When the brain is working its minute, indeed sub-microscopic, component parts act on each other in specific, co-ordinated ways; the sequence of their movements is timed
with precision; they behave like the component parts of a
finely constructed, very complex man-made machine. A
result of this co-ordinated performance is that specific, co-ordinated messages pass to the muscles of the body and lead
to specific, co-ordinated movements. If one considers any
example of order in human activities and attempts to explore
the path along which it came, that path will always lead to a
human brain. If the behaviour of the component parts of
that delicate organ were random instead of being ordered,
there would be no order in our daily lives, none of those
orderly things on which civilization depends, no works of
art, no books or clothes, no houses. To explain the ordered
performance of the brain would be to explain a great deal.
One very significant statement can be made about all the
stimuli that reach the brain. They are not co-ordinated. They
may arrive from anywhere. They are random events, unselected, most of them the result of pure chance. And yet the
response of the brain to these stimuli is not random. Selection,
discrimination, guidance, control, do occur. Where, when,
how?
Monists and dualists offer quite different solutions.
Monists find theirs wholly in the specific structure of the
brain and in the laws of physics. (I use the expression ‘laws
of physics' here to cover those of chemistry as well as all the
others that belong to the physical sciences.) According to
monism the nature of matter, which is defined by the laws of
physics, constrains the component parts to behave as they
do when they find themselves in the particular kind of configuration that constitutes a human brain.
Dualists deny that the structure of the brain and the
nature of its component particles suffice to explain the behaviour of the particles. They deny that the stimuli provided
by the environment are the only things that act on the brain.
They claim that in addition a diathete, mind, acts. Thus
they regard the brain as being simultaneously subjected to
two kinds of action, one from matter and the other from a
diathete and they attribute the ordered behaviour of the
component parts of the brain to the selecting, discriminating,
guiding, co-ordinating, control of the diathete. In short,
monists say that the source of order is matter, dualists that it
is a diathete.
For some inexplicable reason monists always insist that
a living organ such as the human brain is in all essentials
analogous to a man-made machine. They often construct
models in the hope thereby of proving their hypothesis. And
dualists rather vehemently reject the analogy. But a moment's
thought shows that neither can have thought matters out
very clearly.
Monists say that the impact of random events causes the
brain to behave in an ordered manner, because it is in
the nature of its component parts to do so. But it is not the
impact of random events that causes the ordered behaviour of
a man-made machine. Its component parts do not behave
selectively because it is in their nature to do so. The reason is
that a machine operator is in control. The random events do
occur in the environment. What a motor-car does depends
certainly on the twists and turns of the road, on the incidence
of patches of slipperiness, on the random succession of
vehicles that must be avoided. But the car would not behave
as it does if it were driverless.
Law and Order
Let us leave the example of the brain and consider in more
general terms what is necessary that order may result. In
human affairs one of the necessary things is law. This is why
the words law and order are often coupled. The rule of the
road provides an illustration. It has legal sanction and without it the behaviour of traffic in our streets would be chaotic.
Here the law requires a selection between two simple alternatives, left and right. Some laws are more complicated.
The Factory Acts, for instance, are concerned with many
possible ways of building and running a factory; they require
some ways and prohibit others. Some laws again are not codified. They constitute what is called the unwritten law. This
governs our code of conduct in many ways and civilization
owes much to it. Occasionally some of it may eventually be
written down and find its place in a statute book. But whether this happens or not, all those laws that make for order in :
human affairs can conveniently be described as of the statute
book kind.
Are the laws of physics of the same kind? Is there, to put
it concisely, such a thing as a Cosmic Statute Book? Of
course I am not asking whether there is literally such a
volume; I am asking whether the laws of physics are, like
those in statute books, of the kind that make for order. If
they are, one might say that textbooks on physics, in which
these laws are mentioned, constitute a transcription into
human language of the Great Statute Book by means of
which the whole material universe is governed. I believe that
if people were asked about it the inquiry would show opinions
to be sharply, even bitterly, divided on this question. But it
has not been debated as thoroughly as its great importance
deserves. Its bearing on the dispute between monists and
dualists is but one, and I hardly think the most important, of
its many implications. But let me dwell a little on this one.
