The idle ramblings of a Jack of some trades, Master of none

[We continue the paraphrased transcript of Allan Chapman’s Gods in the Sky, episode 2, from Channel 4]

The Ancient Greeks were by far the finest astronomers of the ancient world. This was because they were free. And because they were sailors. To see why, we have to understand the country’s geography. It is a mixture of islands, bays, inlets and headlands. It’s a country of boats, of sailors. Think of Jason and the Argonauts, the Odyssean voyages. The way the Greeks tackled the sea from the earliest times made them a free people.

As well as being farmers, the Greeks were merchants who enjoyed the limitless independence of the seas, an independence that comes from trade. It is here in Greece that one finds the first real concept of Law, a set of rational rules governing society and constructed by its own people who formed a democracy. This Law guaranteed freedom and the rights of the individual. Here Law was used not as a tool of oppression, but as a tool of freedom. In the courts, people could guarantee their own rights and see to justice. The Greeks had the right to be politically incorrect, to follow their own argument, and if they said something that someone else disagreed with, they had the right to argue the others down. They couldn’t be muzzled. That is one of the greatest contributions of the Greeks to the modern world.

The Greeks were free to disagree about the structure of the heavens; their disagreements were to be resolved not by reference to sacred texts, but by disputation and reasoned analysis. Greek astronomy was dominated not by priests but by philosophers, whose names resound through the ages. Anaximander argued, for example, that the universe was not created by a god at all, but was eternal and infinite, and that our own world was one among many. Aristarchus suggested long before Copernicus that the Earth moved around the Sun, and not the other way.

The sea not only gave the Greeks the freedom to think but also a freedom to think in a completely different way. Because they were a maritime people, they were the first in the ancient world to realise that the Earth was round, a sphere. It was Pythagoras in the fifth century BC who first put forward a systematic argument for why our planet was shaped like a ball. After all, if you were sailing away from land in a ship, you noticed that the beach vanished from sight first, then the headland, and finally everything dips below the horizon. But if you climb to the top of the mast, you can see the beach vanish again, and then the headland, and everything else disappeared again. You realised that you were sailing around a great curve.

So it wasn’t Columbus who discovered that the Earth was round: it was ancient Greek traders lugging their olive oil around the Aegean. And as they set off on their voyages, they needed to know where they were going, how to get there, and how to get back. And so it was that in the sixth century BC, the philosopher Anaximander produced the world’s first ever map. To construct this map, the Greeks needed to develop a set of intellectual tools with which to compute distance and direction. So a new science was born to map the world, but which could be used as well to chart the heavens. The Greeks called it Geometry.

The power of Greek Geometry is best demonstrated by Pythagoras. It was he who realised that there are eternal properties in shapes. If you take the radius of a circle, you will find that it will always divide the circumference exactly six times. And if you take the angles of a triangle, you will find that they always add up to 180 degrees, which happens to be as well the number of degrees in a semicircle. Now these are absolute truths, not subject to opinion or fiat. You can’t disagree with them; they are as perfect as laws can ever be, and that recognition was one of the supreme achievements of the human mind.

The sea-faring Greeks already knew with remarkable accuracy the distances between the great cities of the ancient world. With their knowledge of angles and circles, they were able to develop their knowledge in an extraordinary way. An example: Eratosthenes, a mathematician of the 3rd century, made a fascinating discovery when looking into a well. In one particular place in North Africa, he noted that the sun shone right down to the bottom of the well. At the same time, in Alexandria, the sun cast a shadow. Since it was the same sun that shone on both places, there was no reason not to use the angle between the two places to compute the size of the Earth. If you measured the distance between the two spots – one where there was a shadow and one there wasn’t – you realised that the line from the well and the line from the shadow both coincide at the centre of the earth; by knowing that distance as a fraction of a circle, you could calculate the diameter and then the circumference of the rest of the circle, and thereby obtain the exact size of our planet.

Geometry means to measure earth, but the Greeks soon realised that to make maps and chart the seas, they also needed to measure the heavens… We know very little about the astronomers of ancient Greece, except their names and the discoveries that are forever attached to those names. One of the greatest of these astronomers was a man from Rhodes – Hipparchus. He developed the modern constellations that we use today. Aries the Ram; Taurus the Bull; Gemini the Twins… He related particular stars to particular geometric points in the sky to create a science of astronomic measurement. He discovered that astronomical measurements taken centuries ago were not accurate today. The reason 005 tricutumis the Precession of the Equinoxes, which makes the position of the so-called fixed stars move ever so slightly each year, the result, we know now, of a small wobble in the rotation of the Earth. Hipparchus gave us an astonishingly accurate value for the length of the year: he said it was 365 days and 1/300th part of a day long. (He was wrong – it is actually 365 days and 1/128th part of a day long. But how astonishingly close!) He effected this computation from detailed perusal of old Babylonian records, and from study of the movement of the Sun among the stars.

But how did Hipparchus make his observations? Although the Greeks had no telescopes, they were able to make remarkably detailed observations of the movement of astronomical bodies by using a number of ingenious instruments. To make measurements of angles, they used three rulers that were hinged together and worked like a rifle-sight. 006 armillaryIt was called a tricutum, meaning ‘three rods.’ They wouldn’t look at the sun directly, but would let its rays shine through the top sight into the bottom sight, moving the lower rod till the sun’s rays were in exact alignment through the sights. They could then work out basic facts about the year: when was the longest day or the shortest day.

Measurements taken with instruments such as this could be used to chart the movements of heavenly bodies. Another ingenious device was an armillary sphere. This consisted of a spherical (!) Earth placed within a number of spheres of heaven, and a north and a south polar axis. And from wherever you were on the Earth’s surface, you could tilt the instrument such that it represented your local latitude. The outermost ring, called a meridian ring, would be ninety degrees to the horizon; you could then track particular astronomical bodies rising in the east, ascend to their greatest height in the south, and set in the west. You thus had the basic coordinates for the universe, and you can model the rotations of the heavens.

007 hipparchus earth moon dist Indeed, Hipparchus managed to calculate the distance from the Earth to the Moon. He did this by bringing together a number of observations of the shadows cast during eclipses at different parts of the world. He realised that there were times when the Sun, the Moon, and the Earth were all lined up. If you stood in the centre of the shadow, the Sun would be completely obscured by the moon. Now in 129 BC, if you were on the Hellespont near Athens, you would be in total darkness as you were in the middle of the shadow. Hipparchus found out that in Alexandria, people were only seeing a 4/5ths partial eclipse. Of course, Hipparchus knew the distance between Athens and Alexandria. He also knew that the moon orbited the earth in 28 days, and that the earth cast a shadow into space. He knew that at certain times the moon moved through this shadow, causing a lunar eclipse, and that this eclipse takes about six hours. Finally, thanks to Eratosthenes, Hipparchus also knew the radius of the earth. Using geometry, he was able to calculate that the moon was 67-and-a-third earth radii from our world. This is amazingly accurate, and marked the first time that geometry was used to measure distances between heavenly bodies.

[To be continued.]


Post a Comment