CHAPTER I

THE ORGANISATION

OF THOUGHT

THE ORGANISATION

OF THOUGHT

EDUCATIONAL AND SCIENTIFIC

BY

A. N. WHITEHEAD, Sc.D., F.R.S.

FELLOW OF TRINITY COLLEGE, CAMBRIDGE, AND PROFESSOR OF

APPLIED MATHEMATICS AT THE IMPERIAL COLLEGE OF

SCIENCE AND TECHNOLOGY

LONDON

WILLIAMS AND NORGATE

14 HENRIETTA STREET, COVENT GARDEN, W.C.2

1917

_The rights of translation are reserved_

PREFACE

THE discourses included in this volume have been delivered as addresses

on various occasions which are duly noted; the only exception is

_The Anatomy of Some Scientific Ideas_, which is now published

for the first time. These discourses fall into two sections, the first

five chapters deal with education, and the remaining three embody

discussions on certain points arising in the philosophy of science.

But a common line of reflection extends through the whole, and the two

sections influence each other.

I have left in each chapter the reference to the particular occasion of

its first production, and I have not sought for a verbal consistency

covering perplexity. But the various parts of the book were in fact

composed with express reference to each other, so as to form one whole.

I have to thank the Syndics of the Cambridge University Press for

permission to republish the contents of Chapter V.

_Imperial College of Science and Technology,_

_April 1917._

TABLE OF CONTENTS

CHAP. PAGE

PREFACE v

I. THE AIMS OF EDUCATION--A PLEA FOR REFORM 1

(Presidential Address to the Mathematical Association,

January, 1916.)

II. TECHNICAL EDUCATION AND ITS RELATION TO

SCIENCE AND LITERATURE 29

(Presidential Address to the Mathematical Association,

January, 1917.)

III. A POLYTECHNIC IN WAR-TIME 58

(Address at the Prize Distribution, Borough Polytechnic

Institute, Southwark, February, 1917.)

IV. THE MATHEMATICAL CURRICULUM 69

(Presidential Address to the London Branch of the

Mathematical Association, 1912.)

V. THE PRINCIPLES OF MATHEMATICS IN RELATION

TO ELEMENTARY TEACHING 92

(Paper read in the Educational Section of the International

Congress of Mathematicians, Cambridge,

1912.)

VI. THE ORGANISATION OF THOUGHT 105

(Presidential Address to Section A, British Association,

Newcastle, 1916; also read subsequently before the

Aristotelian Society.)

VII. THE ANATOMY OF SOME SCIENTIFIC IDEAS 134

VIII. SPACE, TIME, AND RELATIVITY 191

(Paper read to Section A at the Manchester Meeting of

Section A, 1915; also, with the appended Commentary,

read subsequently before the Aristotelian

Society.)

ORGANISATION OF THOUGHT

CHAPTER I

THE AIMS OF EDUCATION--A PLEA FOR REFORM

(_Presidential Address to the Mathematical Association, January,

1916_)

WHEN I had the honour of being made President of the Mathematical

Association, I did not foresee the unusual responsibility which it

entailed. It was my intention to take as the theme of a presidential

address the consideration of some aspect of those special subjects to

which my own researches have principally been directed. Events have

forced me to abandon that intention. It is useless to discuss abstract

questions in the midst of dominant practical preoccupation. We cannot

disregard the present crisis in European civilisation. It affects every

function of life. In the harder struggle for existence which lies

before the nation, all departments of national effort will be reviewed

for judgment. The mere necessity for economy in resources will provoke

this reformation.

We are concerned with education. This Association, so rich in its

membership of educationalists, with the conception of reform as the

very reason of its being, is among those bodies which must take the

lead in guiding that educational reconstruction which by a sociological

law follows every social revolution. We do not want impracticable

ideals, only to be realised beyond the clouds in

"Some wild, weird clime,

Out of Space, and out of Time."

We require to know what is possible now in England, a nation conscious

of its high achievements, and of great failures, shaken to its

foundations, distrustful of the old ways, and dreading fantastic

novelties.

