Creativity in Science - Ernest Nagel (1968)

My theme is creativity in science

and I think I ought to say at the

beginning that uh there are a great

number of aspects of this problem

about which uh it would be desirable to

talk but uh the subject itself is vast

and I don't don't wouldn't have the time

even if I had the ability to

uh span the relevant issue that are

raised. I do want to say uh also that uh

I will address myself pretty much to

science as we know it today. Science

itself is something that has had a very

long history.

uh it had undergone various kinds of

changes

and uh the fact of change itself of

course is one symptom of one indication

of creative tendencies within or in

science itself.

Perhaps a person who ought to talk about

this subject is someone who has taken

part in uh the sciences.

uh I myself have had no firsthand an

experience within the sciences and

cannot report on any personal exposure

that I've had.

On the other hand, there may be some

advantage in an outsider

to deal with this topic because uh while

he may

not have very much to say about the

individual trees, he may see a bit more

of the forest.

uh as I indicated there are so many

aspects of the subject uh that I've been

compelled really to select uh a few

about which I want to say something and

the three main subordinate questions to

which I do want to address myself is

first

uh what is creativity

particularly in science that is what

does the word creativity mean?

Secondly, uh what are the mechanisms

psychological and other which may be

involved in the creative process?

And thirdly, and this is perhaps the

aspect of it that I'd like to dwell on

at greater at the greatest length is it

at what points in science

is creativity involved?

So let me begin with the first uh issue.

What is creativity? I think it's uh

pertinent to raise this question because

the word itself is vague

and there appear to be uh various sorts

of things that people do understand by

creativity and I like to uh canvas some

aspects of this uh many meaning the

meanings of the many of this manysided

word in the first place I suppose

everybody would agree that in some

fashion or other creativity in science

as well was elsewhere but certainly in

science is

uh associated with what is new, what is

original.

And so for example, we say that Heayen

was a creative musician.

uh not merely because he composed more

than 100 symphonies and other works of

of music but because he introduced and

developed novel patterns of uh symbolic

composition. [clears throat]

Uh similarly, Newton would generally be

regarded as being a creative scientist

and a great creative scientist because

among other things he developed

a general method for

obtaining the tangents to a curve. That

is he was one of the

discoverers of what is now known as the

differential calculus.

And then in the empirical science in

physics in particular he analyzed light

that comes from the sun in a way that uh

no one did before him. So that

originality novelty in this sense is

certainly a mark or at least one of the

essential ingredients of being creative

in science.

But then if we stop to think a moment, I

think we would say that uh it isn't just

originality

that counts to be regarded as being a

creative

in uh in science.

Uh for example, would we be inclined to

say that a man lacks creativity

if his achievements have been

anticipated by somebody else?

And I don't think we could have a

straightforward answer on this. In some

cases, we would say yes. In other cases,

not.

Uh the history of science is full of

what have been called independent

discoveries of the same thing. That is

two or more

uh scientists have found out the same

things. So they worked in ignorance of

one another.

As a matter of fact, one of my

colleagues at Colombia, Professor

Mertton, has a general thesis that uh

uh simultaneous discoveries

are the rule and uh discovery by of

something by just one individual is he

thinks is somewhat of an exception.

But in any case, we can cite it some

familiar examples of independent

discovery. For example, Newton and

Linets both discovered the calculus

simultaneously independent of one

another. There used to be a great

controversy as to who stole from whom

and then now I think everybody's agreed

that uh

there was no plagiarism involved that

each one made the discoveries

independently.

Again in more recent days uh great

American physicist uh Willard Gibbs

developed a branch of physics that is

known as statistical mechanics

and then a few years after that but

independently of Gibbs Einstein did

something pretty much the same. He

wasn't familiar with uh Gibbs's work

certainly not in detail.

Now in this case I think we would agree

that uh both of them were original

uh

that they were creative

but there are other cases I suppose that

uh we would say that a man doesn't

really have originality

if he was anticipated if his discoveries

remain dormant that is nobody pays any

attention to them or if the

anticipations of it have been made have

made no impact

on science. I think we would say he is

not a creative figure in science.

Uh take one illustration. It's an absurd

one but uh it'll make the point uh if

for example I had never heard of Newton

and somehow I was able somehow to

reconstruct

the content of Newton's great work from

Mathematica.

uh in one sense I think we would all say

well I really had an original mind.

Uh on the other hand uh since uh

a discovery of this kind would have no

impact on science because Newton made

the impact and any if I were to simply

uh rediscover the same thing that he did

independently of him I would not really

be contributing anything to the ongoing

process of science. This has already

been done.

So that uh in this case though I was

original

I think the title of being a creative

scientist would normally be denied to

me.

Then there are also a great number of

individuals who think well they really

have very original ideas. Sometimes they

regard as being cranks.

But if they make no impact on the

science even though nobody else had the

idea or if they present their ideas in

such a way that uh doesn't conform to

certain standards that are generally

accepted by the scientists again the

title of being creative minds would

probably be denied to them. And so it

isn't entirely clear under what

conditions an individual is said to be a

creative scientist.

Or take a somewhat slightly different

aspect of it. Uh if a man were to write

but a single poem even though we would

regard it as being really a magnificent

uh composition

uh we would not normally I think call

him a a creative poet.

And uh similarly I think if a man were

to make one contribution to science that

nobody else did uh again I think we

would deny the title of of of of

creative scientist to him. That is we

seem to be reserving the term creative

for those who either make a fairly large

number of new contributions

or if they don't make a very large one

a large number at least they make a

contribution

that is in some sense regard as being

very important.

