A Strange New Universe

For the last 2000 years, the two most studied books in western civilization have been the Holy Bible and Euclid's Elements. Western thinkers have relied on the Bible to tell us what is true about God and the spiritual realm. On the other hand, Euclid's text describes what is true about the physical universe. I have spent much of my life studying these two books.

Euclidian geometry had another more practical purpose in schools of the western world. It was the tool educators used to train young minds to think deductively. Teaching young people to think about if-then statements and writing proofs develops the brain in valuable ways that one might apply to every life path. The premise is that if A is true, then B is true. And if B is true, then C is true, and so on. But how do we know A is true? If you follow any geometric proof to the first link in this chain, you reach an idea so simple it is unprovable. In this sense, geometry is a system of faith. In geometry, these faith statements are called postulates. They are, by definition, unprovable. In Euclidean geometry, there are exactly five postulates upon which the whole system rests. Like a Jenga tower where each of the bottom five layers has just one brick, the entire structure tumbles if one removes the brick from any of the five bottom layers.

Of course, throughout the centuries, mathematicians have tried to prove the fifth postulate. Essentially this postulate, and allow me to paraphrase, states: through a point not on a line, there is exactly one line parallel to the first line. Three men get credit for arriving at a kind of non-proof at roughly the same time. One of these math guys, Janos Bolyai, began falling down this rabbit hole after his father had tried the proof without success. Upon hearing his son was starting down the same path he had previously failed in, the father wrote to his son:

"You must not attempt this approach to parallels. I know this way to its very end. I have traversed this bottomless night, which extinguished all light and joy of my life...For God's sake, I beseech you, give it up. Fear it no less than sensual passions because it too may take all your time and deprive you of your health, peace of mind, and happiness in life."

https://blogs.scientificamerican.com/roots-of-unity/hyperbolic-quotes-about-hyperbolic-geometry/

But, as young men are apt to do, the younger Bolyai ignored his father's advice. The attempt to prove the postulate did yield something else, however. Bolyai’s approach was to assume the postulate was false. He planned to follow that logical path to the point of contradiction. Then, if the idea could not be false, it must be true. Mathematicians call this approach an “indirect proof.” But, I assume with some surprise, Bolyai never reached a contradiction. He instead found a whole new geometry that has come to be known as hyperbolic geometry where a point not on a line can have many parallels to the original. The math that westerners had relied on for more than 2000 years to describe and explain the physical universe was not the only valid geometry. The younger Golyai wrote back to his father and exclaimed: “Out of nothing, I have created a strange new Universe.”

The thing that Tertullian and Clement had in common with Gaus and Bolyai, was that they appreciated the importance of the foundation of any system or structure. Tweek the foundation and the whole thing falls apart, or you end up with something strange and different. Clement and Tertullian knew that a change to the Rule of Faith would ultimately lead to a strange new Christianity that would be no Christianity at all.