Now, let’s talk about whether such a redaction is really possible, and if so, what kind of thinking is needed to develop a perspective that changes everything in the world into immanence. Let me talk about it.

Now, this is where quantum dynamics comes in. The two divisions of four dimensions in the Noosology, “The Inside and the Outside of a human”, that we have been talking about, will allow us to organize a geometric relationship between two spaces, which in physics are called Minkowski spacetime and Hilbert space in complex two dimensions.

In other words, it becomes possible to think of the relationship between objective space, or external space, and subjective space, or immanent space, as a relationship between relativistic space-time and quantum dynamics space.

Since the quantum is considered to create the basis of matter, this thought can be said to be the launch of idealism thought, which attempts to integrate matter and spirit through space. I will briefly explain its fundamental parts.

First of all, the location observed by the four dimensions created by 0 (zero) to S in the previous figure corresponds to Minkowski space-time. Minkowski space-time is given by the following equation in special relativity.

s^2=c^2t^2-x^2-y^2-z^2

It is commonly referred to as a four-dimensional invariant equation. s^2 is the time interval, c is the speed of light, t is the time coordinate, xyz is the spatial coordinate in three-dimensional space. This equation is used in special relativity to describe the universal interval between two events in space-time. In this figure’s case, the interval between the origin O and the observer’s position S corresponds to this time interval.

On the other hand, the inverted direction of time from S to the origin O can be viewed mathematically as a transformation from four-dimensional space-time to four-dimensional space. This corresponds to what is called a Wick transformation in physics. The Wick transformation is a mathematical technique used in quantum field theory, among others, which transforms the time coordinate T in Minkowski spacetime to the imaginary dimension iT, thereby transforming from the framework of special relativity to four-dimensional Euclidean space. It is a mathematical operation.

Imaginary time means that it is time, T, multiplied by an imaginary number i. It is simple: T multiplied by i equals iT. Therefore, the inversion in four dimensions from “The Inside of a human” to “The Outside of a human”, introduced earlier, means the inversion from time T to the imaginary time iT. The mathematical expression is as follows. Many calculation processes are written, but the final result is s^2=c^2t^2+x^2+y^2+z^2, very simple, isn’t it? By converting time T to imaginary time, iT, all marks become positive, and the space is transformed into a five-dimensional Euclidean space.

The four-dimensional Euclidean space that emerges here corresponds to what the wheelchair-bound genius Stephen Hawking called the imaginary time universe in his theory of the Boundaryless Hypothesis. In his Boundaryless Hypothesis, Hawking showed the way of thoughts that it is wrong to think that the universe “began” at a particular moment in time, and that there is no such place in time, no boundary called “beginning”. In other words, he showed that the universe does not have a definite beginning, nor does time go back infinitely, and that the beginning of the universe is everywhere in a sense, as something atemporal, in this no-boundary hypothesis.

The universe has no beginning. Well, time has no beginning. Although it has no beginning, time does not go back infinitely far. Do you understand?　Hawking must have done a lot of calculations to find out that it started out as something non-temporal, and since non-temporal realm is non-temporal, it exists everywhere in the world of time and space. The pre-Big Bang world exists everywhere, as a kind of latent thing, hidden in the shadow of space-time, he showed such idea.

In fact, when we look at this Wick transformation geometrically, there is no longer any distinction between time and space, and this three-dimensional space, which was thought of as an infinite expanse, is transformed into a three-dimensional spherical surface S^3　embedded in a four-dimensional space. The three-dimensional spherical surface S^3 may not be familiar word for you, but you can think of it as a one-dimensional upper version of what we usually call spherical surface.

The two-dimensional spherical surface is in three-dimensional space, and we call it S^2. This is a two-dimensional plane turned into spherical surface. On the other hand, a three-dimensional spherical surface S^3 can be said a closed three-dimensional space, where the three-dimensional space itself is a circle that returns in any direction. So, it is not infinitely open like normal three-dimensional space. It is a circle in the x-direction, a circle in the y-direction, and a circle in the z-direction. Such kind of spatial form. Our current human brain can’t imagine it. If I give you a hint, I may say, we cannot capture it as an object.

