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-   -   The tenth digit (http://cellar.org/showthread.php?t=16852)

HungLikeJesus 03-18-2008 03:43 PM

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.

Flint 03-18-2008 04:09 PM

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.

SteveDallas 03-18-2008 04:14 PM

Quote:

Originally Posted by HungLikeJesus (Post 439693)
It's just not right. . . It's crazy.

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?

Quote:

Originally Posted by HungLikeJesus (Post 439693)
Rather than present derivation of decimals and negative numbers, I'll leave those as exercises for the reader.

No, I want to see you do decimals.

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

HungLikeJesus 03-18-2008 04:14 PM

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

Flint 03-18-2008 04:17 PM

Quote:

Originally Posted by SteveDallas (Post 439706)
Are the numerals customarily used to represent individual digits arbitrary?

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.

Flint 03-18-2008 04:20 PM

Quote:

Originally Posted by HungLikeJesus (Post 439707)
But you wouldn't count something beginning with zero, would you?

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

monster 03-18-2008 04:24 PM

Starting out with nothing makes you stronger.

HungLikeJesus 03-18-2008 04:25 PM

Quote:

Originally Posted by SteveDallas (Post 439706)
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.

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.

Flint 03-18-2008 04:26 PM

Quote:

Originally Posted by monster (Post 439715)
Starting out with nothing makes you stronger.

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

HungLikeJesus 03-18-2008 04:27 PM

Quote:

Originally Posted by Flint (Post 439710)
Yes, I would. My workstations, servers, the drives in my tape libraries, etc. all begin their respective naming conventions with device zero.

So your first child is really child number zero?

Flint 03-18-2008 04:30 PM

:::head explodes:::

milkfish 03-18-2008 04:35 PM

Quote:

Originally Posted by HungLikeJesus (Post 439720)
So your first child is really child number zero?

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.

HungLikeJesus 03-18-2008 04:55 PM

Quote:

Originally Posted by monster (Post 439715)
Starting out with nothing makes you stronger.

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

Happy Monkey 03-18-2008 05:05 PM

Quote:

Originally Posted by HungLikeJesus (Post 439707)
But you wouldn't count something beginning with zero, would you? You always start with one.

Unless you don't have any.

SteveDallas 03-18-2008 05:09 PM

Quote:

Originally Posted by HungLikeJesus (Post 439717)
Logically, after 9þ (ninety-ten) comes þ1 (tenty-one).

What comes after þþ?
Quote:

Originally Posted by HungLikeJesus (Post 439717)
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'm speechless. Help me out here, what's 0.1? 0.01?

Why does the concept of zero bother you so much?


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