A Sleepless Odyssey
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.
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.
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.
Thank you...
ReplyDeletePuts into perspective and helps to understand some experiences I was having this morning during meditation....the duality of normal linear experience of time on the "edge of reality" and a not so much inner (ie, on the periphery of normal awareness - maybe akin to Castaneda's 'heightened awareness') existence more harmonious than its reflection on the outer linear experience ( edge of reality) but some of it's history and occurrences gets to impinge and affect the outer linear history..
It's hard to put into words that experience, which is still ongoing...🤞
Same for me: hard to put into words. Especially when the devil is in the details.
Delete🙏
DeleteI've always wondered what keeps track of progress, even when we are stuck in cyclical time. Similarly, when a fractal is infinitely subdivided or replicated, is there something which distinguishes each "slice"? It wouldn't make much sense if there wasn't some "circuit breaker" which allowed "quantum jumps" from one cycle to another.
ReplyDeleteSo far, I have noticed that there are two main "tracks" in whatever we do: accumulation (i.e. truth, organization, composition) and disintegration (i.e. falsehood, chaos, splitting). One "track" cannot live without the other. If you know the truth, you can discard (infinitely) many lies. When you lie, you know the truth, and you can generate (infinitely) many lies. Lying without knowing the truth is a bit of a paradox - in that case, I would argue that "lying" would take the shape of ignorance (an undesirable, but necessary state or transition for progress).
Could the same concept be applied to gravity and consciousness?
Gravity would be the cup, and consciousness would be the water.
When water is poured into a cup, it takes the shape of the cup.
When water overflows the cup, it needs to go somewhere... into another cup! The water and the cup represent all that is and is not. The cup symbolizes "what could be" and water symbolizes "what is." The goal of a cup is to find water, and the goal of water is to grow and overflow the cup. There are local imbalances (more water, less water) which create opportunities for progress (unstable gravity waves?), even though the total quantity of cups and water remains unchanged. Dynamic balance, yin-yang.
"When you lie, you know the truth, and you can generate (infinitely) many lies."
DeleteThis is what AI does when it "hallucinates." For example, yesterday, I asked ChatGPT about papers published on a specific mathematical topic. I received a list of papers, complete with authors, journal names, titles, and abstracts. After some "discussion," the AI admitted, with an apology, that none of these papers actually exist—it was all fabricated.
This is an example of lying without awareness, where the lie is programmed into the system, and there's no need for the AI to "know" anything at all.
From today's email:
ReplyDelete"On your blog about hopf-fibration there are 2 drawings at the end. I am looking for such a schematic 3D drawing to make such a model on a 3D printer.
Do you perhaps know where I can find such a model?
Thank you in advance and best regards,
XXX"
Probably this Reader has in mind this:
https://arkadiusz-jadczyk.eu/blog/tag/hopf-fibration/
I have no idea what kind of food 3D printers require to be fed with, so I do not know how to help this person....
Thanks. I wasn't using B;lender. I was using POV-Ray for creating my images of the Hopf fibration.
Delete"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."
ReplyDeleteКак-то несимметрично. Можно к четырём добавить ещё четыре и получим восьмимерное пространство - финслерово произведение двух пространств Минковского. Но гравитация это "ветер", который деформирует только первые четыре оператора. Операторы изоморфны линейным векторным полям, а набор из восьми операторов генерирует алгебру Ли векторных полей Киллинга 8-мерного пространства с нейтральной метрикой (то есть финслерова произведения пространств Минковского). Гравитация прячется в локальных алгебрах векторных полей, которые локально деформируют квадратичную форму изотропного конуса пространства Минковского. Подробности смотрите в ранее упомянутой книжке.
Если позволите, то добавлю к этому посту ещё одну картинку. 8-мерное пространство с нейтральной метрикой эволюционирует так, чтобы тангенс телесного угла изотропного конуса был пропорционален эволюционному параметру (абсолютному времени существования вселенной). А поскольку в этом пространстве отклонение от вакуумного векторного поля в 4-мерном подпространстве формируют гравитацию, а отклонения от вакуумного векторного поля в дополнительном 4-мерном пространстве с инверсной метрикой формируют поля калибровочной связности, то можно предположить, что постоянная тонкой структуры и тангенс телесного угла эквивалентны. Загляните ещё в раздел заключения ко второй главе, где рассматривается вывод формулы Барута для масс поколений лептонов.
DeleteIgor, do you have a place for consciousness in your 8-dimensional world? Or is you world all purely materialistic?
DeleteАркадиуш, похоже я утомил вас своим 8-мерным пространством. Вопрос, конечно, убойный, но я попробую ответить. В моём понимании сознание это эволюционирующий (и вместе с тем турбулентный) поток материи на семимерной сфере, но локализован он в носителях этого сознания.
DeleteНо откуда взялась эта семимерная сфера?
DeleteА откуда взялась математика? Откуда взялись уравнения?
DeleteДля меня это важнее лептонных масс!
DeleteВ математике разрешены всякие сферы (гиперсферы), любых размеров и размерностей, и в математике разрешены любые векторные поля на этих сферах. С другой стороны, существует объективная реальность, которая совпадает с потоком материи на семимерной сфере, который эволюционирует (но вместе с тем и флуктуирует) от менее устойчивого состояния к более устойчивому состоянию. Отсюда и берутся физические уравнения. Я так думаю.
ReplyDeleteА откуда взялась математика?
DeleteМатематика это плод сознания, то есть это результат образного мышления, который можно выразить в виде строгих математических текстов.
DeleteОткуда взялось сознание когда математики ещё не было?
DeleteSo, mathematics is the result of human consciousness. Human consciousness is the result of flows on 7-dimensional sphere. Seven-dimensional sphere is a concept of mathematics. So there was no seven-dimensional spheres before spheres before humans appeared. But there were leptons as it seems. I cannot see how you can deal with these contradictions? Igor, do you understand what I have in mind?
DeleteКонечно понимаю. Вы исходите из того, что потоки на сфере это плод фантазии человека, а я утверждаю, что это объективная реальность. Чтобы проверить кто из нас прав надо посмотреть к каким следствиям ведёт эта математика. Если следствия будут похожи на физику, то понятно кто будет прав.
DeleteThis comment has been removed by the author.
DeleteСознание не генерируется математикой, сознание это результат работы мозга человека.
ReplyDelete