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Quadrivium is a method for cultivating human wisdom brought to us by Pythagoras in about 500 BC. It was developed for about two thousand years until the scientific method was discovered as a way to understand the universe we live within.
The difference between the classical method and our modern science seems to pivot on how one tests the truth of the assumptions made by an exploring mind. Science is tightly bound to physical reality by reproducible experiments testing assumptions. The ancient method was more dependent on creating beautiful concepts and then stretching them over the real world to find what fits best.

There is testability in both methods but science is presently providing a finer-grained approximation to reality. One thing becomes apparent when studying the ancient methods of thought: these people tried really hard to find beauty in their search for truth. They sought simplicity, symmetry, and elegance, and they found it in so many things. It is mathematical and musical, it is a harmony of the spheres that is very real and very beautiful. Perhaps in the not distant future, the scientific method will have discovered all that is measurable and with that knowledge integrated into our thoughts, we will return to the beauty of the Classic ways.

I love and fear the Quadrivium for its discovery of obvious truths, once perceived, and its obvious limitations, also once perceived.