# Numerical harmonies, stars and elements

June 27, 2021One of the most important discoveries of Pythagoras is the relations between numbers, ratio and proportions.

This was an idea born out of the relationship between the notes he experienced as a result of his research in music, producing pleasant sounds. It is said that the idea first came to Pythagoras’ mind when he watched two blacksmiths at work. While watching these blacksmiths, Pythagoras noticed that the sounds the blacksmiths made when they hit the anvil with a hammer were exactly in the range of one octave. This may be true; but Pythagoras most likely determined the proportions of homonymous intervals (the number of notes between two notes that determines whether they sound harmonious when struck against each other) by experimenting with broken strings. What he discovered is that these intervals are congruent because the relationship between them is a simple and precise mathematical ratio.

This sequence, which we now know as the harmonic sequence, provided a confirmation for Pythagoras that the mathematical grace he found in abstract mathematics is also found in nature.

stars and elements

Pythagoras has now proven that not only can the structure of the universe be explained in mathematical terms – “numbers are the rulers of forms” – but also that acoustics is an exact science, and that numbers govern harmonious proportions. He then begins to apply his theories to the entire cosmos, demonstrating the harmonious relationships of the stars, planets, and elements. The idea of a harmonious relationship between the stars was eagerly taken over by medieval and Renaissance astronomers, who produced holistic theories around the idea of the music of the spheres, with the assumption that the elements were harmoniously arranged even 2000 years after his death.

In 1865, British chemist John Newlands discovered that when chemical elements are arranged according to their atomic weights, those with similar properties appear once in every eight elements, just like in music. This discovery is known as the Octave Law and helped develop the Periodic Table of chemical elements, which is still used today.

Pythagoras also found the principle of deductive reasoning, which is to arrive at a new conclusion or truth by stepping up from obvious axioms (like 2+2=4). Deduction was later developed by Euclid and formed the foundations of mathematical thought in the Middle Ages and later.

One of Pythagoras’ most important contributions to the development of philosophy was his idea that abstract thought is superior to the evidence of the senses. This was also used by Plato for the Theory of Forms and resurfaced as the philosophical method of rationalists in the 17th century. The attempt of the Pythagoreans to unite reason with religion is the first attempt to confront a problem that has brought philosophy and religion against each other since time immemorial.

Prepared by: Sociologist Ömer YILDIRIM

Source: Omer Yıldırım’s Personal Lecture Notes. Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM); Open Education Philosophy Textbook