I also want to stress the point that I’m a bit biased(?) when it comes to understanding concepts. Surely I could accept any mathematical method or algorithm at face value. After all I’m also able to use WolframAlpha. But I feel that doesn’t count. At least I do not value such understanding. If you taught a prehistoric man to press some buttons he would be able to control a nuclear facility.
Many people are bothered by the counter-intuitive nature of probability. I have never been more confused by probability than by any other branch of mathematics. I believe that people regard probability as more difficult to understand because they learn about it much later than about other mathematical concepts. For me that is very different because it is all new to me. For me P(Y) ≥ P(X∧(X->Y)) is as (actually more) intuitive than a^2 + b^2 = c^2. The first makes sense in and of itself, the second needs context and proof (at least regarding my gut feeling). I just don’t see how 2 + 2 = 4 is more obvious than Bayes’ theorem. You just learnt to accept that 2 + 2 = 4 because 1.) you encounter the problem very often 2.) you can easily verify its solution 3.) you learn about it early on. But it is not self-evident.
I also want to stress the point that I’m a bit biased(?) when it comes to understanding concepts.
This is something people have noticed and it influences their responses. Aggressive “not understanding” is often considered a sign of bad faith, for good reason.
I also want to stress the point that I’m a bit biased(?) when it comes to understanding concepts. Surely I could accept any mathematical method or algorithm at face value. After all I’m also able to use WolframAlpha. But I feel that doesn’t count. At least I do not value such understanding. If you taught a prehistoric man to press some buttons he would be able to control a nuclear facility.
Many people are bothered by the counter-intuitive nature of probability. I have never been more confused by probability than by any other branch of mathematics. I believe that people regard probability as more difficult to understand because they learn about it much later than about other mathematical concepts. For me that is very different because it is all new to me. For me P(Y) ≥ P(X∧(X->Y)) is as (actually more) intuitive than a^2 + b^2 = c^2. The first makes sense in and of itself, the second needs context and proof (at least regarding my gut feeling). I just don’t see how 2 + 2 = 4 is more obvious than Bayes’ theorem. You just learnt to accept that 2 + 2 = 4 because 1.) you encounter the problem very often 2.) you can easily verify its solution 3.) you learn about it early on. But it is not self-evident.
This is something people have noticed and it influences their responses. Aggressive “not understanding” is often considered a sign of bad faith, for good reason.