CHAPTER 5
THE INFORMATION CONTENT OF
LAWS
In a letter to a scientific colleague
Newton spoke about what he considered to be the best method in natural
philosophy (science):
For the best and safest method of philosophizing
seems to be, first diligently to investigate the properties of things and
establish them by experiment, and then to seek hypotheses to explain them. [1]
Fact finding comes first, then comes the search for
"hypotheses" which will explain the facts. Newton found that the same set of experimental facts could
be explained by quite different hypotheses. It was impossible to resolve an
argument about which hypothesis was right provided all the hypotheses did was
fit the known facts. In the heat
of one argument he swore off making hypotheses (in Latin, of course, by "hypotheses non fingo"
which means "I do not make hypotheses"). In fact, he went right on making hypotheses but avoided
arguments. This remark of Newton's
is sometimes interpreted as meaning that we should not try to explain laws by
devising some underlying mechanism but be content that the facts are explained
when the law has been formulated that fits the facts. Newton's law of gravitation is usually taken as the example;
we tend to accept the law as the final explanation of gravity without asking
further questions as to why this particular law holds. In a way, Newton is pressing for
empiricism here, telling us to skip the theorizing because all it does is lead
to arguments. Newton himself made
many hypotheses. To have a model of what is going on - a theory, if you will -
can be useful. Often a theory (law or hypothesis) not only fits facts that have
been found by observation and experiment but also indicates (or predicts) that
other facts, not known at the time, should be true. The theory contains then some part that is not strictly
empirical; it contains assumptions about what might be the case. Often we can make a choice between two
alternative theories that fit the known facts by looking for consequences of
the theories that differ from each other.
An experiment is then performed to resolve the argument about which
theory is better. Bridgman
describes the process:
If we can show that any of the indirect consequences
are opposed to experiment then the assumption is false. But the concept of true is not
applicable. I think we would want
to invent a new concept to cover the situation: probably the word
"possible" has enough of the required connotations to meet our needs...
Doubtless a great many alternative theories will be possible and we shall have
to choose between them on grounds of simplicity or convenience of calculation
or perhaps on purely aesthetic considerations. [2]
I have already indicated that I am
accepting as scientifically "true" any law, or theory, that fits the
facts. False to me applies to one
that does not fit the facts.
Several different theories can be true as far as I am concerned. Bridgman wants to call theories that
fit the facts "possible theories", thus avoiding the problem of
calling two alternative theories true.
It is just a matter of words here.
He indicates that if we have two equally good (possible) theories, in
the sense that they explain the facts, we choose one or the other on some
arbitrary grounds such as "simplicity or convenience of calculation".
The choice in favor of the simple, or the beautiful law was made originally
because scientists, like Newton, believed that it accorded better with the mind
of the Creator. It was thus more likely
to be "really" true.
Mach also said the simpler explanation should be chosen but for an
entirely different reason. This is
how Feuer summarizes Mach:
Natural laws were economical summations of
experience, labor-saving devices, that enable the labor of other men to be
substituted for one's own... Occam's Razor, the so-called principle of
simplicity in scientific method, was no longer to be founded on a metaphysical
belief in the simplicity of the universe; rather it was a principle of economy
expressive of man's biological aim to do things with the least expenditure of
energy. [3]
Or in Mach's own words:
Science itself, therefore, must be regarded as a
minimal problem consisting of the completest possible presentment of facts with
the least possible expenditure of thought. [4]
It is a pragmatic point of view. Again Mach:
Those ideas that hold good throughout the widest
domains of research and that supplement the greatest amount of experience are
the most scientific. [5]
This reason of Mach's for choosing a simpler theory
over a more complicated one, because the simpler theory is more scientific, has
little force when the simpler theory emerges some time after the more
complicated one and does not predict anything different from the original
theory. Louis de Broglie makes
this clear:
Indeed, we may assert it as a sociological law of the
scientific community that no new theory, whatever its appeal of elegance or
simplicity, will generally supersede the old unless it leads to new
experimental discoveries of fact; such resultant discoveries may, with the help
of auxiliary hypotheses, be rendered consistent with older doctrines, but would
not have been foretold by the latter's adherents. [6]
A theory becomes established and will not easily be
deposed by a new simpler theory
which fits the same facts, even though, from Mach's standpoint (and mine), it
is better.
