
There are many ways to represent a number and the three I mentioned aren’t the only ones. If you want base5, your numbers are 0,1,2,3,4, or [0..4]. The number 8d would be 13 in base5. The number 54d in base 33 [0..9,A..W] would be 1L. Obviously, you have to define what your characters represent with numbers from another base. (In this case, A = 10d, L = 21d and W = 32d. 10 = 33d, 1W = 65d, 20 = 66d, and so on.)
Anyway, here is the reason this came up in my mind. There is an easy program which was needed at work. So they hacked out a simple VB (Visual Basic) script to get the necessary information. I would have preferred a “real” language which is also easy to program (such as C#). This would have the advantage of being fewer lines of code, not as bloated (still bloated), and can be compiled to an executable file (.exe).

Here’s the wrap-up. The second to last sentence of their section on Base (what I explained above) is “Base-0 does not exist and you cannot do much with base-1.” Base 1 is easy, there is only one number – 0, if you will. Or 1. It doesn’t matter, there is only one character to represent the entire numbering system and there is nothing or that character – that’s it). In base 1, you could even make your only value, your only digit, Ψ.
This got me thinking about base 0, though. Base 0 has no values. It will have no characters. It is nothing – not even 0. It’s what happens when you divide by 0 – you can’t (excluding 0/0 which is ∞).

This base system is really, completely useless… except to explain it like I have here.
Surprisingly, my little thought process here is not at all off, in fact it is quite on. Here is a post by someone else who has put in a lot more thought on off-beat numbering systems (a system based on pi, e, or i?!) . Scroll down a bit, he calls Base 0 “truly worthless” where I said “completely useless”. Funny.
On dwheeler’s closing remark about base 0 potentially representing all numbers (ie. 0/0), I disagree. A base 0 system has no characters to represent it. It is nothing (which is the same as not nothing, that is – doesn’t exist).
To close this up, enjoy two (10b) videos by They Might Be Giants which do a surprising good job of explaining ZERO and ONE
3 comments:
I suspect that the purpose of this entire post was to share They Might Be Giants "Zero" and "One."
Actually, that popped into my mind as a last minute item. I went back to edit the post to put those links in. But they are great songs!
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