Coincidence (2)

To walk around and observe, to take in what is presented to you, to enjoy playfulness, is part of relaxing. Sometimes, coincidences just make it more enjoyable, so awareness is something that causes coincidences to be observed. It does not mean that when you do not observe them, they are not there... Well, maybe they then aren't because you just did not observe them?

So, when you start seeing more coincidences it says something about your interaction with reality, which in turn is the interaction of reality with you. It says that if you pay more attention to reality, reality pays more attention to you. It increases the mutual awarenes until everything your senses communicate to you have become the coincidence that makes up the totality of you and your reality, who become one.

So, today I walked around and observed something I had never observed in a way that I became aware of it. I just took it in as if I walked there for the first time. I stood in front of a school building, observed the wall and at first did only recognize a colored wall. Looking better, I saw different sizes of balls sticking out of the wall, with diameters ranging from about 3 to 13 cm. Looking better still, I saw a round clock and the balls were positioned around the clock. I noticed that there was a slight asymmetry in the balls: more balls to the left as to the right of the clock. Then I noticed that the balls had different colors and that they matched the colors of the numbers of the clock. More precisely, the clock itself consisted of balls as well, each of them had a number (indicating the hours) but these balls were not solid; only their circumference was colored. That made it a bit harder to put it together. Then I noticed that for each number, the balls with the same color as that number were close to that number and were in the same amount as the number. So, there was one solid ball of a certain color near the ball with 1, there were two solid balls of a certain other color near the ball with 2, and so on. It was fun to check that indeed for every number of the clock, the corresponding amount of balls were positioned near that number. As I progressed towards the 12, I understood why there were more balls to the left of the clock, since obviously the numbers at that side of the clock were larger.

I asked myself:
1. How many balls are there in total (the solid ones and the ones with numbers)?
2. How many balls are positioned around the clock?

Instead of counting them again, risking a counting error, I quickly computed that number and at that point decided to put it here on the blog. You will see why. But I will explain the computation here in full detail.

The same computation is necessary when you want to compute the amount of numbers 1 in the triangular figure below:

1 1
1 11
1 111
1 1111
1 11111
1 111111
1 1111111
1 11111111
1 111111111
1 1111111111
1 11111111111
1 111111111111

The first 1 in each row corresponds to the ball with a number of the clock; it is drawn on a single ball. The other 1's in each row correspond to the amount of balls in the color of that number. I left out the colors and sizes...

Note that there are 12 lines and the last row has 13 1's. Suppose we call O the total number of 1's. Then the answer to question 1. is O and the answer to question 2. is O-12. (You agree, don't you?)

Let's compute O by adding zero's as follows:

1 100000000000
1 110000000000
1 111000000000
1 111100000000
1 111110000000
1 111111000000
1 111111100000
1 111111110000
1 111111111000
1 111111111100
1 111111111110
1 111111111111

We have constructed a rectangle so that it becomes easy to compute the number of 1's and 0's together as

12 (rows) x 13 (length) = 156 = 1 x 3 x 13 x (1+3).*

Let's call Z the number of 0's. We can relate Z to O by relating the triangle of 0's to the triangle of 1's as follows. There are just 11 rows of o's against 12 rows of 1's. The 1's are arranged in a triangle with rows of lengths ranging from 2 to 13, while the 0's are arranged in a triangle with rows of lengths ranging from 1 to 11. So, if we compare both triangles, the triangle of 0's has an extra row of length 1 and misses two rows of length 12 and 13. This means that

Z = O + 1 - 12 - 13.

We know that O+Z = 156 as noted before. We can compute O+Z in a different way by using the previous relationship:

O+Z = O+O+1-12-13 = 2O-24,

and so, since a number can only have a single value, we infer that

2O-24 = 156,

which means that we can compute O as follows:

O = (156+24)/2 = 180/2 = 90.

Remember, that O equals the total number of balls on the wall, the answer to question 1. To compute the number of (solid) colored balls, we can now subtract 12 from this number, arriving at a total of 90-12 = 78, the answer to question 2.

Note that 78 = 156 / 2 = - 1 x 3 x 13 x (1-3).**

*, **: Compare with previous post, where the number
1 x 3 x 13 x 103
came up.

Explanation.
Ghimmel combines and switches from Aleph to Beyt and from Beyt to Aleph. Ghimmel is the principle of action; it causes the movement of Beyt, the container of Aleph. The triangle Aleph-Beyt-Ghimmel can be examplified as follows.

The principle of quantity (corresponding Aleph) is expressed by different numbers (corresponding to Beyt) that are manipulated by computations (corresponding to Ghimmel).

Without computations, numbers would be static (just a sequence of different symbols) and could not be related, added or multiplied.
Without numbers, quantity could not be expressed.
Without quantity, neither number nor computation would exist.

Without Ghimmel, Beyt would be motionless.
Without Beyt, Aleph could not be expressed.
Without Aleph, neither Beyt nor Ghimmel would exist.