Which brings us back to logarithms. We need them because it’s always useful to have tools that can undo one another. Just as every office worker needs both a stapler and a staple remover, every mathematician needs exponential functions and logarithms. They’re “inverses.” This means that if you type a number x into your calculator, and then punch the 10x button followed by the log x button, you’ll get back to the number you started with. Logarithms are compressors. They’re ideal for taking numbers that vary over a wide range and squeezing them together so they become more manageable. For instance, 100 and 100 million differ a million-fold, a gulf that most of us find incomprehensible. But their logarithms differ only fourfold (they are 2 and 8, because 100 = 102 and 100 million = 108). In conversation, we all use a crude version of logarithmic shorthand when we refer to any salary between $100,000 and $999,999 as being “six figures.” That “six” is roughly the logarithm of these salaries, which in fact span the range from 5 to 6. As impressive as all these functions may be, a mathematician’s toolbox can only do so much — which is why I still haven’t assembled my Ikea bookcases.
more from Steven Strogatz at The Opinionater here.