Love that quote: "the main job of theoretical physics is to prove yourself wrong as soon as possible."
I try and apply it to programming and computer systems. Test test test, prototype before you commit millions of dollars and hours to something that might not work very well.
It's a beautiful way to approach problems. But one problem I find with it is that I get a bit paranoid with my solutions. Sure, it's not being rejected by any of my experimentation, but is it ready for millions of dollars of commitment? How do I know when I'm confident enough? After all, I went into this trying to prove myself wrong, so my mind is in a place where I'm expecting for it to fall apart.
As long as you do some experimentation that's fine. You might be legitimately be criticised for not doing the right experiment or not enough. Take it on the chin, learn, move on.
There's another story about Feynman, somewhat related to this issue. He had worked out the V-A structure of the weak force which had been an outstanding puzzle for some time. At some later point he was visiting CERN and they during the tour the guide said something along the lines of "Oh! Professor Feynman! This [huge experiment and expensive detector] is to test your theory of [such and such blah blah blah]."
Feynman smiled and said, "What, you don't trust me?"
Beautiful! Of course, no finite probability could ever prove that no solution exists, but being able to say that the odds of a solution are 10^-31 is, for all practical purposes, a guarantee there is none.
Well, having such a probably could indicate that the possible solutions "could" happen from 10^31
What a lot of people don't know is that the theorem was already proven for several expoents before the final solution (including for 3 and some others - and multiples of those cases)
Love that quote: "the main job of theoretical physics is to prove yourself wrong as soon as possible."
I try and apply it to programming and computer systems. Test test test, prototype before you commit millions of dollars and hours to something that might not work very well.
Unfortunately not everyone sees it my way.
It's a beautiful way to approach problems. But one problem I find with it is that I get a bit paranoid with my solutions. Sure, it's not being rejected by any of my experimentation, but is it ready for millions of dollars of commitment? How do I know when I'm confident enough? After all, I went into this trying to prove myself wrong, so my mind is in a place where I'm expecting for it to fall apart.
As long as you do some experimentation that's fine. You might be legitimately be criticised for not doing the right experiment or not enough. Take it on the chin, learn, move on.
There's another story about Feynman, somewhat related to this issue. He had worked out the V-A structure of the weak force which had been an outstanding puzzle for some time. At some later point he was visiting CERN and they during the tour the guide said something along the lines of "Oh! Professor Feynman! This [huge experiment and expensive detector] is to test your theory of [such and such blah blah blah]."
Feynman smiled and said, "What, you don't trust me?"
I love Fermats Last Theorem.
It just looks so innocuous. Especially given early exposure to a^2 + b^2 = c^2
I've always had the unreachable goal to prove Fermats Last Theorem with high school based math.
One day... One day!
Have you read Fermat's Enigma by Simon Singh? It's a great book on how Andrew Wiles went about solving it. Great book. Highly recommend you give it a read! https://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-...
Previous discussion:
https://news.ycombinator.com/item?id=14940636
Beautiful! Of course, no finite probability could ever prove that no solution exists, but being able to say that the odds of a solution are 10^-31 is, for all practical purposes, a guarantee there is none.
Well, having such a probably could indicate that the possible solutions "could" happen from 10^31
What a lot of people don't know is that the theorem was already proven for several expoents before the final solution (including for 3 and some others - and multiples of those cases)
No, there is a chance of 10^-31 that there is any solution
The article doesn't say the odds are 10^-31. It says 10^-31 percent. So really the odds are less than one in 10^33.