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Ehrenfest sought relentlessly what he called der springende Punkt, the leaping point, the heart of the matter, as for him deriving a result by logical means was never enough: “That is like dancing on one leg,” he would say, “when the essence lies in recognizing connections, meanings and associations in every direction.” For Ehrenfest, true understanding was a full-body experience, something that involved your entire being, not just your mind or reason.
Speak the truth, write with clarity, and defend it to your very end was Boltzmann’s personal motto, and Paul, his disciple, took it to heart.
What if nature cannot be cognized as a whole? Our civilization had yet to come to terms with this terrifying possibility, and she very much doubted that it could, for it would be a death blow to science, philosophy, and rationality.
The mathematical universe is built much like the pyramids of the ancient pharaohs. Each theorem rests on a deeper and more elementary substrate. But what supports the bottom of the pyramid? Is there anything solid to be found there, or does it all float on the void, like an abandoned spiderweb blowing in the morning wind,
Lost faith is worse than no faith at all, because it leaves behind a gaping hole, much like the hollow that the Spirit left when it abandoned this accursed world. But by their very nature, those god-shaped voids demand to be filled with something as precious as that which was lost. The choice of that something—if indeed it is a choice at all—rules the destiny of men.
“Every chaos is a wrong appearance,” wrote Gödel; he was of the firm belief that there was a reason for everything. If you think that way, it’s a small step to begin to see hidden machinations and agents operating to manipulate the most common, everyday occurrences. But it was not just a psychological imbalance that undid him, he was also affected by the ideas that he brought into the world, ideas from which we have yet to recover. Truths that cannot be proven, contradictions that cannot be avoided—these self-referential nightmares of logic preyed on him as powerful demons that, once called
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