It all starts with imagination:
The Bible tells us that our imagination is responsible for all human evil:
Gen 6:5 And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
Gen 6:6 And it repented the LORD that he had made man on the earth, and it grieved him at his heart.
Later on the evil is forgiven:
Gen 8:20 And Noah builded an altar unto the LORD; and took of every clean beast, and of every clean fowl, and offered burnt offerings on the altar.
Gen 8:21 And the LORD smelled a sweet savour; and the LORD said in his heart, I will not again curse the ground any more for man's sake; for the imagination of man's heart is evil from his youth; neither will I again smite any more every thing living, as I have done.
Gen 8:22 While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease.
But not entirely.
Is our imagination really so evil? What about these thoughts of great minds:
Logic will get you from A to B. Imagination will take you everywhere.
Read more at https://www.brainyquote.com/quotes/george_bernard_shaw_113045
Imagination is the beginning of creation. You imagine what you desire, you will what you imagine and at last you create what you will.
And so I have imagined Gaussian fractions. These are complex numbers which are complex fractions of two Gaussian integers
z = (m+n i)/(p+q i),
where m and n and p and q are integers. Then I took those of them which have positive imaginary part. And then plotted so obtained numbers on the complex plane z=x+iy, x horizontal, y vertical. Here is the result
You can download the scalable vector image as pdf from here.
Then I followed my imagination and made the Cayley trnsform z -> (z-i)/(z+i) of these points:
Now my imagination tells me to consider the case of the conformal group SU(2,2), where the Shilov boundary of the eight-dimensional complex domain is our (compactified) four-dimensional space-time of events, and not just a circle of time surrounding the disk as above. This will come step by step in the following posts.
P.S.2 To enhance our imagination we are using at home hyperbaric chamber. Here it is:
Clicking on the image will give you a full resolution photo.
Let me comment in this post on the blowing up of a grenade launcher at the Polish Police Headquarters in Warsaw.
ReplyDeleteI do this because of the fact that you (@Ark) sometimes add news from Poland and the World on various topics, not necessarily related to Physics.
"Imagination" tells me that the whole thing is a set-up. At first, they get the grenade launcher illegally smuggled into Poland (it was indeed illegal). Then they recruited the chief commander of the police to fire such a grenade launcher understanding how it works and the damage it could cause. They gave him assurances that he would not face legal consequences under Article 163 on bringing an event that endangers health and life, where the prosecutor's office considers him a victim (and that's authentic now). And he will subsequently be rewarded for this (yeah this is real, because he had to "go through it"). As we know from Mariusz Kaminski's official Twitter account, the scapegoat is Gen. D. Bondar. [ https://twitter.com/Kaminski_M_ ]
The purpose of this situation is to share a message, not directly, to the Polish population, whose defense is handled by the Police, that their defense is against the Ukrainian military forces ineffective and they have to subordinate - remember that this fired grenade launcher is the German anti-tank grenade launcher, donated by the Ukrainian security forces.
Soon they will do the DeuthsPol (western-northern) and UkrainPol (Eastern-Southern). The only one satisfactional way out of situation is help from Russian brothers and sisters.
Anonymous: Someone
ReplyDeleteThe article you linked to is really great! Thank you!
Anonymous: Someone
ReplyDeleteThere are many similarities to Hegel's concepts in this work.
Anonymous: Someone
ReplyDeleteIt is very difficult to clearly interpret the ideas in this article, such as:
„We discuss a non-materialist view called the self-simulation hypothesis, wherein everything is information, which we define as thought. The universe self-actualizes itself into existence via self-simulation using a mathematical code and a simulation game rule called the principle of efficient language. The salient idea is “timeless emergentism”, wherein the total simulation run can be viewed as one grand thought.”
or
„Idealistic holistic panpsychism [12] (herein, panpsychism) is related to ontological idealism [13]. It says that everything is thought or consciousness. Panpsychism philosophy does not explain how the panpsychic substrate comes to exist. It just is. We propose a panpsychic self-simulation model, which attempts to describe the origin of the panconsciousness.”
Nevertheless, in Hegel's philosophy, the basis of everything is spirit (thought). The spirit is self-developing, there are processes of self-organization, there is continuous emergence (these are also aspects of the philosophy of Plato and Plotinus).
Is everything spirit/thought/mind?
I think this article is also worth reading: https://www.sci.news/astronomy/human-brain-cosmic-web-similarities-09066.html
What modern physics needs is a spirit. Spirit always comes in the same form. It can be found when we change our understanding of time. Einstein's revolution is related precisely to time. Einstein meant that time is relative and flexible, and the dividing line between past, present, and future is an illusion. So, reality is ultimately timeless. The general theory of relativity is beautiful precisely because of its departure from the classical perception of time.
The spirit hides just in time. It is time that creates the greatest paradoxes, it is also illusory, it does not exist in itself, but only because of the existence of consciousness. In addition, time should also expand, as should space. The universe increases in scale because it adds "memories." In fact, it is probably not an increase in scale, but a densification of space, which we perceive as an increase in scale.
I recently read this paper: https://arxiv.org/abs/1606.07975
This is very simple mathematically.
There is no "spirit" here yet, but its author recognizes some important issues that have always been close to my heart. He points out, for example, the artificial correlation between time and entropy.
In terms of physics itself, I have recently become interested in Planck scales. I am learning about quantum groups just in connection with them.
