1.1 Pythagoras and Empedocles
Scientists and philosophers have wondered what light is made of for thousands of years. For most of that time, they have discussed whether it is made of waves, which are infinitely divisible, or atoms, which are not. The fact that light is made from neither, but of something that can display the properties of both, was not discovered until the 20th century and this is the basis of quantum mechanics.
The ancient Greek mathematician Pythagoras first described waves in about 550 BCE. Pythagoras showed that music can be expressed mathematically. This is said to have happened 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, and he discovered a similar effect when he applied the idea to the length of strings, which can be modelled as waves.[1]
Figure 1.1 |
The fundamental and the first six overtones of a vibrating string. |
Pythagoras thought that that mathematics is universal, and so he extended his theory of music to objects in space. He believed the paths of the seven ‘wandering stars’, composed of the five known planets - Mercury, Venus, Mars, Jupiter, and Saturn - and the Sun and Moon, follow the same pattern.[2]
Pythagoras also tried to explain how our vision works. He thought that something was emitted from our eyes that illuminates our surroundings.[3] The ancient Greek philosopher Empedocles, a follower of Pythagoras who was born five years before his death, suggested that something is also emitted from the objects we perceive and that we only see things when the two emissions meet. Empedocles also believed that there are four elements: fire, earth, air, and water.[4]
1.2 Zeno of Elea
The ancient Greek philosopher Zeno of Elea considered whether objects could be infinitely divisible in about 470 BCE. Zeno’s Dichotomy suggests that if distances are infinitely divisible, then motion should be impossible.
Zeno said that to cross a distance, we would first have to reach half the distance. We would then have to reach half of that distance, and so on. If a distance can be divided an infinite number of times, then crossing it would require crossing an infinite number of finite distances.
Zeno concluded that this should take an infinite amount of time[5] and since we can cross distances in a finite time, space cannot be infinitely divisible. The mathematics used to add up an infinite series was not derived until the 19th century.
Figure 1.2 |
An illustration of Zeno’s Dichotomy. |
1.3 Leucippus and Democritus
The ancient Greek philosopher Leucippus and his student Democritus first considered the concept of the atom in about 430 BCE. Democritus described atoms as indivisible objects and stated that everything in the universe could be made of atoms.[6]
Democritus thought that we see things because objects emit thin layers of atoms that are carried through the air until they reach our eyes. He suggested that the more air an image passes through, the more distorted it becomes.
Democritus argued that our other senses work in a similar way; taste, for example, is caused by the atom's shape, where bitterness is caused by jagged atoms that tear the tongue and sweetness by smooth atoms that easily roll over it.[7]
1.4 Aristotle
The ancient Greek philosopher Aristotle disagreed with Zeno and the concept of atoms. Aristotle popularised the idea that objects can be infinitely divisible, like waves, in about 360 BCE.[8] Aristotle didn’t accept Empedocles’ theory of perception because he believed that if vision is caused by emissions from the eye, then objects should be visible in the dark.
Instead, Aristotle argued that perception occurs when light travels through a medium like air or water, and then reflects from objects and interacts with a sense organ associated with sight.[9] In order to explain how starlight travels to Earth, Aristotle relied on a fifth element, besides fire, earth, air, and water, which fills space: the aether.[10]