The Man Who Shaved the Universe

 kw: book reviews, nonfiction, science, astronomy, philosophy of science

I was a developer of scientific software for forty years. One bit of my "Coder's Credo" is, "A complex system that works began as a simple system that works." In practical terms, this meant that I had to first "get the science working", which was usually simple, at least conceptually. The complications that had to be added all derived from the user interface (making the software usable for humans) and the data interface (coupling it to the database or knowledge base). I built my career on a minimalist approach: Add new stuff only when there is a clear advantage.

Millennia ago, the Universe seemed simple compared to the Earth. In the night sky, stars were thought of as distant lamps stuck to a "firmament". The Sun, Moon, and five rather bright "wanderers" (in Greek, πλανόδιοι, which became "planets") were a complication that most folks ignored. But certain curious ones began to theorize; they wanted to figure out how the sky worked.

Fast-forward to a mere 21-22 centuries ago. The prevailing theory of the sky, at least in Europe and north Africa, was a nest of concentric, "crystalline" spheres. The outer sphere held the "fixed stars", and the seven wanderers were each ensconced in its own sphere. Over time, observations of the motions of these "planets" showed something odd: they didn't all march across the face of the "fixed stars" at a steady rate, and some looped back on themselves. Also, the Moon's apparent size changed a little. By about 150 AD, a system of epicycles attached to the spheres had been developed to better model the movements of the planets, including the Moon and Sun.

This illustration from an Arabic document of the 1300's shows the epicycles needed to model the motion of Mercury, shown at four times during a particular year. This image is from Alamy (a commercial site), where its epigraph says,

"Ibn al-Shatir's model for the appearances of Mercury, showing the multiplication of epicycles using the Tusi couple, thus eliminating the Ptolemaic eccentrics and equant."

This shows that Arabian astronomers went beyond Ptolemy. At its height in the first half millennium of the Christian era, about 80 epicycles were needed for a "good" model, and the notion of "crystalline" spheres was politely ignored. Here, I count six epicycles needed to produce motions for Mercury that matched astronomical observations.

We all know that Copernicus tried to simplify the Solar system by recognizing the Sun as its center. However, he also needed epicycles to model planetary motions accurately, because he thought all orbits were perfect circles centered on the Sun…or, at least, the rotational center of a cluster of circular epicycles followed a circle about the Sun.

Leaving behind circles in favor of ellipses, Kepler, using Tycho Brahe's data for positions, produced a greatly simplified model of the Solar system, such as that seen here (this one leaves out Saturn, at twice the distance as Jupiter).

This particular image also shows the orbits of several major asteroids and three comets. Comet Halley's ellipse extends to 35 AU, seven times as far as Jupiter. The orbit that just brushes past Jupiter belongs to Comet Kopff, one we never hear of because it is visible only with a telescope at least 4" in diameter.

The older tradition of natural philosophers, exemplified by Ptolemy, resulted in models of natural phenomena with steadily increasing complexity. Something happened about the time that Ibn al-Shatir began writing his astronomical manuals, that began to turn the study of nature from natural philosophy to science as we know it.

Here I turn to a better authority on science history, Johnjoe McFadden. In his book Life is Simple: How Occam's Razor Set Science Free and Shapes the Universe, Professor McFadden traces the progressive simplification of science and scientific theories, based on a 14^th Century meme we call Occam's Razor. This is expressed in several ways, as it was by William of Ockham in the early 1300's. I like, "Do not multiply entities beyond necessity." This statement does not disallow complexity, it discourages unneeded complexity. Einstein's version is, "Make things as simple as needed, but no simpler," which looks at the matter from the other end.

Either way one looks at it, the principle known as Occam's Razor slices away unnecessary encrustations from scientific models. Before reading Life is Simple, that's about all I knew of the matter. I didn't even know that William, born in Ockham, lived in the early 1300's, about 700 years ago. This was just before the era of Geoffrey Chaucer (Canterbury Tales), who was born just a few years before William of Ockham died. The "English" of the day was Middle English, when the use of "thee" and "thou" and "doest" for "does", still found in the King James Bible, were at their height. But William wrote in Latin, which requires just a tad more translation than Middle English.