I will take my courage in both hands, and put before you an outline of

educational principles. What I am going to say is of course entirely

without your authority, and does not pledge or prejudge any action of

the Association. We are primarily concerned only with the intellectual

side of education, and, as mathematicians, are naturally concerned to

illustrate details more particularly by reference to mathematics. Thus

much to explain deliberate omissions in what follows.

Consider now the general and special education of two types of boys,

namely those in secondary schools who in after life must form the

professional and directing classes in commerce, industry, and public

administration, and again those in junior technical schools and later

in advanced continuation classes, who are going to form the class of

skilled artisans and foremen of workshops. These two sets compose the

educated strength of the nation. We must form no ideals which include

less than these entire classes within their scope. What I shall say,

will in phraseology apply more directly to the secondary schools, but

with unessential changes it will apply equally to the other group.

What is the first commandment to be obeyed in any educational scheme?

It is this: Do not teach too many subjects. The second command is this:

What you teach, teach thoroughly. The devil in the scholastic world

has assumed the form of a general education consisting of scraps of a

large number of disconnected subjects; and, with the artfulness of the

serpent, he has entrenched himself behind the matriculation examination

of the University of London, with a wire entanglement formed by the

Oxford and Cambridge schools' examination.

Culture is activity of thought, and receptiveness to beauty, and humane

feeling. Scraps of information have nothing to do with it. A merely

well-informed man is the most useless bore on God's earth. What we

should aim at producing is men who possess both culture and expert

knowledge in some special direction. Their expert knowledge will give

them the ground to start from, and their culture will lead them as deep

as philosophy and as high as art. We have to remember that the valuable

intellectual development is self-development, and that it mostly takes

place between the ages of sixteen and thirty. As to training, the most

important part is given by mothers before the age of twelve. A saying

due to Archbishop Temple illustrates my meaning. Surprise was expressed

at the success in after-life of a man, who as a boy at Rugby had been

somewhat undistinguished. He answered, "It is not what they are at

eighteen, it is what they become afterwards that matters."

In training a child to activity of thought, above all things we must

beware of what I will call "inert ideas"--that is to say, ideas that

are merely received into the mind without being utilised, or tested, or

thrown into fresh combinations.

In the history of education, the most striking phenomenon is that

schools of learning, which at one epoch are alive with a ferment of

genius, in a succeeding generation exhibit merely pedantry and routine.

The reason is, that they are overladen with inert ideas. Education

with inert ideas is not only useless: it is, above all things,

harmful--_Corruptio optimi, pessima_. Except at rare intervals

of intellectual ferment, education in the past has been radically

infected with inert ideas. That is the reason why uneducated clever

women, who have seen much of the world, are in middle life so much

the most cultured part of the community. They have been saved from

this horrible burden of inert ideas. Every intellectual revolution

which has ever stirred humanity into greatness has been a passionate

protest against inert ideas. Then, alas, with pathetic ignorance of

human psychology, it has proceeded by some educational scheme to bind

humanity afresh with inert ideas of its own fashioning.

Let us now ask how in our system of education we are to guard against

this mental dry rot. We recur to our two educational commandments,

"Do not teach too many subjects," and again, "What you teach, teach

thoroughly."

The result of teaching small parts of a large number of subjects is the

passive reception of disconnected ideas, not illumined with any spark

of vitality. Let the main ideas which are introduced into a child's

education be few and important, and let them be thrown into every

combination possible. The child should make them his own, and should

understand their application here and now in the circumstances of his

actual life. From the very beginning of his education, the child should

experience the joy of discovery. The discovery which he has to make,

is that general ideas give an understanding of that stream of events

which pours through his life, which is his life. By understanding I

mean more than a mere logical analysis, though that is included. I mean

"understanding" in the sense in which it is used in the French proverb,

"To understand all, is to forgive all." Pedants sneer at an education

which is useful. But if education is not useful, what is it? Is it a

talent, to be hidden away in a napkin? Of course, education should be

useful, whatever your aim in life. It was useful to Saint Augustine

and it was useful to Napoleon. It is useful, because understanding is

useful.

