the zeroth place

numbers are weird when it comes to how we name them.

there is no zeroth place, but the way we name our numbers, there almost should be. ..let me explain.

it's best if i start with how i got on this train of thought. today is 1/1/2010. brand new decade. i asked myself, how many decades have i been through? let's see.. the 80's, the 90's and the 00's. that's three decades. so this is my fourth decade.

but wait - 4 decades?! how can this be my fourth decade? each decade is 10 years! that means i've gone through 30 years and this is my 40th. but im not even 30 years old, let alone 40.

.. kind of get it?

i think the confusion arises because of the digit used in the tens column. for instance, the number 8. it's really 08. the tens are 0. but why? does 8 fall under the zeroth ten? there is no zeroth. why not, 18, as in the number 8 of the 1st ten.

interesting.

if we follow through, '99' is 89, but then 90 would be '100' ? no we still have one more ten to count, but we need to represent it with one digit. so let's invent a digit, A. so 'A0' is 90. then we get to A9, then 100. hmm, but 100 shouldn't be '100'. it should be '110'. since we're on the first ten of the hundred. but wait, this is our second 100. so it should be '210'. and really, instead of starting with 0, we should start with 1. after all, that's what we do, we start with 1. 1 is the 1st digit. argh!

maybe 100 should be the highest number expressed in two digits. so we get to A9, then it's AA. so to recap, we count like:
1,2..,9,A
21,22,..29,2A,
..
91,92,..99,9A,
A1,A2,..A9,AA,
then 211,212,..219,21A..
hmm

not sure this is better. now when you have one hundred dollars, you have AA dollars. hehe. which i guess makes sense. i mean A = 10, so AA is ten 10's, or 100. but instead of saying you have one hundred, you say you have ten tens.

but then two hundred, that would be 2AA.. two ten tens. hehe
and if you were counting money, say a dollar at a time, then when you got to 2AA, you can say 'thats my 2nd hundred' and it shows in the number, rather than 200 which is just 2 zeros.

ok now i sound silly to myself. hmm ah ok a good test. does this new system improve the original confusing situation?

let's see, three decades past, working on the fourth. so 1-A past, 21-2A, 31-3A.. that's three decades. working on 41-4A.. blah! still sounds like im forty. hmm however, 41 in that number system is actually 31.. so it's accurate.. since i would be turning '3A' and then '41' soon in that number system.

but in the normal number system.. 1-9 past, 10-19, 20-29.. working on 30-39.. bah wait now the normal numbers sound right. hrm.


numbers are weird.