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The deeper hidden message in Maxwell’s Equations By Ivor Catt, Electronics & Wireless World, dec85 Why have Maxwell’s Equations survived for so long? http://www.ivorcatt.com/em_test04.htm In my November 1985 article I investigated Maxwell’s Equations, generally regarded as the greatest mathematical achievement in science. (And if mathematics is the highest flowering of science, then Maxwell’s Equations become the greatest achievement in all science.) In
the 1830s, Faraday discovered electromagnetic induction, thus closing the
loop between electricity and magnetism. This discovery paved the way toward the
rapid growth of electricity-based industrialization and the high technology
which shapes today’s world. By
making the key discoveries pf their era, uneducated technicians like Michael
Faraday and James Watt threatened the scholastic myth, that all progress,
including scientific progress, needs must use the rigour and discipline
controlled by academics in places like Cambridge University. The ultimate in
scientific rigour (rigor mortis?)
was held to be mathematics. Biography and History of Science writings spawned
in academia present the thesis that, lacking mathematics, Faraday could not
and did not really effect his discovery of electromagnetic induction. Rather,
he stumbled into it, but it could only be properly exploited decades later,
after Professor Maxwell had placed a mathematical structure upon Faraday’s
fumbling, unscholarly ideas. Thus, according to the Platonic interpretation
of history, Professor Maxwell, not Faraday the technician, paved the way for
massive exploitation of electromagnetism in transformers, motors and
generators. The deeper message in Maxwell’s Equations is that, do what they
will, the local yokels will not replace mathematical academia as the fount of
knowledge and progress. In
my previous article I posed two questions: Do Maxwell’s Equations
contain any information about the nature of electromagnetism? Why do academics and
practitioners think that Maxwell’s equations are useful? I am sure you will have found my answers unsatisfactory. The reason is that they were based on certain assumptions, and failed to dig deeply enough into the underlying motivation, psychoses and myopia within contemporary science. The underlying battle for the soul of science is between the practical engineer on the one hand and the Platonic pure mathematician on the other. For his part, the mathematician sees this battle as more important than search after truth or technology-fuelled search after new sources of wealth. For him, the important thing is Form; the purity and beauty of his world, and his ability to control and manipulate it intellectually. (The profane aspect of this idea is the desire to impose a structure onto any ‘discipline’ such that it is easy to teach and, more importantly, easy to set exam questions on.) One FRS [Howie] told me that physical reality was composed of sine waves, and this encapsulates the mathematician’s attitude to our world. A
good example of an academic with the mathematician’s attitude is Sir James
Jeans. He was highly regarded in the 1930a both as a Cambridge academic and
as a populist, much like Sir Fred Hoyle in the 1950s [and Hawking today]. In
his [1931] book, The
Mysterious Universe, p113, Jeans gives a clear view
of the platonic mathematician discussed in the last paragraph. By “pure mathematics” is meant those departments of mathematics which are creations of pure thought, of reason operating solely within her own sphere, as contrasted with “applied mathematics” which reasons about the external world, after first taking some supposed property of the external world as its raw material. On
the next page, Jeans goes on to write, …. The universe appears to have been designed by a pure mathematician. The
important thing is not to ponder over the possible contradiction between
these two statements, but to grasp the mentality underlying them. This
mentality, usually in a better camouflaged and less grotesque form, is what
made possible the survival of mathematical absurdities like Maxwell’s
Equations for such a long time. ( www.ivorcatt.com/2804.htm ) Jeans
then goes on helpfully to point out the flaw in his argument: This [last] statement can
hardly hope to escape challenge on the ground that we are merely moulding
nature to our pre-conceived ideas. The musician, it will be said,
may be so engrossed in music that he would contrive to interpret every
piece of mechanism as a musical instrument; the habit of thinking
of all intervals as musical intervals may be so ingrained in him that
if he fell downstairs and bumped on stairs numbered 1, 5, 8 and 13
he would see music in his fall. In the same way, a cubist painter
can see nothing but cubes in the indescribable richness of nature
– and the unreality of his pictures shews how far he is from understanding
nature: his cubist spectacles are mere blinkers which prevent his
seeing more that a minute fraction of the great world around him.
