Dangerous Math: A Tale of Perilous Pursuits

The Mystery Unfolds

I pondered over the title: Dangerous Relationships? Dangerous Operators? Are the Lizards Awake? Ultimately, I settled on "Dangerous Math." Can math be dangerous? It depends on which kind. Some mathematics seem more perilous than others. This post attempts to delve into that eerie realm.

The Allure of the Unexplainable

My sample size is small, too small for statistical significance. It's like investigating the paranormal or UFOs—phenomena that elude systematic scientific study. Are these occurrences merely coincidences or Jungian synchronicity? Why do circumstances align in one way and not another? Humans excel at spotting patterns, even where there might be none. Are these patterns truly absent? Consider the "Ulam Spiral"—a seemingly random arrangement of integers revealing prime number patterns. What qualifies as a genuine mathematical regularity?

The Curious Case of Mathematicians

Below is a list of mathematicians, their contributions, and their mysterious demises. Is there a pattern, mathematical or perhaps... lizard-like?

Felix Alexandrovich Berezin (April 25, 1931 - July 14, 1980)

Felix Alexandrovich Berezin, my hero, tragically drowned while rafting near Magadan in 1980. 

He was known for his novel approach to the quantization of dynamical systems with non-Euclidean geometry. Berezin was a bridge between modern mathematics and physics, emphasizing the importance of geometrical ideas.

Stephen Mark Paneitz (March 24, 1955 - September 1, 1983)

Stephen Mark Paneitz, a disciple of Irving Ezra Segal, was exploring applications of conformal geometry. He drowned in a shallow lake near the Institute of Theoretical Physics at the Technical University of Clausthal, Germany, during a conference. His death was a heavy loss to the scientific community. Paneitz left behind significant work on conformal differential geometry, known today as the Paneitz operator.

Pertti Lounesto (1945 - June 21, 2002)

I met Pertti Lounesto at the ICCA6 conference in 2002. He showed me how quantum fractals connect to conformal geometry. Lounesto was notorious for pointing out errors in mathematical publications. Tragically, he drowned in the Mediterranean Sea a few months later.

Thomas P. Branson (October 10, 1953 - March 11, 2006)

Thomas Branson, a continuator of Paneitz's work, died suddenly of a heart attack at age 52. The operator he worked on is now known as the Paneitz-Branson operator. His death adds to the list of those mysteriously linked to this dangerous line of research.

Conclusion

I am not here to fascinate, excite, or frighten you with tales of mathematical dangers. I am merely sharing what struck me as curious. These cases, once unrelated and buried in data, now present a pattern worth pondering.

So, why not take a closer look at Segal's life-threatening idea? Perhaps, in these mathematical mysteries, lies a truth stranger than fiction.

The Spinor Enigma

While studying some intriguing papers by Vadim Varlamov (refer to my penultimate post, "The Quantum Leap: A Journey Beyond Reality"), I visited his Russian blog. I couldn't resist translating one of his posts about spinors into English. Here it is:

"What is a Spinor ???"

The Shocking Revelation: 11,000 "Peer-Reviewed" Papers Retracted – What This Means for Trusting Science

All that is required for evil to prevail is for good men to do nothing.

Recently, a headline caught my attention and struck me deeply:

“Trust The "Science"...That Just Retracted 11,000 "Peer-Reviewed" Papers”

The online article begins with a stark reminder that blind trust in science might not always be wise. According to the article, the 217-year-old Wiley science publisher had "peer-reviewed" over 11,000 papers that were later found to be fraudulent. These papers were described as "naked gobbledygook sandwiches."

Naked gobbledygook sandwiches

This revelation underscores a troubling reality: even in the realm of science, errors and deceit can infiltrate. This notion hit home for me just yesterday. As a member of the Editorial Board for a nascent quantum physics academic journal, I was asked to review a paper that had already received two positive reviews. Upon examining the paper and its references, I felt compelled to share my concerns with the Editor-in-Chief. Below is my carefully crafted response:

Dear Editor,

I harbor suspicions that this paper, along with a series of treatises by this author, is based on a grave error that originated in Reference [17]. Upon scrutinizing the citations of Reference [17], I discovered eleven citations, ten of which are self-citations, with one citation in a thesis by a pupil of the author.

I will provide a concise description of what I believe to be the error, which may assist the next reviewer in their evaluation. Would you agree to this?

