ELI5: How did the human race get more and more precise in its instruments, starting from say, a stone hatchet to an electron microscope?

You start by defining a single measurement, then use math to define other measurements relative to your base measurements.

Example: architectural measurements, you start by defining the length of one meter. It doesn't matter how long one meter is, so long as you tell everybody so that you're using the same measurements.

So you find a stick, or a log, and you cut it and decide that it is one meter long. With this one meter stick, you can make things square using a simple triangle that is 3x4x5, because a triangle of that size will always give you a right angle.

Next, if you have some string, you can put it at the top of your stick and hang a rock from it, giving you an accurate vertical line, to keep things straight up and down. If you can find an accurate vertical line, then you can use your square to make sure the horizontal is straight as well. Now you can create square blocks and boards and build large structures that won't fall down.

Let's say you get tired of these big structures and want to make smaller things, like boxes or chairs. But you've only got a one meter stick, how do you make something that's a half meter? You don't know where the exact middle of your stick is, and if you break it you won't be able to show people how long one meter is.

Levers! You take a one meter stick, and measure out a three meter stick, marking off each meter. If you nail down at the one meter mark, you now have a rotating stick that is one meter one the left, and two meters on the right. That means the right side will move twice as far as the left. If you lower the right side by one meter (which you can accurately measure with your one meter stick) , the left side will raise by 1/2 meter. You can now measure 1/2 meter! And so on, smaller and smaller for most physical measurements.

/r/explainlikeimfive Thread