So, it may be suggested, the mathematician only sees nature through
the mathematical blinkers he has fashioned for himself. We may be
reminded that Kant, discussing the various modes of perception by
which the human mind apprehends nature, concluded that it is especially
prone to see nature through mathematical spectacles. Just as the man
wearing blue spectacles would see only a blue world, so Kant thought
that, with our mental bias, we tend to see only a mathematical world.
Does our argument merely exemplify this old pitfall, if such it is? A moment’s reflection will
shew that this can hardly be the whole story. The new mathematical
interpretation of nature cannot all be in our spectacles – in our subjective
way of regarding the external world – since
if it were we should have seen it long ago [my
italics]. The
human mind was the same in quality and mode of action a century ago as now;
the recent great change in scientific outlook has resulted from a vast
advance in scientific knowledge and not from any change in the human mind; we
have found something new and hitherto unknown in the objective universe
outside ourselves. Our remote ancestors tried to interpret nature in terms of
anthropomorphic concepts of their own creation and failed. The efforts of our
near ancestors to interpret nature on engineering lines proved equally
inadequate. Nature refused to accommodate herself to either of these man-made
moulds. On the other hand, our efforts to interpret nature in terms of the
concepts of pure mathematics have, so far, proved brilliantly successful. It
would now seem beyond dispute that in some way nature is more closely allied
to the concepts of pure mathematics than to those of biology or of
engineering, and even if the mathematical interpretation is only a third
man-made mould, it at least fits objective nature incomparably better than
the two previously tried. Professor
Einstein argued similarly in 1949: …. The approach to a more profound knowledge of the basic principles of physics is tied up with the most intricate of mathematical methods. (In passing, it is worth noting from page 62 of the
same book, where Einstein writes: “The special theory of relativity owes its
origin to Maxwell’s equations of the electromagnetic field.” In the
literature we repeatedly come across assertions that Maxwell’s Equations play
a pivotal role in science. - Ivor Catt) [Also see Feynman below in red] I
have put the weak point in Jeans’ argument in italics. The mathematicization
of science developed with a vengeance as a result of the professionalization
of education. Dr. Ivor Grattan-Guinness once pointed out to me that the
decline, or ossification, of science into ‘maturity’ was a necessary result
of the introduction of universal education in the midt-19th
century, because it caused the growth of a powerful group with a vested
interest in knowledge, the professional teachers. Basil
Bernstein says that knowledge is property, with its own market value and
trading relationships, to be protected by the social group who administer
that body of knowledge. If
only those who lived off a body of knowledge could make their knowledge more
secure, their careers and pensions would be protected. Two stratagems were
open to them: -
to freeze the knowledge base so that it
would not be a prey to the ebbs and flows of the real world, and -
to develop the thesis that any change in,
or extension of, the knowledge base could only be properly effected by the
professional ‘knowledge doctors’ or ‘knowledge brokers’, with their special,
occult ways of pushing forward the boundaries of knowledge. It
would of course be less effective for the professional group of knowledge brokers
merely to bless or condemn influxes of new knowledge. (Admittedly they do do
that. All my attempts to publish work on electromagnetic theory and on
computer architecture (US patents 3913072 and 4333161) were blocked
for more than ten years [which is now thirty years] by learned
journal referees, who are by definition knowledge brokers.) The knowledge
brokers’ power would be greater if they required that new knowledge arise in
their own prescribed style, preferably devised by one of their members, a knowledge
professional. An early example of this in my own publications is that under
threat of firing by my boss [Dr. Jan Narud], who was a Fellow of the
IEEE, I was compelled to include a ghastly, recondite, mathematical last
