[gforge]

While I knew the concepts of log I first truly understood it when I started looking at everything as log2. In hindsight I feel like a moron, obviously it is about doubling and halving risks is what it's about (I'm an MD so everything is a risk ratio in my field).

I remember a colegue that was presenting results during their defense of a thesis where one risk ratio 0,45 and the other 2,1. I asked which effect was biggest and they automatically replied 2,1. I'm pretty sure that 80%+ of my colegues would make the same mistake. Everyone understands double/half - we should try to teach people this as the word log is just too intimidating for so many.

[WorldMaker]

The word "logarithm" is an interesting accident of how they were calculated for so long. Exponentiation is easy: at its core it's just repeated multiplication. But doing the "opposite" is much harder, it is not just, say, repeated division. Some of the oldest algorithms were logarithms. Some of the most complex algorithms an average person might study for a large swath of history were algorithms.

One of the most complex functions a slide rule enabled was simply some logarithms.

When such computations were hard and slow, people filled entire books with logarithms tables. Multiple volumes sometimes filled entire stacks in early engineering libraries.

I feel like this illustrates one of the biggest problems when we teach math from a "pen and paper first" perspective: exponents are easy to teach with pen and paper as soon as people are used to multiplication, logarithms which are intricately linked to exponents (as the reverse relationship) get saved for one of the last things to be taught, if they are taught at all, because not only is teaching them with pen and paper hard, it's now even harder that slide rules and logarithms tables are out of fashion, so a lot of teachers skip them.

Computers make long slow calculations so much easier. We have the power to give people some very deep visualizations into things like how directly exponents and logarithms are related, we maybe shouldn't let the historic complexity hide the visual simplicity so much when we teach these early concepts. Logarithms are always going to feel complex and ugly to those that study them with pen and paper alone. We have the technology to improve that.