I pass lightly over that understanding which should be given by the

literary side of education. It is not peculiarly the function of this

Association to consider it. Nor do I wish to be supposed to pronounce

on the relative merits of a classical or a modern curriculum. I would

only remark that the understanding which we want is an understanding

of an insistent present. The only use of a knowledge of the past

is to equip us for the present. No more deadly harm can be done to

young minds than by depreciation of the present. The present contains

all that there is. It is holy ground; for it is the past, and it is

the future. At the same time it must be observed that an age is no

less past if it existed two hundred years ago than if it existed two

thousand years ago. Do not be deceived by the pedantry of dates. The

ages of Shakespeare and of Molière are no less past than are the ages

of Sophocles and of Virgil. The communion of saints is a great and

inspiring assemblage, but it has only one possible hall of meeting,

and that is, the present; and the mere lapse of time through which any

particular group of saints must travel to reach that meeting-place,

makes very little difference.

Passing now to the scientific and logical side of education, we

remember that here also ideas which are not utilised are positively

harmful. By utilising an idea, I mean relating it to that stream,

compounded of sense perceptions, feelings, hopes, desires, and of

mental activities relating thought to thought, which forms our life.

I can imagine a set of beings which might fortify their souls by

passively reviewing disconnected ideas. Humanity is not built that

way--except perhaps some editors of newspapers.

In scientific training, the first thing to do with an idea is to prove

it. But allow me for one moment to extend the meaning of "prove"; I

mean--to prove its worth. Now an idea is not worth much unless the

propositions in which it is embodied are true. Accordingly an essential

part of the proof of an idea is the proof, either by experiment or by

logic, of the truth of the propositions. But it is not essential that

this proof of the truth should constitute the first introduction to

the idea. After all, its assertion by the authority of respectable

teachers is sufficient evidence to begin with. In our first contact

with a set of propositions, we commence by appreciating their

importance. That is what we all do in after-life. We do not attempt,

in the strict sense, to prove or to disprove anything, unless its

importance makes it worthy of that honour. These two processes of

proof, in the narrow sense, and of appreciation do not require a rigid

separation in time. Both can be proceeded with nearly concurrently. But

in so far as either process must have the priority, it should be that

of appreciation by use.

Furthermore, we should not endeavour to use propositions in isolation.

Emphatically I do not mean, a neat little set of experiments to

illustrate Proposition I and then the proof of Proposition I, a neat

little set of experiments to illustrate Proposition II and then the

proof of Proposition II, and so on to the end of the book. Nothing

could be more boring. Inter-related truths are utilised _en bloc_,

and the various propositions are employed in any order, and with any

reiteration. Choose some important applications of your theoretical

subject; and study them concurrently with the systematic theoretical

exposition. Keep the theoretical exposition short and simple, but

let it be strict and rigid so far as it goes. It should not be too

long for it easily to be known with thoroughness and accuracy. The

consequences of a plethora of half-digested theoretical knowledge are

deplorable. Also the theory should not be muddled up with the practice.

The child should have no doubt when it is proving and when it is

utilising. My point is that what is proved should be utilised, and that

what is utilised should--so far as is practicable--be proved. I am far

from asserting that proof and utilisation are the same thing.

At this point of my discourse, I can most directly carry forward

my argument in the outward form of a digression. We are only just

realising that the art and science of education require a genius and

a study of their own; and that this genius and this science are more

than a bare knowledge of some branch of science or of literature. This

truth was partially perceived in the past generation; and headmasters,

somewhat crudely, were apt to supersede learning in their colleagues

by requiring left-hand bowling and a taste for football. But culture

is more than cricket, and more than football, and more than extent of

knowledge.

Education is the acquisition of the art of the utilisation of

knowledge. This is an art very difficult to impart. Whenever a

text-book is written of real educational worth, you may be quite

certain that some reviewer will say that it will be difficult to

teach from it. Of course it will be difficult to teach from it. If it

were easy, the book ought to be burned; for it cannot be educational.

