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More About Symmetry, Or Lack Thereof - by John Prytz

Mathematics is the foundation of all of the sciences, and with some exceptions tends to reflect symmetrical operations and relationships. Easy examples are 1 + 2 = 3; 2 + 1 = 3; 3 = 2 + 1; 3 = 1 + 2. However, mathematics is still an intellectual and abstract field that exists within the realm of biological (perhaps artificial) intelligence. It’s not an obvious part of nature.


Physics & Chemistry: On the micro scale, there is indeed a great deal of symmetry. An electron is symmetrical with its antimatter counterpart, the positron. It’s like the yin and yang. The electric charge of a proton matches that of an electron. Many molecules are symmetrical, like methane, though the water molecule isn’t. Also, physics and chemistry tend to have reversible (symmetric) actions. You can combine hydrogen and oxygen to form water; you can turn water into hydrogen and oxygen. Energy can turn into matter; matter can turn into energy.


There are obvious cases at the macro level where there is symmetry – for every action there’s and equal and opposite reaction. But, as a general rule however, the transition from the micro to the macro tends to also be a transition away from symmetry to the asymmetrical.


Space: Space appears symmetrical. Up balances down; left balances right; back balances front; north vs. south; east vs. west.


Time: There is in physics this phenomena that time ‘moves’ or flows in one direction – from the past to the future, although that’s only apparent on the macro scale. Any one fundamental particle looks and acts the same whether filmed from past to future, or run in reverse, from the future to the past. However, when grouped together, it would be odd for thousands of particles to start from a position of uniform distribution then all move such as to clump together. That is to say, you won’t find a box full of air where all the air is clustered or huddled together in one of the eight corners. 


Energy: Energy is like time – left alone it flows overall in just one direction – from high concentration to low concentration. That is to say, your cup of tea, left standing, doesn’t further warm up left to natural processes or forces, but rather cools down.


Matter: Whether matter exists in a gaseous, liquid or solid state, you’ll never find absolute symmetry. One cubic centimetre of air wouldn’t be absolutely symmetrical with respect to the mixture. Even if it were just a cubic centimetre of say oxygen, the density of the molecules will vary from location to location. The same applies to say sea water, even pure distilled water. And as for solids, well we all know any diamond has some flaws or imperfections, even the best of them. Snowflakes on the surface look like perfect six-sided symmetry, but up-close-and-personal, there again will be slight flaws.


The Earth Sciences: Geology, Oceanography and Meteorology don’t tend to be associated very much with symmetry. Some rock crystals will be symmetric, but more likely as not with flaws that spoil the perfection as noted above. I suppose if you drop a rock into the ocean, the ripples will spread out in a symmetrical fashion, but quickly become distorted due to differing local factors operating at different points. I guess water evaporating is sort of symmetrical with rain falling, but that’s a bit of a stretch.


The Universe: Our Universe is asymmetric with respect to antimatter vs. matter. The Universe is 99 and 44/100’s % pure matter – probably more. This is strange since theory predicts that there should be equal amounts of matter and antimatter at large. The Alpha and the Omega of the Universe isn’t symmetrical either. The Universe started with a Big Bang, yet will expand forever and end in a Heat Death. A Head Death is when the overall temperature of the entire cosmos is uniform. In contrast, our Universe would have exhibited far greater symmetry had the Alpha been the Big Bang, and the Omega the Big Crunch – a cyclic universe.


Most of the objects within the Universe aren’t symmetrical. You have the irregular galaxies, but even normal spiral or elliptical galaxies aren’t symmetrical down to the last nitty-gritty detail. Stars aren’t perfect little spheres, but seethe with solar activity which distorts perfect symmetry. On the other hand, a Black Hole should exhibit near perfect symmetry, except, like stars, they too can seethe with activity and give off energy in the form of Hawking radiation which won’t be uniform at the quantum level.


The Solar System: There’s certainly no symmetry with respect to the bodies that orbit Mr. Sun either with respect to spacing between the planets, or the size of the planets. And you get one-off bits like the asteroid belt (of rocky stuff), the Oort cloud (of cometary stuff), and the Kuiper Belt (more icy stuff in the main). Asteroids and all the smaller bodies tend not to have enough gravity to pull them into a uniform spherical shape and so have irregular shapes.


Planet Earth: Well for starters, there’s this tilt to the Earth’s axis. Then too the division between land masses and oceans isn’t symmetrical, and never really has been due to plate tectonics. The Earth isn’t even a perfect sphere due to its rotation.


Life: Terrestrial biology is composed of biochemicals, complex molecules usually composed of various arrangements of carbon, hydrogen, oxygen and nitrogen, which can have a right or left handedness to them. Our biology, or rather biochemistry, is in the main left-handed. 


Humans: Humans have no top-bottom symmetry; nor front-back symmetry; only left-right symmetry, and that is only superficial. The right and left sides of our outer shell aren’t quite identical, as in, for example, the way we part our hair. The left and right side of our faces are ever so slightly different as you can see if one matches two right sides together and two left sides together, then view both at the same time. They don’t look absolutely identical. Of course on the inner anatomical level you are well aware there’s no real left-right symmetry, since our heart leans to the left; our stomach and liver are on opposite sides, etc. And the left and right sides of our brains aren’t apparently the same with respect to the bits and pieces they hold sway over.


Human Technology: Relatively few manufactured goods are totally symmetrical. Certainly not our automobiles which have left-right symmetry, except for the steering wheel and location of the gas cap. Your house may look symmetrical from the outside, but the interior layout most certainly isn’t (although a typical dog house probably has near perfect left-right symmetry). A dice is apparently symmetrical left-right, front-back, and top-bottom, but the faces have different patterns. A bowling ball has those finger holes to offset otherwise perfect symmetry. However, even when things are totally symmetrical, say ball bearings (though on a micro scale there would be irregularities – peaks and troughs), that’s of little interest to the physicist or other scientists who look for symmetry in the natural world.


Further reading:


Gleiser, Marcelo; Imperfect Creation: Cosmos, Life and Nature’s Hidden Code; Black, Inc.; Melbourne, Victoria; 2010:

Science librarian; retired.

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