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 10^{1}, 10^{2}, 10^{3} 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).