I can’t help but love logarithmic scales. Most graphs and images that we see are drawn using a linear scale. By that I mean that the axes (axises? axis’?) count using the basic numbers so that it goes 1, 2, 3, etc… Logarithmic images, on the other hand, have axes that count using the exponents, usually with a common base number like 10. In this way it counts 101, 102, 103 or more commonly (amongst us non-mathematical types) 10, 100, 1000. In this way, things that are of greatly differing size or values can be compared.
One great example of this is the XKCD comic Height. It uses a logarithmic scale with a base of 2 so that every tic represents twice the height of the previous one. I fell in love with that image when I first saw it. But of course, “real” scientists have done him one better. Below is a (slightly and ineptly edited…by me) image of the logarithmic universe which apparently was posted waaaay back in 2005. It shows pretty much the entire universe. I’ve limited this image here to just the area near the earth. Click on it to see the complete image (warning it’s a big image…remember it’s the entire universe).
I’m not sure that this is related the way that I think it might be, but the latest Radio Lab Podcast had a segment on the fact that very young children think of numbers logarithmically. Perhaps our difficulties with scale and magnitude are a reflection of this natural understanding of numbers (rather than our “unnatural” understanding of numbers as serial).
Until now I thought I was the only person who was silly enough to teach myself calculus just for the fun of it. It turns out there is at least one other person as crazy as I am.
Most people who find out that I did such a thing immediately assume that I’m some kind of math whiz, when in fact I did it precisely because I suck so bad at it. In college I took some math classes because I love science and I knew that a good mathematical base could help a whole lot. I got to pre-calculus and scored a hard won D, the lowest score I’ve ever gotten in any class I’ve ever taken in my entire life*. I HAD to take it again, if for no other reason than to erase that blight from my academic record. The second time around, through much hard work and perseverence I was able to raise that D to a D+. Okay, actually it was the same D. I gave up going to math classes, but I never really gave up trying to learn the math. Over the years I’ve built up quite a collection of math books, which I revisit every once in awhile in a renewed attempt to power through my mathematical mental block. It looks like it might be time to add to that collection. The Manga Guide to Calculus sounds interesting.
And by the way I was right. It really has helped me a lot in thinking about and understanding much of science.
* In reality I’ve gotten many D’s and F’s in my academic career. The difference here was that I was actually trying, where all the other bad scores were classes that I didn’t give a damn about.