I’m unable to detach my mind from the linear scale imbedded in my head, how to make sense of a logarithmic increase?
In: 13
Take some graphing calculator. Throw up two functions: y=x and y=2^x
Now, stretch the paper it’s drawn on so that the 2^x line is straight. Your original y=x line will be very bent. Your new ‘paper’ is a log scale.
These scales are useful, broadly, when comparing multiplication instead of addition. Going up one line in a linear scale means something is bigger by 1 (or some other fixed number), but on a logarithmic scale it means *multiplying*.
Say you want to compare the height of an ant, a human, and the burj khalifa. On a linear scale, the ant and the human are right next to eachother, while the BK is *really far away*.
This can be sort of misleading, though, as the ant is 500x smaller than the human, who is 450x smaller than the BK. An ant looking up at a human sees us towering above them, much like we see this huge skyscraper towering above us. The experience is similar; the size relationship between the ant and the human is like the size relationship between the human and the BK.
On a logarithmic scale, this is represented well. The ant and the human are about as far apart as the human and the BK, as opposed to the linear scale which would tell you that an ant and human are “about the same size”.
Latest Answers