Surveying the history of science at a macroscopic level, we find that progress consists of a series of revolutions in understanding, each greatly simplifying the description of the field under study.\u00a0 These revolutions are then followed by decades or centuries of elaboration, discovery of apparent exceptions, and gradual expansion of the existing dominant theory to accommodate those exceptions.\u00a0 Eventually, the structure of the theory becomes deeply intricate and unwieldy, increasingly complex and difficult to comprehend.\u00a0 This situation is eventually the impetus behind a fundamental reconsideration of the phenomena under study, leading, typically, to another revolution in understanding.<\/p>\n
In more recent times, one of the major criteria for accepting a new theory has become the inner simplicity, or “beauty” of the mathematics involved in the description of phenomena.\u00a0 In fact, this factor has become so important in modern physics that theories are often defended against challenges in part by citing their inner mathematical simplicity as evidence of correctness.<\/p>\n
Aristotelian physics was based on a preconceived natural order – the heavier a substance, the nearer to the center of the universe, the center of an unmoving Earth, it would tend to move. \u00a0Hence all solids were on Earth, denser solids more strongly resisted motion away from the center than lighter solids, water lay on the Earth’s surface, air above the water, and fire, from which all lights in the sky were made, sought the sphere above the air. \u00a0everything revolved in spheres about a motionless Earth. \u00a0A very simple, beautiful system that could be accepted, unless someone started looking into the real world in detail.<\/p>\n
Ptolemy (and before him, Eudoxus, Hipparchus and others), \u00a0examining observations of the real motion of the Sun, moon and planets, devised a series of interlocking circular motions to explain the observed positions. While insistent on preserving the “perfection” of uniform motion along ideal circles, the circles became decentered from Earth, and the motion uniform from a vantage point other than their centers. \u00a0The circles were tilted with respect to each other, and the number of circles needed steadily increased as the desired precision of predictions became smaller. \u00a0The beauty of the Ptolmeic system became very questionable by the time of the Renaissance. \u00a0 A revolutionary advance was due.<\/p>\n
Copernicus supplied the revolution, \u00a0though by recalling the work of Aristarchus, who was born 12 years after Aristotle’s death, and was exiled for teaching that the Earth rotated and orbited the Sun. \u00a0Copernicus supplied compelling evidence, but even in the 1500’s he feared for his safety, and wished publication of his revolutionary work only after his natural death. That he was very wise to be concerned was shown soon after, as Giadorno Bruno burned at the stake in 1601 for promoting anti-Aristotelian physics, and Copernicus in particular, \u00a0and the father of physics, Galileo Galilei, suffered house arrest and the banning of his published work at the end of his life in the 1630s.<\/p>\n
A very similar pattern on a much larger theoretical scale played out through the development of electromagnetic theory, \u00a0chemistry, and Newton’s mechanics and gravitation theories. \u00a0Starting from the simplicity of Newton’s three laws and gravitational force, Maxwell’s 4 equations of electromagnetism, and the atomic element theory, 19th century observations lead to increasingly difficult explanations of phenomena of optical absorption and emission, \u00a0thermal properties of matter, the undetectable ether, and the apparent wave-like yet particle-like behavior of light.<\/p>\n
The early 20th century brought the anticipated revolution in the form of Einstein’s geometrical interpretation of gravitation, \u00a0and the insane (and unfounded) theory of quantum mechanics to describe phenomena at very small scales. \u00a0Later in the century, the attempt to unify these theories – the quest for beauty and simplicity – brought us the Standard Model, along with String theories involving 13 or more dimensions, \u00a0the “Theory of Everything”, and the (conveniently) undetectable concepts of dark matter and dark energy to allow this modern simplicity to survive in the face of observations not fitting the accepted theories.<\/p>\n
And so we may be reaching the point of another revolution. \u00a0But that is not my central theme here. \u00a0My question is much more fundamental, and difficult to address (at least I am finding it so).<\/p>\n
Is it necessary that the actual Universe follow a set of “laws”, a patten of existant behavior, that Man can describe accurately in a small set of mathematical expressions? \u00a0Is “mathematical beauty” required of the Universe? \u00a0The “obvious” answer I have had for this question for many years has been an adamant No. \u00a0I could find no metaphysical reason why simplicity, and from a human perspective, comprehensibility, \u00a0would be required. \u00a0But I now wonder if I have been lead astray in my thinking.<\/p>\n
More will follow. \u00a0Think about the problem in the meantime.<\/p>\n","protected":false},"excerpt":{"rendered":"
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