Ultimate Geometry

The shape of closing—why does the circle appear at the root of the world?

Since I was twenty, I have been thinking about two shapes: the "circle" and the "triangle".
The circle closes.
The triangle opens.
At the time, it was just an intuition.
But as the years passed, I began to feel that this intuition was quietly resonating not only in philosophy but also in mathematics, physics, and even Buddhism.
Of course, they are not the same thing.
However, it is very striking that the shape of "closing" appears repeatedly in different fields.
I was once strongly drawn to Euler's identity.
It was not that I understood the mathematical formula.
I simply felt a strange beauty in the fact that "1" and "π" are deeply connected to a single circular motion.
For me, "1" was the moment existence is decided.
On the other hand, "π" was an endless continuity, a movement that keeps approaching perfection.
At the time, I was thinking about it while superimposing it on the images of "open strings" and "closed strings".
Looking back now, that intuition was by no means explaining string theory.
However, after I learned about string theory later, I was surprised by one thing.
In one of the most advanced mathematics attempting to describe the universe, the structure of a "closed string" truly appears.
Of course, it is not the same thing as the "circle" I am thinking of.
Physics has its own rigorous meaning.
Even so, it was very impressive to me that the shape of "closing" appears in a theory that speaks of the root of the universe.
Recently, this feeling has expanded even further.
In philosophy, it is continuity and discreteness.
In physics, it is continuous symmetry and discrete symmetry.
In Buddhism, it is the circle (enso) and discrimination.
I do not mean to say that each is the same concept.
Rather, I feel that each is looking at the "oneness" and "separateness" of the world from different standpoints.
The circle I have been thinking about for many years may not have been a mere figure.
Closing.
Circulating.
Losing boundaries.
Holding the beginning and the end at the same time.
Humanity has entrusted such qualities to the shape of a "circle" since ancient times.
That is why my thinking has changed a little recently.
Previously, I was thinking about "what is a circle?"
But now,
"Why does humanity, every time it thinks about the root of the world, arrive at the shape of 'closing' again and again?"
I am more interested in this question.
There is no answer to this question yet.

---

Consciousness is made of waves and particles—a closing world, an opening world

Since I was twenty, I have been thinking about two shapes: the "circle" and the "triangle".
The circle closes.
The triangle opens.
As the years passed, that intuition began to quietly connect to philosophy, mathematics, physics, and Buddhism.
Of course, they are not the same thing.
But I feel that different disciplines are looking at the same structure over and over again.
My hypothesis is very simple.
Could it be that consciousness itself is composed of the simultaneity of waves and particles?
Usually, wave-particle duality is discussed as a property of quanta.
However, I think that this structure might also appear in consciousness itself.
A wave is a continuous possibility, a field without boundaries.
A particle is a localized experience, an event where "this very moment" arises.
In my own words,
the wave is a circle, and
the particle is a triangle.
With only a circle, the world continues to expand in an undifferentiated state.
With only a triangle, the world shatters into fragments.
Is life not an existence that lives both of these simultaneously?
I have long thought that the universe and consciousness were not born separately, but were born simultaneously at the Big Bang.
The world contained the possibility of being experienced from the very beginning.
I call that very possibility of experience the "consciousness field."
The consciousness field is a single field that continuously expands throughout the entire universe, and each of our individual consciousnesses appears as a local excitation of it.
Here, I feel a special role for gravity.
This is not a conclusion established in current physics.
It is strictly my own philosophical hypothesis.
If gravity is deeply involved in the collapse of quantum superposition, then gravity might be the action that slightly tilts the continuous field toward discrete events.
The world goes from wave to particle.
From particle to wave again.
It constantly repeats closing and opening.
Recently, this shape of "closing" has become even more meaningful to me.
In Buddhism, there is the enso (circle).
The enso symbolizes perfection, emptiness, and oneness.
On the other hand, humans divide the world through discrimination, recognizing "me" and "you," "good" and "evil."
In mathematics, there are continuity and discreteness.
In philosophy, this problem appears repeatedly within epistemology and ontology.
And in string theory, which attempts to describe the universe, the structures of "open strings" and "closed strings" appear.
Of course, these are not the same concepts as the circle and triangle I speak of.
However, every time we think about the root of the world, humanity encounters the shape of "closing" again and again.
Is that a coincidence?
I cannot help but feel that there is some deep structure there that human cognition is repeatedly touching.
That is why I will not discard the "circle" and the "triangle."
Continuity or discreteness?
Wave or particle?
Emergence or reduction?
Enso or discrimination?
I will not choose one or the other.
I have called this "true contradiction."
It is a perspective where things that are mutually opposed simultaneously establish the world, rather than resolving the contradiction.
In that sense, I feel it quietly resonates with what is called "emptiness" in Buddhism.
The world is a movement that is one while being divided,
and while being divided, it becomes one again.
The universe might be the activity of a giant consciousness field continuously experiencing itself locally.
This text is not a scientific proof.
It is a philosophical hypothesis and my own worldview.
However, I feel great surprise and hope that the simple intuition of the "circle" and "triangle" that I have been thinking about since I was twenty is quietly beginning to build a bridge to philosophy, mathematics, physics, and Buddhism.

---

A Philosophical Essay
—The world is a movement that is one while being divided, and while being divided, it becomes one again

My philosophy begins with the extremely simple intuition of the "circle" and the "triangle."
The circle is a closed shape.
The triangle is an open shape.
However, this is not a theory of figures.
The circle is...

• Continuity

• Oneness

• Closing

• Disappearance of boundaries

• Circulation

• Wholeness

On the other hand, the triangle symbolizes...
Discreteness,

• Discreteness

• Articulation

• Boundaries

• Individual

• Cognition

• Difference

The world is established by these two movements.
The world is not one from the beginning, but is one while being divided.

The world is not one from the beginning, but is one while being divided
I doubt the very dichotomy of:
"Continuity or discreteness?"
"Wave or particle?"
"Emergence or reduction?"
The world is not one or the other.
The world is...

continuous while being discrete, and discrete while being continuous.I call this simultaneity "true contradiction."
True contradiction is not a philosophy that resolves contradictions.
Rather, it is the position that...

the contradiction itself establishes the world.

Life proliferates. Consciousness expands
Recently, I noticed a correspondence.
Life,
once born,
heads in the direction of proliferation.
On the other hand,
consciousness,
increases experience,
expands meaning,
and expands the world.
I do not think of
life and consciousness as separate things.
I think that both are
the movement of the same field,
appearing in different layers.

Gravity is the gradient that tilts the world toward experience
I, too,
feel a special significance in gravity.
Of course,
this is not a conclusion of physics.
It is a philosophical hypothesis.
Could gravity be the gradient that slightly tilts
waves into particles,
the continuous into the discrete,
possibility into events?
Because of that tilt,
the universe possesses events,
and life can experience the 'now'.

Why does the form of 'closing' appear so often?
In recent years,
my interest has shifted to a single question.
Previously,
I was thinking about
'what a circle is'.
But now,
why is it that every time humanity contemplates the roots of the world, it arrives at the form of 'closing'?
I am more drawn to this question.
Ensō.
Circular motion.
Closed strings.
Euler's identity.
Continuum.
Of course,
these are not the same concepts.
However,
it is highly striking that different disciplines
repeatedly encounter the structure of 'closing'.
I feel that
behind this,
there may be a deeper structure that human perception is repeatedly touching.

Conclusion
I
do not consider this thought to be a scientific theory.
Also,
it is not a religion.
This is
a philosophical worldview born from continuing to gaze at the world.
To me, the world is
an endless movement that is one yet divides,
and while dividing, becomes one again.