From Manjit Kumar, Quantum , Einstein, Bohr and the Great Debate About the Nature of Reality-Icon Books (2008):
Max Born, 38, a key figure in the future development of quantum physics, had arrived in the small university town from Frankfurt just six months before Pauli. Growing up in Breslau, capital of the then Prussian province of Silesia, it was mathematics, not physics, that attracted Born. His father, like Pauli’s, was a highly cultured medical man and academic. A professor of embryology, Gustav Born advised his son not to specialise too early once he enrolled at Breslau University. Dutifully, Born settled on astronomy and mathematics only after having attended courses in physics, chemistry, zoology, philosophy and logic. His studies, including time at the universities of Heidelberg and Zurich, ended in 1906 with a doctorate in mathematics from Göttingen.
I was walking the same stairs in the same building that Max Born was walking, when studying theoretical physics in Breslau ( after WWII renamed Wrocław ).
And then I was walking the same stairs during my year long stay in Gottingen.
So I feel some affinity with Max Born. And surely I feel lot of affinity with mathematics.
"The belief that there is only one truth, and that oneself is in possession of it, is the root of all evil in the world."
"I am now convinced that theoretical physics is actually philosophy."
"Intellect distinguishes between the possible and the impossible; reason distinguishes between the sensible and the senseless. Even the possible can be senseless."
Mathematics exercises the brain better than anything else. Yesterday I realized I need such exercises, since my unlawful use of a hammer (which may have been a kind of a self-punishment for past mistakes in my life) resulted in a psychic shock to my nervous system that I am still not quite able to completely overcome.
And so when the opportunity appeared, and it appeared, I decided to use it to its full. Here is my exercise, from N. Bourbaki - Elements de Mathematique. Algebre. Chapitre 9-Springer (2006) :
At the moment I have no idea how to solve these problems. But I will not cease until I solve them.
15-02-23 18:51 My guess is that Bourbaki defines here the Hodge star operator. Usually it is defined for bilinear forms, but in 9d Bourbaki is asking the reader to extend its properties to sesquilinear forms (so that it works also in quantum theoretical environment, for Fermionic systems), like those we are dealing with discussing twistors. It strikes me that these twistors do not twist. How to make them twist? Something to think about.
It occurred to me today, while reading Kumar, that energy is not in general quantized, contrary to misleading statements in some popular books. But angular momentum IS! It looks like angular momentum is more primitive than energy, perhaps more fundamental than space and time.... Godel rotating universe allows for time travel. Another hint?
Niels Bohr has no idea how to make his model of an atom until he earned from a mathematician John Nicholson that angular momentum may be quantized.
"Bohr had met Nicholson during his abortive stay in Cambridge, and had not been overly impressed. Only a few years older at 31, Nicholson had since been appointed professor of mathematics at King’s College, University of London. He had also been busy building an atomic model of his own. He believed that the different elements were actually made up of various combinations of four ‘primary atoms’. Each of these ‘primary atoms’ consisted of a nucleus surrounded by a different number of electrons that formed a rotating ring. Though, as Rutherford said, Nicholson had made an ‘awful hash’ of the atom, Bohr had found his second clue. It was the physical explanation of the stationary states, the reason why electrons could occupy only certain orbits around the nucleus."
Thus even mathematicians making "awful hash" may be sometimes useful....
16-02-23 17:43
P.A.M. Dirac, Heinrich Hora, J. R. Shepanski, "Directions in physics: lectures delivered during a visit to Australia and New Zealand August/September 1975", Wiley 1978
ISBN: 0471029971,9780471029977
17-02-23 8:37 While searching for articles related to Gryzinski and Eganowa accidentally found A. Guts, "Metaphysics of time and eventology": Александр Константинович Гуц, "Метафизика времени и эвентология" (2011) I love the term "eventology".