In education, as elsewhere, the broad primrose path leads to a nasty

place. This evil path is represented by a book or a set of lectures

which will practically enable the student to learn by heart all the

questions likely to be asked at the next external examination. And I

may say in passing that no educational system is possible unless every

question directly asked of a pupil at any examination is either framed

or modified by the actual teacher of that pupil in that subject. The

external assessor may report on the curriculum or on the performance

of the pupils, but never should be allowed to ask the pupil a question

which has not been strictly supervised by the actual teacher, or

at least inspired by a long conference with him. There are a few

exceptions to this rule, but they are exceptions, and could easily be

allowed for under the general rule.

We now return to my previous point, that theoretical ideas should

always find important applications within the pupil's curriculum. This

is not an easy doctrine to apply, but a very hard one. It contains

within itself the problem of keeping knowledge alive, of preventing it

from becoming inert, which is the central problem of all education.

The best procedure will depend on several factors, none of which can

be neglected, namely, the genius of the teacher, the intellectual type

of the pupils, their prospects in life, the opportunities offered by

the immediate surroundings of the school, and allied factors of this

sort. It is for this reason that the uniform external examination

is so deadly. We do not denounce it because we are cranks, and like

denouncing established things. We are not so childish. Also, of course,

such examinations have their use in testing slackness. Our reason of

dislike is very definite and very practical. It kills the best part of

culture. When you analyse in the light of experience the central task

of education, you find that its successful accomplishment depends on a

delicate adjustment of many variable factors. The reason is that we are

dealing with human minds, and not with dead matter. The evocation of

curiosity, of judgment, of the power of mastering a complicated tangle

of circumstances, the use of theory in giving foresight in special

cases--all these powers are not to be imparted by a set rule embodied

in one schedule of examination subjects.

I appeal to you, as practical teachers. With good discipline, it is

always possible to pump into the minds of a class a certain quantity of

inert knowledge. You take a text-book and make them learn it. So far,

so good. The child then knows how to solve a quadratic equation. But

what is the point of teaching a child to solve a quadratic equation?

There is a traditional answer to this question. It runs thus: The

mind is an instrument, you first sharpen it, and then use it; the

acquisition of the power of solving a quadratic equation is part of

the process of sharpening the mind. Now there is just enough truth in

this answer to have made it live through the ages. But for all its

half-truth, it embodies a radical error which bids fair to stifle the

genius of the modern world. I do not know who was first responsible

for this analogy of the mind to a dead instrument. For aught I know,

it may have been one of the seven wise men of Greece, or a committee

of the whole lot of them. Whoever was the originator, there can be no

doubt of the authority which it has acquired by the continuous approval

which it has received from eminent persons. But whatever its weight of

authority, whatever the high approval which it can quote, I have no

hesitation in denouncing it as one of the most fatal, erroneous, and

dangerous conceptions ever introduced into the theory of education. The

mind is never passive; it is a perpetual activity, delicate, receptive,

responsive to stimulus. You cannot postpone its life until you have

sharpened it. Whatever interest attaches to your subject-matter, must

be evoked here and now; whatever powers you are strengthening in the

pupil, must be exercised here and now; whatever possibilities of mental

life your teaching should impart, must be exhibited here and now. That

is the golden rule of education, and a very difficult rule to follow.

The difficulty is just this: the apprehension of general ideas,

intellectual habits of mind, and pleasurable interest in mental

achievement can be evoked by no form of words, however accurately

adjusted. All practical teachers know that education is a patient

process of the mastery of details, minute by minute, hour by hour, day

by day. There is no royal road to learning through an airy path of

brilliant generalisations. There is a proverb about the difficulty of

seeing the wood because of the trees. That difficulty is exactly the

point which I am enforcing. The problem of education is to make the

pupil see the wood by means of the trees.

The solution which I am urging, is to eradicate the fatal disconnection

of subjects which kills the vitality of our modern curriculum.

