amazing

Math Fact: All numbers are equations; 9 is a Fixed Point.

You may be wondering why we count numbers the way we do. If you’re not wondering that, well, now you are, because by subliminal suggestion, you read that first sentence and were forced to ponder it.

Wait I’m supposed to be talking about math.

Right.

Okay, so numbers. Numbers are easy to count. 1…2…3…4…and so on. You don’t even have to think about them. But we’re gonna do just that, because numbers are magical mystical beings from another realm actually an incremental series of one basic equation.

(10n0-1)(Yk0) + (10n1-1)(Yk1) + (10n2-1)(Yk2) + (10n3-1)(Yk3) + ….

Where Yk is defined as an integer digit to the left of the decimal point, and n is defined as the placement of Yk0 with respect to the decimal point.

As an example, let’s take the number 49.

Yk0 = 9
Yk1 = 4

In this case, Yk0 is located 2 spots in front of the decimal point, thus:

n = 2
n-1 = 1

Let’s put all of this together:

(100)(9) + (101)(4)
= (1)(9) + (10)(4)
= 9 + 40
= 49

Let’s try another number, say, 283.

Yk0 = 3
Yk1 = 8
Yk2 = 2
n0 = 2
n1 = 3
n0  – 1 = 1
n1 – 1 = 2

So, putting these into the equation, you get:

(100)(3) + (101)(8) + (102)(2)
= (1)(3) + (10)(8) + (100)(2)
= 3 + 80 + 200
= 83 + 200
= 283

Now, you’re probably wondering why you can’t just count numbers and be done with it. And that’s all fine and dandy. But this shows you something fundamental about the WAY we count numbers: all of our numbers can be simplified down to a base of 10. This explains WHY we use decimal points (you can use this same equation on the flipside of a decimal, but you always have to keep Yk0 on the left side. Yk0 will ALWAYS be the first digit to the left of the decimal.

This also explains why the standard logarithmic base is 10, as compared to 2 in some variations (if you tried to replace the “10″ in the above equations with “2,” you would have a VERY different system of counting).

Finally, this also explains why the number “9″ is what is defined as a “fixed point” under Brouwer’s Theorem. If you add up the integers of any two-or-more digit number and subtract them from the original number, the resulting number will be divisible by 9. If you repeat this process, eventually the digits will ALWAYS add up to 9 or a multiple of 9, until you reached the number 9 itself and could no longer subtract away a value.

For example, take the number 697.

6 + 9 + 7 = 22
697 - 22 = 675
675 / 75 = 9

6 + 7 + 5 = 18
675 - 18 = 657
657 / 73 = 9

6 + 5 + 7 = 18
657 - 18 = 639
639 / 71 = 9

6 + 3 + 9 = 18
639 - 18 = 621
621 / 69 = 9

Now watch…. 6 + 2 + 1 = 9
621 - 9 = 612
6 + 1 + 2 = 9
612 - 9 = 603
6 + 0 + 3 = 9

I could go on all the way down to 9, but as you can see, the added values keep switching back and forth between 9 and 18, and every single number is wholly divisible by 9.

This property is specifically due to the fact that we count by base 10. Each time you subtract, you remove one of the integers multiplied by 10. That is to say, the number 37 isn’t 30 + 7, it’s really 3+3+3+3+3+3+3+3+3+3+7 (ten 3s and a 7). By removing one of the 3s, you now only have 9, and thus, 9 remains a fixed point on the number line.

Brouwer’s Theorem doesn’t just apply to numbers, but to any closed system without holes. If you stir your coffee, no matter how you stir it, there will ALWAYS be one point that NEVER leaves it’s original position. A fixed point. No matter how you translate, scale, or twist a closed system without holes, without fail, exactly one point will NEVER change.

That’s math, people. Pretty amazing, huh?

In terms of an individual, not so much, but it’s kind of like, it’s kind of got a double meaning I guess. It’s my home town, you know it’s funny how things never change in this home town, uhh, but everything comes back to you, you know, like going home and stuff like that. It's also got that double meaning and people can, people from small towns can understand. There’s always that one individual that you end up seeing when you go home or whatever.
—  Niall talking about the meaning behind ‘This Town’ 

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