As the sun moves across the sky, the shadow cast by the gnomon will move. But how do you turn that shadow into time? You got it—you measure the distance of the shadow from the noon position. The sundial above is pointing to 2:10 pm.

(Interesting footnote: The hour labels had to be inscribed differently from city to city because the shadow changes by latitude and longitude. If you moved from Sparta to Athens and took your sundial with you, you’d be five minutes late to class at the Lyceum.)

Here's another time-measuring device you might have seen, which shows the same time, 2:10, in a different way:

I love this old clock. It's fun to remember that “IBM” stood for International Business Machines, which weren’t just computers. Anyhow, you read the time from the location of the hands. Yup, that's a distance measurement—the information is conveyed by how far a hand has traveled around the dial. But wait! There's more! Here are some other things that measure using distances:

That force gauge above, for instance, has a calibrated spring inside. When you hang a mass on it, the spring stretches proportionately to the force exerted, and the length of extension indicates how many newtons of pulling force were applied. The result is displayed as a distance on a dial.

Sometimes we just do comparisons without a distance measurement. Here is a balance scale. You put an unknown mass on one side and add known masses to the other side until they’re equal. That’s how assayers measured gold during the California Gold Rush.

Why didn’t they use a spring scale, which would be faster? Because spring scales, like your bathroom scale, measure the gravitational force acting on an object—that’s what “weight” really is. Mass is a different concept; it’s the amount of physical matter in an object. Because the gravitational field is not uniform all over the world, a weight measurement could differ from place to place. But a balance scale will give the same measure of mass anywhere you go, since the local gravity affects both sides equally. It’s also probably harder to cheat with a balance scale.

But aside from a few similar exceptions, almost all analog devices use comparison and length measurements to get a value.

Counting and Digital Instruments

What if you wanted to model the populations of wolves and rabbits? You could show that without wolves, the number of rabbits grows exponentially until they reach the resource limit. Obviously now you’re counting, not comparing.

Here’s an old laboratory timer that counts off tenths of seconds. See how that’s different from the clock? It’s not continuous like a sweeping second hand—it can only take certain discrete values. That’s the key property of a “digital” instrument: It’s like counting on your fingers, aka digits!

This might be confusing at first; we’re used to thinking of digital as synonymous with electronic. But what makes electronic systems digital is that information can only be represented by discrete values—the binary digits 0 and 1. So yes, even though the timer above operates by ratcheting physical gears, this is a digital device.

Or consider a digital voltmeter, like the ones below.

How do you get a digital voltage reading? I’ll demonstrate one rudimentary method. Now, because voltage is the difference in electrical potential between two points, it can’t be measured in absolute terms at a single point; we need a reference voltage for a baseline. (Comparison!)

In my hacked-together voltmeter below, I’m starting with a 9-volt battery. Then I can connect this reference voltage to nine equal resistors in series. From Ohm's law and the voltage loop rule, each resistor will have a 1-volt potential difference.

Now I can use an unknown voltage along with the 9-volt battery. If three of my 4 LEDs light up, we have (3/4) x 9 = 6.75 volts. So this gives us a digital value of the unknown voltage, obtained by counting the lights. Sure, voltmeters don’t really use blinky lights, but you get the idea.

Once we can measure voltage, we can get digital measurements of many other things, like temperature or magnetic field strength or even carbon dioxide levels. The trick is to find something with electrical properties that depend on its environment. For example, a thermistor is a semiconductor whose resistance varies precisely and predictably with temperature. You just run a current through it and measure the voltage to get a temperature reading.

See, anyone can do science! It all comes down to counting or comparing—or both.