Question

What are some non-character representations of numbers?

Answer 1

Voltages in analogue circuits are an, well, analogue to numbers of different sizes

Answer 2

Some forms of vector algebra basically let you do math with arrows. You can add and subtract two arrows together. You can find a parallelogram between those arrows. You can rotate them, and then extrude that parallelogram along a third arrow into a parallelepiped. You can project one arrow, or other object, onto another object, and then find what was left over.

Answer 3

When someone asks my daughter how old she is, she proudly holds up three fingers. You could conceivably make any number with fingers.

Answer 4

Tally marks

Answer 5

I'm wondering about visual or physical representations of numbers that aren't written symbols/characters, things like groups of objects, or polygons or polyhedrons come to mind.

Are there more? Do you have any favorites?

Answer 6

You could represent binary numbers in the form of electrical potentials in semiconductors like computers do.

Or unary is essentially non-symbolic -- a group of some number of objects (e.g. beads or something) would be the represntation of that number.

Answer 7

In Papua New Guinea, the Mountain Ok people (not a single community, but a cultural cluster of different linguistic communities with several aspects of culture in common) use a system for counting on their bodies. There is some variation, but the most use a system of 27 points going from the right thumb, through the arm, head, other arm, and the other set of fingers.  Google "Oksapmin counting system" for images.

So aside of using more of the body this system is equivalent to holding up fingers, except for the fact that they have no words for numbers other than these gestures. To indicate a given quantity you point at the corresponding body part.

Answer 8

Or, you could do an empty bowl for 0, A bowl containing an empty bowl for 1, a bowl containing an empty bowl and a bowl containing an empty bowl for 2, and so on…

Answer 9

NaN maybe? Epsilon in automaton theory? Or am I totaly wrong, with my suggestion?

Answer 10

The ancient Greeks did math almost purely in terms of geometry with almost no numbers. It was all visual. They discovered some very advanced concepts like limits but had no way to express it other than drawing them.

That is one reason why Pythagoras was so freaked out over the square root of 2. They had no decimal representation and they figured out that it could not be written as the proportion of two other things. According to what they knew at the time, it shouldn't exist.