Carl Sagan : What Pythagoras Believed

Summary

The transcript discusses Pythagoras' groundbreaking contributions to the understanding of the universe, including his belief in a spherical Earth, the mathematical harmony underlying nature, and his influential concept of the cosmos. It explores the Pythagoreans' focus on mathematical thought rather than experimentation, their fascination with regular solids, and their mystical associations with elements and the heavens. The discovery of the irrational square root of two challenged their worldview, leading to a crisis in doctrine. The Pythagoreans suppressed certain knowledge, such as the dodecahedron, fearing it threatened their beliefs.

Takeaways

• 😀 Pythagoras was likely the first person to propose that the Earth is a sphere, potentially through observation of lunar eclipses or disappearing masts of ships.
• 😀 Pythagoras believed in a mathematical harmony that underlies all of nature, influencing modern scientific thought and the concept of 'cosmos' as a well-ordered universe.
• 😀 Pythagoras coined the term 'cosmos' to describe a harmonious and well-ordered universe, a concept still used today.
• 😀 Pythagoras did not prioritize observation or experimentation like other Ionian thinkers but believed that the laws of nature could be deduced purely through thought.
• 😀 The Pythagoreans were mathematicians and mystics, interested in five regular solids, which they associated with the elements and the cosmos.
• 😀 Four of the regular solids represented the classical elements: earth, fire, air, and water, with the cube symbolizing earth.
• 😀 The fifth regular solid, the dodecahedron, was considered to represent the cosmos and was thought to be too dangerous for the general public to understand.
• 😀 Pythagoreans believed that all things could be derived from whole numbers, a philosophy that was challenged by the discovery of irrational numbers like the square root of two.
• 😀 The discovery that the square root of two is irrational contradicted Pythagoras's belief that all numbers should be expressible as whole-number ratios, leading to a crisis in their worldview.
• 😀 The Pythagoreans suppressed knowledge of the square root of two and the dodecahedron, keeping these discoveries hidden from the public to protect their mystical beliefs.

Q & A

What was Pythagoras' contribution to the understanding of the Earth?

Pythagoras was one of the first to propose that the Earth is a sphere, possibly based on observations such as the curved shadow of the Earth during a lunar eclipse or the disappearance of ship masts from sight.

How did Pythagoras' view of the universe differ from the Ionian philosophers?

Unlike the Ionian philosophers, who emphasized observation and experimentation, Pythagoras believed that the laws of nature could be understood through pure thought and mathematics, rejecting the experimental approach.

What was the significance of the 'music of the spheres' concept?

The 'music of the spheres' was an idea derived from Pythagoras, suggesting that the movement of heavenly bodies followed a harmonious, mathematical order, akin to music. This concept reflected his belief in mathematical harmony in the universe.

What was the meaning of the word 'cosmos' according to Pythagoras?

Pythagoras was the first to use the term 'cosmos' to describe the universe, meaning a well-ordered, harmonious, and beautiful whole that could be understood by human beings.

What was Pythagoras' method for understanding the laws of nature?

Pythagoras and his followers used deductive reasoning and pure thought rather than empirical observation or experimentation to understand the laws of nature.

Why were the five regular solids important to Pythagoras and his followers?

Pythagoras and his followers were fascinated by the five regular solids because they were seen as embodying harmony and order. Each solid was associated with one of the classical elements, with the fifth solid, the dodecahedron, symbolizing the cosmos itself.

What did the Pythagoreans believe about the elements and the regular solids?

The Pythagoreans believed that the four classical elements—earth, fire, air, and water—were represented by four of the regular solids, while the fifth solid, the dodecahedron, was mystically linked to the cosmos and the heavens.

What was the significance of the dodecahedron for the Pythagoreans?

The dodecahedron was considered a sacred object by the Pythagoreans, symbolizing the cosmos, and it was believed to be too dangerous for the public to know about. Ordinary people were kept ignorant of its significance.

What was the crisis that Pythagoras and his followers faced regarding numbers?

The crisis occurred when the Pythagoreans discovered that the square root of two is an irrational number, meaning it could not be expressed as a ratio of whole numbers. This challenged their belief that all numbers could be derived from whole numbers.

How did the discovery of the square root of two affect the Pythagoreans' worldview?

The discovery of the irrationality of the square root of two was a serious threat to the Pythagorean worldview, which was based on the belief that all things could be explained by whole numbers. It hinted that their understanding of the universe might be incomplete or flawed.