A Temple to the Gods - Pythagoras

Blog Post 3: c. 510 BCE A Temple to the Gods

My Dear Mathematikoi,

Many of you are due to receive this letter of welcome into my tutelage, and with the grace of the Gods, all of you will join me in Croton to form the “semicircle.” I have invited you to study, under my guidance, the questions of goodness, justice and expediency. What ensues in this letter is an exploration into the ideas we will expand and examine.

First, however, let me explain my qualifications. I have seen life in all its beauty and death in its all-consuming darkness. I have studied the holiest rites with the Maogi and the Egyptian Priesthood. I have known the truths of the number language; and if you wish to work with me, I too, will instruct you in the language of the Gods.

If you choose to join me, you must hold these truths holy as I do: everything is mathematical in nature, philosophy is the act of purifying the spirit, our souls can join with the Gods and reside in the heavenly halls, certain symbols hold divine significance and we must hold them as sacred, and finally; and most importantly, all members of the “semicircle” must observe a very strict code of secrecy. We will live together in holy matrimony with the Gods and we shall live through a code of purity. We must abstain from unholy foods, wearing the skins of the dead, and engaging in any unholy acts. And finally to enter my school, all of you must take a two-year vow of silence to quiet your minds and open your mental ear to the song of the Gods.

I encourage you to take time out from your studies to realize how surrounded and immersed in numbers we all are. Look about you and count; and if you can, identify all these holy numbers and their meanings. Numbers are not just for counting the coppers after a hard day at the market. No, numbers are like us; they think and feel, they have strengths and weakness, aspirations and loves. My friends gaze into the hall of the Gods on a clear night and see how their wisdom rains down upon in the form of these such numbers. Look for such wisdom even in the triangular façade of your magistrate’s stronghold.

In this message, I leave for you a gift of sorts. Triangles, yes, those stubborn and mathematically heretical structures are, in fact, beautiful. I will attach an illustration alongside this description, yet I beseech you to bear with the process. Imagine that you have three squares, and that one is larger than the other two; carefully, place the square so that two vertices of each are connected to one of the other two squares. Now examine the space in between this new structure of squares. A triangle is it not? But look more closely; see that this triangle has a much larger side formed from the largest square. Let us call that the hypotenuse. Now each side must be in a relationship with the other, yes? However, notice that it is the square from which these side are formed that provides the relationship, yet if you attempt to find the length of the hypotenuse if its square is thirteen suddenly our commonsensical numbers fail us.

I challenge you to prove this theorem for yourself, and upon deliverance to me I will grant you full access to the years of work I, too, have performed upon such beautiful shapes as triangles.

I wish you the best of luck and the expediency of the Gods in your journey,

Pythagoras

Look at how a triangle need not be matter filling space, but the space between matter.