Thus, if uh

a physicist were to spend his life in

obtaining increasingly more precise

measurements

of the velocity of light, let's say he

might have made a valuable contribution

to science. I mean, it's important to

know a precise value for the speed of

light. But I think we would not regard

him as being a a creative scientist

or to take an example

from mathematics.

There were two great mathematists in the

19th century. One of them was a German

by the name of Gaus

who really frucified the field because

he worked in so many different areas. He

contributed uh important work in in in

geometry, in number theory,

uh in electricity and magnetism.

Uh he was undoubtedly a creative

creative mind

uh both because of the number of his

contributions but also because of the

importance of each of them or at least

of many of them. On the other hand,

there was a French mathematician by the

name of Galwa,

G A L O I S, who died at the age of 19,

I think it was. It was short of 20, I

believe. He died in a duel.

Uh he had submitted a paper to a

outstanding French periodical some year

before.

It was not accepted for publication.

But the night before he went to a duel,

he wrote out some of his ideas

and this was really just in one area of

mathematics.

Now though his contributions partly

because of the brevity of his life

uh were few in number,

it dealt with uh what is now known as

group theory. And this uh has important

application to solving equations in

algebra.

He opened up a tremendous area of

research. [snorts] And so the sheer

number of his contributions is not

important and not important in in in his

case. Yet I think no one would hesitate

to deny him the title of being a

creative a creative mathematician, a

creative scientist.

And then you read I think we all it's

generally

uh recognize that there are degrees of

creativity

and of course if there are degrees of

creativity and if there are no firm

rules for measuring them then it's a

certain in a certain sense arbitrary

whether an individual is going to be

called creative or not. I mean there's

this kind of a difficulty.

Now uh let me turn from this to another

aspect of the question as to what we

mean by creativity.

I think by and large when we talk about

creativity in science

we associate the characterization with

the introduction of new ideas. new

ideas.

Somebody who was an insiduous gatherer

of miscellaneous facts though would be

there would be a very large number of

such facts would certainly not be

regarded as as a creative scientist.

Uh an explorer in geography uh may make

very valuable contributions

and he was involved of course in uh

great deal of activity in his

explorations.

But I think he would perhaps not be

called creative

a creative scientist unless

some

important idea

underlyed

uh his explorations

or if his explorations in some way

challenged

some accepted ideas about various

aspects of the earth's surface.

Take a slightly different illustration.

I doubt whether anybody would call Sir

Edmund Hillary who was the first

man to scale the southwest face of Mount

Everest creative explorer or mountaineer

and I think we would not call him

creative because in way he didn't

contribute any ideas.

So I I think uh

uh in some way creativity and science is

associated

with uh not so much in what you do by

way of some kind of a action that you

engage in but what kind of ideas you

either uh introduce into uh science or

what kind of ideas you tend to disprove

by some thing that you do. Take one

other illustration that I think bears on

this. Uh anybody who is an experimental

scientist obviously is involved in

activity. He's got to use his hands

uh

his his muscles often.

Uh experimentation surely involves

action.

But I think we wouldn't call an

experimentter a creative scientist

merely because he's able to manipulate

various sorts of instruments

but because he designed an experiment

and the the design of the experiment may

be the more important than the actual

physical labor of executing it. Uh take

one uh example of each kind. uh Newton

was not only a creative theoretical

uh physicist, he was also a creative

experimental physicist. uh he did

experimental work in optics

and uh he used a prism in order to show

that uh light coming from the sun is

dispersed and that there are various

colored rays that uh uh are contained in

the apparently white light that comes

from the sun. Now Newton not only

designed the experiment but he also

actually performed it.

On the other hand, uh there are very

great very distinguished experimental

physicists

some alive today. One of my colleagues

at Colombia who was a recipient of a

Nobel Prize for uh experimental physics

is very inept in handling apparatus

but uh he supplied uh the basic ideas

for constructing the various instruments

for running them and so on. And so again

I think uh an experimental is said to be

a creative experimental

not primarily because of his overt

behavioral activity so to speak but

because of the kind of ideas that he

contributes to the design of experiment

to evaluating the significance of the

experiment and so on.

One other uh point I'd like to make in

this uh connection with this first issue

as to what we all understand by

creativity is connected with the uh

distinction that we often make between

creativity and discovery.

Now we often distinguish between

creation

or invention on one hand and discovery

and in many cases this distinction is

very clear.

Uh

Captain Cook I think everybody would say

discovered Australia.

He didn't invent it. He didn't create

the continent.

uh we would say I suppose that Edison

invented the electric light

although sometimes we say he discovered

it but if we say that he discovered it

we don't quite mean the same thing that

we mean when we say that let's say

Columbus discovered America I mean the

electric flight was not there so to

speak for him to find

but he had in some way to uh reconstruct

material that was available to him and

put into some kind of a new form so he

invented

But in other cases, especially in the

realm of ideas,

it is more difficult to say whether a

man

been a creator or whether he's been a

discoverer.

Uh take some examples from very

elementary uh

uh mathematics. uh I suppose we all

heard about so-called negative numbers

or imaginary numbers. I mean numbers

like minus2 or minus7

these are the negative numbers and then

there are the so-called imaginary

numbers like the square root of minus1.

Now what shall we say about these? Did

the mathematicians of the 15th 16th

century who

introduced these notions did they

discover

uh the negative numbers or did they

invent them?

Or take an example from geometry when we

are given a problem and we are asked to

prove some theorem and we do give a

proof. What what did we do? Did we

discover the proof or did we invent the

proof? Did we create the proof?

Uh mathematicians themselves don't uh

are not of of like minds on this. At

least certainly psychologically.

you have a feeling of discovering

something that if you if if you devise a

proof or something that you didn't know

be a proof that you didn't know before

many people have a feeling that uh well

they're sort of exploring a continent in

the same way in which Columbus explored

uh uh various parts of the surface of

the earth

on the other hand many mathematicians

claim that no they are not discovering

they are really inventing. They're

inventing the things that other people

sometimes say they discover.

