Euler on the left and Diderot on the right.
False Stories With True Lessons
It has been pointed out to me that the story about Pythagoras and Hippasus that I wrote about in my previous post was probably not historically accurate. I certainly hope so for Hippasus… Though the events might never have happened, the moral of the story is true, and you should be careful to keep “truth” as your ultimate goal instead of “being right”.
The French philosopher Denis Diderot was visiting Russia on Catherine the Great’s invitation. However, the Empress was alarmed that the philosopher’s arguments for atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, “Sir, (a+b^n)/n = x, hence God exists—reply!”. Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress.
This has been debunked, but the reason why it was told and retold for centuries is probably because it has a ring of truth. We can all imagine a debate between two people where one of them says something that the other does not understand, and instead of asking for clarifications, he simply admits defeat.
Pride vs. Truth
That’s self-defeating pride for you. You are too proud to admit that you don’t understand something, and that perversely leads to the very thing you were trying to avoid, which is humiliation. If your goal is to look for truth, you should want to understand all the arguments from the other side. But if your goal is to look right and superior (humans are social animal that seek social status), you will be reluctant to ask for help because that in itself can make you look wrong (even if you aren’t), and there’s always the danger that the clarifications will just end up making it extra-obvious that you are wrong.
But that’s not a real problem: If you are wrong, you should want to know it so you can change your position. There is nothing noble about sticking to false ideas because of how changing your mind might make you look. The more ego you invest in your positions, the harder it is to abandon them. That’s the difference between “I think X because it is correct to the best of my knowledge” and “X is correct”; you need to keep in mind that you believe the things you believe because of some data that pointed in that direction, and that new data could change that. Not because your positions are intrinsically correct.
So if you are ever faced with an argument that you don’t understand, it is win-win for you to admit you don’t understand and either ask for help or go do some research and come back to it. Once you fully understand it, maybe you’ll find out that the argument wasn’t actually a good one, and you wouldn’t have helped your search for truth by forfeiting to it. And if the argument turns out to actually be convincing, it’ll be a good thing for you to evaluate it and see if you need to change your position. This new information also brings you closer to your search of truth. Win-win.