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| Eugene Wigner |
Eugene Paul Wigner was a Hungarian physicist who received the Nobel Prize in Physics in 1963 for his contribution to the theory of the atomic nucleus and elementary particles. In a famous article published in 1960, Wigner said:
It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. (“The unreasonable effectiveness of mathematics in the natural sciences”. Communications on Pure and Applied Mathematics 13: 1-14).
He later notes
that scientific advances based on mathematics are often applied to previously
unsuspected fields. For example, Maxwell’s equations, proposed to unify
electricity and magnetism, also apply to radio waves, whose existence was not
suspected when Maxwell formulated his laws. Newton’s laws of Universal
Gravitation predicted the existence of the planet Neptune. Wigner sums up his
argument in the article mentioned above:
[T]he enormous usefulness of mathematics
in the natural sciences is something bordering on the mysterious, and… there is
no rational explanation for it.
And in the conclusion,
he adds:
The miracle of the appropriateness of
the language of mathematics for the formulation of the laws of physics is a
wonderful gift which we neither understand nor deserve. We should be grateful
for it and hope that it will remain valid in future research and that it will
extend, for better or for worse, to our pleasure, even though perhaps also to
our bafflement, to wide branches of learning.
However, Bertrand
Russell, although he fundamentally agrees with Wigner, said in this quote
something that seems to weaken this conclusion:
Physics is not mathematical because we
know much about the physical world, but because we know very little; we can
only discover its mathematical properties. (An Outline of Philosophy. George Allen and Unwin, 1927).
In an article on
the history of science published in
this book in 2011, entitled Creation and
Inertia: The Scientific Revolution and Discourse on Science-and-Religion,
William E. Carroll notes that mathematics and physics have been distinct
sciences since ancient times. It is true that mathematical principles can be
applied to physics, but what is practiced in this way is neither physics nor
mathematics, but a different science, mathematical physics. This distinction is
also very old: In his second book on Physics, Aristotle recognizes the
existence of mixed sciences, which he considers branches of mathematics,
including optics and astronomy. And St. Thomas Aquinas, in his Commentary on
Boethius, writes this:
It does not belong to the mathematician
to treat of motion, although mathematical principles can be applied to motion… The
measurements of motions are studies in the intermediate sciences between
mathematics and natural science (i.e., Physics). So there are three
levels of sciences… Some treat of the properties of natural things, like
physics… Others are purely mathematical and treat of quantities absolutely… Still
others are intermediate, and these apply mathematical principles to natural things,
[like] music and astronomy. These sciences… have a closer affinity to
mathematics, because in their thinking what is physical is… material, whereas that
which is mathematical is… formal. (Material and formal
are understood here in the Aristotelian sense.)
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| Isaac Newton |
Isaac Newton was
very clear about the difference between physics and mathematical physics. It can
be seen in the title he gave to his most famous work: Philosophiae Naturalis Principia Mathematica,
(Mathematical Principles of Natural Philosophy). Natural
Philosophy was the name given to Physics at that time. He says it more clearly
in an article that was not published until 1978: De
Gravitatione et Aquipondio Fluidorum (On Gravitation and
the Aquipondium of Fluids):
Moreover, since body is here proposed
here for investigation not in so far as it is a physical substance endowed with
sensible qualities but only in so far as it is extended, mobile and
impenetrable, I have not defined it in a philosophical manner, but abstracting
from the sensible qualities… I have postulated only the properties required for
local motion.
Unfortunately,
today this distinction has been partly lost. Many mathematical physicists act
as if their elucubrations were immediately and undoubtedly applicable to the
real world. Hence all those dead ends of current physics that I have denounced
in other
posts in this blog, which make one think that physics is losing touch with
reality. The extreme case of this tendency is provided by Tegmark’s
mathematical multiverse, which states that every coherent mathematical
construction is a universe that must exist somewhere. It is not entirely clear
what the phrases exist and somewhere may mean in
this context.
Mathematical
physicists should be aware of the limitations of their science. In his article,
Carroll agrees with this diagnosis: Principles
of mathematics, although applicable to the study of natural phenomena, cannot
explain the causes and true nature of natural phenomena.
Thematic Thread on Science and History: Previous Next
Manuel Alfonseca
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