Or to take one other illustration taken

from the physical sciences, uh Kepler is

often said to have been the discoverer

of the law that the planets move on

ellipses

around the sun.

But one could ask about Kepler 2, did he

discover this law

or did he invent it? I mean after all

the planets don't move actually on

elliptic orbits you know precisely

and uh the supposition that well

there were the uh planets moving around

and all that you had to do was somehow

get at to a point which is sufficiently

far away and there you would see the

planets moving on elliptic orbits. This

is a very naive view. Even if you were

in that position you wouldn't see this

happen.

uh in some sense uh Kepler introduced

something into the material a way of

looking at this and it was he himself

who introduced this way of looking at

things. So in this sense he could be

said to have been an inventor of a new

perspective and not just a discoverer of

something or was already fully there.

Now these questions as to whether what a

scientist does is creation or discovery.

These are are difficult questions to

answer and they certainly raise very

fundamental issues in understanding the

nature of science. And I want to come

back to some of these matters a little

bit later on.

But in this connection I think it might

be helpful. I'm not sure how far it is,

but it occurred to me that it might be

helpful to distinguish between what

seemed to be at least on the face of it

two different types of creativity. And

let me begin by kind of a biological

analogy.

Every individual as we know uh possesses

uh certain genes

uh many of which he inherits

[clears throat] from his parents.

And the genes that a man has, those he

inherited from his parents are a

selection from the genes that his

parents had.

Uh but the genes that are selected

appear in new combinations. The genes

were already there so to speak. And what

he did what what happened to him was a

new combination of elements that were

already there

uh what were transmitted to to the

individual.

Uh now this is one sense in which uh

every biological individual is a unique

individual. namely that uh part of his

uh gene stock uh consists in a

recombination of some of the genes that

his parents have. But there's also

another feature about an individual that

he may possess genes

that is if a gene undergoes a mutation

some kind of a change because of various

sorts of influence upon it. For example,

if if uh he was exposed to a uh

radiation of various kind

gene mutates and then the gene that he

possesses then uh would be unlike

anything like his parents possessed.

So that the novelty that an individual

in some way represents

uh one can distinguish two sorts of

things. that which involves some kind of

a recombination

of what is already there and that which

involves the introduction of something

that is brand new that is a component

that wasn't already there.

Now taking this uh as an analogy I think

we might perhaps distinguish two kinds

of creativity in the realm of ideas.

one which would the kind of creativity

which consists in putting older and

familiar ideas into new combinations.

Take some very familiar illustrations uh

uh there are no unicorns that is there

are no animals that have the appearance

of a horse with a single horn and a

forehead. On the other hand, the notion

of a horse and the notion of a of a

horn, these were familiar notions. And

whoever first introduced the notion of a

unicorn and simply combined these two

ideas which are already in some way

available.

Or if you have read any of the Dr.

Doolittle stories or seen the movie, I

haven't seen the movie, but I I know

that some of the books there is a animal

which is known as push me pull you. It

has

roughly the appearance of a a

four-legged animal, but it has two

heads, one in each direction.

Or think of a winged horse

in antiquity or a flying man such as

Icarus. I mean, these are obviously

at one time they were new ideas, but

they represented a putting together of

ideas that were already available.

Now if you turn to uh uh more scientific

material

uh whoever first introduced the notion

of a corpuscular theory of light could I

suppose in a certain sense to have

really put together ideas that were

already available and formed a new

combination of them. I mean the idea of

there being particles which move with

with various speeds that these particles

would collide with other particles that

they move in straight lines that they

are reflected when they hit some kind of

a war

that they are defracted. Uh these are

familiar phenomena. Uh

uh and then this theory then to be sure

represented something that is novel. But

I think one could say that in case of

some of the theories they do involve

this recombination of notions that uh

were already available. On the other

hand, there are uh uh kind of novelties

uh creative

uh activities which do seem to involve

the introduction something that

corresponds to this kind of a mutant

gene that is intro [clears throat] in

introducing a mutant idea which is not

just a rearrangement of older ones.

Although I admit it's rather difficult

to be sure which ideas are of this sort.

Uh

let me mention some that may be of

[clears throat] this kind and I'm sure

at one time they must have been uh novel

in this sense. You know the notion of

proof such as we find it in geometry

where you start out with a set of axioms

and once you accept the axioms and

everything unrolls from the axioms by

the application of logical rules.

This of course as far as we know was a

Greek invention.

Nobody had it before. The Babylonians

knew some mathematics. The Egyptians

knew some mathematics. But the idea of

of proof of a rigorous logical proof was

something that to the best of our

knowledge was the product of Greek

genius.

And

deductive proof is nothing like anything

else that you can think of. Of course we

sometimes say well a theorem is

contained [clears throat] in the axioms

but contained is a kind of a spatial

metaphor. Uh the sense in which a a

theorem is contained in the axum is not

like the sense in which this room

contains this uh this table.

Uh it's only by kind of a metaphor that

we talk this way. And so at one time it

seems to me that the notion of

deductive proof was a mutant idea,

something that was brand new, not just a

rearranging the familiar things.

Or take the notion of uh

action at a distance when Newton

introduced the not uh the idea of bodies

attracting each other universally to

square the distance with and that this

happens instantaneously.

uh that is one body acts upon another

body in such a way that the action takes

no time whatsoever.

This was apparently a a novel idea which

scandalized many of Newton's

contemporaries and as a matter of fact

was unhappy with it.

uh one of his friends and correspondents

wrote to him and asked him uh do you

think uh that gravitation is an inherent

body an inherent property of body

something that is intrinsic to it? Is it

something that is ultimate?