The ability of a theory to predict facts
that can be later verified is perhaps overemphasized. Certainly, if a theory does predict facts beyond the known
facts that it was designed to fit, we should check to see whether or not the
additional facts can be verified.
If they cannot, we would have to alter the theory or get a new one. The alteration of a theory is quite
possible - we could for instance, impose additional restrictions so the theory
would not predict the non-existent facts.
Schrodinger, the scientist who invented the wave mechanical model of the
atom, is quoted by Feuer as saying:
The following process is recurrent in physical
science. A certain amount of
special knowledge, empirically accumulated and asserted, is tentatively cast
into a comprehensive theoretical aspect.
The theory, after having been gradually corrected by further
experiments... tends to acquire an unforeseen general validity. But, strangely enough... the knowledge
which its proportions are supposed to convey turns out to be more and more
tautological.
Schrodinger is indicating that the theory which
emerges after the processes of fact fitting and correction are ended begins to
seem more than just a "possible' explanation (in Bridgman's terminology).
It becomes stamped with an authenticity that makes it practically inevitable,
if not obvious, or true by definition.
It becomes established and any change from the established view is taken
only if the established view is proved false.
Louis de Broglie hints that the choice
between equivalent theories is often made on the basis of personal
philosophical beliefs in
"hidden harmonies" in the universe (the order of things):
A few examples don't suffice to prove that there are
always an infinite number of possible theories for explaining the same
experimental facts, and it seems certain to us that even, when there are a
great number of logically equivalent theories, the physicist has the right to
believe that one of them conforms more to underlying physical reality, and is
more capable of generalization, more apt to reveal the hidden harmonies. [7]
I will be writing in a later chapter about the
philosophical beliefs of a number of modern scientists which slanted their
science towards certain types of theories and made those theories, to them,
seem inevitable. Tzara, a Dadaist
philosophically, wrote:
Science throws me off as soon as it pretends to be a
philosophical system; for it loses its useful character... I detest that pat
objectivity and harmony with which science finds all in order. [8]
The Dadaists hated the idea of design and logic, and
featured chance in all their thinking and art. I must admit that science throws me off sometimes with
concepts such as the "wave-particle duality of matter and radiation",
as if duality were of the essence of nature.
Sometimes after a theory has been
established for a while there are alternative approaches which contain much the
same information, in that they explain the same facts, that are accepted by the
scientific community. For example,
the energy point of view in mechanics (which is the study of motion of
interacting objects) was formulated a considerable length of time after Newton
first devised his laws of motion.
There is absolutely no additional information provided by the
introduction of the concept of energy, but often greater insight into a
physical situation can be gained by using it. It is a labor saving device in
some computations. So we have two alternative viewpoints on motion, the
force-acceleration viewpoint and the energy viewpoint. Sometimes the new
viewpoint leads to the discovery of new information. In studying the
electromagnetic interaction, the concept of the electromagnetic field used by
Maxwell helped him to add a piece to the theory that was not based on any
experimental evidence. Maxwell's
enormous success has meant that the field concept has dominated thinking about
electromagnetism, and the electric charge, as the source of the field, has been
somewhat neglected. Scientists
frequently introduce concepts, like energy or electromagnetic field, which are
defined in terms of other, more fundamental, concepts. These others are more
fundamental only because they are closer to our own sense experiences. Newton introduced the concepts of force
and mass which he defined in terms of the prior and more fundamental concepts
of position, velocity, and acceleration.
Einstein explains this all rather well:
We shall call "primary concepts" such
concepts as are directly and intuitively connected with typical complexes of
sense experiences. All other notions are - from the physical point of view -
possessed of meaning, only in so far as they are connected, by theorems, with
the primary notions. These
theorems are partially definitions of the concepts (and of the statements
derived logically from them) and partially theorems not derivable from the
definitions, which express at least indirect relations between the
"primary concepts", and in this way between sense experiences. Theorems of the latter kind are
"statements about reality" or laws of nature, i.e. theorems which
have to show their usefulness when applied to sense experiences comprehended by
primary concepts. The questions as
to which of the theorems shall be considered as definitions and which are
natural laws will depend largely upon the chosen representation. It really becomes absolutely necessary
to make this differentiation only when one examines the degree to which the
whole system of concepts considered is not empty from the physical point of
view. [9]
Einstein indicates that concepts like energy and
electromagnetic fields must be connected with primary concepts through
definitions. As well as the definitions, there will be other (usually
mathematical) statements that can be made. These are often called laws of
nature, for example, the law of conservation of energy. But in fact there is
always confusion about what is a definition and what is a law of nature. We
tend to think that a definition does not contain any information about the
physical world in it but that a law of nature does. Einstein points out that it
is "the whole system of concepts" that must be thought of as
containing information about the world. When I speak of the "information
content of laws", I mean the same thing as what Einstein calls "the
degree to which the whole system of concepts considered is not empty from the
physical point of view". Here
is another opinion, this time from Richard Feynman:
Although it is interesting and worth while to study
the physical laws simply because they help us to understand and to use nature,
one ought to stop every once in a while and think, "What do they really
mean?" The meaning of any
statement is a subject that has interested and troubled philosophers from time
immemorial, and the meaning of physical laws is even more interesting, because
it is generally believed that these laws represent some kind of real knowledge.
