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Joe Bauman
The spiral galaxy M101, photographed in Tooele County, Utah, June 28, 2017.

Editor's note: A version of this was previously published on the author's website.

The first time I read "Walden" all the way through, I thought Henry David Thoreau was stretching a comparison beyond its breaking point. In the chapter "Spring," he writes, with quotations chosen from two separated paragraphs:

"Few phenomena gave me more delight than to observe the forms which thawing sand and clay assume in flowing down the sides of a deep cut on the railroad through which I passed on my way to the village. … Innumerable little streams overlap and interlace with one another, exhibiting a sort of hybrid product, which obeys half way the law of currents, and half way that of vegetation."

Cory Bauman
Nature's geometry is seen in a hibiscus flower.

But the more I learn about the underlying structures of the universe, the more I agree with Thoreau. To start with geometry alone, we find spirals, spheres, ovals and other geometric patterns, even straight lines, underpinning much of the cosmos. For the least obvious of these, straight lines, consider the path covered by light from a supernova blast, assuming it's not bent by a vastly massive object like a black hole or a galaxy cluster. From the instant of that blinding, searing explosion, light travels outward in a sphere that expands by 186,000 miles every second. The bright point that an astronomer sees is made evident by light that has traveled, by wave and particle, in a straight line for possibly many millions of years.

Blind happenstance isn't responsible for these phenomena. Photons from the explosion don't just waft around every which way willy-nilly, eventually winding up in your telescope. An underlying law directs them to head in a straight line to where you'll happen to be millions of years later while its kin go forth in their straight lines, out in every direction, the energy scorching a nearby planet here, lighting up a dusty nebula there, astonishing alien civilizations over yonder.

Spirals dominate hurricane systems. For a good example of a spiral, watch your kitchen sink drain water. Sunflower seeds form spirals in the flower's centers; pine cones scales make spiral patterns.

NASA asserts that more than two-thirds of all galaxies, the Milky Way included, are spirals. Others may have been deformed by collisions, becoming gigantic elliptical galaxies or assuming other odd shapes like rings.

The earliest galaxies were clumps of stars, which merged with other clumps and formed large galaxies. "In particular, the formation of spiral galaxies is thought to be a complex process in which the stellar halo, bulge and disks are formed at different times and through different mechanisms," according to Swinburne University in Melbourne, Australia.

"Typical spiral galaxies like the Milky Way are usually made up of three principal visible components," say experts with NASA's Hubble Space Telescope. These are "the disk where the spiral arms and most of the gas and dust is concentrated; the halo, a rough and sparse sphere around the disk that contains little gas, dust or star formation; and the central bulge at the heart of the disk, which is formed by a large concentration of ancient stars surrounding the Galactic Center."

Joe Bauman
In one of the 60-second raw sub-exposures made for an image of spiral galaxy M101 (and not incorporated into it for an obvious reason), a meteor streaks through most of the frame. Here is an example of a spiral and a straight line, both natural geometric forms, in the same picture.

The Milky Way's central bulge is dominated by old stars that more than 7 billion years, but some younger examples are present too, believed to have evolved within the bulge. As the Australian site says, the most striking feature of spiral galaxies are the two or more arms that sweep out, either from the center or from the ends of a bar formation across the middle. The Swinburne astronomers believe the arms must not be ancient and permanent or they would have wound tighter and tighter until they merged. "It is now thought that spiral arms arise due to the passage of a density wave around a spiral galaxy." Alternatively, Swinburne's astronomers add, maybe spiral arms are stretched into existence when star-forming areas are pulled out by the effects of the galaxy's "differential rotation" (parts of the galaxy rotating at different speeds).

In 1609, the German scientist Johannes Kepler published the first two of his three laws of planetary motion. The first was that planetary orbits are ellipses, not circular. The second holds that an imaginary line between a planet and the sun will sweep out equal areas in equal times.

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Not to intrude into other physical laws that are expressed by mathematics — like those governing gravity, magnetic attraction, acceleration, electricity and others — these are a few examples of geometry in nature. The laws aren't accidents. They are part of the fabric of the universe.

Writing of the leaf-shapes taken by thawing sand and clay in the railroad cut, Thoreau adds, "No wonder that the earth expresses itself outwardly in leaves, it so labors with the idea inwardly. The atoms have already learned this law, and are pregnant with it."