Uh Newton replied saying only a fool

only a beginner in philosophy

would suppose that gravitation is an

inherent property of matter. He hoped

eventually that some explanation would

be given for this.

But the idea of action in a distance is

something that appeared to be very novel

and to be a kind of a mutant idea.

Now thus uh uh thus much I think for the

question as to what we mean by

creativity and I've indicated that uh

creativity involves originality

uh but that this has to be qualified in

a number of ways and [clears throat]

creativity in some cases associated with

discovery

in other cases perhaps not and the

creativity could involve simply a

recombination of things that are

familiar here while in other cases

introducing something that is entirely

unlike anything that had happened

before.

Let me turn very now to something that I

will talk about very briefly namely the

mechanisms that are involved in creative

thought or the psychology of creativity.

Now this question as many of you I'm I'm

quite sure know has been very much

discussed by psychologists

and there have been various theories

have been suggested

as to how to account for this creative

process. But despite the fact that the

submit has been of interest for so many

years, I think it is not an exaggeration

to say that we know very little about

the process, very little about it that

is really firmly established.

Uh there are various uh theory that have

been advanced. Let me very briefly uh

mention three [clears throat]

kinds that uh have been employed. uh one

of them is sometimes called an

associationist explanation for

uh creativity. The general idea being

that uh human beings being exposed to

various sorts of things in experience

uh develop some ideas of one thing being

connected with something else because

these things really come together.

So uh like Potta's dog uh you uh hear a

bell and you and and you uh smell a

smell and then one of the you hear the

bell and that brings to mind the smell

of the food. Uh and so in this way these

connections are uh are formed because of

the experiences that individuals have.

And on this theory, the the creative

mind is one which has the largest store

of such uh associations or connections.

And that uh what happens in the case of

a creative mind is that he has such a

fund of connections that he can then

select much more readily than can a man

who has a fewer number of such uh uh

such connections.

Now this doesn't really explain an awful

lot. Uh in the first place when a person

does have these associations these might

[clears throat] become so habitual

that they instead of being an aid to

novelty and creativity might serve as a

block to new combinations of ideas.

And the associationist account does not

really explain how it is that these

blocks [snorts] which prevent the

development of new combinations really

arises.

Moreover, and this is perhaps the uh the

crucial point, even if we suppose now

that the creative mind selects from the

association that it has already formed,

how do we explain the selection itself?

Which is really the the crucial

question. How are these selections made?

And uh we don't really have a clear

answer on this. A second type of

explanation is a kind of a gestalt

explanation in terms of gestalt

psychology

that uh uh the creative mind uh

transforms the ideas. If it has a

problem to solve, for example, it

instead of sort of adding a little bit

of idea here and a little bit of idea

there, it has a kind of an initial

insight into the total structure.

Uh and then this initial insight somehow

guides him in filling in the details. So

that the stress here is upon having some

sort of an insight into the structure.

But then calling it an insight is simply

to baptize it but doesn't really tell us

as to how these insights are obtained or

what the psychological mechanisms are by

means of which it is uh achieved.

Moreover, while this account might be

fairly plausible in some cases, namely

if I want to go from A to B, that is

starting from a a given situation, I

want to get to a a certain objective,

reach a certain objective,

uh then perhaps I ought to have some

sort of a a general overall picture of

the situation and try to fill in the

details. But this uh account doesn't

tell us how these objectives themselves

are conceived or entertained. And these

sometimes really are crucial elements in

the work of science.

Then the third approach that I want very

briefly to mention

is a so-called psycho dynamic approach

which is associated with the name of

Freud and

uh uh sort of dynamic psychology in

general where the general point is that

the creativity that people engage in are

involved in that this is located in in

in the unconscious mind.

uh it doesn't appear on a conscious

level and on the conscious level we are

so

uh bound by our habits and the routines

that we cannot free ourselves from these

firm bonds that are uh have been

developed but the the in the unconscious

the ideas can mingle without constraint

and uh this is how the originality

appears. Now again this is kind of a

dramatic uh uh formulation of what

happens but really doesn't tell us much

either because to say that these things

happen in the unconscious is to baptize

our ignorance and not to tell us how

these things operate. Let me mention uh

the kind of explanation that some

mathematicians give physicists too but

uh creativity in mathematics has been uh

studied by some mathematicians

themselves. There was a very

distinguished French mathematician. He's

no longer alive. Jacqu Adamar

was in this country during the Nazi

occupation of of of uh France. And he

published a book while he was in this

country called the psychology of

invention in the mathematical field.

And he asked a number of mathematicians,

you know, h [laughter] how how they got

their

big ideas, how how they got their uh

their their solutions, how they got

their important problems. And in many

cases he found the following that people

in some way

uh were interested in a problem. They

worked hard at it and got nowhere and

then they went to bed

and

in in some fortunate cases they woke up

uh with a solution

and then uh Adomar himself says well you

see of course you have to introduce the

unconscious to explain this. That's all

very nice but then uh what do we really

know?

Uh

or take a a different kind of a an

illustration uh a great uh French

physicist and mathematician Henri Ponare

in a very famous essay which he

describes his first contribution to

mathematics he said well he had a

problem the details of which we do not

have to go into and he worked at it for

several weeks and he got nowhere. This

was his doctor dissertation.

[clears throat]

Then uh he went for a holiday

and then on his way home from the

holiday he stepped on a bus to take him

from where he was back to his home. And

as he put his foot on the step of the

bus, the solution flashed upon him.

Well, this is an interesting uh tidbit

as to how to the circumstances under

which this idea happened to to Pankare.

