the most fundamental and basic insight is, that everything around us is perceived through our senses. they work logarithmically, and even encode the "natural" logarithm in their fundamental workings. e.g. the cochlea in our inner ear makes about 2.71 turns (text books say 2.5, but that's also only an approx) ... which is exp(1). the reason why they do this is because energy/frequency doubling is mapped into onto a "linear" scaling, which reflects what the underlying fundamentals are about. with musical sound, doubling the frequency is an octave and sequences of octaves sound linear to us. therefore, applying a logarithm just transforms the data in a way such that we can grasp it better …

Very interesting stuff!

But then how will we scare people into selling us their coins for cheaper than we're predicting that they will some day be worth?

hehe.