[ARTS] Pi for a Penny
Greetings everyone!
Dogen once wrote:
"Enlightenment is like the moon reflected on the water.
The moon does not get wet nor is the water broken.
Although its light is wide and great,
The moon is reflected in a puddle even an inch wide.
The whole moon and the entire sky
Are reflected on one dewdrop in the grass."
A very elegant way of expressing Indra's net. "Indra's net" is an infinitely large net and is considered as having a multifaceted jewel at each vertex, with each jewel being reflected in all of the other jewels.
What does any of this have to do with drawing, Pi, and a penny?
When I was in my late teens I worked at a hotel as a dishwasher. One day in the dish-pit I wondered if I could make an equilateral triangle, without a protractor, compass, or the like. I thought, maybe I could use a penny in some way, and pi crossed my mind. A way of dividing the circumference into three parts.
Do follow along and draw this if you can.
I found a piece of paper and pen, then drew a circle around the penny. Seen in example 1 below.
Next I found the exact center of that circle by folding the paper and aligning the two halves of the circle to create a central line.
Next I divided that line in two to find the center. Seen in example 2.
Next I took the penny and lined up one edge with the center of the first circle and traced the edge. Seen in example 3.
Next I lined up the edge of the penny with the center of the original circle, and the exact point the second circle intersects with the first circle. Seen in example 4.
Next the three circles naturally create three points for the next circle to go, two intersection points along the edge of the first circle, and a center point. Seen in example 5.
And there you have it, three points along the edge of a circle, connect them all and you have an equilateral triangle. Seen in example 6
Then I thought back to example 3, and wondered what would happen if we mirrored it. Seen in example 7.
Then mirrored the rest of the steps. Seen in example 8.
Indeed I found many ways to create a sort of art out of it, as seen in 9 and 10.
pattern 1-00f.jpg
From there I was inspired to research Pi a bit more. At the time I knew relatively little about it. It's relatively simple of course, if you take the length of the circumference and see how many times the diameter can fit into it, you will find that it perfectly fits three times, with a tiny fraction left over. If you then subdivide the circumference by that tiny bit, you will find there is a tiny bit left over again. You can repeat this forever and there will always be a tiny bit left over.
It was from this study that I figured out a way to describe the nature of form. Form is just like Indra's net, and so is Pi.
Pi is a transfinite number, and the sequence it produces contains all possible combinations endlessly. This has a very profound meaning that seems to be often overlooked.
Indeed, if we articulate Dogen's poem into a numerical representation, classifying each letter to a number, that poem is found in the digits of Pi before Dogen ever wrote it out. In fact, this entire post, and all posts in this forum are contained within the digits of Pi. Your DNA, what you ate for lunch yesterday, and in a numerical sense the entire activity of the universe is contained in the digits of pi. Not only that, much more is contained in the digits of Pi than merely this universe. All possible articulations, realities, or universes which could be represented in a number sequence, is contained already, in the digits of Pi.
To be clear Pi is just a numerical representation of a fundamental of reality. Often it is said that mathematics is the language of nature, but in my view, reality is the language of nature, and mathematics is merely a partial interpretation of it. The fundamental source of Pi is merely pointed at by the number we get when examining a circle's circumference and its diameter.
There are endless insights that studying this can illuminate, but one of them is the interesting nature of the circle as it relates to knowledge, understanding, and Zazen.
We have never directly observed a circle in this universe. We have only observed the appearance of a circle, what looks good enough to get an idea of what a circle is. If we were to zoom into the edge of whatever circle we create, we would find that it isn't perfectly round, but has little variations, or sides. Indeed a perfect circle is so at the infinitesimal level. Smaller than even atoms or subatomic particles can articulate.
There is a simple reason for this. Any circle we make is actually a polygon with many many sides that give the appearance of a circle. And while we can think of a circle as a geometric feature having one single side, a circle can also be considered as a polygon with an infinite number of sides.
I like to think about notions, feelings, experiences, formations and so on, like adding a side to a polygon. At first it looks like a triangle, then a square, eventually a pentagon, and so on. Looking more and more like a circle with the more sides we add to it. Now if someone's goal was to make their life like a perfect circle, they might believe they need to experience many things, they need to pile up notions, like adding side after side to the circle. Yet no matter how many sides they add, it isn't going to make a circle. No matter how much intellectual knowledge they gain, it isn't going to ever be complete.
However, there is a sort of hack. Or trick. What if, instead of adding sides, you were to instantly unattach all the sides at once. Letting go, or not grasping any notion, experience, or formation. Clear in all the infinite directions, no boundaries anywhere. In this sense, to practice Zazen is the embodiment of the perfect circle. Containing all forms, yet itself traceless. Inherently complete without beginning or end. A clear mind like the sky, in all directions, awareness becomes a singular side and all things the cite of enlightenment.
Just some insights I thought I'd share with you all for fun. I put it here because it involves drawing, and wasn't sure where it would best go. At any rate I hope you enjoyed.
Much love,
Salem
sala
Dogen once wrote:
"Enlightenment is like the moon reflected on the water.