Do we really know what uh what went on?

I I don't think we do. Well, let take as

my uh other illustration of this sort of

a thing and then I'll I I'll I'll turn

to another matter. There was a very

distinguished physiologist. Uh he was a

German by birth. He was a Nobel Prize

winner in physiology.

He received his Nobel Prize for having

uh determined uh uh what is the process

by means of which uh

a stimulus passes along a nerve. He once

told I I heard him once tell this story

but he was also published uh his account

much pre-erformed than he did when when

he told it. And I thought you might be

interested in if I took the liberty of

reading just a

one short passage in which he describes

uh how he was able to establish the fact

that the transmission of of nerve

impulse has a chemical origin not an

electronic origin but according to him a

chemical one

and this is what he says. This is a

little book called from the workshop of

discoveries.

The uh the uh man Dr. Otto Lurvy L O E W

I

he died about 2 three years ago. He was

in his 80s.

He said the possibility of a chemical

transmission of nervous impulses had

been considered before the time of my

experiment.

Accordingly, one may perhaps be inclined

to say that the idea of such a mechanism

was in the air at the time.

I personally, he continues, am of the

opinion that what may be in the air at

any time is not ideas, but rather

desires or general views of

possibilities or probabilities. An idea

apparently means much more, something

much more concrete. An idea, in my

opinion, must already include the way to

be followed in order to solve a problem.

If in an age of piety a painter feels

the desire to paint a Madonna, I don't

think one can call this an idea. He has

got an idea only in the moment when he

has formed a definite mental image of

the type of Madonna he wants to paint.

Consciously I never before had dealt

with a problem of the transmission of

the nervous impulse.

It therefore will always remain a

mystery to me that I was predestined and

unable to find the mode of solving this

problem. Consider for decades to be one

of the most urgent ones in physiology.

And like me, you will find it still more

mysterious when I now tell you the story

of how the discovery happened.

In the night of Easter Saturday 1921, I

awoke, turned on the light, and jotted

down a few notes on a tiny slip of

paper. He had some kind of a dream.

Then I fell asleep again.

It occurred to me at 6:00 in the morning

that during the night I had written down

something most important.

But I was unable to decipher the scroll.

And so he was in great agony.

And he says here that that Sunday was

the most desperate day in my whole

scientific life. And I remember hearing

him say that he left the house in the

morning without food and wandered for

something like 14 hours trying to think

of what it is that he he dreamt.

He came home dog tired, refused any

food. He went to bed

and now I continue from the reading.

During the next night, however, I awoke

again at 3:00

and I remembered what it was. This time

I did not take any risk. I got up

immediately went to the laboratory, made

the experiment on a frog's heart which

he had described early in this essay and

at 5:00 the chemical transmission of

nerve impulse was conclusively proved.

So the whole process [snorts] the

psychology of of of discovery something

that we know really very little about.

Uh some of you may know a book that was

published I think about a year and a

half two years ago by Arthur Kistler the

novelist essaist called the art of

discovery in which he offers a theory of

his own. But I think if you look at it

uh you find that uh it remains as much a

mystery after some 600 pages as it was

at the outset. Book is interesting. I

mean it's full of nice [clears throat]

stories and anecdotes.

But uh I don't believe that you will get

a really uh clear answer to the

question.

Then let me turn uh to my third uh

question uh uh third aspect of this

problem of creativity in science. Namely

at what points in science does

creativity arise?

Now there are very many points and I

just want to restrict myself to uh uh

three in number and point of fact but uh

uh I ought to perhaps say just a few

words by way of introduction to this

uh what are the objectives or the aims

of science

and I think we want in this connection

to distinguish between the individual

motives of scientists

and the large overall objectives of the

scientific enterprise. The individual

motives of a scientist might differ. A

man might be motivated to make money and

so it goes into science because he

thinks this is going to be a way of

getting it. He might be motivated by

fame. Perhaps he thinks he'll get a

Nobel Prize. Uh these are motives

but the objectives of science are not to

be identified with the motives. I mean

different individuals have different

motives but by and large I think if you

think of science as a institution that

has been going on

for many many centuries

uh in the main I think we could say that

uh uh the objective of science is to

find explanations

or to find some understanding

of the way in which various parts of the

world work whether it is inanimate

nature or whether it is the animate part

of it and I stress the importance of

explanation and understanding

even though in many cases the objectives

of scientific inquiry are narrowly

practical

because even when the objectives are

sort of I mean when we're dealing with

applied science engineering for example

especially in our own Today

uh even the achievements of applied

science cannot be obtained unless there

is at least some understanding of how

different parts of nature operate.

[clears throat]

So I'm supposing now that the aim of

science is really to achieve some kind

of an understanding.

Now the second point I think that has to

be said about the the locus of

creativity in science is that

every scientific inquiry is uh

controlled by some sort of a problem.

That is one doesn't just investigate in

the blue but one investigates uh in

order to find answers to fairly definite

problems or questions.

And the question one question about the

kind of questions or problem that a

scientist discusses is what problems

does a scientist work on.

Now here the answer is very difficult to

give. In part it is determined by the

intellectual and social climate in which

a scientist happens to be born or in

which he operates.

So for example, I think it would be

absurd to suppose that if Newton had

been born and continued to live in uh

central Africa

in the 16th in the in the 17th century

that he would have been concerned with

astronomical or with optical problems.

I mean the intellectual climate and the

social requirements were not adequate

for that. So in part they're determined

by the society

uh and the kind of ideas that are

prevalent but in part they're also

determined by the personal inclination

of scientists and after all Newton was

interested in physics gravit in in

astronomical theory in uh optics he was

also interested in in chemistry but he

was never successful in getting anywhere

in chemistry.

uh he had no interest in linguistics

although he was interested in the Bible

and made study of of of Bible and so on.

