Negatives Stack; Positives Don't: The Number Line Model Of Communication
An extended metaphor shining light on the problem of having to use humans in groups to agree on things that eventually need to be coded into a formal system.
Do you know about pi (π)? π is the ratio of a circle's circumference to its diameter. This ratio is the same for any circle. Pi is a neat little number most kids learn about in school. People have known about it for thousands of years, ever since we started drawing circles and doing math with them.
Here's a fun game: ask a friend what pi is. Some people will say "3". Many have learned that π is the ratio 22/7. Still others, probably the kids who think they're smart, will say "3.14". If you were to ever ask me, ever since I was a little kid, I'd tell you that it is "3.141592863". That's because I tend to be a pretentious jerk who found things like this impressive, but I only learned that about myself as I got older. At the time, I thought it was pretty cool to know that many digits. I have many friends that know π out to 10, 50, even 100 or more digits. What can I say? We usually had no problem picking up the girls at parties. It's a gift.
π is what's called an irrational number. Technically irrational numbers are those numbers which are not rational. (Mathematicians get paid for saying such things!) Rational numbers can be expressed as p/q, like 4/1, 2/3, or 19/28. You can also express any rational number as a couple of fractions banged together with an arithmetic operator, like 1/2 + 1/4, or 33/17 * 3/17, because math. If you can't express a number as a ratio of numbers, or a combination of ratios, then by definition it's not rational. It's still a number, or course, and it still exists on the number line. So where is it?
