Just a quick note on your main example - in math, and I'm guessing in theoretic areas of CS as well, we often find that searching for fundamental obstructions to a solution is the very thing that allows us to find the solution. This is true for a number of reasons. First, if we find no obstructions, we are more confident that there is some way to find a solution, which always helps. Second, if we find a partial obstruction to solutions of a certain sort, we learn something crucial about how a solution must look. Third, and perhaps most importantly, when we seek to find obstructions and fail, we may find out way blocked by some kind of obstruction to an obstruction, which is a shadow of the very solution we seek to find, and by feeling it out we can find our way to the solution.
Thank you for all these interesting references. I enjoyed reading all of them, and rereading in Thurston's case.
Do people pathologize Grothendieck as having gone crazy? I mostly think people think of him as being a little bit strange. The story I heard was that because of philosophical disagreements with military funding and personal conflicts with other mathematicians he left the community and was more or less refusing to speak to anyone about mathematics, and people were sad about this and wished he would come back.
One thing that most scientists in these soft scientists already have a good grasp on, but a lot of laypeople do not, is the idea of appropriately normalizing parameters. For instance dividing something by the mass of the body, or the population of a nation, to do comparisons between individuals/nations of different sizes.
People will often make bad comparisons where they don't normalize properly. But hopefully most people reading this article are not at risk for that.
Conservation gives a local symmetry but there may not be a global symmetry.
For instance, you can imagine a physical system with no forces at all, so everything is conserved. But there are still some parameters that define the location of the particles. Then the physical system is locally very symmetric, but it may still have some symmetric global structure where the particles are constrained to lie on a surface of nontrivial topology.
Do you often read physicist's response to claims of FTL signalling? It seems to me like there is not much value in reading these, per the quote.
No, you should focus on founding a research field, which mainly requires getting other people interested in the research field.
I don't think that's really relevant to the original quote.
True, but that doesn't mean we're laboring in the dark. It just means we've got our eyes closed.
I would be interested in a post about how to acquire political knowledge!
10% isn't that bad as long as you continue the programs that were found to succeed and stop the programs that were found to fail. Come up with 10 intelligent-sounding ideas, obtain expert endorsements, do 10 randomized controlled trials, get 1 significant improvement. Then repeat.