We generally use ten digits for counting: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Everybody knows that. "Normal" math is said to be in "base 10" because we make numbers by counting through these ten digits, then adding a digit to the left and starting over again. This process is so familiar that we never really think about it. It's just "how counting goes."

    0,   1,     2,     3,     4,   5,     6,     7,    8,    9, --> 10
  30,  31,   32,   33,   34,  35,   36,   37,  38,   39, --> 40
520, 521, 522, 523, 524, 525, 526, 527, 528, 529, --> 530

But you don't have to use ten digits for counting. You can use two digits or five digits or sixteen digits or as many as you want, just as long as you keep cycling through them in the same kind of pattern.

For a short example, let's say you want to count in base 3. That gives you three digits to work with: 0, 1, and 2. So you start at zero (0), then you count one thing (1), then you count a second thing (2), and already you're out of counting room because you've run out of digits! So just like in base ten, you make more room by moving the "high" digit (in this case, 2) back to zero and adding one to the left.

0, 1, 2, --> 10

So you go from "2" to "10" (don't think "ten", think "one, zero") - and that's three. Now you can go from 10 to 11 (for four things) and from 11 to 12 (for five things), and you can see that the right-hand digit is up to 2 again.

10, 11, 12, --> 20

The pattern may be easier to see in the chart below. (To see it even more easily, when you see a number like 12 or 110 on the chart, don't think "twelve" or "one hundred and ten," think "one-two" or "one-one-zero.")

base 10    "actual" number     base three
0 ---------------  zero ----------------- 0 (zero)
1 ---------------  one  ----------------- 1 (one)
2 ---------------  two  ----------------- 2 (two)
3 ---------------  three  -------------- 10 (one, zero)
4 ---------------  four  --------------- 11 (one, one)
5 ---------------  five  --------------- 12 (one, two)
6 ---------------  six  ----------------- 20 (two, zero)
7 ---------------  seven  -------------- 21 (two, one)
8 ---------------  eight  --------------- 22 (two, two)
9 ---------------  nine  --------------- 100 (one, zero, zero)
10 --------------  ten  ---------------- 101 (one, zero, one)
11 --------------  eleven  ------------ 102 (one, zero, two)
12 --------------  twelve  ------------ 110 (one, one, zero)
13 --------------  thirteen  ---------- 111 (one, one, one)

You see? In base three, whenever you get through all three digits (0, 1, 2) you have to start back around at zero again, just like you have to do in base ten whenever you get through all ten digits. Simple enough.*

And now we're getting to the joke. Notice that in base three, "100" is nine, which is three times three. And in base ten ("normal" math), "100" is one hundred, which is ten times ten. Whatever base you're working in, "100" is always that base times itself.**

Here's a small chart of what "100" stands for in a few different base systems, translated into "normal" math:

"100" in base 2 (2 X 2) is 4.
"100" in base 3 (3 X 3) is 9.
"100" in base 4 (4 X 4) is 16.
"100" in base 5 (5 X 5) is 25.
"100" in base 6 (6 X 6) is 36.
"100" in base 7 (7 X 7) is 49.

So there's the joke. In base 7, the number forty-nine is written "100." So the 49th post is the "100th" post if you're counting in base 7. (Hey, I said it was a little math humor. I never said it was hilarious...)

So what was all this math talk supposed to illustrate? There are many, many things we do every day that we never think about. We don't have to do them the way we do. It just feels like the only way to do them. It feels like the "real" way because that's how we've always done these things - because that's how everyone does them. But the way we do things isn't necessarily the best way to do them. It's just what's familiar.

"100" doesn't have to stand for one hundred. That's nothing more than a convention. We use base ten out of habit. Originally we probably chose to base our math system on ten digits because we have ten fingers. But we could just as easily have used base three or base five or base seven. (Base five could have been a natural choice, since we have five fingers on each hand.)***

This problem of the familiar is worth keeping in mind when we look around at how we do just about everything. For example... Do people really have better ideas when they're wearing business suits than they do when they're wearing blue jeans? Does the name on the label of your favorite pair of blue jeans really reflect your personality? Does a school "uniform" that allows children to wear different brand names really eliminate the awareness of social "class"? Does a person's level of "class" really have anything to do with their level of income?

Most of the "thinking" that we do every day isn't really active thinking. It's just popular (and familiar) programming that goes streaming through our minds unquestioned. We make assumptions about other people based on all kinds of social cues that have few, if any, ties to reality. We make assumptions about the appropriateness of policies based on "common sense" that may be more common than logical.

The list goes on and on and on... As difficult as it is, try not to assume in life that "familiar" is the same thing as "necessary." Look around. Question everything. Just because "it's the way everybody does it" doesn't mean it's the best way. Every parent tries time and again to teach this to their children. ("If your friends jumped off a bridge, would you do it?") It's time we remembered it for ourselves.

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*You might have noticed that "10" is how you write the number ten in base ten and it's also how you write the number three in base three. That always happens because you always have to roll over to 10 (one, zero) when you run out of single digits. So "10" is also how you write five in base five, and seven in base seven, and sixteen in base sixteen. That's how it works.

**Technically, that's because when you get to "100" you've run out of that many digits that many times. Look at the base three chart above - when you get to "100" in base three, you've gone through all three digits three times.

***Just to blow your mind a little more, if we did use any of those bases, then in each case that's what we would be calling "base 10" - because "10" is three in base three, and five in base five, and seven in base seven. If we all used base three math, for example, then base three math would be called "base 10 math" -  and everyone would think that was "real" math and that 22 things was "really" this many: ||||||||. And then base ten math would be called "base 101 math" (because ten is represented as "101" in base three - see the chart above), and everyone would think that wasn't "real" math because they would think there weren't "really" enough digits for base 101 math since everyone would know that zero, one, and two were the only "real" digits and the rest were just "made up" by mathematicians. Strange, huh?