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It doesn't make you a weirdo but you are throwing away the baby with the bathwater. I can't tell you how many times I've looked at a proof or a solution to a pr
by dkarapetyan 12y ago
It doesn't make you a weirdo but you are throwing away the baby with the bathwater. I can't tell you how many times I've looked at a proof or a solution to a problem and thought to myself that it just feels wrong and ugly and that there should be a more elegant approach. And sure enough after a bit of digging and thinking there is a better and more elegant approach.
That feeling of ugliness is not formal or logical in any way. It is a visceral and emotional reaction and there is no specific set of formal reasons I can point to that gives rise to it. The history of science and mathematics is full of examples of such emotional insights so seems to me your theory of "enlightenment" is incomplete.
- yummyfajitas 12y agoOne shouldn't ignore intuition, empathy, or a gut feeling. It's a useful signal. But that's all it is. There are true results that go against emotion, intuition, and just feel wrong. In math, Banach Tarski is a perfect example. http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox If you want to use empathy as a hint to keep digging for a better solution, be my guest. I just object to using empathy as a basis for morality. Similarly, mathematical intuition isn't a substitute for a proof.