The development of cosmology and the scientific method

This was originally five separate Facebook posts. It's been republished by the Astronomical Society of Victoria and in a couple of other places as well. Although I think it was originally a pile of notes that got saved after my university course in History and Philosophy of Science from the mid 1980s.

1: Introduction

4 October 2019

What happens when objective observation comes up against hubris? Hubris wins.

At first.

I'm going to spin out a yarn. It's quite a good one, about how humans figured out how the planets move through the sky. It also shows a lot about how humans began asking the big questions: of "what?" and more importantly "why?"

That humans ask themselves these questions about pretty much everything is, I think, the thing that sets us apart. That these questions are unanswerable doesn't matter - it's a goal that drives our understanding, not only of astronomy, but in fields as diverse as psychology and economics.

But it's also a story about what happens when people see things that don't agree with their understanding of the world.

The story is fairly long, so I've split it into five parts.

The first part starts with how the ancient Greeks thought the heavens worked. I'll talk about Aristotle and Ptolemy and the crystal spheres that circled the stationary Earth, each one moving in graceful harmony.

The second part discusses what happened when the planets didn't move as predicted. The astronomers tried harder and harder to save their cosmology, to the point of developing whole new branches of mathematics.

In the third part I'll talk about the revolutionary, Copernicus. I'll include Tycho and Galileo, two of the new breed of astronomers who valued observation over beliefs, and who helped finally bring down Ptolemy's model of the solar system.

The second-last part starts with the stupid and horrible death of Tycho. But out of this, the mathematician Kepler finally got the data he needed. His critical discovery about Mars opened the scientific floodgates.

Finally, I'll talk about Newton, one of the crankiest nut-jobs in history. He also pushed the theory further, inventing more mathematics as he went. Newton enabled the likes of Einstein and Hawking to continue the work.

The wonder of the heavens is truly amazing; but so too is the fact that as a result of gazing at the sky, our civilization has developed and been transformed. Amazing, too, that the process will continue. One or more present-day Australian kids might take their places on the shoulders of these giants.

2: Ancient Greek cosmology

7 October 2019

The ancient Greek society and culture was based on logic and reason - that's the impression they gave. Philosophers and intellectuals were influential; they wrote the history that tells us they were.

The Greeks used astronomy to try to understand humans' place in the cosmos, and, predictably, they placed the Earth at the centre of the universe.

Probably the most influential philosopher, Aristotle, established as a principle that the Earth was surrounded by perfect immutable heavens and that these heavens could not be influenced by the Earth. From there, simple observation indicated that the Sun and the Moon rotated around the Earth.

Using this cosmology, the astronomer Hipparchus accurately predicted a solar eclipse. Surely this achievement confirmed the Greeks understanding of cosmology.

But what of the other planets? These star-like creatures wandered the ecliptic in ways similar to the Sun and the Moon. These planets, reasoned the astronomers, also rotated on concentric spheres, with the Earth at the centre of all.

Closest to the Earth was the Moon. Beyond that the spheres spread, their order determined by their orbital periods - the time the planet appeared to take to get back to its starting point. First was Mercury and Venus. Then came the Sun, and after that, the spheres of Mars, Jupiter and Saturn.

Outside Saturn was one final sphere, that of the fixed stars, immutable, unreachable, beyond earthly influence, the reciprocal of earthliness, the pinnacle of perfection.

After that: the "unmoved mover", the object immovable producing forces irresistible. The realm of the gods.

It was a beautiful cosmology, geometric, harmonious and symmetrical, its perfection reinforcing hubris. A true paradigm, a father theory, guiding other theories.

But the planets were doing things that the astronomers just couldn't explain.

What then happened to the paradigm?

3: When planets don't move as predicted

11 October 2019

The Ptolemaic cosmology, with its crystal spheres within crystal spheres rotating around the Earth, was a beautiful idea, harmonious, poetic, geometric and geocentric.

But it was flawed. And what do normal humans do with a faulty paradigm? Tear it down or prop it up?

Unexpected behaviour

The planets moved through the night sky - on crystalline spheres, according to the astronomers. They just didn’t behave like they were.

For most of the time, Mars and planets further out move eastward against the stars. However, occasionally, they pause and drift back westward, before resuming their eastward progress. While moving backwards, they also appear brighter. The inner planets, Mercury and Venus, spend around half their time moving backwards, oscillating from morning to evening objects. Astronomers call these backward steps "retrograde motion".

You can look up charts of retrograde motion for yourself. As at September 2019 none of the visible planets are in retrograde. During 2020, Jupiter and Saturn will retrograde together.

Were the spheres changing direction? The idea of the apparatus grinding to a halt, backing up and starting again was an affront to the perfection of the idea. What was going on?

Adherents to the Ptolemaic cosmology (with the notable exception of Aristarchus) couldn’t bear the idea of abandoning such a beautiful idea.

So they didn’t.


They developed the epicycle. This was an offset, a second sphere. The planet was on the epicycle, and the centre of the epicycle was fixed on the principal sphere.

Epicycles explained retrograde motion and changing brightness. But with better observations, epicycles couldn’t explain the new errors. Then again, mathematics was becoming more sophisticated, so astronomers could add more epicycles to the crystal spheres.

And the wrestling went on for centuries.

