Wednesday, October 12, 2005

Amount of information and Display length needed (The Story of Locapoint: 2)

To express ANY location on earth with about one meter (or 3.28 feet) precision, I calculated following.

Meridian of the earth is 40,000,000 meter, thus it needs 40,000,000 steps for 1 meter precision. Actually, it requires

20,000,000 steps in latitude direction (a half of meridian),
40,000,000 steps in longitude direction
= 8*10^14 steps

is required.

From technology's point of view, 8*10^14 steps is 49.507 bits of information.
To express this data, following length of digits is needed in various radix.

50 digits: binary notation (radix = 2)
15 digits: decimal (radix = 10)
13 digits: HEX (radix = 16)
11 digits: radix=26
10 digits: radix=36
9 digits: radix=60
4 digits: radix=10000

If I choose to create a code which is only using number, it requires at least 15 numbers. Like a credit card number (16 numbers), this is not easy to remember for human.

If I choose HEX notation (0-9 and A-E as 10-15), it needs at least 13 digits. it is shorter, but "28a6f6b021cf3" is NOT as easy to remember as telephone number.

If you know Chinese characters, and know 10000 characters, you may use only four letters for a code. This is much sorter, but it seems inconvenience. In addition, increasing in radix base doesn't look effective in decreasing display digits.

So, I had a two choice.
1. Decrease amount of information
with lower precision (like 30 meter or 100 feet)
by limiting cover area of the code (US only, Japan only, etc.)
2. Keep amount of information
but try to create a "Easy" code for human

Many existing code chose the first one. For example, "map code" by Denso Co. can express any location in Japan with 30 meter precision by 10 numbers. Or 3 meter precision by 12 numbers.

I wanted to create UNIVERSAL geographic code, then I had to choose the second one.
But at this time, I had no idea how to do it.