The moon does not get wet nor is the water broken.
Although its light is wide and great,
The moon is reflected in a puddle even an inch wide.
The whole moon and the entire sky
Are reflected on one dewdrop in the grass."
A very elegant way of expressing Indra's net. "Indra's net" is an infinitely large net and is considered as having a multifaceted jewel at each vertex, with each jewel being reflected in all of the other jewels.
What does any of this have to do with drawing, Pi, and a penny?
When I was in my late teens I worked at a hotel as a dishwasher. One day in the dish-pit I wondered if I could make an equilateral triangle, without a protractor, compass, or the like. I thought, maybe I could use a penny in some way, and pi crossed my mind. A way of dividing the circumference into three parts.
Do follow along and draw this if you can.
I found a piece of paper and pen, then drew a circle around the penny. Seen in example 1 below.
Next I found the exact center of that circle by folding the paper and aligning the two halves of the circle to create a central line.
Next I divided that line in two to find the center. Seen in example 2.
Next I took the penny and lined up one edge with the center of the first circle and traced the edge. Seen in example 3.
Next I lined up the edge of the penny with the center of the original circle, and the exact point the second circle intersects with the first circle. Seen in example 4.
Next the three circles naturally create three points for the next circle to go, two intersection points along the edge of the first circle, and a center point. Seen in example 5.
And there you have it, three points along the edge of a circle, connect them all and you have an equilateral triangle. Seen in example 6
Then I thought back to example 3, and wondered what would happen if we mirrored it. Seen in example 7.
Then mirrored the rest of the steps. Seen in example 8.
Indeed I found many ways to create a sort of art out of it, as seen in 9 and 10.
pattern 1-00f.jpg
From there I was inspired to research Pi a bit more. At the time I knew relatively little about it. It's relatively simple of course, if you take the length of the circumference and see how many times the diameter can fit into it, you will find that it perfectly fits three times, with a tiny fraction left over. If you then subdivide the circumference by that tiny bit, you will find there is a tiny bit left over again. You can repeat this forever and there will always be a tiny bit left over.
It was from this study that I figured out a way to describe the nature of form. Form is just like Indra's net, and so is Pi.
Pi is a transfinite number, and the sequence it produces contains all possible combinations endlessly. This has a very profound meaning that seems to be often overlooked.
Indeed, if we articulate Dogen's poem into a numerical representation, classifying each letter to a number, that poem is found in the digits of Pi before Dogen ever wrote it out. In fact, this entire post, and all posts in this forum are contained within the digits of Pi. Your DNA, what you ate for lunch yesterday, and in a numerical sense the entire activity of the universe is contained in the digits of pi. Not only that, much more is contained in the digits of Pi than merely this universe. All possible articulations, realities, or universes which could be represented in a number sequence, is contained already, in the digits of Pi.
To be clear Pi is just a numerical representation of a fundamental of reality. Often it is said that mathematics is the language of nature, but in my view, reality is the language of nature, and mathematics is merely a partial interpretation of it. The fundamental source of Pi is merely pointed at by the number we get when examining a circle's circumference and its diameter.
There are endless insights that studying this can illuminate, but one of them is the interesting nature of the circle as it relates to knowledge, understanding, and Zazen.
We have never directly observed a circle in this universe. We have only observed the appearance of a circle, what looks good enough to get an idea of what a circle is. If we were to zoom into the edge of whatever circle we create, we would find that it isn't perfectly round, but has little variations, or sides. Indeed a perfect circle is so at the infinitesimal level. Smaller than even atoms or subatomic particles can articulate.
There is a simple reason for this. Any circle we make is actually a polygon with many many sides that give the appearance of a circle. And while we can think of a circle as a geometric feature having one single side, a circle can also be considered as a polygon with an infinite number of sides.
I like to think about notions, feelings, experiences, formations and so on, like adding a side to a polygon. At first it looks like a triangle, then a square, eventually a pentagon, and so on. Looking more and more like a circle with the more sides we add to it. Now if someone's goal was to make their life like a perfect circle, they might believe they need to experience many things, they need to pile up notions, like adding side after side to the circle. Yet no matter how many sides they add, it isn't going to make a circle. No matter how much intellectual knowledge they gain, it isn't going to ever be complete.
However, there is a sort of hack. Or trick. What if, instead of adding sides, you were to instantly unattach all the sides at once. Letting go, or not grasping any notion, experience, or formation. Clear in all the infinite directions, no boundaries anywhere. In this sense, to practice Zazen is the embodiment of the perfect circle. Containing all forms, yet itself traceless. Inherently complete without beginning or end. A clear mind like the sky, in all directions, awareness becomes a singular side and all things the cite of enlightenment.
Just some insights I thought I'd share with you all for fun. I put it here because it involves drawing, and wasn't sure where it would best go. At any rate I hope you enjoyed.
Much love,
Salem
sala
Lovely!
In Zen math, every number and fraction of a number is every other number and fraction fully ... 22749255210059682 is Pi is 3457934/22048884 is 0 is 1 is -1 is infinity. It is a math where literally 2+2=7 and every other possible answer.
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