4: The Copernican revolution

16 October

In the battle between Ptolemaic cosmology and physical observation, Ptolemy wasn’t giving up without a fight. In fact, adding multiple epicycles to circular orbits can very nearly describe the planets' true orbits.

Copernicus the revolutionary

Then Nicholaus Copernicus upended it all by putting the sun at the centre of the solar system. Retrograde motion was an illusion caused by the Earth orbiting with other planets.

Nicholaus Copernicus

The concept that the Earth was just another planet was anathema to nearly everyone. Where were the spheres? Were we on a sphere? Where is it? If there aren’t any spheres, how do the planets know where to go?

One patch that was proposed was that of aether, which was a mystical current that supported the planets. The aether guided the planets around allowing moons to cross the orbits of their planets without crashing through any crystal.

But the Copernican Revolution was underway, and once shaken, the Ptolemaic cosmology began to crumble. New precision observations began to guide astronomers' thinking.

Tycho the ammunition maker

Tycho Brahe

The Great Dane, Tycho Brahe, never had a telescope, but built massive machines for measuring the position of stars and planets. His accuracy was, on average, around five times better than anything previous. Mars was a puzzle because it seemed to change speed at various times in its journey.

Tycho's model was geocentric with the planets still orbiting the Sun, which in turn orbited the Earth. Mathematically it was the same as the Copernican model without the controversy. Tycho hedged.

At about the same time, Galileo saw planets with his new telescopes. His observation that Jupiter had moons that orbited the planet was the final falsification of the crystal spheres.

More critically, he recorded the phases of Venus and discovered that they appeared in a way that none of the Ptolemaic arrangements could explain. It's a fantastic story, but too long for here - perhaps another time.

All this was as destructive to Ptolemaic cosmology as Jupiter's moons crashing through crystal spheres.

5: Tycho and Kepler: hubris and genius

21 October

Ptolemy was doomed.

New and more accurate findings were being made by astronomers who had the equipment to make the observations and the will to understand what they meant.

Copernicus had shaken the Ptolemaic cosmology by placing the Sun at the centre of the solar system. Galileo had seen planets, their phases and their moons and explained that what he saw was inconsistent with the crystal spheres.

But these scientists were not the heroes of this story. They rode on the shoulders of giants who had gone before.

Neither was Tycho a hero.

Tycho had accurately plotted the motion of Mars and documented its deviation from predicted course and strange changes in velocity. He also measured the supernova of 1572 and realised it was further away than the moon (disproving the immutability of the heavens). His observations of the comet of 1577 showed that it shattered the crystal spheres.

But Tycho was jealous. He knew that his data was of ultimate value and would not allow others to use it.

Kepler and the death of Tycho

Tycho's assistant, the mathematician Johannes Kepler, pleaded with Tycho to try to make sense of the observations of Mars. Tycho consistently refused.

Johannes Kepler

Ultimately, Tycho was a victim of hubris. At a banquet in 1601 he felt bound by protocol not to go to the toilet, and ruptured his bladder. Kepler finally received the data, with Tycho's dying wish not to have lived in vain.

Equal areas in equal time

Kepler slaved over the data. He found the area swept out by Mars was constant over time - explaining its velocity. The orbit was an ellipse with the Sun at one focus. These were the first of his three laws of planetary motion.

Kepler is only the penultimate hero of this story. He proved the value of data, relieved science of the crutch of epicycles and explained Mars' motion. But he'd needed Tycho's data and the iconoclasticism of Copernicus and Galileo.

But there was still a detail Kepler hadn't found. He knew that the attraction between bodies decreased with distance, but not how much.

6: Newton's shoulders

25 October 2019

Newton was, by all accounts, a nutter. Paranoid about others' motives, picking arguments where no argument was necessary, vindictive and over-sensitive to criticism, he must have been a difficult man to know.

Isaac Newton

The short name for Newton's magnum opus is the "Principia". This was published later in his life, and incorporated a lot of his work, so the order in which he developed it is not really clear.

Following a written conversation with Robert Hooke, and then a comet in 1681, Newton became intrigued with Kepler's laws of planetary motion. Kepler knew that the attraction between bodies decreases with distance between them. Newton found that the attraction decreased in proportion to the square of that distance.

Newton developed this into his "law of universal gravitation", which states that the attraction between two bodies is proportional to the product of their masses divided by the square of the distance between them. Finally, Tycho had not lived in vain.

Standing on the shoulders of giants such as Aristarchus, Copernicus, Galileo, Tycho and Kepler, Newton was able to see further, and developed calculus and three laws of motion. He furrows brows of students even today.

While Newton wasn’t the first person to have used the analogy of standing on the shoulders of giants, he certainly used it in a letter to what we might call his "frenemy" Robert Hooke. Here's the relevant fragment.

The concept of gravity was the final piece of the puzzle of the motion of the planets. Newton was the ultimate hero of the story.

Shoulder standers

But the story continues. Einstein stood on Newton's shoulders. Hawking stood on Einstein’s shoulders.

As long as there are iconoclasts willing to hold theories to account, as long as we encourage curious minds to foster and develop new ones, and as long as there are empirical scientists to gather data, there should be no shortage of giants. Perhaps one of our young Australian astronomers will be next to stand on a shoulder and take their place in history.

Further reading:

Thomas Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought

Arthur Koestler, The Sleepwalkers: A History Of Man's Changing Vision Of The Universe