It’s hard to understand! So they are invisible? How does the invisible create the visible universe? Is it vanity? Why does nothing create duplicate existence? Then, after many long years, I gradually realized.
When I was in high school, I read in a geometry illustration book: Point (as) a “something” has no “thickness, breadth, breadth”, straight lines are infinitely “long”, infinitely “thin” and infinitely “thin” and infinitely “wide”. It’s hard to understand! So they are invisible? How does the invisible create the visible universe? Is it vanity? Why does nothing create duplicate existence? Then, after many long years, I gradually realized. It turned out that the introductory lesson on geometry was a mathematical illustration of the idea of Dependent Origination in Buddhism.
EUCLIDE GEOLOGICAL Axioms SYSTEM
Point: = A, B, C… Line: = a, b, c, d… Plane: = (P), (Q), (R)
Element x belongs to set A: =
Set A is contained in set B: =
1) Through 2 distinct points there exists only 1 straight line d.
2) Through 3 points not on the same line, there exists only 1 plane.
3) If the line d has 2 points in the plane (P), then d is contained in (P).
4) If 2 distinct planes have 1 point in common, then they share a line called the intersection of those 2 planes.
5) In the plane, through a point not on the line d, there exists only one line that has no point in common with d.
Thus, in order to “know” points, lines, and planes, language cannot tell them what they are, but must describe how (how) by an axiomatic system in which “points, lines, faces flat” are just terminological symbols, conventions accompanying other “relationships” concepts (existence, belonging, contained) to connect them through axioms (justice) that we recognize. receive not prove. One exists because the other exists. Nothing has an existence in itself. This is strangely similar to the Buddhist thought of “Dependent origination”: “phenomena are nothing in themselves. The reason they get their nature is because of their interdependence. All are dependently arising from emptiness. One of all, all in one!” (quoting Trinh Xuan Thuan – Infinite in the palm of your hand).
With the basic “particles” (points) and “interactions” (relationships), in the above axioms, through the coincident design of new concepts and new theorems, mathematicians create a universe. Deep, magical Euclidean geometry. Please reveal one of the countless impressive rooms of that magnificent castle:
“The three intersections of opposite sides of a hexagon inscribed in a conic lie on a line (Pascal’s line of the hexagon)” (Blaise Pascal – French mathematician)
Corresponding to 6 points on the conic, we have 60 different hexagons, generating 60 different Pascal lines. Of those 60 lines, every 3 lines pass through 20 points called Steiner points, these points every 4 points lie on 15 lines called Plucker lines. Pascal’s curves converge every 3 in a set of 60 other points called Kirkman points. For each Steiner point, there are 3 Kirkman points such that all 4 points lie on a straight line called the Cayley line. There are 20 such straight Cayley lines, of which every 4 lines pass through 15 points called Salmon points … Just like that, coincident with Dependent Origination, Pascal’s theorem opens the realms of unlimited use. All coexist in a perfect “Local – Whole” connection.
The science of the law of cause and effect
This reminds us of the “Net of the Heavens of God” in the Buddhist scriptures. It was a net made of countless transparent jewels. When we stand in front of the universe made of these bright mirror-like jade particles, our images are reflected in each jade-mirror microsphere and each jade-mirror microsphere reflects each other, forming a world of identical images. presently. All is one, one is all! As expressed by Zen master Khanh Hy during the Ly dynasty:
The universe ends with the top of the head,
The sun and moon include the middle and the dead.
(Wisdom is on the head of a hair.)
The sun and moon are contained in the heart of a mustard seed).
Or as the English poet William Blakes:
“To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour”.
(To see the universe in a grain of sand
And heaven in a wildflower
Hold infinity in the palm of your hand
And eternity in the present moment).