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The analogy is not meant to be applied further than “sometimes we invent new mathematical tools solve problems that were impossible to solve previously.”
by baddox 9y ago
The analogy is not meant to be applied further than “sometimes we invent new mathematical tools solve problems that were impossible to solve previously.”
- pvg 9y agoYes, and my point is 'it's not a good analogy (nor analogue) for the thing being discussed'. The nature of the things being compared is too dissimilar. Here's a trivial counter-analogy - angle trisection with compass and straightedge. Known since antiquity, proved impossible by Pierre Wantzel, a piddly 180 years ago (with the requisite invention of new mathematical tools).
- alphaalpha101 9y ago>Here's a trivial counter-analogy - angle trisection with compass and straightedge. Known since antiquity, proved impossible by Pierre Wantzel, a piddly 180 years ago (with the requisite invention of new mathematical tools). That's not a 'counter analogy'. It's the same analogy. Nobody is saying 'we have solved other problems therefore this one is solvable even though it appears not to be'. People are saying 'we can't say it's impossible just because it looks to be impossible'.