So part of these things are matters of

personal inclination

but I think the the point I want to make

is that uh there is a great creative

element involved in finding problems.

One thinks well it's very easy to find

problems but it isn't and as a matter of

fact it's one of the difficulties that

graduate students have uh in finding

some kind of a problem on which they

could work and write a dissertation

and hopefully they come to their

instructor and ask for some suggestions.

In many cases the instructor is in

exactly the same boat

and he has no ideas himself.

But uh what I think is certainly true

that science as we have it organized

today places a a great deal of emphasis

upon the ability

to think of uh fertile or significant

problems. And so one important aspect of

the creative activity of a scientist is

to think of problems

uh that uh will not be only of sort of

personal interest but will have some

significance for the further development

of science and more will be kind of a

problem that are manageable uh within

the uh the means available at the time

that is uh you know a long time ago

people thought of flying to the moon and

so one might then somehow generate the

problem well we have the problem of

getting to the moon or we might have the

problem of getting to one of the very

[clears throat] distant stars.

Well today the problem of uh getting to

the moon is one that is at least viable.

But to say well now let's throw out the

problem of how do you get to the to one

of the stars. This is not a significant

problem for us at at the moment.

And similarly in different areas of of

uh of science uh to find problems that

in some way extend

uh present knowledge in a in a

significant way. That is it that will

deepen our knowledge or will uh enable

us to correct it or establish some sort

of a connection between what we already

know in one area and what we already

know in some other area and bring about

some kind of a fusion and synthesis.

These are the kind of problem that

people would like to uh to to find and

uh to be able to find them is to make a

creative contribution to the work of

science even if you do not find an

answer to them.

Now there is a widespread conception

which despite the amount of that had

been written on this uh still continues

to hold to capture the the belief of

many people that uh science is a kind of

a fact grubbing enterprise

that uh every investigation somehow

begins with amassing a tremendous amount

of facts

uh and then Somehow once you got the

facts you will look at them and then out

of this will spring the answer to

whatever problem that you had.

Uh now the difficulty with this is of

course is that well facts what are what

facts I mean there are such a large

number and we have in some way to select

what facts we are going to look for and

gather and how we're going to interpret

them. There have been again as many of

us know uh

uh attempts which have been going on for

many many centuries

to find uh formulate rules of discovery

uh to formulate rules such that if you

can learn those rules then anybody who

follows them will be able to make

significant discoveries in the sciences.

One name that is associated with this

conception is Francis Bacon, a very

influential

British philosopher, lawyer who had

certain definite ideas as to how science

could progress. And although this is

somewhat oversimplified and it's almost

a caricature of what Bacon said in

essence, he did hold something like

this. He gave an example. Suppose you

want to know what is the cause of heat.

This is his own example. Well, what you

do is first of all collect all cases

where heat is present.

And so there will be uh the heat

produced by uh an artificial flame, the

heat produced by uh sun, uh the heat

produced when some kind of chemical uh

reactions take place and so on and so

on. Then you gather together all cases

where heat is absent

and uh then he had a third table where

heat is present in various degrees. But

if you just consider the first two

tables, tables of presence of heat and

tables of absence of heat, then bacon

thought, well, all that you require now

is let's see what all those cases where

heat is present, what they have in

common. That is sort of sift sift out uh

all the differences and find what is

common to them and then turn to the

table where heat is absent

and then be sure that the thing that you

find common in all the cases where heat

is present is also absent when heat is

absent. Now

Bacon had great hopes for this method.

unfortunately didn't work and certainly

if it had worked then anybody could

become a great scientist and we know

this is alas not the case not all

workers in the science are really

creative figures in it and what's wrong

really with this whole conception well

and this brings me to my second point

about where creativity is involved that

uh you have a problem you've got to have

a problem to start an inquiry going but

it's not sufficient just to make gather

facts because you don't know what facts.

What you have to have is uh some kind of

a hunch, some kind of a guess or if you

want to use a more respectable word, you

have to have some kind of a hypothesis

as to what might be an answer to the

problem in which you are interested in.

And there is a tremendous creative

element in finding adequate hypotheses

for dealing with the problems at hand.

Now, one of the features of modern

science is that the hypotheses that turn

out to be extremely successful

are often very remote from the familiar

facts of common experience.

I mean if you think for example even of

relatively familiar hypotheses such as

the atomic theory and if you come down

to more more complicated theories like

relativity theory or theories about the

particulate nature of all matter I mean

electrons protons mezons and so on these

are not things that you encounter in

everyday experience. It really involves

a tremendous flight of imagination. uh

uh something that requires you somehow

to look away from what is familiar to

something which some way is fantastic,

fanciful, highly imaginative

and in this respect there is I think a

marked difference between ancient

aretilian science and modern science. Uh

it is sometimes said that to a scientist

must really stick uh you know observe

the facts. The trouble with much of a

healing science, it's it it restricted

itself much too much to the familiar

facts. That is take the well-known

illustration, you know, the freely

falling body. According to Aristotle,

uh a heavier body will hit the ground

faster than a a lighter body. And uh I

think if you make the the the proper

observation, you will find that by and

large in many cases Aristotle was right.

That is for you know take the obvious

case of a cannonball and a piece of

paper. You drop them from the same

altitude and it's the cannonball that

will hit the ground before the the piece

of paper.

What Gallo required was the supposition.

He invented this idea that well you have

to think of these bodies as falling

through

a vacuum.

Something which is a vacuum. Nothing

that offers any resistance.

And of course the whole idea of vacuum

was something that was entirely foreign

to Aristotle.