[10]
Feynman uses the phrase "some kind of real
knowledge" where I speak of "information content".
In the next chapter I will examine
Newton's laws of motion which are one of the expressions of the information
about the motion of objects as they interact with each other. In performing this analysis, I must consider
the whole system, both laws and definitions, because, as Einstein indicates,
the boundary between them is very fuzzy.
Then there is the confusion about information content when there are
alternative formulations. Because there are alternative systems for mechanics,
I would have to say that one is as true as another. That brings up another related problem. If the whole of
mechanics can be explained without any reference to the concept energy, is
there anything "real" about energy? If you could explain mechanics without the concept of force
is there anything "real" about force? And what about explaining
electromagnetism without the concept of the electromagnetic field? Then there is the other side of this.
Newton said that he would make no hypothesis about the law of gravity. Was he
saying that he would not try to explain why the force of gravitation produced
by an object depended on its mass and fell off inversely as the square of the
distance from the object? Why
should it depend on the mass, a concept he introduced to express his laws of
motion? And why should it vary as
the inverse square of the distance?
Explain that Sir Isaac! (Answer: "Hypotheses non fingo".) No,
his real answer is that it is the will of the Creator who designed the universe
by laying down a set of universal laws from which everything follows. End of explanation. When you have this
attitude perhaps you shut doors that should remain open. Newton hated controversy but science
must have differences of opinion or it cannot survive. Kuhn points this out:
The resolution of revolutions is the selection by
conflict within the scientific community of the fittest way to practise future
science... And the entire process [development of science] may have occurred,
as we now suppose biological evolution did, without benefit of a set goal, a
permanent fixed scientific truth, of which each stage in the development of
scientific knowledge is a better exemplar. [11]
Kuhn, like me, doubts that there is an absolute
scientific truth to which science is approaching closer and closer.
So that is my program; in the next
chapter I will look at Newtonian mechanics and see what I can read into it as
far as information content is concerned.
Then, in the following chapter, I will examine electromagnetic
theory. I will be acting somewhat
as a critic in that I will be tearing the laws (and definitions) apart hunting
for meaning (content). Bridgman
describes this kind of activity as follows:
The material for the physicist as critic is the body
of physical theory just as the material for the physicist as theorist is the
body of experimental knowledge. [12]
Remember that my aim is twofold: first,
to show that the idea of general
laws is an illusion and second, to offer some explanation as to why any
specific facts are simple, if they are.
One of the dangers of this sort of
exploration is that, in trying to present a coherent world view, I must plug
some of the holes with suggestions that I perhaps have not thought out
carefully enough. Actually, most
of the suggestions have already
been made by other people and I am merely selecting ones that fit in
with my scheme.
These suggestions have not had widespread
interest shown in them because they departed from the orthodox view and were in
a sense contradictory to that view, even though they had features that were
appealing. At the end of each of the following chapters I will try to list
those unorthodox ideas that I am including in my world view, both those of
others and my own. It must be remembered that the point of this investigation
is to see whether it is possible to construct a world view based on the premise
that there are no general laws. Each particular suggestion must not be taken as
being the only one that might serve.
I have a somewhat similar aim to Mach who
in the preface to his book on the "Science of Mechanics" said:
The present volume is not a treatise upon the
application of the principles of mechanics. Its aim is to clear up ideas, expose the real significance
of the matter and get rid of metaphysical obscurities. [13]
By "significance of the matter" I mean the "information content". By getting rid of "metaphysical obscurities" I mean that my aim is to show that there is no evidence in physics for or against an underlying pattern of things.
Copyright © 1983 J.N.P. Hume All rights in this book reserved