I’m gander.

I used to post on usenet under that name.
you might also know me as a c++ programmer of that name.

I’ll try to publish here some thoughts I have on the mathematics I learned at uni.

but also other random topics related to abstraction I will post.

my ultimate goal in life is to learn abstract thinking.

I learned c++ but realized I need to learn object oriented programming instead.
I learned formulas and algorithms but realized I need to learn maths instead.

people call mathematics and category theory “yet another language”. but in reality it is so much more than that.

imagine the language of logic. with its true, false, equals and some additional operator.

just 4 symbols and lots of variables.
of course it’s just a language.
along with a “meaning” we apply to it.

but in addition to that it also is a way of thinking.
a style, a path we walk on.

mathematics is exactly the same, although with much more freedom.

in some blog I read about Jensen’s Paradox:

take 2 points, situated diagonally to each other.
draw a horizontal and a vertical line to connect them.

length of the connection is 2.

you may insert more and more horizontal and vertical lines till you get something resembling a diagonal line.
but the length still is 2 and not \sqrt 2.

the reason is because regardless of how the path does look like, it’s the way you walk on it that counts.
when you see mathematics as a language, it’s as if walking in this 2-sized zig-zag way.
you must think abstractly to get the shorter distances!
maths is about taking shortcuts!

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