There is only one subject-matter for education, and that is Life

in all its manifestations. Instead of this single unity, we offer

children--Algebra, from which nothing follows; Geometry, from which

nothing follows; Science, from which nothing follows; History, from

which nothing follows; a Couple of Languages, never mastered; and

lastly, most dreary of all, Literature, represented by plays of

Shakespeare, with philological notes and short analyses of plot and

character to be in substance committed to memory. Can such a list be

said to represent Life, as it is known in the midst of the living of

it? The best that can be said of it is, that it is a rapid table of

contents which a deity might run over in his mind while he was thinking

of creating a world, and had not yet determined how to put it together.

Let us now return to quadratic equations. We still have on hand the

unanswered question. Why should children be taught their solution?

Unless quadratic equations fit into a connected curriculum, of course

there is no reason to teach anything about them. Furthermore, extensive

as should be the place of mathematics in a complete culture, I am a

little doubtful whether for many types of boys algebraic solutions of

quadratic equations do not lie on the specialist side of mathematics.

I may here remind you that as yet I have not said anything of the

psychology or the content of the specialism, which is so necessary a

part of an ideal education. But all that is an evasion of our real

question, and I merely state it in order to avoid being misunderstood

in my answer.

Quadratic equations are part of algebra, and algebra is the

intellectual instrument which has been created for rendering clear

the quantitative aspects of the world. There is no getting out of

it. Through and through the world is infected with quantity. To talk

sense, is to talk in quantities. It is no use saying that the nation

is large,--How large? It is no use saying that radium is scarce,--How

scarce? You cannot evade quantity. You may fly to poetry and to music,

and quantity and number will face you in your rhythms and your octaves.

Elegant intellects which despise the theory of quantity, are but half

developed. They are more to be pitied than blamed. The scraps of

gibberish, which in their school-days were taught to them in the name

of algebra, deserve some contempt.

This question of the degeneration of algebra into gibberish, both in

word and in fact, affords a pathetic instance of the uselessness of

reforming educational schedules without a clear conception of the

attributes which you wish to evoke in the living minds of the children.

A few years ago there was an outcry that school algebra was in need

of reform, but there was a general agreement that graphs would put

everything right. So all sorts of things were extruded, and graphs were

introduced. So far as I can see, with no sort of idea behind them,

but just graphs. Now every examination paper has one or two questions

on graphs. Personally, I am an enthusiastic adherent of graphs. But I

wonder whether as yet we have gained very much. You cannot put life

into any schedule of general education unless you succeed in exhibiting

its relation to some essential characteristic of all intelligent or

emotional perception. It is a hard saying, but it is true; and I do

not see how to make it any easier. In making these little formal

alterations you are beaten by the very nature of things. You are pitted

against too skilful an adversary, who will see to it that the pea is

always under the other thimble.

Reformation must begin at the other end. First, you must make up your

mind as to those quantitative aspects of the world which are simple

enough to be introduced into general education; then a schedule of

algebra should be framed which will about find its exemplification in

these applications. We need not fear for our pet graphs, they will

be there in plenty when we once begin to treat algebra as a serious

means of studying the world. Some of the simplest applications will be

found in the quantities which occur in the simplest study of society.

The curves of history are more vivid and more informing than the dry

catalogues of names and dates which comprise the greater part of

that arid school study. What purpose is effected by a catalogue of

undistinguished kings and queens? Tom, Dick, or Harry, they are all

dead. General resurrections are failures, and are better postponed.

The quantitative flux of the forces of modern society are capable

of very simple exhibition. Meanwhile, the idea of the variable, of

the function, of rate of change, of equations and their solution, of

elimination, are being studied as an abstract science for their own

sake. Not, of course, in the pompous phrases with which I am alluding

to them here, but with that iteration of simple special cases proper to

teaching.

