Before the Curtain Falls

An oracle machine was something that could never be constructed. Its nature was closer to the "thought experiments" and "ideal conditions" of physics—things that could never be reproduced in reality.

An oracle machine concerning undecidable problems was even more impossible to construct from the very beginning.

This was merely using an imaginary concept to probe a possible one, in order to obtain a result that was undeniably real.

Yet that result sounded utterly despairing.

"Even the Great Dao's sacred voice of fantasy cannot complete this proof?" Feng Luoyi forced a smile, but the disappointment in his eyes could not be concealed.

Even with the strongest cheat imaginable to humanity, it was still impossible to bypass the boundary drawn by "self-reference."

Turing took a sip of tea and said softly, "I think perhaps we need not continue down this path..."

"A concept that even listening to the Great Dao's sacred voice cannot explain..." Feng Luoyi seemed unable to let it go, repeating himself.

"Teacher, perhaps our imagination has limited our methods," Wang Qi said. "Turing's ideas truly exhausted the limits of imagination. But Turing's 'imagination' was still inferred from his 'experience'—deduced from finite experience. Perhaps there truly is a method in this world that can bypass self-reference. It is simply that our present way of thinking cannot perceive it at all."

There was a trace of despondency in Feng Luoyi's voice. "Infinity and finitude... once we involve 'arbitrariness,' once we involve 'the infinite,' every step becomes difficult... Is the leap from finitude to infinity the limit of our understanding? Or was that bastard Master of Calculation right again? Does infinity simply not exist in this world?"

In the universe, the mass of matter was finite—otherwise, given gravity's property of extending without limit, every point in an infinite universe would possess infinite