first encountered humans who couldn’t understand basic arithmetic at university
When I first saw a fraction, e.g. 1⁄4, I had real trouble to accept that it equals .25. I was like, “Uhm, why?”...when other people are like, “Okay, then by induction 2/4=.5″...it’s not that I don’t understand, but do not accept. Only when I learnt that .25 is a base-10 place-value notation, which really is an implicit fraction, with the denominator being a power of ten, I was beginning to accept that it works (it took a lot more actually, like understanding the concept of prime factorization etc.). Which might be a kind of stupidity, but not something that would prevent me from ever understanding mathematics.
The concept of a function is another example:
f:X->Y (Uhm, what?)
f(x) : X → Y (Uhm, what?)
f(x) = x+1 (Hmm.)
f(1) = 1+1 (Okay.)
y = f(x) (Hmm.)
(x, y)
(x, f(x))
(1,2) (Aha, okay.)
(x,y) is an element of R (Hmm.)
R is a binary relation (Uhm, what?)
x is R-related to y (Oh.)
xRy
R(x,y) (Aha...)
R = (X, Y, G)
G is a subset of the Cartesian product X × Y (Uhm, what?)
...so it goes. My guess is that many people appear stupid because their psyche can’t handle apparent self-evidence very well.
When I first saw a fraction, e.g. 1⁄4, I had real trouble to accept that it equals .25. I was like, “Uhm, why?”...when other people are like, “Okay, then by induction 2/4=.5″...it’s not that I don’t understand, but do not accept. Only when I learnt that .25 is a base-10 place-value notation, which really is an implicit fraction, with the denominator being a power of ten, I was beginning to accept that it works (it took a lot more actually, like understanding the concept of prime factorization etc.). Which might be a kind of stupidity, but not something that would prevent me from ever understanding mathematics.
The concept of a function is another example:
f:X->Y (Uhm, what?)
f(x) : X → Y (Uhm, what?)
f(x) = x+1 (Hmm.)
f(1) = 1+1 (Okay.)
y = f(x) (Hmm.)
(x, y)
(x, f(x))
(1,2) (Aha, okay.)
(x,y) is an element of R (Hmm.)
R is a binary relation (Uhm, what?)
x is R-related to y (Oh.)
xRy
R(x,y) (Aha...)
R = (X, Y, G)
G is a subset of the Cartesian product X × Y (Uhm, what?)
...so it goes. My guess is that many people appear stupid because their psyche can’t handle apparent self-evidence very well.