# Tagore – Einstein Conversations – What is the Pythagorean Argument?

## A Critical Evaluation

(Image Credits: Courtesy of the Leo Baeck Institute)

## What is the Pythagorean Argument?

“Numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception.”

What seems certain is that Pythagoras developed the idea of mathematical logic. He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths that were independent of the opinion of prejudice and which were more absolute than any previous knowledge.

Now if we follow the development of the scientific theory of Einstein, we would find Lorentz transformation from Pythagoras’ theorem, where:

• Pythagorean Theorem for 2 dimensions is $h^{2}=b^{2}+p^{2}$
• Pythagorean Theorem for 3 dimensions can be stated like this: $ds^{2}=dx^{2}+dy^{2}+dz^{2}$
• For a rod of a given length $L$. For any observer $L=\bigtriangleup x^{2}+\bigtriangleup y^{2}+\bigtriangleup z^{2}$. This $L$ is constant irrespective of how different observers rotate (their coordinate axes) with respect to each other. If an observer rotates with respect to another, one or 2 of the 3 components decrease and the third one increases keeping the length constant.
3. For 4 dimensions, Lorentz Transformations give us the in-variance relation. For a given pair of events $\bigtriangleup s^{2}=(\bigtriangleup x)^{2}+(\bigtriangleup y)^{2}+(\bigtriangleup z)^{2}-(c\bigtriangleup t)^{2}$

The reason for citing the above example is that based on the Pythagoras’ theorem, the Lorentz factor can be derived, which is one way to show, why Einstein believed in the Pythagorean argument that numbers exist independently.

This is quite like a Pythagorean theorem in 4 dimensions but with time having a $-ve$ sign.

So, Einstein’s Lorentz transformation and hence the calculations of Special Theory of Relativity and then his magnum opus GR or General Theory of Relativity, changed our entire outlook of space-time and gravity resulted from Pythagoras.

Pythagorean philosophy believed that for all things which are ordered in the world by nature according to an artificial course in part and in whole appear to be distinguished and adorned by Providence and the All-creating Mind, according to Number; the exemplar being established by applying (as the reason of the principle before the impression of things) the number pre-existent in the Intellect of God, maker of the world.

‘This only in intellectual, & wholly immaterial, really a substance according to which as being the most exact artificial reason, all things are perfected, Time, Heaven, Motion, the Stars and their various revolutions.’  (Pythagoras – His Life & Teachings by Thomas Stanely)

What we see is that “numbers” which constitute the mathematical world, where all the equations lie, are independent of the tangible world – the world where we live in, the world where Truth lies – the world where Apollo Belvedere lies. Hence, Einstein argues on this.