Джон Гриббин – Science: A History in 100 Experiments (страница 5)
That, it seems, is exactly what happened. Archimedes did the experiment (or something very similar) and found that the jeweller had indeed cheated the king. About five centuries after Vitruvius, the story was re-told in a Latin poem ‘
Archimedes’ Principle also explains why a ship made of steel can float. A solid lump of steel displaces a relatively small amount of water, much less than its own weight, and sinks. But if the same amount of steel is spread out in the shape of a boat, or even a simple bowl (like a coracle), a larger volume of water is displaced, weighing more than the weight of the steel, resulting in a large enough upwards force to make the boat float.
The first scientific attempt to measure the size of the Earth was made by a Greek polymath, Eratosthenes of Cyrene (276–194 BC), who was in charge of the Library of Alexandria in the third century BC. He was a contemporary and friend of Archimedes. His experiment involved some observations of his own, made in Alexandria, but combined with evidence from a far away place, the city then known as Syene (now Aswan), which he had never visited.
Eratosthenes learned that each year on the day of the summer solstice, when the Sun is at its highest in the sky, it was exactly overhead at Syene, south of Alexandria. Travellers told how the reflection of the Sun could be seen at the bottom of a deep well in Syene on that day. Even at the summer solstice, the Sun is not directly overhead at Alexandria, because, as Eratosthenes appreciated, the Earth is round. So he made careful measurements of the difference between the angle made by the Sun and the vertical at the time of the solstice, working out that this corresponded to one-fiftieth of a circle, or 7º 12ʹ of arc. Simple geometry told him that this meant that the distance from Alexandria to Syene was one-fiftieth of the circumference of the Earth, assuming (which is not quite true) that Syene lies due south of Alexandria.
The distance from Syene to Alexandria was well known even in Eratosthenes’ day (it is about 800 kilometres in modern units). Egyptian records gave the distance as 5,000 stades, and Eratosthenes checked this by asking camel train drivers how long it took them to make the journey (some sources say he hired a man to pace out the distance; but this may be apocryphal). This gave him a figure of 694 stades per degree, which he rounded off to 700. Multiplying by 360 gave him the circumference of the Earth – 252,000 stades (he could have just multiplied 5,000 by 50 to get the ‘answer’ 250,000, but apparently he did it the hard way).
So what is this in modern units? Unfortunately for us, the Greeks and Egyptians used slightly different stades, but the likelihood is that Eratosthenes, being Greek, used the Greek measurement, where one stade corresponds to 185 metres, which gives a circumference of 46,620 kilometres, only 16.3 per cent too big. In the unlikely event that he used the Egyptian measurement, with one stade corresponding to 157.5 metres, he would have come up with a figure of 39,690 kilometres, just a bit too small (less than 2 per cent smaller than the actual distance, 40,008 kilometres). Either way, it is impressive.
© Sheila Terry/Science Photo Library
Eratosthenes (
That was by no means the only impressive achievement of Eratosthenes. He used the information he found in the books in the Library of Alexandria to produce a three-volume book of his own in which he mapped and described the entire known world. He used grids of overlapping lines, like modern lines of latitude and lines of longitude, to locate places, and invented many of the terms still used by geographers today. More than four hundred cities were named and located in the book. Unfortunately the book itself, called
© Collection Abecasis/Science Photo Library
The World by Eratosthenes. 1886 replica of a map of the known world according to the Ancient Greek geographer, mathematician and astronomer Eratosthenes.
Eratosthenes was very much an all-rounder, so much so that he had the nickname ‘Beta’, because he was second best at everything, according to his contemporaries. The Greek geographer Strabo, who lived from about 64 BC to AD 24, described Eratosthenes as the best mathematician among the geographers, and the best geographer among the mathematicians. In mathematics, he is known for a technique called ‘the sieve of Eratosthenes’, used to find prime numbers. This simple method, which he invented, involves making a list (or grid) of all the numbers up to the biggest one you are interested in (for example, 1 to 1000). Then, you cross off from the list all the multiples of 2, the first prime number (4, 6, 8 and so on, but not 2 itself), and check that the next lowest number not crossed off is prime (if it isn’t, you have made a mistake!). If it is, cross off all the multiples of that number (but not the number itself), and so on. Once you get to the end of the list, the numbers that have not been crossed off form the list of primes.
After the decline of classical civilization and before the European Renaissance, scientific knowledge was preserved and improved in the Arabic world. Greek texts were translated into Arabic and later from Arabic into Latin, which is how they became known to Europeans. But the Arabs also carried out original scientific work. The greatest scientist of the Middle Ages, the ‘Arabic Newton’, was Abu Ali al-Hassan ibn al-Haytham, known for short as Alhazen, who lived from about 965 to 1040 and carried out experiments in optics on either side of the year 1000. His influential book was published in Europe in Latin as
© Science Source/Science Photo Library
Abu Ali al-Hassan ibn al-Haytham (known as Alhacen, or Alhazen) (965–1040).
Alhazen’s key insight was that sight is not the result of some influence reaching out from the eyes and sensing the world outside, but is caused by light entering the eye from outside. In his own words, ‘from each point of every coloured body, illuminated by any light, issue light and colour along every straight line that can be drawn from that point’. This was not an entirely original idea. Philosophers had discussed whether vision was caused by an outward influence (emission) or an inward influence (intromission) since the time of Euclid and Aristotle. But Alhazen put together a complete, coherent package of ideas which he then proved correct by experiments based on the idea of a ‘camera obscura’ (literally, a ‘dark room’; the Latin term is the source of our modern word camera). In a dark room with a heavily curtained window, if a tiny hole is made in the curtain on a sunny day an image of the outside world will be projected, upside down, on the wall opposite the window. The phenomenon had been known to the ancients, but Alhazen was the first person to describe it clearly and explain what is going on.
Alhazen realized that light travels in straight lines. Light from the top of a tree in the garden outside the window of the camera obscura will go through the hole in the curtain to the bottom of the wall opposite. Light from the base of the tree will go through the hole and up to the top of the wall. Straight lines from other points on the tree, and from other objects outside the window, go through the hole in straight lines to corresponding places on the wall to make the image.
He might have stopped there. Before Alhazen, those philosophers who thought about such things at all, such as Euclid and Aristotle, usually stopped at this stage, without actually doing experiments to test their ideas. They tried to persuade people that they were right by logic and reason, without getting their hands dirty (Archimedes, of course, was a notable, but rare, exception). What made Alhazen a real scientist was that he went a stage further. It was one thing to show how a camera obscura worked, but something else to prove that the eye works in the same way. A thousand years ago, many people would have assumed that living things were not subject to the same rules as inanimate objects. To test whether this was so, he took an eyeball from a bull, and carefully scraped away at the back of it, thinning it down until he could see on the back of the eyeball an image of what was in front of the eye, almost exactly like a tiny camera obscura. He had proved that light travels in straight lines, shown how a camera obscura works, and established that no mysterious life force is needed to explain vision, just the same physical laws that apply to non-living things. And he had done so using what became known (eventually) as the scientific method – thinking up ideas (hypotheses) about how the world works based on observation, then testing those ideas by experiment. Today, an idea that passes the experimental test is upgraded to the status of a theory, while those that fail the experimental test are discarded. As the twentieth-century physicist Richard Feynman pithily put it, ‘if it disagrees with experiment then it is wrong’. Because he understood this and put it in to practice, Alhazen was arguably the first modern scientist.