And so he in in ordinary experience we

don't encounter vacuum. He had to

manufacture them. And Gallagher really

had to stretch his imagination in such a

way that in terms of this idea he was

able to formulate a law of motion which

was very different from that of uh that

of Aristotle.

So there's this tremendous creative

element involved in finding hypotheses.

Now how do you find how how are these

hypotheses found? Again we don't really

know too much about this. One can say a

few things in sort of a general way. And

one of the things perhaps I I I I have

time to to to mention is that analogies

and resemblances often play an important

role in suggesting hypotheses.

Let me mention two examples. Both of

them are very familiar. I mean they're

oft tales. Remember the story about

Arimedes

who uh lived in Syracuse and there was a

king of Syracuse received a crown or he

he ordered a crown to be manufactured

and it was to be made of pure gold but

he suspected that perhaps some uh less

precious metal was involved. He thought

that maybe maybe some silver was mixed

in it.

and he asked Archimedes to find out

whether this crown uh was made of pure

gold or whether it contained some kind

of an alloy. Now, of course, uh

Archimedes could have sort of melted

down the crown, found out its volume and

then uh he knows you know what the

density of gold is and then if you could

somehow make one solid chunk out of this

gold crown,

u he'd be able to give the answer. But

of course his problem was to determine

without destroying the crown whether uh

it was made of pure gold or not. And the

story goes that he once took went to a

bath and he noticed that as he sat down

in a bath bathtub or whatever it was

that he used

uh that the level of the water rose by

how much? Well, by the amount of volume

that he himself was immersed in. So that

the more of him was dunked into this

bath, the higher the level of the water

in a bathtub rose.

And then the story is in great elation.

He jumped out of the bath and ran

through the streets crying, "Eureka!

I've got it." And what was the point?

Well, he said, "Well, just as my own

body put into a a volume of water

raises the level of the water by the

amount of my own the volume of my own

body. So, I can find out what the volume

of the crown is without destroying the

shape of the crown. But by putting it

into some volume of water and see by how

much the level of the water arises, in

this case, I will know exactly how much

volume the gold occupies. If I divide

the uh the uh if I if I I know the

volume, if I know the the weight, I can

calculate its density and if it differs

from the density [clears throat] of pure

gold, then I know that this is not pure

gold. This is one example where we say

well there's kind of an analogy here

between the crown and the human body.

Now here this seems like an easy analogy

but surely you have to have the right

kind of a mind to recognize it. The

other illustration I want to mention is

a well-known story about uh Newton and

the fall of the apple. The story is

sometimes told in this way that Newton

was sitting under apple tree and uh

apple

fell and hit him on the head and this

somehow developed in him the idea that

there's a force of gravitation between

the earth and the apple. No, this is

this wasn't it really. I mean this is

this is only a small fraction of the

story assuming that there's any basis

for the story at all. The real point is

that uh the apple falls to the ground.

And it was known of course by other

people in Newton that apples fall if

they're left unsupported and other

objects fall if they're unsupported.

But what Newton said, well, if there is

a force of gravity between the Earth and

uh and the apple, this gravity ought to

extend

all the way out. And it ought also

affect the moon.

And so the analogy that Newton

uh thought of was the analogy between

the fall of the apple and the fall of

the moon as the moon moves around the

earth. That is a fall of the moon in

this sense that of course if the moon

went off on a straight line

eventually would disappear but it

doesn't moon doesn't do that. It

circulates around the earth and as it

circulates it moves away from a kind of

a straight line motion and the amount of

deviation from the straight line motion

is the amount of force that the moon

suffers

uh because of the force of gravity. And

what Newton then had to do a little

calculation and showed that since uh the

moon is uh six diameter uh six the

distance of the moon uh from the center

of the earth is about 60 times of the

distance of the apple from the center of

the earth then uh the moon ought to fall

toward the center of the earth by an

amount which is

13,600 hundreds the amount that the

apple falls and in making the

calculation he found that these things

checked and so he had some evidence for

a supposition that there was this force

of gravity so that there are these

analogies

uh which uh suggest

hypothesis

another very famous analogy of course is

the you is the behavior of water there

waves on water and it occurred to some

people to say well look I mean here we

have light phenomena

uh maybe we can explain why it is that

light behave the way it does by

supposing that there are the light is

made up of various kinds of waves. This

again was an analogy to what had been

observed elsewhere.

But uh

uh having these analogies though they

might involve some kind of flash of

insight the insight itself is not

sufficient. It's not self-certifying.

The insight must be tested.

Uh no modern scientist would take the

view that Aristotle held. Uh Aristotle

too said well you got to have this flash

of insight but then Aristotle thought

that well yes you start out with making

observations and then after a while you

somehow intuit some sort of a connection

between what you observe and this

intuition is something that is final and

definitive and in a way becomes sort of

self-evident. Nobody today would say

that these flashes of insight, these

hypotheses are self-evident but they

have to be tested. And this brings me to

to the third element, third point where

a creative element is involved in

science namely

uh the creative effort that is involved

in testing in testing hypothesis.

Let me give uh one uh or two examples

and I think I I'll I'll stop.

You remember Galileo was interested in

studying the way in which a body falls

and according to him the the body falls

in such a way that uh the distance that

a body falls depends upon not simply the

time of its fall but the time multiplied

by itself. So that for example if a body

falls

uh 1 second

and if the distance that it traverses in

1 second is uh let's say 1 ft then if a

body were to fall 2 seconds the distance

would be would be four times that that

it would be two times two not just twice

the original one. If the body falls 3

seconds, it would be 3 * 3 or 9 times

the original one. So that the distance

is proportional to, as the phrase goes,

a square of the times. Now fine, how do

you test this?

If you had a nice clock, if you could me

measure small intervals of time, you

might be able to do this.

