Chapter 1. Atoms and Waves

1.1 Pythagoras and Empedocles

Scientists and philosophers have debated the nature of light for thousands of years. For much of that time, the debate has been over whether light 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.

Ancient Greek mathematician Pythagoras was fascinated by the connection between mathematics and nature, and is thought to have been the first to discover that music can be expressed mathematically in about 550 BCE. This is said to have happened when he noticed that anvils of different weights produced different musical notes when they were struck.

Pythagoras realised that the weights have to be exact ratios to sound pleasing to the ear, and discovered a similar affect when he applied the idea to the length of strings, which can be modelled as waves.[1]

Depiction of overtones on a string.

Figure 1.1
Image credit

The fundamental and the first six overtones of a vibrating string.

Pythagoras claimed that mathematics is universal and so extended his theory of music to objects in space. He believed the seven ‘wandering stars’, composed of the five known planets - Mercury, Venus, Mars, Jupiter, and Saturn - and the Sun and Moon, move in orbits that correspond to this scale.[2]

Pythagoras claimed that perception occurs when emission from our eyes illuminates our surroundings.[3] Ancient Greek philosopher Empedocles, a follower of Pythagoras who was born five years before his death, extended this theory by arguing that emission also occurs in the objects we perceive, and that perception only occurs when the two emissions meet. Empedocles also believed that there are four elements: fire, earth, air, and water.[4]

1.2 Zeno of Elea

Ancient Greek philosopher Zeno of Elea first considered whether objects could be infinitely divisible in about 470 BCE. Zeno’s Dichotomy, for example, argues that if distances are infinitely divisible, then motion should be impossible. This is because 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] Since we can cross distances in a finite time, this suggested that space cannot be infinitely divisible.

Illustration showing that distances can be halved an infinite amount of times.

Figure 1.2
Image credit

Illustration of Zeno’s Dichotomy.

1.3 Leucippus and Democritus

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 can be explained by the interaction of atoms.[6]

Democritus claimed that vision is caused by objects emitting thin layers of atoms that are carried through the air until they reach our eyes. He suggested that the more air an image passes though, the more distorted it becomes.

Democritus 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 by smooth atoms that easily roll over it.[7]

1.4 Aristotle

Ancient Greek philosopher Aristotle disputed Zeno’s claims, and popularised the idea that objects may 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. This is known as quintessence, or the aether.[10]

1.5 References

  1. Caleon, I., Ramanathan, S., Science & Education 2008, 17, 449–456.

  2. Godwin, J., The Harmony of the Spheres: The Pythagorean Tradition in Music, Inner Traditions/Bear & Co., 1992.

  3. Kuehni, R. G., Color: An Introduction to Practice and Principles, John Wiley & Sons, 2015.

  4. Parry, R., Empedocles, Stanford Encyclopedia of Philosophy, 2012.

  5. Huggett, N., Zeno’s Paradoxes, Stanford Encyclopedia of Philosophy, 2010.

  6. Berryman, S., Ancient Atomism, Stanford Encyclopedia of Philosophy, 2011.

  7. Berryman, S., Democritus, Stanford Encyclopedia of Philosophy, 2010.

  8. Bell, J. L., Continuity and Infinitesimals, Stanford Encyclopedia of Philosophy, 2013.

  9. Wade, N. J., Perception and Illusion: Historical Perspective, Springer Science & Business Media, 2006.

  10. Wildberg, C., John Philoponus’ Criticism of Aristotle’s Theory of Aether, Walter de Gruyter, 1988.

Back to top