section, written by someone else, in my 1967 IEEE paper. We have reached the following point in the argument. Under cover of claiming to maintain standards of scholarship, or to maintain rigour, knowledge brokers (1) block the ingress of new knowledge, particularly revolutionary knowledge in the Kuhnian sense, and also (2) they make a last-ditch, bitter defence of old, discredited knowledge, like Maxwell’s Equations. “Unfortunately, however, when the body of knowledge is bigger and the rate of inflow of new knowledge is smaller, more and more of the activity within the knowledge [base] becomes ‘celebration’, more and more ceremonial rather than exercise in depth. As a result, a different calibre of person is attracted to that large knowledge, lacking the ability to understand and defend a body of knowledge with many levels of meaning. They are ‘maintenance men’ rather than ‘builders’. The central body of knowledge ossifies, becomes brittle and then disintegrates.” We
need to realise that the cardinals who suppressed Galileo did not need to be
competent theologians or scientists; they only needed a much narrower
competence, the ability to distinguish between the orthodox and the
heretical, in both content and in style. As to style, it is worth pointing
out that possibly the ability to publish radically new, revolutionary
knowledge in the old accepted style would prove that after all the new
knowledge was not truly revolutionary. So arguments about style, which are
regularly lodged against my writing, including my last article, create a
beautiful Catch 22 situation where no new knowledge can be published. In
this penultimate paragraph I mention in passing The Lateral Arabesque,
‘Arabesque’ having the meaning ascribed to it by Dr Peter rather than its
dictionary meaning. In the engineering sense, the supposed situation where
academia controlling a discipline – electromagnetic theory for example – maps
onto the real subject, is unstable. If at any moment the professors administering
a discipline happen to be weak in one branch of it, they will tend to not
examine their students in it, and so will tend to select out those up and
coming students who have that sub-discipline as their strength. Positive
feedback down the generations of students will further the retreat from that
particular sub-discipline. (Sir James Jeans and Einstein could be said to be
telling us that academia have selected out budding scientists who showed a
grasp of the physics, rather than the maths, of their subject.) Similarly,
the whole of academia will move deeper and deeper into any misconception or
aberration, and there is no corrective force. In my view, ‘The Lateral
Arabesque’ makes it possible for an academic subject’s content to end up with
no overlap at all onto the real
subject from whence that branch of academia sprang. I have just completed
four years as Principal Lecturer in a College of Further Education, where I
was struck by the lack of any significant link between the Higher TEC
syllabus that I taught and the real subject, electronic design, in which I
had been earning my living in industry for the previous 20 years. As a minor
example, academia evolved the myth that dissatisfaction among logic designers
with the indeterminate state of an R-S bistable if driven on both its inputs
at the same time led to the development of the J-K bistable: then that the
instability of the J-K led to the development of the Master-Slave J-K,
regarded by academia as the Rolls-Royce of bistables. A nice idea, but with
no historical foundation. A
large example would be academia’s fixation on Quine-McClusky, something net
even heard of, let alone used, by engineers in the real world of logic
design. Although I was in the best position possible to introduce or alter
syllabuses, being on the County Committee, during my four years as a P.L. I
failed to change one word of one syllabus. I struggled very hard to do so. To sum up. Professionaliztion of knowledge leads to a vested interest in knowledge, which leads to the disintegration of competence among knowledge professionals as well as the prevention of the ingress of new knowledge. Something like this syndrome is needed to explain the survival of Maxwell’s Equations for so long. For
references, see original article in Electronics and Wireless World, dec85.
"From a
long view of the history of mankind – seen from, say, ten thousand years from
now – there can be little doubt that the most significant event of the 19th
century will be judged as Maxwell’s discovery of the laws of electrodynamics.
The American Civil War will pale into provincial insignificance in comparison
with this important scientific event of the same decade." – R.P.
Feynman, R.B. Leighton, and M. Sands, Feynman
Lectures on Physics, vol. 2, Addison-Wesley, London, 1964, c. 1,
p. 11. Oops! – Ivor Catt |
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A Mathematical Rake’s Progress. www.ivorcatt.com/2809.htm |
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The
Conquest of Science. http://www.electromagnetism.demon.co.uk/wbdanbk8.htm |