When Gallry was doing this thing, there

were no clocks.

They came much later partly as a result

of his own discoveries. He had a water

clock that is the amount of water that

dripped out of a of a pan which there

was a little hole and these are very

inaccurate.

So how was going to test this assumption

that the distance depends upon the

square of the times? Well, he had the

brilliant idea of as phrase now goes of

diluting the force that the earth uh

exert on earth by not not by having a

body fall directly but he devised the

idea of having an incin plane so the

ball would roll down the the plane with

a speed that was much less than the

speed with which a body would to fall if

it were not supported by the plane. Now

you say well once Gallio showed you how

to do this it's very easy but the idea

of trying to think of some way of

testing this of of trying to think of an

experiment which will enable you to test

the assumption involves a great uh uh

creative uh creative step

or to take uh one other illustration

without mentioning the details.

when uh the question arose as to whether

uh the earth

uh is moving through an ether. This was

a question that was came up in the 19th

century.

Uh some people believed it did and some

people believed it didn't. And the

question is how do you test the

assumption that the earth does really

move with respect to an ether that

supposedly fills all space? Well, it

wasn't an easy thing to do. and required

a great creative acting, creative

imagination to devise an experiment. And

this was done by Michaelelsson and

Molly, two American physicists who

indicated in what way you could set up

an experiment in order to see whether

there is any noticeable effect in the

way in which light moves when the earth

supposedly moves through the ether.

one other example uh to indicate really

this kind of uh uh creative imagination

that is involved. I mean let me uh uh

sort of end with with that. Uh some

people sometimes think that uh if you

really have to just do sort of formal

deduction

uh this is a purely routine matter of uh

drawing consequence in accordance to

rules.

But I think those of us who are

experienced in trying to construct

proofs know that this isn't by any means

easy that you require considerable

imagination.

Uh consider the following very simple

sort of mathematical puzzle. Let's

suppose that we have dominoes. Each

domino is 1x 2 in long.

And now let's construct a board

uh which is uh 8 in long and 8 in wide

and we rule it. So it's made up of

squares.

So we have 64 squares on this board. Now

if I take a domino, a domino will fill

exactly two squares, right? That would

be eight squares in the first row, eight

squares in the second row, and there'll

be eight rows in all. And if I ask the

question, could I

uh take eight? [clears throat] Could I

could I take dominoes which will uh fill

all the squares without overlapping?

And the answer is very easy. Sure. I

mean, if each domino is 2 in long,

uh I can get uh four dominoes into the

first row, four dominoes into the second

row, and so on down the line. So that

there will be four * 8 or 32 dominoes

will completely fill this board. Now

this is very easy. Anybody can do this.

Now now here's the problem. Suppose I

want to take one of these squares at the

uh uh northwest corner of the board and

take it out, sort it out. That is the

the the upper uh right uh accord where

I'm standing upper leftand corner. I I

cut out that little square. And I do the

same thing with the bottom right hand

corner and cut out square so that I no

longer have uh

60 uh four, but I've taken out two and

uh uh I just have 62 left. Question,

could I fill this board with these

dominoes?

Well, you say, well, why shouldn't one?

I mean there each domino is only 2 in

long. Uh so the amount of space seems to

be divisible by two and so on the face

of it looks as if I could do this. You

try and you try and you don't succeed.

Could you prove that it couldn't be

done?

And now let me just indicate what kind

of a creative step that has to be has to

be taken in order to show that it could

not be done. Imagine that the board

before I take out these initial these

these two squares are painted black and

white like a chess board or a

checkerboard.

Then there will be as many

uh uh black squares as there are white

squares, right?

And each domino if it's going to fill uh

uh this will occupy half of it is going

to cover a black and half it is going to

cover a a white square. Right

now, if I were to take out the upper

leftand corner and lower right hand

corner, it turns out that if I paint

these alternately, then the upper

leftand corner, if that's black, then

the lower right hand corner must also be

black.

And so

although originally I had 32 white and

32 black squares, when I've taken out

these two squares, I've

no longer have 32 black squares, but I

have just 30 black squares and 32 white

ones. But in order to fill this entire

thing, a domino has to cover both a

black and a white square. And so we see

now that you couldn't do this. But

somebody had to think of this idea. I

didn't think of this myself. I' I've

I've heard I've heard this once so that

I don't credit myself with this creative

imagination. But somebody had to think

of this surprising idea of well just

this was not given as part of the

problem. It was given uh in such a way

that say well all that you have are

these 64 squares. Somebody thought they

are painting them alternately black and

white and when you saw that this was the

way to do it then somehow the answer

came out. that this again involves a

great creative step not entirely unlike

the great creative steps that are

involved in putting to test the very

complicated theories. Now let me then

finally just say one more thing and and

and I'll stop.

>> Yeah, just one word. I've been I've been

saying I've been talking about

creativity in science and I've left out

of consideration entirely the creativity

of science and this of course is a

terribly important point because as we

know science today and it has been for a

long time and and certainly is going to

continue to be this one of the transform

transforming forces of modern

civilization.

uh these transforming

uh what it transforms is not only our

physical and our social environment but

also has altered our conceptions of the

kind of world that we live in and

although science is a human enterprise

uh it's something that we have

introduced something that we have

developed in the process of developing

it uh we not only change science itself

but in in in it we change ourselves and

let me conclude then with this Uh I'm

not sure that I can repeat the words

exactly Churchill's remark when they

propo when they proposed to rebuild the

House of Parliament in England when he

said we

uh construct our buildings

and our buildings in turn reconstruct

us.

We make science but in the process of

making and developing it we ourselves

become transformed. Thank you very much.

>> [applause]

>> Goodbye.