If there is a Cosmic Statute Book, it provides much
stronger support for monism than the unfortunate machine
analogy. That all living substance, be it in the brain or elsewhere, unfailingly conforms to the laws of physics must be
agreed by both sides to the dispute. For it is by conformity
to these laws that we recognize substance as material. Matter
does not cease to be matter when it acquires the epithet
living. What characterizes living matter is, according to
dualism, not what it is but what is being done to it.
Dualists do not say that a particle changes its nature or any
of its properties on entering a living body but that it then
comes under a control from which it was previously free.
Dualists, at least if they are logical) do not say that a
particle in living substance is not subject to the laws of
physics; they say that it is subject to these laws and, in
addition, to the laws imposed by the diathete life. Monists
say that it is subject to the laws of physics and to no others.
If a monist can prove that the laws of physics make for
order he has a very strong case. These laws are, so far as can
be ascertained, absolutely universal; they apply everywhere
and at all times. If they make for order they must do so
everywhere and at all times. And if so there can be no such
thing as a random event, however much some events may
seem to be random. There are many, indeed, who think so.
I have often been told, particularly by pious people, that
there is no such thing as chance, that there is order everywhere, that even the most insignificant event has been
ordered. Anyone who believes this must consider it wrong
to pinpoint the problem of order at the junction between
stimulus and response, or at any other place. For he cannot
think that there is any problem. If he believes that everything is subject to law and order, he believes this of the
stimuli; in his view they are not random, however much they
may appear to be so. The component parts of the brain behave in a co-ordinated manner, he will say, because the laws
of physics ensure that the stimuli received by the brain are
co-ordinated; and the fact that these stimuli seem to be unselected, unguided, uncontrolled is, in his opinion, a mere
delusion arising from our incomplete knowledge of all the
circumstances.
A dualist who believes in a Cosmic Statute Book has, on
the other hand, a very weak case. He represents the component parts of the brain as conforming to two kinds of law
and he believes that each makes for a different kind of order.
He has to explain why this does not lead to some odd conflict.
He will not find it easy to justify his contention that two sets
of law have to be obeyed by the same particle at the same
time. A monist would be fully justified in pointing out that
it is irrational to invoke two sets of law when one will serve.
If I were satisfied that the laws of physics do make for order
I should support monism.
It is quite consistent with the paradoxical logic that pervades our theme that supporters of dualism tend, on the
whole, to believe in a Cosmic Statute Book and supporters
of monism to reject that notion. A person whose temperament makes him like to think that there are 'higher and
better' things than mere impersonal matter also likes to think
that all things, however remote and impersonal, are beautifully ordered and law abiding. And a person who feels
resentful at the attacks from religion from which science has
often suffered likes to cling to two hypotheses that, I am
showing, cannot be reconciled: that matter is the only
reality and that chance controls all events. And so dualists
often clog their cosmology with too much order while monists
admit too little. Neither side can reach a logically consistent
view of reality without the sacrifice of a cherished conviction.
The monist must sacrifice the conviction that every aspect of
reality, including order, can be brought within the field of
study of the physicist. And the dualist must sacrifice the
conviction that law and order are omnipresent throughout
the universe. Here we meet one of the occasions when the
criterion of attractiveness comes into conflict with the
criterion of truth. And when this happens there is always an
unwillingness to face a question the answer to which might
destroy one of the cherished convictions. The question
whether there is a Cosmic Statute Book is of this disturbing
kind. It will, I fear, prove equally unwelcome to many
dualists and to many monists.
One of the least worthy reasons for clinging to belief in a
Cosmic Statute Book is that it provides opportunities for
some attractive rhetoric. It sounds well in a peroration when
a speaker proclaims such sentences as: 'Nature's sublime
plan is revealed everywhere, no less in the tiniest grain of
sand than in the most distant star.' 'When I contemplate the
wonders of science and the beautiful consistency of those
supreme and eternal laws that are implicitly obeyed by our
vast majestic universe how can I doubt that there is meaning
in everything?' 'The laws of physics and chemistry, no less
than those of wise governments must prove to everyone
capable of understanding higher things how well everything
was meticulously ordained at the very beginning of time.'
'The more profoundly one immerses oneself in the great
scientific verities the more must one admire the simplicity of
Nature's immutable laws.'
