Green
Lion Press
NEWTON
/ MAXWELL / MARX
(forthcoming
from Green Lion Press)
Newton, Maxwell, Marx:
three pillars of our western intellectual inheritance, yet each more celebrated
in encyclopaedias and histories than read. It is the thesis of this new volume
forthcoming from the Green Lion Press that there is much to be gained from a
fresh reading of these authors. Three extensive essays are collected here, each
reflecting a re-reading of a work of one of these authors: respectively,
Newton's Principia,
Maxwell's Treatise on Electricity and Magnetism, and Marx's Capital. A commentary has been
added, linking them and proposing a dialectical thread that begins in the 17th
century, and develops an unfolding vision of science still challenging in our
own time.
The account begins with
the recognition that Newton's Principia constitutes overall a polemic against
mechanism, and specifically a refutation of Descartes' vision of nature as a
mathematical machine. Newton embraces, certainly, the conviction that the natural
world is mathematical throughout, but he distinguishes from the outset what is
inert—as all nature is for Descartes—from a second principle that
he calls active force. Newton in this way opens spaces throughout the Cartesian
plenum in which spirit, this second principle, can operate. It is difficult
today, in our world of universal engineering, to see again with Newton's eyes
the significance of this distinction, and to recognize that a law of force,
though strictly mathematical, is not thereby rendered mechanical. Newton shapes his
geometrical mathematics as a rhetorical instrument rich in meaning; in such a
world the statement that a system is mathematical throughout is by no means a
reductive proposition. This distinction is of first importance to Newton, as it
may well be for us, since it becomes clear that within the realm of nature the
scope of the Principia is altogether universal. Thus the justly celebrated System
of the World,
Newton's account of the heavenly motions, becomes hardly more than an example,
a first instance of the new system. Force is exactly the domain of what alchemy
calls spirit,
and Newton as master alchemist, as we now know him to have been, is surely on
the track of the ultimate of the spirits in nature, the vital force. We once
approached the Principia as the founding work of modern physics; now we see it as
the culminating work of serious alchemy—a mathematical biology of all
natural functions, inclusive of the very cause of life itself—and indeed,
as Newton's book of life. The unity of Newton's thought may astound us,
as we ourselves try to piece together in our own time a coherent picture of the
world; thus, the Principia holds a central place in Newton's theology,
since the concept of force restores scope for God's active presence in the
world, a presence crucial to Newton's faith, for which mechanism had left no
room.
Newton's successors have
not of course understood his project in the terms he intended. The term force soon became a mere tool
in the engineering of the industrial revolution, retaining nothing of Newton's
sense of spirit. By the time James Clerk Maxwell had embarked on the study of
natural philosophy in the middle of the 19th century, he was
confronted at Cambridge University with a challenging but sterile mental
discipline, in which a Newtonian law of force appeared merely as the blank
formalism of an action-at-a-distance. Maxwell was at heart a Scotsman,
curiously out of place at Cambridge for all his ironic skill at mastering the
English ways, and his own revolution, more fundamental perhaps than is often
realized, began with a dramatic turn away from this sterile system. Maxwell
embraced in its place the apparently naïve insights of Michael Faraday,
who as a commoner with virtually no formal education, represented to all
appearances, and indeed in his own terms, the most unmathematical of natural
philosophers. Yet Maxwell maintained, publicly and to the end of his life, that
of them all it had been Faraday who was the real mathematician!
The nature of mathematics,
and of mathematical physics, is seriously in question here. Maxwell carefully
shaped his own electromagnetic theory, and the symbolic structure of the vector
calculus, to reflect as fully as possible the patterns that Faraday was
perceiving in the magnetic lines of force traced by his iron filings. It was
the field
as a whole that had become primary, caught in its totality by the intuitive
mind, with symbolic mathematics following behind. Maxwell was openly delighted
when, well into his scientific career, he first encountered Lagrange's
equations of motion, which characterize, in terms of energy rather than force,
the motion of a connected system as a whole. Maxwell retained a
deep concern for metaphysics, and this primacy of the whole is clearly a matter
of first importance to him. He made certain to derive his own system of
equations by beginning with Lagrange's, and from them moving toward
electromagnetism by carefully specifying the values of the coefficients that
would apply in this case.