If this course be followed, the route from Chaucer to the Black Death,

from the Black Death to modern Labour troubles, will connect the tales

of the mediæval pilgrims with the abstract science of algebra, both

yielding diverse aspects of that single theme, Life. I know what most

of you are thinking at this point. It is that the exact course which

I have sketched out is not the particular one which you would have

chosen, or even see how to work. I quite agree. I am not claiming that

I could do it myself. But your objection is the precise reason why a

common external examination system is fatal to education. The process

of exhibiting the applications of knowledge must, for its success,

essentially depend on the character of the pupils and the genius of the

teacher. Of course I have left out the easiest applications with which

most of us are more at home. I mean the quantitative sides of sciences,

such as mechanics and physics.

My meaning can be illustrated by looking more closely into a special

case of this type of application. In my rough catalogue of the sort

of subjects which should form the schedule for algebra, I mentioned

Elimination. It was not put there by accident, for it covers a very

important body of thought.

In the first place, there is the abstract process of algebraic

elimination for suitable simple cases. The pupil acquires a firm grasp

of this by the process, inevitable in education, of working an adequate

number of examples. Again, there are the graphical solutions of the

same problem. Then we consider the significance in the external world.

We consider the velocity, time, space, acceleration diagrams. We take

uniform acceleration; we eliminate "_t_" between

_v_ = _u_ + _ƒt_, and _s_ = _ut_ + ½_ƒt_^2,

and eliminate "_s_" between

_v_^2 = _u_^2 + 2_ƒs_, and _s_ = _ut_ + ½_ƒt_^2.

Then we remember that constant acceleration is a very special case,

and we consider graphical solutions or empirically given variations of

_v_ or of _ƒ_. In preference, we use those empirical formulæ

which occur in the pupil's experimental work. We compare the strong and

weak points of the algebraic and graphical solutions.

Again, in the same connection we plot the statistics of social

phenomena against the time. We then eliminate the time between suitable

pairs. We can speculate how far we have exhibited a real casual

connection, or how far a mere temporal coincidence. We notice that

we might have plotted against the time one set of statistics for one

country and another set for another country, and thus, with suitable

choice of subjects, have obtained graphs which certainly exhibited mere

coincidence. Also other graphs exhibit obvious casual connections. We

wonder how to discriminate. And so are drawn on as far as we will.

But in considering this description, I must beg you to remember what I

have been insisting on above. In the first place, one train of thought

will not suit all groups of children. For example, I should expect that

artisan children will want something more concrete and, in a sense,

swifter than I have set down here. Perhaps I am wrong, but that is

what I should guess. In the second place, I am not contemplating one

beautiful lecture stimulating, once and for all, an admiring class.

That is not the way in which education proceeds. No; all the time the

pupils are hard at work solving examples, drawing graphs, and making

experiments, until they have a thorough hold on the whole subject.

I am describing the interspersed explanations, the directions which

should be given to their thoughts. The pupils have got to be made to

feel that they are studying something, and are not merely executing

intellectual minuets.

In this connection the excellence of some of the most recent text-books

on elementary algebra emanating from members of this Association,

should create an epoch in the teaching of the subject.

Finally, if you are teaching pupils for some general examination,

the problem of sound teaching is greatly complicated. Have you ever

noticed the zig-zag moulding round a Norman arch? The ancient work is

beautiful, the modern work is hideous. The reason is, that the modern

work is done to exact measure, the ancient work is varied according

to the idiosyncrasy of the workman. Here it is crowded, and there it

is expanded. Now the essence of getting pupils through examinations

is to give equal weight to all parts of the schedule. But mankind is

naturally specialist. One man sees a whole subject, where another can

find only a few detached examples. I know that it seems contradictory

to allow for specialism in a curriculum especially designed for a

broad culture. Without contradictions the world would be simpler, and

perhaps duller. But I am certain that in education wherever you exclude

specialism you destroy life.

We now come to the other great branch of a general mathematical

education, namely Geometry. The same principles apply. The theoretical

part should be clear-cut, rigid, short, and important. Every

proposition not absolutely necessary to exhibit the main connection

of ideas should be cut out, but the great fundamental ideas should

be all there. No omission of concepts, such as those of Similarity

and Proportion. We must remember that, owing to the aid rendered by

the visual presence of a figure, Geometry is a field of unequalled

excellence for the exercise of the deductive faculties of reasoning.

