Atoms and Waves (500-300s BC)
The concept of the atom was first devised by Ancient Greek philosopher Leucippus and his student, Democritus, in 530 BC. Democritus described atoms as indivisible particles and argued that everything in the universe can be explained by the interaction of these basic objects. He argued that vision is caused by the fact that objects give off thin layers of atoms which are carried through the air until they reach our eyes (Berryman, 2004). Democritus suggested that the more air an image passes though, the more distorted it will become. He argued that the other senses work in a similar way. Taste, for example, is caused by different shaped atoms, bitterness is caused by jagged atoms that tear the tongue and sweetness is caused by smooth ones that easily roll over it.
Around the same time, another Ancient Greek philosopher, Pythagoras, was developing the first wave equations. Pythagoras did not accept that Democritus' atoms were the fundamental components of nature and argued that numbers are true representatives of reality, not objects. It is said that when Pythagorean philosopher, Hippasus, showed that the square root of two was an irrational number - a number which cannot be described as a fraction - Pythagoras' followers were so shocked that they had him killed.
Pythagoras is said to have discovered that music could be expressed mathematically when he noticed that anvils of different weights produce different musical notes when they are struck. He realised that the weights have to be exact ratios to sound pleasing to the ear, the second anvil must be half the weight of the first, the third must be two thirds of this weight and the forth must be three quarters of this. He found that the same was true when he applied the idea to the length of strings.
Pythagoras was fascinated by the fact that the musical scale is built from ratios containing the first four whole numbers. He already considered them to be mystical as they form a perfect triangle and add up to ten, which he considered to be the holiest of numbers. Pythagoras devised the tetractys to illustrate this and it became an important religious symbol for his followers.
The Star Garden
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The tetractys
Pythagoras believed that mathematics is universal and so extended his theory of music to the heavens. He believed the seven 'wandering stars', composed of the five visible planets and the Sun and Moon, move in orbits that correspond to this scale.
Unlike Democritus, who argued that objects emit atoms which interact with our eyes, Pythagoras argued that our eyes emit waves which illuminate their surroundings (Huffman, 2009). Empedocles, a follower of Pythagoras who was born five years after his death, extended this theory by arguing that light emanates from our eyes as well as from other luminous bodies like the Sun and that perception only occurs when the two rays meet (Parry, 2005).
In the 4th century BC, Aristotle popularised the idea that the elements are all infinitely divisible, like waves, and so cannot be composed of indivisible atoms as Democritus had thought. Another Greek philosopher, Zeno of Elea, had already raised problems for atomism with his paradox of the arrow, one hundred years before. Zeno argued that an arrow must be at rest in order to occupy any particular spatial and temporal coordinates, yet this is contradicted by the fact that we experience movement. Zeno's paradox of the arrow asks how a body at rest can instantaneously move from one set of spatial and temporal coordinates to the next. Zeno believed that motion must be an illusion but Aristotle did not agree and argued that Zeno's paradox is based on the false assumption that time and space are atomised. Aristotle argued that time and space are in fact infinitely divisible and so there is no single 'here and now' for the arrow to rest in.
Aristotle did not accept Empedocles' theory of perception and argued that objects emit rays of colour which travel through a medium like air or water. He claimed that perception is caused by the rays interaction with a sense organ associated with sight (Aristotle, 1966). In order to explain how starlight travels to Earth, Aristotle relied on a fifth element - besides fire, earth, air and water - which fills space, this was known as quintessence or the aether.
References
Aristotle, 1966, 'Physics', Books V and VI, Ross, W.D. (Ed.), Clarendon Press, Oxford
Berryman, S., 2004, 'Democritus', Stanford Encyclopedia of Philosophy
Huffman, C., 2009, 'Pythagoras', Stanford Encyclopedia of Philosophy
Parry, R., 2005, 'Empedocles', Stanford Encyclopedia of Philosophy