Archytas of Tarentum

Biography of Archytas of Tarentum

Archytas was born in the Greek city of Tarentum around 428 B.C. and died in 347 B.C., at the age of 81. He was a pre-Socratic philosopher, astronomer, scientist, mathematician, with major contributions to the science of optics and mechanics, and teacher of the renowned mathematician Eudoxus of Cnidus.

He was also a renowned and powerful politician in Tarentum, being elected 7 times as general of the city, although legally reelection was not allowed in Tarentum, which shows how prestigious he was. According to Aristoxenus, Archytas never lost a battle.

Archytas of Tarentum is often linked to the doctrine of the Pythagoreans, although Aristotle considered him an independent thinker. He is also believed to have been a disciple of Philolaus of Croton, one of the leading Pythagorean philosophers.

He developed a Pythagorean theory of harmony, and devised mathematical structures of musical scales used by musicians of his time.

In addition, he was a close friend of Plato. When Plato fell under the tyrant Dionysius II of Syracuse, Archytas sent a ship to his rescue. However, despite their close friendship, there were strong philosophical differences between them.

Works

Archytas wrote three works:

• on Mathematical Science
• on Harmony
• on Mechanics

However, only a few fragments remain in which he deals with Mathematics and Music.

Many works are attributed to Archytas, but most are considered inauthentic. It was common practice in ancient times to write works and attribute them to renowned philosophers in order to sell them for a higher price. Many inauthentic texts have been attributed to the Pythagoreans in general.

Philosophy of Archytas

Archytas’ philosophy was based on the doctrine of the Pythagoreans. Like all Pythagoreans, he believed that mathematics was the main factor in understanding all things.

Mathematics and knowledge

According to him, mathematics provided the most beautiful and excellent knowledge of the things of the world. He said:

It seems to me that mathematicians have acquired excellent knowledge, and it is not strange that they think correctly about the properties of particular things. For having acquired beautiful knowledge about the nature of the whole, they could naturally attain a beautiful insight into particular things as well.

In one of his fragments, Archytas identified 4 main sciences:

• arithmetic
• astronomy
• geometry
• music

Such disciplines became, in the middle ages, the structure of the quadrivium, sciences that integrated the teaching method in medieval universities.

Arithmetic and its predominance

For him, the most important science, because of its superiority, is Arithmetic. He says:

And Arithmetic has predominance over the other sciences as well as over Geometry, because it can demonstrate more clearly what it wants. For geometry proves, where the other sciences remain in difficulty. And when Geometry fails, Arithmetic presents demonstrations, as also the exposition of forms, if there is a science of forms.

Human action and mathematics

Mathematics would also serve for him to explain moral action as well as political relations. He says:

Once the calculus is found, this ceases discord and concord increases. There is no longer any place for competition, for equality reigns. For through calculation we will seek reconciliation in our relations with others. Through this, the poor receive from the powerful and the rich give to the needy, both in the confidence that they will get what is just.

Quotes

One must arrive at the knowledge of what one ignores by learning from another or by one’s own research. Learning is done with another or by strange means; research is done by oneself or by one’s own means. Finding without research is difficult and rare; when one researches, it becomes easy and accessible; and he who understands nothing of research can find nothing.

There are three proportions in Music: the arithmetic, the geometric, and the counterpoint, so called harmony.