Believers in dualism often find comfort in phrases of the
kind that I have caricatured only very slightly in the foregoing quotations. There is no harm in that if the phrases
represent true facts. But if they are no more than a substitute
for disciplined thinking they can do much harm. Theologians
and scientists would agree about that. And I doubt whether
belief in a Cosmic Statute Book can really be justified even
on religious grounds. Its implications are surely too deter-
ministic to be sound theology. Whether the Cosmic Statute
Book is supposed to have been the work of an impersonal
Nature or of a personal God it is supposed to govern every
detail of the material universe. It must be hard for anyone
who believes that the behaviour of every particle of matter in
all its details has to conform to immutable laws laid down at
the Creation also to believe that such particles can conform
to the present will of a living God. To accept the Cosmic
Statute Book seems to deny God's guiding hand. But the
theological implications are a little confusing. For there is
another side. To deny that the laws of physics make for order
is to deny that they are God's work. And to do this may seem
to detract from the omnipotence and ever-presence that is
attributed to the Diety. However, I am not qualified to judge
the theological implications of the concept Cosmic Statute
Book. I have little doubt that theologians have considered
them very thoroughly, be it with the use of a different set
of words. All that I can ask is that you consider the question
without allowing any disturbing thoughts about its implications to cloud your judgement. If I, myself, have, after long
cogitation, reached the conclusion that there is no Cosmic
Statute Book, it is not because I set myself the task of knocking away the strongest prop of monism. Nor is it that I
wanted either to support or to defy any theological doctrine.
It is that I think it of the utmost importance that some of
us should try to achieve a clear understanding of physical
laws, and not be restrained by fear of the consequences to
our tranquillity. And to ask about a Cosmic Statute Book is
my way of prompting thought about a theme that has been
too much neglected. I have noticed that even scientists are by
no means consistent in the way they talk about the laws of
physics. The remarks of a person will often imply at one
moment that he accepts the notion of a Cosmic Statute Book
and at another moment that he rejects it. I am hoping that
use of this term will focus attention on an aspect of the
philosophy of science that needs thorough consideration.
The Laws of Physics
To ask whether there is such a thing as a Cosmic Statute
Book is, of course, to tackle along new lines a subject that
has its accepted place in the methodology of science. Physicists have succeeded with much labour in formulating a number of statements about the material universe; some of these
statements are called laws. They are the foundation on which
the magnificent edifice of Western science has been built;
they have led to a profound understanding of the nature of
matter; they make accurate predictions possible. It is important that we should gain insight into their meaning; we
ought to know what we are doing when we formulate the laws
of physics. Many of man's greatest achievements in this field
have been reached intuitively. But it is as well from time to
time to test intuition by the discipline of reason. Hence the
value of considering carefully what is happening when a law
of physics is being formulated.
The methodology of science can be approached along
many different paths. It is only after much deliberation that
I have decided in these lectures to follow one that tradition
has not signposted. My reason is that traditional questions
about the laws of physics tend to conceal conflicts of opinion
in this subject and I want to show as clearly as possible how
sharp a conflict there is. It is not only between rival schools of
thought; it is, as I have just hinted, within the mind of every
one of us. Whether we decide that there is a Cosmic Statute
Book or that there is not, we have to sacrifice some theory
that we find attractive. It is better to face that fact than to
evade it.
From the way in which the laws of physics are often
spoken of I must conclude that belief in a Cosmic Statute
Book is rather more orthodox than disbelief. I think that the
following fairly represents the views of many about the laws
of physics: 'These laws resemble those in the statute books
at Westminster in their effect, which is to make for order.
This is proved by the certainty with which physicists make
predictions from their laws. When one knows the laws of a
country one can predict some of the things that the inhabitants will do, such as on which side of the road they will most
often drive. Similarly it is because physicists know the laws
of the material universe that they can predict how a particle
of matter will behave in given circumstances. But the laws of
physics differ from those in man-made statute books in five
ways. They are more ancient. They are more detailed. They
are completely unalterable. They are completely binding.
They are implicitly obeyed.'
Only on the reason why a particle of matter implicitly
obeys the laws of physics may there be difference of opinion
between a theologian and his atheistic opponent. The theologian might say it was because matter does not possess Free
Will and cannot therefore sin against the laws that the
Creator has ordained for the material universe, while man,
on the other hand, does possess Free Will and so does some-times sin against God's moral law. The atheist might object
that the laws of physics were not ordained by God but by
Nature and that a particle of matter obeys them implicitly
because it is made in Nature's image and cannot do otherwise. But that matter would behave differently if the laws of
physics were different would be agreed by many theologians
and many atheists.
