Was there anything wrong with the idea of having a complete and consistent set of axioms on which to base all of our mathematical knowledge? No, there wasn’t. Hilbert’s programme seemed a sensible one, but Kurt Gödel proved it is not possible.
Was Newton’s idea of describing the movement of every particle specifying its position and speed a bad one? No, it was a bold idea, but Werner Heisenberg showed there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as its position and speed, can be known simultaneously.
How could the idea of ranking the preferences of individuals into a community-wide ranking be a bad one? It would have made democracy simply the best possible form of government (and not just the worst possible one excepting the rest.) Unfortunately, Kenneth Arrow proved there is no fair way to do that.
Wouldn’t it be great if we could take full advantage of cooperation to solve collectively our most pressing problems? It would be great indeed, but the full benefits of cooperation cannot be reaped unless there is endless trust among the cooperating parties.
Every step we take toward ultimate causes or enlightened ideals, ends up in a thousand new open roads to explore, or just in a conundrum. There seems to be always a fundamental limit that prevent our greatest ideas to fully realise. Like chimeras.
So, let me ask a silly question: Can Google’s mission to organize the world’s information and make it universally accessible and useful be an evil idea? It sounds formidable, but on a second thought, don’t you think it might also belong to the same category of La-la land’s chimeras?
Let me suggest a possible formulation:
Total Information Conjecture: There cannot be a world’s information system which is both universally accessible and useful, and Pareto Efficient
I am just looking forward to learning the name of the man or woman who proves it formally. Oh, if that were actually possible!