HOW_TO_MAKE_A_DISCOVERY_OF_PRINCIPLE (2)
There is an innate ordering principle to numbers which Gottfried Leibniz called “preestablished harmony.” According to him, such harmony was created by God for a purpose that has not yet been made clear to mankind, and which remains to be investigated as to its purpose. Here, in substance, is what he wrote about it:
“It is good to give an example. Let us take in order the numbers: 0 1 2 3 4 5 6 7 8 9 10 etc. and then their squares: 0 1 4 9 16 25 36 49 64 81 100 etc., and the differences between these squares: 1 3 5 7 9 11 13 15 17 19 etc. We find that the differences between the squares of the numbers taken in order are the odd numbers, again in order; and after having tested a long sequence of numbers, and found that this holds good, we justifiably presume that it will always continue to hold good to infinity; but we do not thereby see either the necessity or the cause of it, which depends on certain demonstrative reasons taken from the source, or a priori. Souls capable of these reasonings are called ‘minds,’ and it can be rightly said of them that they are made in the image of God, and that there is a society between God and them, so that with regard to them, God is not only what an architect is to his building, but also what a Prince is to his subjects.” [ Leibniz and the Two Sophies: The Philosophical Correspondence]
Why would such preestablished harmony exist among numbers? And what makes it necessary to have such a divine a priori ordering? Why were numbers the chosen ones to represent such a preestablished harmony? What is its purpose and what does it tell us about the lawfulness of the universe? What was God’s Intention? You may want to try to understand the following biquadratic geometrical construction and see if my hypothesis for the coincidence of opposites of Nicholas of Cusa and of the I Ching (Book of Changes) is on the right track.