Maxwell's equations,
which result from this process, speak to the field as a whole. The individual
bodies and the forces between them with which Newton had begun are for Maxwell
the last, and indeed most problematic, concepts to appear. By way of the field
and its patterns Maxwell makes electromagnetism intuitively accessible to every
inquiring mind; his entire approach constitutes an inversion of the concept of
science which undercuts at once both the primacy of mathematical symbols and
the necessity of an aristocratic formal education. It was surely meant as his
gift to Faraday, and more largely to what has been termed the democratic
intellect.
In our faltering efforts to comprehend whole systems in their entireties,
whether environmental systems or the global human community, and in the
austerity with which we still treat mathematics and the sciences as matters
reserved only for specialists, it is clear that we have not altogether caught
the significance of the revolution Maxwell was undertaking in our behalf. We
should note, incidentally, that Maxwell's revolution is against the specter of
Newton, not against Newton himself. For all their evident differences, in truth
a deeper concern for the unfolding human spirit unites them. Newton's notion of
the human spirit, expressed in a paradigm of law and obedience derived
ultimately from the Old Testament, we might think of as essentially feudal;
Maxwell perhaps reflects the larger course of human history when with equal
concern he carries this same human spirit to the level of its democratic
manifestation. Newton describes a layered world, of command, and obedience at a
distance. Maxwell fills all the gaps. Each of his field equations applies
everywhere equally, and as a set, they speak to a coherent cosmos. They are, in
a sense, the very image of a restored and democratic social whole.
An understandable
reaction to the title of this volume, Newton / Maxwell / Marx might be, "Why
Marx?", since, in this country at least, Marx is not often thought of as a
serious scientist. In truth, however, Capital in one giant step
carries forward the very trajectory of the concept of science we have been
tracing. If Faraday and Maxwell have made the science of nature accessible to
the democratic mind, Marx in effect invites his readers to turn this new light
upon the study of society itself. To an extent that is not often remarked, Capital analyzes the system of
capitalism in ways strikingly parallel to Newton's analysis of the motions of
the planets in the System of the World. Thus, as Newton begins with mass as the measure of
undifferentiated matter, so Marx with extreme care defines a corresponding
social quantity, the undifferentiated labor hour. And Capital, similarly, builds upon
a universal law of motion, the law of surplus value, delineated with
precision, whose operations Marx tracks scrupulously through the phenomena of
the system of capital—profit, interest, and rent. It is, of course, not a
system Marx loves, nor in his view one destined to endure. Surplus value, and with
it profit and the driving force of capitalism, arises only through the fact
that labor is never paid at its actual value. Further, since laborers sell what
belongs most essentially to them, their very power of free human activity, Marx
sees this as a system based on a the universal alienation of the human.
This perception, though
it introduces a tone of moral judgment that is sustained throughout the work,
is never allowed to relax its strictly scientific character. In this sense, Capital never descends into
ideology. Instead, Marx reasons with scrupulous care from the system that lies
before him, to an analysis of its future trends. He demonstrates the existence
of certain secular tendencies that are fraught with consequence for the system
itself. Once again, it is striking that Newton in the Principia followed a similar
path. In one magnificent proposition, to which perhaps too little attention has
been paid, Newton directly confronts the fact that a universe that contains
more than two bodies cannot sustain the perfect order which he has so carefully
described. This three-body problem inherently defies solution, but, undaunted,
Newton traces its consequences through argument inevitably blending the
qualitative with the quantitative. Out of it he draws, almost magically, his
theory of the tides, the precession of the equinoxes, and more largely, the
prediction of an ultimate demise of the original order.
Marx, similarly, defines
motions within capitalism that must work to undo its original order. He has shown
how the law of surplus value inexorably leads every manufacturer, wherever
possible, to substitute machinery for human labor. With real awe Marx has
depicted the growth of large industry and the development of machines which
ingeniously replicate human skills. The other side of this coin, however, is
the fact that labor, the sole source of surplus value, is everywhere extruded
from the system. In the long run, therefore, the rate of profit, and with it
the life of the system, must tend to fail.