Then, of course, there follows Geometrical Drawing, with its training

for the hand and eye.

But, like Algebra, Geometry and Geometrical Drawing must be extended

beyond the mere circle of geometrical ideas. In an industrial

neighbourhood, machinery and workshop practice form the appropriate

extension. For example, in the London Polytechnics this has been

achieved with conspicuous success. For many secondary schools I suggest

that surveying and maps are the natural applications. In particular,

plane-table surveying should lead pupils to a vivid apprehension of the

immediate application of geometric truths. Simple drawing apparatus, a

surveyor's chain, and a surveyor's compass, should enable the pupils

to rise from the survey and mensuration of a field to the construction

of the map of a small district. The best education is to be found

in gaining the utmost information from the simplest apparatus. The

provision of elaborate instruments is greatly to be deprecated. To

have constructed the map of a small district, to have considered its

roads, its contours, its geology, its climate, its relation to other

districts, the effects on the status of its inhabitants, will teach

more history and geography than any knowledge of Perkin Warbeck or

of Behren's Straits. I mean not a nebulous lecture on the subject,

but a serious investigation in which the real facts are definitely

ascertained by the aid of accurate theoretical knowledge. A typical

mathematical problem should be: Survey such and such a field, draw a

plan of it to such and such a scale, and find the area. It would be

quite a good procedure to impart the necessary geometrical propositions

without their proofs. Then, concurrently in the same term, the proofs

of the propositions would be learnt while the survey was being made.

Fortunately, the specialist side of education presents an easier

problem than does the provision of a general culture. For this there

are many reasons. One is that many of the principles of procedure

to be observed are the same in both cases, and it is unnecessary

to recapitulate. Another reason is that specialist training takes

place--or should take place--at a more advanced stage of the pupil's

course, and thus there is easier material to work upon. But undoubtedly

the chief reason is that the specialist study is normally a study

of peculiar interest to the student. He is studying it because, for

some reason, he wants to know it. This makes all the difference.

The general culture is designed to foster an activity of mind; the

specialist course utilises this activity. But it does not do to lay too

much stress on these neat antitheses. As we have already seen, in the

general course foci of special interest will arise; and similarly in

the special study, the external connections of the subject drag thought

outwards.

Again, there is not one course of study which merely gives general

culture, and another which gives special knowledge. The subjects

pursued for the sake of a general education are special subjects

specially studied; and, on the other hand, one of the ways of

encouraging general mental activity is to foster a special devotion.

You may not divide the seamless coat of learning. What education has

to impart is an intimate sense for the power of ideas, for the beauty

of ideas, and for the structure of ideas, together with a particular

body of knowledge which has peculiar reference to the life of the being

possessing it.

The appreciation of the structure of ideas is that side of a cultured

mind which can only grow under the influence of a special study. I

mean that eye for the whole chess-board, for the bearing of one set of

ideas on another. Nothing but a special study can give any appreciation

for the exact formulation of general ideas, for their relations when

formulated, for their service in the comprehension of life. A mind so

disciplined should be both more abstract and more concrete. It has been

trained in the comprehension of abstract thought and in the analysis of

facts.

Finally, there should grow the most austere of all mental qualities; I

mean the sense for style. It is an æsthetic sense, based on admiration

for the direct attainment of a foreseen end, simply and without waste.

Style in art, style in literature, style in science, style in logic,

style in practical execution have fundamentally the same æsthetic

qualities, namely, attainment and restraint. The love of a subject in

itself and for itself, where it is not the sleepy pleasure of pacing a

mental quarter-deck, is the love of style as manifested in that study.

Here we are brought back to the position from which we started,

the utility of education. Style, in its finest sense, is the last

acquirement of the educated mind; it is also the most useful. It

pervades the whole being. The administrator with a sense for style,

hates waste; the engineer with a sense for style, economises his

material; the artisan with a sense for style, prefers good work. Style

is the ultimate morality of mind.