Those who think thus picture the physicist as analogous
to an explorer who seeks to discover the laws of a foreign
country. Should he want to know what the rule of the road
was he could place himself at a street corner and watch the
traffic. After he had observed a sufficiently large number of
vehicles he would know whether the law required them to
keep to the right or the left. Similarly, it is thought, Mr. Ohm
observed electric currents in circuits. When he had measured
a sufficiently large number he arrived at the conclusion that
the Cosmic Statute Book contains the famous law that goes
by his name. This is the view that must, I am afraid, be
challenged. I think that it constitutes a danger to the
methodology of science.
With the sole purpose of making my meaning as uncompromisingly clear as I can let me depart even further than I
have done already from the traditional approach. Let us
imagine that an explorer has visited a newly discovered, very
civilized country and brings back an account of its laws. He
reports that they are very ancient and established, never
altered, completely binding and so detailed that his list of
them fills three fat volumes. He reports on them to a learned
society.
'Do the inhabitants always obey these laws?', he is asked.
'Implicitly', is the reply.
'Is there a rule of the road?'
'Certainly.'
'Does traffic have to keep to the right or to the left?'
'The law says that it must either keep to the one side or to the
other.'
'Are there any building regulations?'
'There are many pages of them.'
'What does the clause say in which it is laid down in what proportions cement, sand and aggregate shall be mixed in making concrete?'
'The law says that these shall be mixed in any proportions.'
|
And so it goes on. The audience learns that the laws
require a man to have any number of wives, to pay any proportion of his income in tax, for any number of cubic feet
of space in the factories of the country to be allowed per
worker. Those who hear these travellers' tales are not surprised that the laws of this strange country are obeyed implicitly.
Clauses in human statute books do not contain the word
'any'. To constitute laws the wording must imply 'thus and
not otherwise'. And the prevalent belief that I am now
challenging is the one that the laws of physics do in effect
say 'thus and not otherwise'. Indeed those who believe that
the laws of physics make for order cannot think differently.
So let us review some of those phenomena held to illustrate
the eternal, universal order.
Days and nights succeed each other with absolute regularity and a day and night encompass between them twenty-four hours. Does the Cosmic Statute Book contain a clause
to say that it shall be so? A schoolboy can tell us that it does
not. A clause is not needed to say that days and nights shall
succeed each other. A more general clause to say that planets
shall rotate on their axes would suffice. And a clause to say
that the period of rotation shall be twenty-four hours can
certainly not be there; for the period of rotation of planets is
different for each. A clause about the time that a planet shall
take to rotate about its axis would have to be worded 'any
time'.
What can be said about the length of days and nights can
be said with equal force about the length of the planetary
year, about the size of stars, the height of mountains, the
width of valleys, the speed of rivers, the constitution of the
atmosphere surrounding a planet, the proportions in which
the elements are mixed in rocks, the outline of continents, the
arrangement of stars in the heavens. So long as we look only
on the untouched world of lifeless things we find examples of
every conceivable contour, every degree of simplicity and
complexity, every mixture of ingredients, every possible size
and shape of things. The rugged outline of a mountain range,
the starry confusion of the heavens do provide sublime
beauty. But it is not the beauty of order; it is the beauty of
randomness. How then, it may be asked, can one account for
such examples of regularity and pattern as may undoubtedly
be observed in the untouched world of lifeless things?
There is, for instance, the roundness of stars. A star with
knobs or corners is unknown. Is there, perhaps, a clause to
say that stars shall be nearly spherical and may not be of any
other shape? A student of elementary mechanics can tell us
that no such clause is necessary. The nearly spherical shape
of stars is ensured by gravitation and centrifugal force. We
must look for another example.
There is the beautiful regularity of crystals. Is there a
clause to require that molecules shall be drilled into serried
ranks when a substance solidifies from its gaseous state or
when it precipitates out of a concentrated solution? A
crystallographer could tell us that no such clause is necessary.