Книга, в которой собраны работы О.Ю. Воробьёва, основателя нового междисциплинарного научного направления - эвентологии, связывающего философию и математику с естественными, гуманитарными и социо-экономическими науками: статистической механикой и термодинамикой, теорией вероятностей, теорией информации, теорией решений, эвенто-менеджментом, психологией, экономикой, социологией и др. Эвентология - учение о событиях, возникшее из невыносимо лёгких наблюдений: "материя и разум - это просто удобный способ связывания событий воедино" (Бертран Рассел, 1946; О.Ю. Воробьёв, 2001) и "разум возникает там и тогда, где и когда возникает способность делать вероятностный выбор" (В.А. Лефевр, 2003). Математическая эвентология - основанный на колмогоровской аксиоматике новый раздел теории вероятностей, показавший свою эффективность в математическом описании и эвентологическом обосновании и развитии существующих теорий неопределённости (теории нечётких множеств (Лютфи Аскер Заде, 1965), теории возможностей (Лютфи Аскер Заде, 1978), теории свидетельств (Демпстер-Шафер, 1976)), а также теории перспектив (Канеман, Тверски, 1979, 1992), объединившей экономику и психологию, и теории спроса и предложения ("крест Маршалла"), краеугольного камня современной экономикс. Наряду с философскими и математическими вопросами "со-бытия" и бытия эвентология затрагивает экономические, социальные и психологические вопросы, над которыми каждый из нас задумывается и размышляет на протяжении жизни. В книгу включены материалы, рассчитанные на широкий круг читателей, интересующихся эвентологией и ее приложениями; особый интерес они представляют для специалистов, активно работающих в этой новой области, преподавателей, аспирантов и студентов старших курсов университетов, занимающихся теорией решений, эвенто-менеджментом, искусственным интеллектом, теорией вероятностей, математической статистикой и математическим моделированием гуманитарных, социо-экономических и естественных систем.
Содержание:
Пролог.
Общие эвентологические принципы.
Аксиоматика Колмогорова.
Математические эвентологические принципы.
Множество событий.
Обращение эвентологических распределений.
Зависимость событий.
Парус и ветер Фреше.
Эвентологические распределения.
Эвентологические случайные процессы.
Теория нечётких событий.
Эвентологический портфельный анализ.
Эвентологические обоснования экономикс.
Эвентологические сеточные методы.
Эвентологические модели в психологии.
Эвентологическая теория сет-предпочтений.
Эвентологическая теория принятия решений.
Эвентологическая теория игр.
Эпилог.
Эвентологические обозначения.
Литература.
Zeit ist nur dadurch, daß etwas geschieht und nur dort wo etwas geschiecht.
(E. Bloch)
More papers by the same author, actively searching for the truth, here. Guts gives a quasi-definite answer to the question: "What is Time?". Time is a form of realization of the consciousness.
11:08 It seems to me, but perhaps I am wrong, that Guts assumes, more or less, that Quantum Theory is the Ultimate Truth. That we are supposed to rely on its formalism even when looking for answers for our deepest questions of existence and meaning. Even if nobody understands it, the problem lies with our understanding, not with quantum theory. On this issue I would rather take sides with Gryzinski. But it's my subjective and certainly biased taste and choice.
13:39 Something to think about (apart of Bourbaki): A. Guts, Созидание Мира в Библии и науке Доклад на "Рождественских чтениях-2019" (Омск, ОмГУ, 9 декабря 2019)
P.S. All these links and comments above are exclusively for me. What I am writing is simply my personal journal. I am talking to myself. I am putting links, so that later on I will be able to find them easily. Right now I am stuck with Bourbaki. Can't prove a clear statement in an exercise. I am really disappointed with myself, with my mental/mathematical abilities. Shame!
18-02-23 19:40 Prepared pdf file with the proposition at the end. Will try to add my proof tomorrow. It took me several days. I hope finally today I got the idea how to do it.
I am aware of the fact that a bright student would solve this problem in five seconds instead of five days. On the other hand how can I think of ever solving a really hard problem if I can't solve a simple (as I believe it is) problem? Time needed for solving the problem really doesn't matter.
On the other hand a smart student has billions of problems that are waiting for solutions.... And there are problems of unknown difficulty (like Riemann Zeta) waiting for smart students.
20:30 Decomposable k-vector may be thought of as a non-entagled k-particle (fermions here) state. A generic (entangled) k-vector is a superposition (linear combination, or, simply, a sum) of decomposable ones.
19-02-23 8:37 John G. mentioned Raoul Bott. As I do not believe in coincidences, I checked Bott's "Lectures on K(X)". There is something that I will be needing very soon. Like this type of graphs:
12:15 It occurred to me last night that if I consider EEQT version of QED (I do not care for electro-week interactions for a while), we can shoot perhaps two birds with one shot. First of all we will get rid of the need of renormalization, and we will also have the answer to the question "what are the fundamental primitive events?". Of course we will have to use the conformal structure for that.
