"Surface geometry denied the final postulate of Euclidean Geometry, the Geometric God, and was therefore called 'non-Euclidean.' But did Non-Euclidean Geometry truly deny Euclidean Geometry?"
The question Wang Qi slowly voiced seemed casually thrown out, yet it was in fact an incomparably important matter of perspective.
Was new science built upon the negation of old theories?
The answer to that question was indeed somewhat hazy. There were many scientists who, unable to adapt when new theories emerged, gradually withdrew from the forefront of research.
Yet more often than not, the answer was no.
Did Non-Euclidean Geometry truly negate Euclidean Geometry? No. Non-Euclidean Geometry altered the Fifth Postulate, but its foundation still rested upon the first four major postulates of Euclidean Geometry. It was an important extension of Euclidean Geometry.
Did the system of relativity negate the system of Newtonian Mechanics? Likewise, no. Einstein merely followed Newton's line of thought, combining it with later theoretical achievements to discuss the conditions under which Newton's system operated at high speeds. Newton's system could be called an approximation of relativity at low speeds, while relativity could be called an extension of Newton's system at high speeds.
By the same token, Planck's Quantum Theory was also an extension of Maxwell's system under microscopic conditions.
Yes, the key lay in the concept of "extension."
As Russell said, "The laws humanity has grasped are merely the statistical averages of random events." A theory was only something we summarized from the range we had already observed. When technological methods advanced and the observable domain expanded, the theories we had already mastered would no longer apply.
At that point, we needed "extension"—to revise existing theories and extend them into new fields!
Bo Xiaoya's breathing caught.
Wang Qi's words... "Ignore the law of the excluded middle"... this was... the key