During crystal formation the molecules tumble and dart
about erratically. Occasionally one of them comes near
enough to the growing crystal to be held firmly in position'
and to become a part of the crystal structure. Then it jostles
and tilts with its neighbours until it has fallen in the only
position in which it can pack firmly and not easily become
dislodged. The molecules reach their regular configuration in
the process of rushing aimlessly hither and thither. One need
not invoke a restraining law to explain their behaviour. If
the Cosmic Statute Book says that molecules may form 'any'
configuration, many different configurations will be observed.
Those of crystals will occur occasionally, about rarely
enough to explain the high price of precious stones.
Shall we then turn to the law that requires planets to move
in elliptical paths, to the law of the pendulum, to the law of
inertia, to the laws of the electro-magnetic field? At one time
it would have been thought that each of these has its separate
clause in the metaphorical volume. But Newton applied the
blue pencil to many of them. He showed that the elliptical
paths of the planets, the falling of apples, the law of the
pendulum and much else would be ensured automatically
if there were only clauses calling for the laws of gravitation
and motion. He inherited from his predecessors a very detailed Cosmic Statute Book and bequeathed to posterity a
very meagre volume. That is what people mean when they
say that Newton achieved a great unification of the laws of
physics. He showed how a very large number of special laws
can be deduced from a small number of general ones. The
late Professor Thornton, who gave the second series of these
lectures, meant the same when he spoke in World Power of
'great sweeping laws that gather together masses of apparently unrelated facts like fish into a net'.
Since Newton's day the blue pencil has been wielded again
and again; ever bigger fish have been gathered into the net.
The popular notion that physicists are always adding new
clauses to the Cosmic Statute Book has been belied by
history. On the contrary, they more frequently find that the
fruits of their work enable them to strike out some of
those that they have found there. The General Principle of
Relativity provides a recent example. It ensures the law
of gravitation together with many others. And an even wider
generalization has been achieved with the formulation of
what is called the Principle of Least Action. The late Sir
Arthur Eddington pointed out in his Space, Time and Gravitation that the law of gravitation, the laws of mechanics, as
well as the Jaws of the electromagnetic field are all summed
up in this one principle. Perhaps it spreads its net so wide
that no fish can escape. If so, the Cosmic Statute Book need
contain only this single clause. But it is doubtful if even this
is needed.
Eddington also pointed out that another apt name for the
Principle of Least Action would be the Principle of Greatest
Probability. He inferred from this that 'the law of nature is
that the actual state of the world is that which is statistically
most probable'. This is the state in which the traffic in our
streets would be if there were no rule of the road; it is the
state in which all things find themselves when everything is
allowed and nothing prohibited. Eddington's suggestion
amounts to saying that the Cosmic Statute Book consists
mainly of blank pages.
If this is so a 'thus and not otherwise' type of legislation
in the physical world can apply at most to only a very few so-called cosmic constants. There is, for instance, the greatest
velocity at which energy can be transmitted; it is called the
velocity of light in a vacuum. There is the smallest portion of
ponderable matter, called an electron. There is the smallest
amount by which anything can change, called the quantum
of action, or Plank's constant. So far physicists have not
succeeded in showing that these three constants are the
inevitable consequence of some more general principle in
the sense in which the succession of days and nights is the
inevitable consequence of the earth's rotation. But most of
them expect eventually to be able to do so. There is good
reason for examining the possibility that the few remaining
facts about the material universe that have so far proved
irreducible are not imposed on matter but are the consequence of the way we think about things.
Be that as it may it would take a bold man to build a
doctrine of universal law and order on the slender foundation
of a few cosmic constants. Those who like to believe that
eternal laws govern every detail of the material universe will
gain but little comfort from the thought that these few
constants may, after all, prove to be irreducible. And monists,
in particular, who hope to show that the ordered behaviour
of the component parts of the human brain is the inevitable
consequence of the ordered behaviour of all matter will need
more of a 'thus and not otherwise' than a few such quantities
if their hypothesis is to convince anyone.
It may, however, be objected that I have chosen my
examples unfairly and that one could find in textbooks on
physics another category of law that does require certain
things and prohibits others. In the short time at my disposal
I cannot review the whole of physics and examine every one
of its laws in turn. But I can at least mention some that do
seem to belong to a different category and might be quoted
in support of belief in a Cosmic Statute Book. As examples
I shall mention Ohm's law and the inverse square law of
forces. The true nature of these can be most conveniently
presented to you if I refer again to the imaginary traveller
who returns from a foreign country. He is asked whether
that country has any laws that are of the 'thus and not otherwise' kind.