But above style, and above knowledge, there is something, a vague

shape like fate above the Greek gods. That something is Power. Style

is the fashioning of power, the restraining of power. But, after all,

the power of attainment of the desired end is fundamental. The first

thing is to get there. Do not bother about your style, but solve your

problem, justify the ways of God to man, administer your province, or

do whatever else is set before you.

Where, then, does style help? In this, with style the end is attained

without side issues, without raising undesirable inflammations. With

style you attain your end and nothing but your end. With style the

effect of your activity is calculable, and foresight is the last gift

of gods to men. With style your power is increased, for your mind is

not distracted with irrelevancies, and you are more likely to attain

your object. Now style is the exclusive privilege of the expert.

Whoever heard of the style of an amateur painter, of the style of an

amateur poet? Style is always the product of specialist study, the

peculiar contribution of specialism to culture.

English education in its present phase suffers from a lack of definite

aim, and from an external machinery which kills its vitality. Hitherto

in this address I have been considering the aims which should govern

education. In this respect England halts between two opinions. It has

not decided whether to produce amateurs or experts. The profound change

in the world which the nineteenth century has produced is that the

growth of knowledge has given foresight. The amateur is essentially a

man with appreciation and with immense versatility in mastering a given

routine. But he lacks the foresight which comes from special knowledge.

The object of this address is to suggest how to produce the expert

without loss of the essential virtues of the amateur. The machinery

of our secondary education is rigid where it should be yielding,

and lax where it should be rigid. Every school is bound on pain of

extinction to train its boys for a small set of definite examinations.

No headmaster has a free hand to develop his general education or his

specialist studies in accordance with the opportunities of his school,

which are created by its staff, its environment, its class of boys, and

its endowments. I suggest that no system of external tests which aims

primarily at examining individual scholars can result in anything but

educational waste.

Primarily it is the schools and not the scholars which should be

inspected. Each school should grant its own leaving certificates, based

on its own curriculum. The standards of these schools should be sampled

and corrected. But the first requisite for educational reform is the

school as a unit, with its approved curriculum based on its own needs,

and evolved by its own staff. If we fail to secure that, we simply fall

from one formalism into another, from one dung-hill of inert ideas into

another.

In stating that the school is the true educational unit in any national

system for the safe-guarding of efficiency, I have conceived the

alternative system as being the external examination of the individual

scholar. But every Scylla is faced by its Charybdis--or, in more homely

language, there is a ditch on both sides of the road. It will be

equally fatal to education if we fall into the hands of a supervising

department which is under the impression that it can divide all schools

into two or three rigid categories, each type being forced to adopt

a rigid curriculum. When I say that the school is the educational

unit, I mean exactly what I say, no larger unit, no smaller unit.

Each school must have the claim to be considered in relation to its

special circumstances. The classifying of schools for some purposes is

necessary. But no absolutely rigid curriculum, not modified by its own

staff, should be permissible. Exactly the same principles apply, with

the proper modifications, to universities and to technical colleges.

When one considers in its length and in its breadth the importance

of this question of the education of a nation's young, the broken

lives, the defeated hopes, the national failures, which result from the

frivolous inertia with which it is treated, it is difficult to restrain

within oneself a savage rage. In the conditions of modern life the ride

is absolute, the race which does not value trained intelligence is

doomed. Not all your heroism, not all your social charm, not all your

wit, not all your victories on land or at sea, can move back the finger

of fate. To-day we maintain ourselves. To-morrow science will have

moved forward yet one more step, and there will be no appeal from the

judgment which will then be pronounced on the uneducated.

We can be content with no less than the old summary of educational

ideal which has been current at any time from the dawn of our

civilisation. The essence of education is that it be religious.

Pray, what is religious education?

A religious education is an education which inculcates duty and

reverence. Duty arises from our potential control over the course

of events. Where attainable knowledge could have changed the issue,

ignorance has the guilt of vice. And the foundation of reverence is

this perception, that the present holds within itself the complete sum

of existence, backwards and forwards, that whole amplitude of time,

which is eternity.