Over my life, I’ve learned all these numbers like “mass of a human” (\(\newcommand{\kg}{,\text{kg}} 70\kg\)) and “mass of an electron” (\I9 \cdot 10^{-31}\kg\)) and “mass of the earth” (\I6 \cdot 10^{22}\kg\)). And I know that an electron is small and the earth is big. But I don’t have a clear picture of how small and how big.

So I made pictures!

The pictures use a log scale – for the uninitiated, a log scale is a way of putting tick marks on a line, and assigning them values, like you might on the y-axis of a bar chart. A “linear scale,” which you use normally, has evenly spaced tick marks labeled “0, 1, 2, 3, …”, and it has great intuitive meaning: if one bar-chart bar is twice as high as another, then it represents a number twice as big. A “log scale,” on the other hand, has evenly spaced tick marks labeled “1, 10, 100, 1000, …”. Its intuitive meaning is that if B is halfway between A and C, then “A is to B as B is to C” – for example, “the tallest building in the world is to you as you are to an ant.” This has the great feature that you can show hugely different numbers – say, the masses of an electron, a person, and the earth – on the same chart without the tiny ones being all squished against each other.

I’m not the first person on the Internet to do this: xkcd beat me twice, at the very least. But here are mine.

Mass

mass

Length

length

Time

time

Energy

energy