I will later present more about the meaning of this three-dimensional spherical surface, in terms of consciousness, in this series of research videos, though, in quantum mechanics, in the spin rotation of material particles such as electrons and quarks, this three-dimensional spherical surface S^3 appears as a form of SU(2), the rotation group in complex two-dimensional space.

The space of quantum mechanics is not a simple four-dimensional space, but a four-dimensional space with two complex planes superimposed on it. A complex plane is two-dimensional in one complex dimension, so two of such planes are two-dimensional in complex dimension, creating a four-dimensional space with a structure of four dimensions. This three-dimensional spherical surface appears as the form of the rotation group.

Well, simply put, material particles have this three-dimensional spherical surface. So, in a sense, it is a higher-order entity. And this rotation can be represented by a determinant of four 2×2 complex numbers as shown here. It may be a bit complicated for people who know little about mathematics. SU (2) is a composition of x+yi and u+iv in the complex plane. Here, xyuv is a real number, so it forms four-dimensions. So, these four real number dimensions are the source of the four-dimensional space. In the case of the SU (2) group, the determinant must be 1, and is calculated as follows

Det(SU(2))=(x+yi)(x-yi)-(u+iv)-(u+iv)

In summary, it looks like this.

det(SU(2))= x^2+y^2+u^2+v^2= 1

What do you think? You can see that this area surrounded by red, the area that I just read out in the equation, has exactly the same shape as the equation that was just shown in the Wick transformation, right? What I am trying to say here is that when we discover the fourth dimension as a space of depth that breathes to the direction of “The Outside of a human”, rather than as the space-time of “The Inside of a human”, this depth is somehow connected to the space of complex two dimensions that make up material particles. In other words, we can think of elementary particles as the physical representation of the location of subjective space as our duration.

What Noosology aims to do, although I will not explain in detail today, is to think of subjective space as space of duration and to give mathematical structure to this space of duration. By superimposing the structure that emerges on the mathematical structure of quantum mechanics as I mentioned so far, we will make a concrete argument that this space of duration that supports our immanence corresponds, in the same shape, to the space of elementary particles.

What I would like to indicate by presenting this kind of argument is that the universe is actually created from the subjective space side, that is, from our spirit, and I would like to model the intrinsic cosmology as a new ontology from the perspective of modern physics. In other words, as I mentioned earlier, subjective space as “The Outside of a human” is ontologically prior to space-time as “The Inside of a human”, and the universe is not a physical reality but rather an existence directly connected to the spirit that is rooted in the subjectivity of each one of us. We are trying to construct such ontology as a new worldview and new view of human beings for the coming age.

Until now, we have been looking only at the four-dimensional space-time, “The Inside of a human” and have sought the cause of existence of this universe in the matter objectified in that space-time. On the other hand, although religions and philosophies have talked a lot about the subjective space or mind that is “The Outside of a human”, they have not yet succeeded in finding a clear structure for it. If we continue to have only this perspective on the world of existence, we will be forever trapped in this endless history created by external time. From the perspective of Noosology, this sense of history that linear time creates is the very place of the matrix I mentioned earlier.

These unfulfilled feelings toward human beings, trapped in historical time, are expressed in a very beautiful text by the German thinker Benjamin, inspired by the painting work “New Angels” by Paul Klee. Let me end this research video by introducing that text. This text by Benjamin also seems to wish for human’s escape from space time.

There is a painting by Klee titled “New Angels”. It depicts an angel who appears to be about to move away from something that is staring at him. His eyes are wide open, his mouth is open, and his wings are outstretched. The angel of history must look like this. He turns his face toward the past. Where our eyes see a chain of events, he sees only one catastrophe. The catastrophe is constantly piling rubble on top of rubble and throwing it at his feet. He would like to stay there if he could, to awaken the dead, to gather up what has been destroyed and put it back together. But a storm is blowing from paradise, and it is so fierce that the angel can no longer close his wings. This storm pushes him inexorably toward the future to which he has turned his back, while before his eyes, a mountain of rubble piles up, almost reaching to the heavens. What we call progress, that is what this storm is.”See you next time!