Same thing with logarithms, which were invented to simplify multiplying two huge numbers. Combined with log tables (think paper LUT for humans) that became a simple matter of looking up two log conversions, adding them, then looking up the inverse of the answer.
Is that what we learn in high school? Nope. So everyone is left wondering what the hell they are good for (or were, before we had calculators) the first time around.
(btw, as far as I can tell you don't have that bit of history on your site yet either - might be an interesting addition?)
Well, I learned that at school. It still didn't answer what the hell logarithms are good for. Everyone was left wondering why we were learning something that can be replaced by calculators.
Seeing some modern application of lagarithms would be great. Even just making a log-log graph at some point would answer every question. But those are not at the official curriculum.
It drives me batty because we learn the properties of logarithms before (if ever) internalizing what they mean. Here's my intuition if it helps someone:
Exponents let you plug in time, and get the amount of growth. e^3 ~ 20, which means "3 periods of 100% continuous growth [100% is implied by e, 3 = 3* 1] will grow us from 1 to 20".
Logarithms let us plug in the growth, and get the time it took to get there.
ln(20) ~ 3 means "It takes 3 units of time [growing at 100%, continuously] to grow from 1 to 20".
Exponents take inputs and find the future state, logs take the future state and work backwards to find the inputs that got us there.
Great tidbit, thanks. I forget if I have a mention that logs were developed before e, but I love it because it's a little mosquito in the ear for the over-rigorous mathematicians who define e up front (as a limit) and then say "the natural logarithm is log base e".
e was only discovered because of logarithms, not the other way around! :)
Is that what we learn in high school? Nope. So everyone is left wondering what the hell they are good for (or were, before we had calculators) the first time around.
(btw, as far as I can tell you don't have that bit of history on your site yet either - might be an interesting addition?)