Essays – Cosmology and the History of Wonder

Source: G Kalyakin. Wikimedia Commons. — Source: G Kalyakin. Wikimedia Commons

And some things that should not have been forgotten were lost. History became legend. Legend became myth. And for two and a half thousand years, the ring passed out of all knowledge. — JRR Tolkien, Lord of the Rings

The figure above is a sequence of images of a total lunar eclipse. Note the shape of the Earth’s shadow.

How do we measure distances in everyday life?

There are a variety of ways we judge distances as we navigate the world. Here is a short list (from Wikipedia):

Parallax (binocular vision)
Motion parallax (following moving objects across our field of view)
Depth from motion (change in apparent size)
Perspective (using knowledge of shapes)
Relative size (compared to a known object)
Luminance contrast (distant things appear hazy)
Occulomotor cues (you perceive how much your eye needs to distort to focus on the object)
Occlusion (near things occlude far things)
Texture gradients (details are discerned if close)

None of these will work for measuring the distances to astronomical objects, except for parallax, but even then only by using artificial means. The naked eye cannot judge distances to objects like the Moon or Sun.

How did Aristarchus estimate the distance to the Moon?

By measuring the time it took for a moon to cross the center of the Earth’s shadow during an eclipse. (We’ll use round numbers below for simplicity.)

The longest eclipses take about t = 3 hours = 1/8 day.
Assume the Earth’s shadow is a cylinder with the same diameter as the Earth, d=2 r. (This is a good approximation, if the Sun is much farther away than the Moon. It requires assuming that the Moon shines by reflected light from the Sun.)
The Moon travels around the circumference of its orbit in one month, T = 30 days. Assume the speed along the orbit is constant. Therefore, using ‘speed = distance traveled/time’ we have (2π R)/T = 2r/t.
Solve for R/r = T/(π t) = 30/(3/8) = 80. (Note: I have used π = 3, which in technical mathematical terms is a ‘brutal’ approximation, keeping only the first significant digit.)

This means that the Moon is about 80 Earth radii away from us. The true value is closer to 60, but the order of magnitude is correct.

Naked eye observations of lunar eclipses easily reveal that the Earth’s shadow is curved, not a straight line. Lunar eclipses occur several times a year, so they are fairly common. Why wasn’t it obvious from simple observations like this that Earth was a sphere? Many ancient astronomers, like Aristarchus, understood what they were looking at, and were convinced the Earth was a sphere, but some later cultures did not. Discoveries can be forgotten.

Psychologists and cognitive scientists have found that when a sensory stimulation, an observation, or other piece of evidence, violates our intuition we sometimes don’t see it, or don’t process it. We can memorize a 200 word poem easier than 200 random words. Why? It has something to do with the poem having structures and patterns that help us to understand it (e.g. rhythm, rhyme, as well as imagery, and other aspects that help it to make ‘sense’ to us), where a random set of words does not. Memorizing chess pieces on a board is similar: if the pattern arises from a game, a chess master will do far better than an ordinary mortal at memorization. If the pattern of pieces does not arise from a game, they do no better than anyone else.

We are bombarded all day long with sensory input. If we did not organize this somehow into an internal theory of the world, we would not be able to function. Most of this becomes second nature to us as we grow up, so we stop thinking about it. This internal ‘world theory’ becomes a kind of filter on our experience. It allows us to function and thrive, yet it can also keep us from seeing things that are right in front of us.

One goal of a liberal arts education is to reawaken your sense of newness, to keep you alive to the fact that the way you see the world is not the only ‘right’ way, and to rekindle your sense of wonder so you stay open to new ideas and new ways of doing things.

The ancients were not stupid, or even ignorant in some ways, but they did have an intuition about how the world worked and this could make it difficult to see things right overhead that violated their intuition. This is not uncommon today. Psychologists have a term for this difficulty in integrating new information that runs counter to our intuition: cognitive dissonance. What types of things are right under our nose that we overlook because it doesn’t fit our preconceived notion of how the world works? [1]

Here is one of my favorite literary quotes on this matter:

A pair of wings, a different respiratory system, which enabled us to travel through space, would in no way help us, for if we visited Mars or Venus while keeping the same senses, they would clothe everything we could see in the same aspect as the things of the Earth. The only true voyage, the only bath in the Fountain of Youth, would be not to visit strange lands but to possess other eyes, to see the universe through the eyes of another, of a hundred others, to see the hundred universes that each of them sees…

— Remembrance of things past, by Marcel Proust

The challenge is always to try and see the world anew, to be astonished by it, like a child. The best scientists are often a bit childlike, because they try to preserve this sense of wonder intentionally.

In sum: Aristarchus drew upon evidence that was open and available to everybody. It was above their heads, and available to anybody who was able to see with an open mind.

1] See, for example, “Anomaly and the Emergence of Scientific Discoveries,” Chapter VI of The Structure of Scientific Revolutions by Thomas S. Kuhn. Kuhn describes an experiment by the psychologists Bruner and Postman where test subjects were asked to identify playing cards, having been told they were being tested on how quickly they could correctly identify the card. In fact, some playing cards were anomalous (e.g. a red four of spades, or a black ace of diamonds). Most test subjects did not detect the anomalies, but assigned the cards to one of the familiar — expected — categories. Even when given quite a long time to view the cards, they reported having a sense that something was wrong, but couldn’t articulate what the problem was. Many reported that viewing these anomalous cards was unsettling.

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Einstein won the Nobel Prize for Physics in 1921 for his work on the photoelectric effect, where he first introduced the notion that light was composed of discrete particles he called ‘photons’. However, his Nobel Lecture concerns the Theory of Relativity. By this time the Special Theory had received experimental confirmation, yet apparently not enough for some members of the Prize Committee. The General Theory was considered still more speculative at this time, even though the precession of the perihelion of Mercury was correctly predicted by the theory, and the bending of starlight had been observed by Eddington’s solar eclipse expedition of 1919.

There is a wealth of understatement in the description given in the prize announcement, as summarized on the Nobel Prize website linked above:

“The Nobel Prize in Physics 1921 was awarded to Albert Einstein “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect”.

Albert Einstein received his Nobel Prize one year later, in 1922. During the selection process in 1921, the Nobel Committee for Physics decided that none of the year’s nominations met the criteria as outlined in the will of Alfred Nobel. According to the Nobel Foundation’s statutes, the Nobel Prize can in such a case be reserved until the following year, and this statute was then applied. Albert Einstein therefore received his Nobel Prize for 1921 one year later, in 1922.”

Relativity was still considered a controversial theory in some quarters, even though it had largely been embraced by the leading theoretical physicists. The ‘relativity revolution’ was still underway, and sill incomplete.

A complete bibliography of Einstein’s publications prior to 1922 can be found here. Although many of the titles are in German, it is clear that his early work was on the fundamentals of thermodynamics and statistical physics, and only in 1905 does he begin to publish work on what we now call the Special Theory of Relativity.

For a recent review of tests of the Special and General Theories, see the 2006 article by Clifford Will.