Symmetry Philosophy Quotes

The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

Close to the very beginning of everything, a roughness was imposed on the universe. Its properties-energy, mass, and the forces uniting mass-energy-began in a completely unified state, but they would not stay that way for long and would be profoundly affected by the stretching of quantum irregularities. Quickly, the smooth homogeneity of everything developed waves, lumps, and wrinkles, especially variations of the density of energy and mass that began to structure space and time. Also, superimposed on the enormously magnified quantum effects to further shape the cosmos was a process physicists have termed symmetry-breaking.

The small surplus of matter over antimatter was only one of the asymmetries. Equally profound, engendering structure out of the matter that remained, was gravitational energy that broke out of the unified energy field at the beginning of the universe we inhabit. Following inflation, gravity amplified its effects throughout space in response to the stretched quantum fluctuations that first set the patterns into which structure would evolve. Matter began to concentrate in some regions, leaving other areas relatively less dense. The distribution of galaxies would later correlate with this initial pattern of lumpiness. In other ways, the early shaping of our universe may have progressed through discontinuities emerging out of symmetrical force fields that then took particular forms within the wrinkled "quantum fabric" of spacetime. One seminal example that led out of physics to chemistry and, ultimately, biology was a unified particle symmetry that concerned an electron-neutrino unity. These particles assume a smooth, uniform identity-virtually pure energy at an extremely high temperature-but, upon cooling to a certain threshold, suddenly break into unique entities, with the electron assuming much more of its energy as mass and the potential to build the emergent complexity of chemistry around elemental matter. Thus, the early breaking of symmetries led to various subsequent processes to shape the universe on all scales with an inexorable potential for the emergence of everything.

Knowledge and ability require other bases than this pseudo-brilliant intellect. First of all, they require a healthy body! It is the precondition within which a healthy mind can develop. Greek culture, Greek philosophy would be unthinkable if special care of the body and even of its symmetry and beauty had not been at the heart of it. Degenerates have no high culture, they are not creatively elevated in their thoughts and in their actions.

architecture, as Goethe said, is frozen music; and symmetry is rhythm standing still.

Imagine yourself wealthy and healthy, but getting death threats from an enemy. Or you’re successful—your pay so hefty, but have drug addict in the family. As no symphony without harmony, no true happiness without symmetry. Harmony is the soul of the earth; discord is the sound of the devil’s mirth.

The moment you treat math as an abstraction, as unreal, as manmade, as a branch of logic, as a technical game, as a bunch of axioms, as some mere formalism, you are lost. Math, ontologically, is energy, and the study of math is the study of the existence, relations, interactions and symmetries of energy. That’s exactly why math can replace science wholesale. Anyone who approaches math as anything other than noumenal, ontological energy – energy in itself – will never get anywhere with relating math to reality.

Earth, air, fire, and water," he began. "The ancient Greek philosopher Empedocles says that these four elements are the roots of everything." Here was the garden he inherited from Leah. Celia, who mostly tended it, called it her sculpture in four dimensions, the fourth being time. Perhaps all sculpture changed over time, with decay and dissolution setting in, rust and chipping and breakage. But marble or bronze evolved so slowly, and their changes were unintended, while the garden was always in visible flux, each morning a new unfolding. Celia always said that the flower beds were a progression of looping actions: each plant opening, blooming, fading, setting seed, drooping, falling; and each seed rooting, sprouting, budding, blooming. And the seasons, the moons and days, the pendulum of darkness and light, the beat of the cardinal's song. Was the earth, then, our real timepiece? Stop, Pindar. Pay attention. "But Empedocles also said that our spirits have successive lives, born sometimes as the fair-tressed laurel trees, sometimes as lions who live in the golden grass...." A shifting of the light through the trees made Pindar notice the Queen Anne's lace in its brass vase. Constellations of tiny white stars swirled in a galactic umbrella the size of his hand- who was above? Who below? Beside their lacy flaring explosives symmetry, the black-eyed Susans gazed at him with their fierce yellow. Wide-open, with none of the hidden turns and caverns of the lilies whose trumpets would be deep enough to incubate in, or at least hide one's thoughts in, though their scent would be too strong for the dinner table.

The PSR is reflected in points traveling in complex-numbered Euler circles where no point is privileged over any other. From this motion, we get sine and cosine waves, even and odd functions, symmetry and antisymmetry, orthogonality and non-orthogonality, phase, straight-line radii, right-angled triangles, Pythagoras’ theorem, the speed of mathematics (c), π, e, i, Fourier mathematics … and from all of that we get the whole of mathematics (eternal, necessary and mental; Being), and thus the whole of science (temporal, contingent and material; Becoming). And that is the whole universe explained. Nothing else is required. The PSR gives us mathematics, mathematics gives us science, and that’s all we need for the universe: science with a mathematical and rational core rather than with a material and observable core. What could be more rational and logical?

In the case of Newtonian physics, velocity boosts—transformations where all bodies are increased in speed by the same amount, in the same direction—are, provably, symmetries. And so Galileo is right: velocity boosts are undetectable in Newtonian mechanics. The postulate that velocity boosts are symmetries is called the principle of relativity. In popular culture it is of course associated with Albert Einstein, but the basic idea is hundreds of years older. And it creates a potentially severe problem for Newton’s physics: it tells us that, contra Newton’s suggestion, it is in principle impossible, according to physics itself, to detect whether or not something is moving with respect to the rest frame.