Even leaving aside difficult concepts related to infinity, there are problems whose solution seems obvious, even to highly intelligent and well educated people (including the legendary mathematician Paul Erdős), but the obvious answer is wrong. Fro example, it seems obvious in the Monty Hall problem that your probability of winning a car is the same whether or not you switch your initial choice, but in fact the probability doubles if you switch. Some rigorous analysis is required to see this clearly.
My university math professor’s favorite phrase was “it’s intuitively obvious”.
Even leaving aside difficult concepts related to infinity, there are problems whose solution seems obvious, even to highly intelligent and well educated people (including the legendary mathematician Paul Erdős), but the obvious answer is wrong. Fro example, it seems obvious in the Monty Hall problem that your probability of winning a car is the same whether or not you switch your initial choice, but in fact the probability doubles if you switch. Some rigorous analysis is required to see this clearly.
Common Law versus Natural Law.
Sounds the same but different.
Sometimes both converge and become similar, sometimes different.
Comparable examples are Details-General, Vision-Hearing, Thinking-Feeling, Body-Mind, etc.
The Past and the Future converges on the Present.
Jack of All trades, Master of None or is it possible to be
Jack of All trades, Master of One?
Life is a paradox in a spiral. The answer lies in one's concept of Anthropology.
The fundamental unit of human behavior is called Dimension (not String Theory).