Logarithms are laughably simple once you've fully internalized the meaning of the log function; it simply answers the question:
"To what power must I raise the base to get the argument?"
This is why the output tapers out as you increase the argument; because as the argument grows exponentially, you only need a fixed increment in the power to reach that number.
I remember when was doing algebra with logs many years ago at school, I was applying rules to remove the log from one side of the equation.
Then when I got to uni, I had to revise the rules but it was kind of silly of me because those rules can be trivially derived if you just think about what the log function means. Turns out I had been solving equations with logs throughout school without understanding what they even meant... It's only at university that I actually bothered to learn them.
Actually TBH. I didn't even understand powers even though I was doing calculus with them at school. I only fully understood powers once I properly internalized the concept of k-ary trees as a proxy.
This essay needs a type system. Every time it says “log” it should say: log of what, into what?
It’s like audio where people say "dB" as if it answers the next question. Relative to what, measured how, and weighted for whom?
Author should brush up on https://en.wikipedia.org/wiki/Lie_theory
The first section details how the author thinks of "log N" with no base as an abstract object rather than a number. Or what are you referring to?
Does this answer the question of why we see hyperoperations until exponentiation in physics, but not higher?
That's a lot of ways to think about logarithms.
Logarithms are laughably simple once you've fully internalized the meaning of the log function; it simply answers the question:
"To what power must I raise the base to get the argument?"
This is why the output tapers out as you increase the argument; because as the argument grows exponentially, you only need a fixed increment in the power to reach that number.
I remember when was doing algebra with logs many years ago at school, I was applying rules to remove the log from one side of the equation.
Then when I got to uni, I had to revise the rules but it was kind of silly of me because those rules can be trivially derived if you just think about what the log function means. Turns out I had been solving equations with logs throughout school without understanding what they even meant... It's only at university that I actually bothered to learn them.
Actually TBH. I didn't even understand powers even though I was doing calculus with them at school. I only fully understood powers once I properly internalized the concept of k-ary trees as a proxy.