Neither did I know how the Razor grew and spread among the literate people of Europe and the Middle East. By the time of Kepler, 300 years later, and Newton, a generation later, simplification of theories was accepted throughout the world of the Enlightenment. The thread of the Razor through history is followed in all its excursions, leading to its dominance today.

It has become the ambition of many scientists to determine a Theory of Everything, which can be expressed on a T-shirt as a single equation that unifies not just the Weak and Strong and Electromagnetic forces, but also Gravity and Quantum Mechanics. Such a theory would not be a theory that "explains" everything, for a corollary to the Razor is, "That which explains everything explains nothing." The prolific clusters of epicycles in cosmology are an example. The more cycles you add, to account for refinements in astronomical observations, the less you actually know about them. The laws of orbital areas derived by Kepler, and the three laws of motion of Newton, as modified by Einstein, allow us to calculate exactly where each planet, moon, asteroid, comet, and artificial satellite is going, for decades or centuries into the future, and where they were at any time in the past. The calculations are tedious, but not difficult, and modern computing machinery shoulders the load of the tedious part.

Sadly, many (most?) modern theorists have gotten bogged down in String Theory. Somehow, these mathematical models require calculations in at least 10 or 11 dimensions (some versions, as many as 26 dimensions). None of the string theories so far proffered can be tested experimentally, and the number of possible string theories is a gigantic number with about 500 digits. And we thought 80 epicycles are too many! At the moment, this is a lot more "hair" than the Razor can manage to tame.

I was quite enthralled by the stories, the history, of how modern science developed once it was freed from the cosmogony of Aristotle and Ptolemy, which somehow became the foundation of Roman Catholic cosmology (for the curious: cosmogony is about "what is there", and cosmology is about "how it goes"). In effect, the Razor removed God's hand from the tiller of the Universe, at least so far as science is concerned. William of Ockham was also far ahead of his time in political understanding, which is probably a consequence of his revolutionary understanding of nature: he insisted that rulers' legitimate power came through the consent of everyone. His understanding of natural rights is an embryo of the Bill of Rights in our Constitution.

While I recommend this book for its historical perspective, I have a few quibbles about statements made by the author when he stepped outside his area of expertise, which is molecular genetics. Those who think my objections are TMI can stop here. What follows touches on three items that surprised me the most:

• On p 271, discussing the Planck Law for the spectrum of a heated blackbody, he writes that such bodies "emit light in a narrow band that depends only on the black body's temperature." Not quite. The actual spectrum of a blackbody (note the absence of a space) covers all wavelengths, and the width-at-half-height of the spectrum is about 2.8:1. For example, for a blackbody at a temperature of 7,250K (~12,600°F), the half-height spectrum ranges from 240 nm to 680 nm. The peak of the spectrum for this temperature is at 400 nm. The location of peak radiation depends on temperature, and the relative shape of the spectrum follows. An analogy about whacking a piano and somehow getting only a single note is quite bogus. The range of "notes" so emitted is strongest over more than an octave (18 half-tones), and there is some resonance from every string on the "piano".
• On p 293, about symmetry, "…time symmetry implies energy conservation, translational symmetry implies conservation of momentum, and Newton's third law, that every action has an equal and opposite reaction, is a consequence of rotational symmetry." About the last phrase: Where did that come from? Newton's third law is equivalent to time symmetry, and has nothing specific to do with rotation.
• On p 327, regarding the Bayesian likelihood of a particular combination of numbers being thrown in ten tosses of a 60-sided die, he states correctly that this is the tenth power of 60, or 60¹⁰, but then he evaluates it as 600 million to one. Hardly! 60¹⁰ = 6.05 x 10¹⁷, or 600 million times about a billion, or 600 quadrillion. Really! Don't any of his editors and readers know enough math to punch this out on a calculator?

That's enough of that. I can't blame him too much. Although I strive to be a generalist, I admit I know woefully little about molecular genetics, at least compared to Prof. McFadden. So, if I ever write a book that happens to wander into that arena, I'll see if he's willing to give it a read, and after he stops laughing, make the odd correction here or there.