'Oh yes', he answers. 'One of them helps to regulate traffic in the
streets.'
'How is it worded?'
'It says that stationary traffic shall not move. There is a rider to
define stationary traffic as traffic that does not move.'
|
The audience can well understand that this law, too, is
obeyed implicitly. And what I want to explain to you is that
Ohm's law and the inverse square law are of this kind. They
say no more than what is true by definition. Let us consider
each in turn.
Ohm's law does not say that the current in a circuit shall
have a stated value, for the value depends on the circuit. The
law does not say that the ratio of current to voltage in a
circuit shall have a constant value. This only happens when
the resistance remains constant and other circumstances do
not affect the current. What the law does say is that the ratio
of current to voltage shall equal the resistance when the
resistance is defined as the ratio of current to voltage.
It might be objected that the law does say something more.
For it requires that the ratio of current to voltage shall be
a linear function. Expressed in the form E = IR the law
prevents, for instance, the current from being proportional
to the square of the resistance or to its fifth power or to any
other function of the resistance. If so, Ohm's law, by requiring linear proportionality, does say 'thus and not otherwise'.
True enough. But if the law occurs in this form in the Cosmic
Statute Book it is nearly always disobeyed. For it would be
difficult indeed to find a circuit in nature for which the ratio
of current to voltage was a linear function of the circuit. In
nature every conceivable function between current and voltage can be observed. And even in a laboratory it takes some
care to reproduce Ohm's law, as every teacher of electricity
and magnetism finds out. When he succeeds he proves that
nature, wild and disorderly when left to herself, can on
occasion be made to toe the line and do man's bidding. In
short, one can argue that Ohm's law is no more than a definition of resistance, and one can argue that it is an invention.
But one cannot argue that it is a discovery.
Much the same can be said about the inverse square law.
This applies equally to gravitational, electrostatic, and magnetic fields. So it seems to have some universality. Let us
consider its application to electrostatic fields. The law states
that the field strength around a charged body varies inversely
as the square of the distance. But if a small charged body
were suspended just here in front of you and the field strength
around it were measured it would not vary even remotely as
the inverse square of the distance. Various objects in the
vicinity of the charge would interfere too much. To demonstrate the inverse square law I should have to take sundry
precautions. I might let the charge be on a small sphere and
surround this by a larger concentric sphere made of a conducting material. If I made measurements of field strength in
the space between the two spheres I should be able to show
that the inverse square law was being obeyed. The reason is
that in the field between concentric spheres the field is uniformly divergent, and the law only holds for this special condition. So the clause to ensure the inverse square law must
read: In the space between concentric spheres (or alternatively
'For a uniformly divergent field') the field strength shall be
inversely proportional to the square of the distance from the
centre of a charged body forming the inner sphere.
But this could be predicted without an experiment. When
one speaks of a force one means an influence exerted from
somewhere on some object, one means the kind of effect for
which, as stated in elementary textbooks, action and reaction are equal and opposite. In electricity this could be
expressed by saying that every tube of unit force in our
concentric spheres had one end on one of the spheres and the
other end on the other sphere. It follows from this that the
intensity of the force on the outer sphere is inversely proportional to its area. And as the area is proportional to the
square of the radius the intensity of the force, also called
field strength, is inversely proportional to the square of the
radius for any sphere concentric with the one carrying the
charge. In short, the inverse square law is not a statement
about gravitation, or electricity, or magnetism. It is a statement about geometry. It must be observed whenever there
is a uniformly divergent field and it is never observed when
the field has a different shape.
So the Cosmic Statute Book need not have a clause in
which the inverse square law is mentioned. It would be
ensured by a clause in the section headed 'Geometry'. Such
a clause would have to read: 'For a sphere the area shall be
proportional to the square of the radius.' Are we then to take
it that there is such a clause? The answer is 'No'. For it holds
only when the geometry is Euclidian. And Nature's geometry is not necessarily Euclidian. We know from the
general principle of relativity that the Cosmic Statute Book
allows any geometry. There are, therefore, occasions when
the inverse square law does not hold even for concentric
spheres. The region within the nucleus of an atom may provide an example.
