The tenth digit
 

How many of you are comfortable with our current counting system? You know, 1,2,3,4,5,6,7,8,9,10, etc.

This is something that's been drilled into us for so long that it seems normal, natural, not to be questioned. And what's wrong with that?

Here's an example. Get a sharpie, or other permanent marker. Starting with the pinkie of the left hand, number each of your fingers, including the thumbs. Left pinkie - 1. Left ring finger - 2. And so on. Left thumb - 5, right thumb - 6...

What happens when you get to your right pinkie? Right pinkie is 10 - that takes two digits! It's just not right.

There are other problems with the number 10, and its multiples. For example, most people think that 20 is the bottom of the twenty series. It's not - it's the top of the teens. And 30 is the top of the twenties. It's crazy. But what can we do?

I would suggest that we adopt a single digit representing 10. What will we call it? How about ten? What should it look like? Maybe this: þ. It's like a 1 and 0 combined into one digit.

With the new digit þ we can almost completely eliminate use of the dreaded zero (but not completely).

Counting in new digit is almost the same as counting in old digit:
1,2,...,9,þ, 11, 12, ... ,19,1þ (tenteen), 21, ..., 29, 2þ (twenty-ten), 31

Counting in old digit, we have 9 one-digit numbers, 90 2-digit numbers, 900 3-digit numbers, etc.

Counting in new digit, we will have 10 1-digit numbers, 100 2-digit numbers (from 11 to þþ), and so on.

Doesn't that just feel right?

Rather than present derivation of decimals and negative numbers, I'll leave those as exercises for the reader.

I think of the first ten digits as 0 through 9, with 9 being the 10th single-digit number.

But this does remind me of something that bothers me: Sunday is the END of the week. NOT the beginning. Monday morning, when you clock in at work, is the beginning of the week for most people. Sunday is the last day in the weekend, which is the very last part of the week. Monday begins the next week. . . . It's stupid to have calendars arranged with Sunday as the beginning of the week.

Speak for yourself. I can calculate in any base you care to name. Our current system for representing numbers* with numerals* according to place values is flexible enough to accommodate this. Are the numerals customarily used to represent individual digits arbitrary? Of course. Duh.

What comes after 9þ?

No, I want to see you do decimals.

*Yes, there's a difference between numbers and numerals.

But you wouldn't count something beginning with zero, would you? You always start with one.

No. We have ten clumps of neurons that represent the ten digits. They study stroke and brain injury patients to see what they "lose" when certain parts of the brain are damaged. The ten digits reside just above and slightly behind your ear.

Yes, I would. My workstations, servers, the drives in my tape libraries, etc. all begin their respective naming conventions with device zero.

Starting out with nothing makes you stronger.

Logically, after 9þ (ninety-ten) comes þ1 (tenty-one).

Decimals are a lot of fun, and the representation changes depending on degree of accuracy indicated (i.e. number of significant figures).

1.5 is still 1.5, but 1.50 becomes 1.4þ and 1.500 becomes 1.49þ

In this way, we know that we really mean three or four significant figures, and are not just writing down what the calculator or spreadsheet gives us (I see this error all the time). Of course, there's still plenty of room for human error.

I think that's a brilliant and creative statement in response to this subject.

So your first child is really child number zero?

:::head explodes:::

No, my zeroeth child is child number zero. And a model tyke he/she is, never any discipline trouble after all, and so easy to please.

But my zeroeth wife, she was hard to get along with.

Some crazy people say first floor when they mean one up from ground level, so I guess that would make sense to them.

Unless you don't have any.

What comes after þþ?
I'm speechless. Help me out here, what's 0.1? 0.01?

Why does the concept of zero bother you so much?