19:30 Have finished the proof, updated pdf. A smart student would certainly do it in five lines in five seconds. In fact I asked a mathematician, Marian Fecko, how to prove this property some ten years ago. I have a copy of my email to him, but his answer has been scrambled by some software bug. I do not remember today what was in his answer. What I do know is that, after that, I simply wrote in one of my papers that decomposability of $*_e x$ follows from decomposability of $x$, like it was instantaneous and easy. Can move now on, step by step. Yeah, theoretical physics is actually philosophy. In one of my old papers I was playing a bit with Hodge-star operator. Commenting on it I wrote: "The question is important because light-cone structure determines nine of the ten components of the metric tensor. Thus, in other words, we were asking to what extent is gravity intertwined with electromagnetism?"
20-02-23 21:30 A Reader asked me an apparently unrelated question. He asked me if proving theorems in a particular branch of mathematics can be considered as a way to salvation? I am not an expert in this domain, but as far as I know it is more or less clearly stated in the Bible: The way to salvation is by asking for forgiveness all person that have been hurt by our actions, and do it while they are still alive. And then repent, and repent aloud. But as I said: I am not an expert. Experts should be searched for among theologians
26-02-23 11:20 From my correspondence.
Received while ago:
Good day, Arkadiusz!
In the article sent to you (through Levichev) "Atomic Physics by Gryzinski..." you can immediately see my attitude to his outstanding works: he revived true physics, figuratively speaking, he returned to physics (experimental science!) experiment. Quantum mechanics, in principle, is unnecessary. He demonstrated this convincingly in his numerous writings. The fact that few people understand this is not surprising (most people do not think independently, only imitate scientific activity, without any serious education, both physical and philosophical).
All the best, I.E.
26-02-23 11:23
Part I ( Peter Keating )
Howard Roark laughed.
Chapter I, p. 9 ; opening sentence
"Do you mean to tell me that you're thinking seriously of building that way, when and if you are an architect?"
"Yes."
"My dear fellow, who will let you?"
"That's not the point. The point is, who will stop me?"
"What is mathematics about? Is there a mathematical universe glimpsed by a mathematical intuition? Or is mathematics an arbitrary game of symbols, with no inherent meaning, that somehow finds application to life on earth? Robert Knapp holds, on the contrary, that mathematics is about the world. His book develops and applies its alternative viewpoint, first, to elementary geometry and the number system and, then, to more advanced topics, such as topology and group representations. Its theme is that mathematics, however abstract, arises from and is shaped by requirements of indirect measurement. Eratosthenes, in 200 BC, demonstrated the power of indirect measurement when he estimated the circumference of the earth by measuring a shadow at noon, in Alexandria, on the day of the summer solstice. Establishing geometric relationships, solving equations, finding approximations, and, generally, discovering quantitative relationships are tools of indirect measurement: They are the core of mathematics, the drivers of its development, and the heart of its power to enhance our lives."
15:02 Some Readers of this blog may feel a strong urgency and a compulsive need to express their own views, ideas, and opinions, that are radically different than those I am presenting here - they just wish to go into a completely opposite direction - these readers are strongly encouraged to use their own websites or blogs for a public presentation of their private views, and taking responsibility for these presentations. It is a refreshing, useful, and educating experience. Worth the effort. On their own sites they can open their wings wide and fly as high as they wish feeling completely free.
15:24 Quoted from "Human Front:
"Ethical egoism is a view that one can be self-serving and moral. Writer and philosopher Ayn Rand (pictured) constructed her own egoist theory called ‘Objectivism’. Remarkably, she did this through her works of fiction.
Rand’s philosophical outlook was based on a trichotomy: phenomena inside the mind (subjective), phenomena outside the mind (intrinsic), and phenomena between the two (objective). She then argued that it is ethical to rationally promote one’s own best interests to form objective knowledge on what they ought to do in each situation: what’s best for themselves.
Rand’s view is teleological because it brings purpose into morality. "
I consider such a view, we may call it STS, as in fact existing, and followed consciously or not, by many, if not by most of the people. The opposite view may be called STO or, following Gurdjieff, "external considering.". It is my understanding that for some people external considering may be simply physically impossible. These people simply do not have appropriate wirings. But even without a proper wiring a simulation is possible. We can, for instance, simulate quantum computer on a classical computer. Of course such a simulation needs remarkably more effort and time.