Why exactly that? First of all, it was a sudden and unexpected opportunity. It all happened on days that were of great importance to me. In addition, I am interested in the nature of gravity at this scale. I have a certain suspicion. Moreover, it turns out that in this approach it will probably be possible to use a certain very exotic operator that I once wrote about.
We'll see what comes of it, while what to look for is the spirit. The Heisenberg time-energy principle is not irrelevant either. This "energy" is a little more than the modern understanding of energy. This description is downright theological. Here mysticism is combined with physics.
This is a lot of work. Category theory is also proving useful. Suddenly, some forgotten and distant pieces of a strange puzzle come together.
Yes, the self-simulation hypothesis supposes panpsychism in which everything is a thought within a universal mind.
DeleteI agree that category theory will be useful for many things, including a reformulation of quantum field theory.
Anonymous: Someone
DeleteHow do you see this relationship? How do you see the description of time in terms of morphism?
You hit the point exactly. Category theory and quantum field theory. And how do you see the application of category theory to the Planck scale? Do you think such a description would be better than quantum groups?
Anonymous: Someone
DeleteFor me, the case with category theory appears more or less like this:
Category theory, in addition to offering a universal language, plays an important role in noncommutative geometry.
Structures such as groups, Lie algebras, Hopf algebras, can be characterized in terms of the categories of their representations. For example the category of representations of a group (or a Lie algebra) is a symmetric monoidal category.
For classical geometry, there are so-called strictly monoidal categories. In NC geometry they are generalized to braided monoidal category.
Such a braided structure is given by a quantum R-matrix satisfying the Yang-Baxter equation.
This makes it possible to generalize the concept of statistics for particles.
However, these are the simplest things, I'm more interested in what I see in dreams, and these are certain structures that exist mathematically, but currently I don't know enough about all this to properly translate it all into a formal language. I'm in the testing phase and it's pretty hard. Until now, none of the professors I consulted knew the subject well enough. Some knew more about physical interpretations, others about mathematical structures, although it started to turn out strangely that my dreams weren't as stupid as I thought they were.
In addition, category theory for me is also a consequence of the use of certain theological models. In fact, theological considerations showed me the importance of this discipline. Then I became interested in the Planck scale and then I saw that there is indeed a real possibility of describing what I dreamed about.
It seems plausible to conjecture that q-deformed groups, Drinfeld doubles, and Hopf algebras might play an important role in the category-theoretic reformulation of QFT. For instance, LQG only studies gravity, makes contact with q-deformations of SU(2), but does not focus on other forces. Robert Finkelstein unified Schwinger's dyons as topological preons with QCD and the standard model by adding a q-deformed Lie algebra to describe fundamental particles as knots, which relates to extremal black holes, but did not focus on gravity. Amplituhedra from Nima Arkani-Hamed were found by making a Yangian symmetry manifest, which is an infinite-dimensional Hopf algebra as a type of quantum group. As supersymmetric theories strive towards a nonperturbative realization, it seems reasonable that tools for unified field theory will emerge. A category theorist that passed away named Marni Sheppeard told me that Lagrangians should be completely abandoned; indeed, the new methods for finding amplitudes bootstrap solutions directly from their fundamental symmetries rather than solving equations of motion.
DeleteAnonymous: Someone
Delete@David Chester
Thank you so much for this description! I am not yet familiar with all the structures you described, but I will certainly deepen my knowledge on the subject.
I also have very similar intuitive feelings. For a long time, certain structures have attracted me more than others. Now I can see at every turn that they are exactly what I am interested in using.
Again, thank you very much for your explanation David.
Got another message from Marcelo including this informative part:
ReplyDelete"Taking the opportunity of the contact let me mention some more technical work: We have applied some quantum group at the fifth root of unity to quantum gravity [1,2] and also advancing with a new notion of tiling spaces [3,4] where we hope to find representations of quantum groups.
[1] Marcelo Amaral, Raymond Aschheim, Klee Irwin, Quantum gravity at the fifth root of unity,
Physics Open, Volume 10, 2022, 100098, https://doi.org/10.1016/j.physo.2021.100098.
[2] https://www.journals.elsevier.com/physics-open/highlighted-articles/a-new-model-of-quantum-gravity-from-the-building-blocks-of-grand-unified-theories
[3] https://www.preprints.org/manuscript/202111.0359/v2
[4] https://web.math.ucsb.edu/~kylehansen/Talks/Intro_to_Tiling_Spaces.pdf
"
This morning Alex is sending me a very old paper by M. I. Shirokov about energy and time in quantum mechanics. Irina apparently came to the conclusion that I should study carefully this paper. And I wiil. Thanks to Alex and Irina.
ReplyDeleteThe paper is available here:
http://www.nkozyrev.ru/bd/112.php
Anonymous: Someone.
DeleteArk, thank you for the link.
I am currently reading and recommend:
https://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687
Anonymous: Someone
ReplyDeleteRethinking while reading:
To do mathematics you need knowledge. I have no doubt about that. Imagination, even the best, is not enough. You can't operate in any system if you can't speak the language of that system well enough.
The most important thing, however, is imagination, and I have no doubt about that either. Ideas are born in the imagination. Sometimes there are several alternative descriptions of the same idea in formal ways.
However, everything begins in the imagination, that is the source. One should also beware of becoming too immersed in a given discourse. Sometimes dealing with something abstract for several hours a day for several days detracts from other kinds of thinking.
A dilemma arises. Do you try to get along with people at all, or do you cut yourself off almost completely and only talk to those people who can contribute something to new concepts?