaching in that department.'

Such is the kind of misapprehension which has come of trying to put the new wine of scientific progress into the old bottle of academic rightness. A mistake in grammar is a mere blunder, and should be corrected as soon as possible, so as to prevent the child's eye and ear from becoming accustomed to, and contented with, inelegant diction. But the misapprehension about the gland is not a blunder ; it is the normal impression which the phenomena should naturally make on a mind at a certain stage of development ; and it is the teacher's business to ensure that her pupil's mind shall register that impression before being disturbed by the intrusion of one derived from more recondite investigations. If, indeed, the child were, from carelessness, to make what is for him, at his present stage, a blunder, she would immediately lead him by questions to see his error ; but that is quite another matter. In arithmetic — the most methodized of sciences — we make the child correct his sum if he has made a careless mistake ; but no good teacher interrupts a partial apprehension till the normal time has come. Scientific education is not arrived at, and never can be arrived at, by young people being crammed at School and College ■with ready-made knowledge ; and left to find out, after adult life and its duties have come on them, that they are still very ignorant of how to learn what they now need to know. Nor do they mend the matter then, by turning in disgusted recoil from the sham knowledge with which others crammed them, to cram themselves, from books, with ready-made Theories about the limits of the knowable and the ' Philosophy of the Unknowable.' Scientific culture is the result of a steady life-long habit of friendly and intimate, though reverent, intercourse with the Eternally Infinite Unknown.

We must now go a little further into the questions : — What is that essence of scientific method on which its essential scientific quality depends ? What are the conditions for securing it ? How has it been introduced into science colleges ? How might it be introduced into elementary teaching 1 Are there any special diflficulties in so introducing it ; and, if so, how can they best be overcome ?