For over a week, I've barely slept. I've barely eaten. Without my wife, I might not sleep or eat at all. Work has consumed me. My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world. Something new is forming. At least, it's new to me.
My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world.
Will it be of use to anyone? Right now, I don't care. It's beautiful, and that's enough. A puzzle is unfolding before me.
I don't know what the final picture will be. Many pieces are still missing. The box is vast, overflowing with possibilities. Strangely, I find myself returning to ideas from my doctorate. Back then, they were mysteries. Now, I understand them. Now, I develop them.
The Edge of Reality
To satisfy your curiosity, I'll share what I'm working on. Although, I doubt anyone will understand. But I’ll tell you anyway. Think of it as surrealist poetry.
On the edge, there’s a great concentration (critical density) of Black and White...
Our world—our entire reality—is a complex domain. This domain has an edge, and our lives unfold along this boundary. We have no clear view of its interior. Perhaps, just a glimpse. Deep within the domain, a spotlight of consciousness shines, like a lighthouse, illuminating the edge point by point.
A lighthouse, illuminating the edge point by point.
The Cycle of Time
Each point touched by light marks the passage of our "time." Time is cyclical. Reincarnations. For those who live only on the edge, with no insight into the interior, the cycle repeats endlessly. Every point on the edge has its opposite—somewhere, infinitely distant.
Within the domain, time does not flow. Inside, there is no difference between reality and imagination. Inside, Geometry dwells. Geometry akin to Escher’s devils and angels. Our edge is not the only one. There are others, adjacent to ours, with other "lives" existing in different dimensions.
Not only is our "time" cyclical, but our space also loops back on itself. It closes with a cap shaped like a truncated double light cone.
The Operators of Existence
The domain is filled with operators. Our point on the edge, along with its opposite—the tip of the cap—is also an operator. This operator is anti-commuting with the lighthouse. It remains anti-commuting through all "time." The tangents to the edge are four Dirac gamma operators.
But there is a fifth gamma operator, anti-commuting with the four "normal" ones. Together, they span a five-dimensional space. The domain is "round." But if a "wind" distorts it slightly—it creates unstable gravity waves—that’s GRAVITY.
John Archibald Wheeler proposed The One law for the Universe; Boundary of the boundary is zero - BB Principle.
In symbols:
∂∂ = 0.
From Warner Allen Miller ,"The Geometrodynamic Content of the Regge Equations as Illuminated by the Boundary of a Boundary Principle", (pp. 201-227 in Between Quantum and Cosmos: Studies and Essays in Honor of John Archibald Wheeler, Wojciech Hubert Zurek, Alwyn van der Merwe, Warner Allen Miller, Princeton University Press 1988):
All our laws of nature would be then consequences of this one. Looks nice and simple indeed. In topology and in algebraic topology it holds indeed, either as a theorem or as a postulated fundamental property.
In my vision there is also one law: it is the "Law of Free Fall". Everything moves along a geodesic of some kind of "geometry". Can these two visions, Wheeler's and mine, be merged into one vision? Is free fall another expression of BB? Is BB just another expression of Free Fall? And what about Free Will?
And then: why THIS law and not some other? And why one law and not two or three? Or even an infinite number of laws? Why?
While looking for answers, enlarging my knowledge (and my ignorance as well, but only linearly), I am asking myself: "Am I of this world?"
"And so we wander on our way asking ourselves—if truth be known, muttering to ourselves really—“Am I of this world or the other?” and answering “I am of both.” And we remind ourselves of this as we go along."
"Through this circular river symbol, the moat, the tale warns us that this water is not just any water but a certain kind. It is a boundary water, much like the circle the maiden drew around herself to keep the Devil away. When one crosses into or through a circle, one is entering into or passing through to another state of being, another state of awareness, or lack of one. "
Found by Laura for me to watch. A good one indeed. Recommend for everybody!
P.S.2. Just chceked my researchGate mail. Discovered a message from September:
"Hallo Arkadiusz,
I looked to your your Preprint Time of arrival
operator in the momentum space, it is interesting and please see my
paper (blow) , where one can see the relation to the Fujiwara–Kobe time
operator, sec 4 of your preprint.
Посмотрите, пож., на уравнение 3.16
из статьи Хаотическая динамика электрона. Вы ее легко найдете в моем
профиле. Там речь о динамическом решении для нулей дзета функции Римана."
Riemann Zeta! Beatiful piece of art!
P.S.4 Another worth considering quotation from "Women Who Run With The Wolves" mentioned in the main text of this note:
"The young and the injured are uninitiated. Neither knows much about the dark predator and are, therefore, credulous. But, fortunately, when the predator is on the move, it leaves behind unmistakable tracks in dreams. These tracks eventually lead to its discovery, capture and containment."
"Wild Ways teaches people when not to act 'nice' about protecting their souls. The instinctive nature knows that being 'sweet' in these instances only makes the predator smile. When the soul is being threatened, it is not only acceptable to draw the line and mean it, it is required."
P.S.5. I am back to conformal infinity. It is a part of U(2). Perhaps I will write a note about it.
P.S.6. From the battlefield Planet Earth;
P.S.7. I have on my table these two books. Oh God, how much I would like to know their content and master it!. Why it is not possible for us to bring these books close to our heads and download their content (even if it may take a while), and push the button "Understand" and another button "Now"? Why?
But I clearly realize that different people may have extremely different standards of "understanding"....
Different level of "depth". The next button would be "Integrate". Of course the first book would have nothing to ingrate with. Would be instantaneous. But with each new piece of added knowledge integration would take exponentially longer time.
By integration I mean making the whole more than just the sum of parts. For instance: when we learn about complex numbers, we understand much better real numbers about which we have learned before. We create a huge number of connections and interactions between the old and the new knowledge. Thus, approximately, when we have m pieces of old knowledge and add m pieces of new knowledge we can optimally-ideally gain mxn rather than just m+n. But there is also useless knowledge: a knowledge that cannot be integrated with our other knowledge, because it belongs to a different "species" of knowledge. For instance knowledge of blacksmithing or knitting will hardly add anything useful to your knowledge of algebraic topology. We all have finite resources and we have to choose whether we want to know superficially possibly many subjects, or to know really deeply at least one. People with extremely high IQ seem to be naturally gravitating towards the first option.
And, as John Wheeler has noticed: the more we know about a given subject, the more we are painfully aware of how little we, in fact, know.
