19-01-2026, 12:25 AM
Quote:42
Mathematics & Reality
had a strong appeal, especially for the scientist engaged in
the search for objective truth. He must study nature impar-
tially and investigate how it behaves when left to itself;
when he weighs an object he must not put his hand on the
scales. Therefore all laws are predicated on the assumption
that energy is not being added to or subtracted from a
closed system, and in this way the regularities of nature are
discovered-laws of motion, laws of gas pressure and
temperature, etc. The scientist is understandably impressed
with the remarkable consistency that emerges and with the
predictive power that rewards his labors.
Yet, having found that under these special conditions
matter behaves in this remarkably precise and orderly
fashion, the theoretical scientist tends to disregard the fact
that he had assumed for purposes of his experiment that
no energy was added or subtracted from outside the sys-
tem, and he concludes there can be no addition or subtrac-
tion to mar the predictability and order. It does not occur
to most scientists that the existence of the third derivative
makes possible just this addition or subtraction of energy.
To the mind directed at the discovery of a world order, the
mind trained to avoid human intervention or bias of any
sort, it is abhorrent to turn traitor to this beautiful crea-
tion. Unable to put it to use, unable to take advantage of
the knowledge of law so obtained, the scientist becomes
the chef who has created such a marvelous cake he cannot
bear to eat it.
Thus it is that the sharp line is drawn between technol-
ogy and science. Technology, driven by invention, does not
hesitate to eat the cake or use determinism. This is precise-
ly what technology does. By using nature's laws, it creates
products, and when these products are machines, it takes
for granted that the machines can be controlled.
Mathematics & Reality
Control and Li( e
43
In this reference to use and control, I am assuming that the
third derivative is kept optional. The scientist would admit
that a planet in an elliptical orbit changes its acceleration.
When the planet is close to the sun, the acceleration is
greatest, when far from the sun, the acceleration is least. So
there is in this case change in acceleration, but the accelera-
tion varies inversely with the square of the radius, and is
therefore linked to position; it is not open or optional. The
elliptical orbit, then, does involve the third derivative, but
this is a special case.
The governor of a steam engine or a thermostat that
has been set to a predetermined temperature are also spe-
cial cases. The general case, however, allows control to be
optional, subject only to the limitations of the machine.
(We could not expect a 40 hp car to accelerate with the
rapidity of a 300 hp car.) It allows the householder to reset
the thermostat, the engineer to regulate the governor of the
steam engine, and so on.
I emphasize the importance of the third derivative, or
control, not only because it puts determinism in its place-
as the servant of free will-but because it lays the basis
for a true science of life. The fact that man can control
machines enable us to recognize that he also controls his
body. Even to stand up requires the continual, but largely
unconscious, exercise of control. And if man controls mo-
tion, as I said before, so, too, can animals control their
motions, and plants control the chemicals to store energy
and promote growth.
Here, at last, life enters the picture. Hitherto life has
had no place in the scheme of determinism. Determinism is
a dead picture, a portrait of inert matter obeying fixed
44
Mathematics & Reality
laws, of dead planets repeating their monotonous revolu-
tions. But with the expanded formalism permitting the
addition of control, we can account for life. We realize that
nature creates creatures who, through control, use the laws
of nature for growth and self-maintenance.
our problem here, however, is mathematics, and
the need to challenge that curiously perverse view of
mathematics, at once romantic and irresponsible, that de-
clares that because mathematics is a pure science it has no
bearing or obligation to the real world. Let us now try to
see how this idolatry of formalism has obscured the very
thing that could save science.