Both Newton and Marx
have their eyes fixed on distant futures, therefore, and, remarkably, for
neither is this bad news. Newton foresees a time, not perhaps so distant, when
the Creator will once again exert His hand to reform the work. It is beyond the
scope of Capital,
and of the present study as well, to ask what prospect the demise of capitalism
may hold for Marx. He realizes that the new machines might labor for us,
yielding to everyone resources to live freely in directions which the
individual human mind, released from alienation, could choose for itself. Yet
though Capital
delineates the grounds for this possibility, in this scientific work it appears
as no more than a path which lies ahead, and the briefest glimpse of what Marx
perceives as a light beyond.
Taken together, these
readings constitute three windows on the evolution of the concept of science as
we know it today, yet any suggestion of a single, linear progression would be
misleading. These are complex works, each of lasting value in its own right,
and their relationship is surely dialectical rather than simply linear. Thus
though few today might be comfortable with Newton's own account of theology,
nonetheless the breathtaking scope and unity of his work still reminds us that
the human mind is ultimately one. That department of human activity we now
attempt to isolate as science cannot finally exist in separation from the
universe of our broader concepts and concerns. Similarly, Newton's sense of the
rhetorical role of mathematics, worthy in his view to serve as a vehicle of
spirit and human understanding, might startle us into a new line of thought
about mathematics today. If after all mathematics is neither mechanical nor
reductive, this insight may reassure us as we now tread so closely upon the full
realization of Newton's original vision, the mathematization of all nature, not
excluding ourselves in our natural being, and perhaps even of the very source
of life itself.
In such a dialectical
unfolding, the past is never left behind, but always incorporated in the new.
Thus these overriding insights of Newton's do not dim as we approach that very
different vision of Maxwell, that inversion contained in the idea of the field, in which the whole,
whether social or natural, becomes primary and coherent. The idea of causality
remains, even as the overall pattern becomes explanatory, and Newton's force becomes, literally,
only a derivative concept. With this transformation, science itself becomes a
significantly new concept, an instrument of intelligent, critical thinking
intuitively accessible to all, and a crucial bond of any democratic society.
Yet we are speaking of a vision of science which, though new a century ago,
today exists in our society as no more than an unfulfilled goal. People in our
time on the whole avoid the study of science and think of it still as a remote
domain, reserved for experts. We have not yet risen in practice to the
challenges of Maxwell's insight; we have not even quite caught the significance
of our failure.
Finally, what are we to
make of Marx? It is almost as if we had read Capital until now only as
ideology, failing to confront the vastly expanded concept of science which Marx
is proposing, in which society itself, its institutions and its practices,
become objects of serious scientific thought. We apply, it is true, seemingly
endless quantitative measures to society, proliferating sophisticated methods
of descriptive mathematics, but we do not follow Marx in developing a causal theory comparable to that of
the Principia,
explaining how and why capitalism and its institutions work. It may be hard to
deny outright the possibility of developing such a theory, if indeed we have in
Capital
a paradigm of the completed project. The issue is surely critical to the idea
of science and its role in modern society, for it directly affects our social
behavior. In matters concerning nature and technology, which belong to the
world of what we do call science, we reason together dispassionately and submit
disagreements to the forum of evidence and reason. In the social domain, by
contrast, concerning matters which we say lie outside of science, we
substitute opinion for truth, veil issues in obscurity, act in conflict rather
than cooperation, and resolve disagreement through levels of violence worthy
only of a barbaric age. Marx extends the scope of science, and would have us
reason as a community, intelligently and cooperatively, in matters belonging to
the social domain as we do in those of nature and technology.
Newton / Maxwell / Marx, in exploring these and
other aspects of the concept of science, constitutes an invitation to fresh
thought about these matters; it aims in particular to bring light to bear upon
the most deeply underlying questions. This book shows a way in which serious
study of the history of science can contribute importantly to our thinking
about ourselves and about our world today.
Green
Lion Press