Additionally, should my assessment prove accurate, we face an ethical dilemma. If an entire series of papers is based on a fallacy and we are aware of it, is it right to remain silent? We might consider writing a paper to highlight this error. However, before proceeding, I want to ensure my judgment is sound. I will endeavor to prepare and send a PDF document with the relevant formulas today.

With the utmost respect and warmest regards,

Arkadiusz

Having penned this initial response, I spent the rest of the day and this morning creating a detailed follow-up:

Dear Editor,

Attached is my brief and quickly written note. There may be some spelling errors, but I hope it helps. I would appreciate an independent opinion on the subject.

Best regards,

Arkadiusz

Here is my "short note":

Throughout this process, one thought persistently lingered in my mind:

“All that is required for evil to prevail is for good men to do nothing.”

By sharing this experience, I hope to underscore the importance of vigilance and integrity in scientific endeavors. Let us remain steadfast in our pursuit of truth, even when it means questioning the very foundations upon which we stand.

"When bad men combine, the good must associate; else they will fall, one by one, an unpitied sacrifice in a contemptible struggle."

“There is good and there is evil and there is the specific situation that determines which is which.” [The Law of Three]

The Quantum Leap: A Journey Beyond Reality

 The world around us is not merely changing; it is experiencing a quantum leap. This is not a mere evolution but a dramatic transformation, and we are all participants in this grand phenomenon. Some of us are active players, diving headfirst into the unknown, while others are passive witnesses, watching the spectacle unfold. Yet, many continue their daily routines, blissfully unaware of the seismic shifts happening around them.

In my theory of EEQT (Event Enhanced Quantum Theory), these jumps occur at seemingly random, yet precisely timed moments. When the time is ripe, reality takes a leap, and these jumps, theoretically instantaneous, are in truth processes that transcend our material world, touching upon hyper-dimensional realms beyond our comprehension.

The term UFO (Unidentified Flying Object) has evolved into UAP (Unidentified Anomalous Phenomena). These entities are no longer mere flying objects; they are elusive forms that defy our physical understanding. Despite the media's reluctance to embrace the term "hyper-dimensional," the public is gradually being conditioned for the extraordinary revelations that lie ahead.

A flying flock of gees over the pool in Florida?
Or a "form" of a hyper-dimensional origin?

In this rapidly shifting landscape, propelled by the explosion of artificial intelligence, I find myself pondering the union of matter and spirit. Recently, I delved into the works of a kindred spirit, V.V. Varlamov, a professor at the Siberian State Industrial University in Novokuznetsk, Russia. His paper, "On the Union of Matter and Form: Group Theoretical Approach" (Metafizika, 2023), has captivated my mind.

Varlamov begins by exploring the very fabric of our reality: space and time. Are these the fundamental levels of reality, or mere constructs of our perception? He writes:

“Does spacetime make the fundamental level of reality? First, define what are these ‘space’ and ‘time’ comprising the notion of spacetime. Two different frameworks should be distinguished: aprioristic Kantian understanding of space and time as pure forms of our sensibility and the so-called relativistic view on space and time as the forms of existence of matter. Forms of sensibility versus forms of being. Consciousness versus matter. It seems like we are trapped once again within the eternal duality of spirit and matter - nightmare of a philosopher having to choose between the idealistic and materialistic philosophies. As a matter of fact, this duality is only an illusion caused by the mess of words and concepts, as was noted by Bertrand Russel. These two concepts cannot be deduced empirically but precede any experiment making the ground for all the following constructions. According to Kant, space and time are two pure forms of sensory contemplation and principles of a priori knowledge. They are the first and fundamental attributes of our perception, derived from the integrated sensorial experience of human being. Form of contemplation is just an obscure and strongly curved lens mediating our perception of the world. Hence, defining the space and time concepts from experience makes no sense, while defining them by other means yields anything but not space and not time. Here we come to a very important conclusion: space and time are nothing but forms of human conscious contemplation.”

As I read these profound words, I see a reflection of my own thoughts. Varlamov, a mathematician, weaves his contemplations in the language of Real numbers, Quaternions, Spinors, Twistors, and the Conformal Group, even delving into the enigmatic anti-de Sitter space with its two time-like dimensions. He is, in essence, another version of myself, more mathematical in spirit.

In this quantum leap, we are bound not just by the physical world but by a tapestry of consciousness that stretches into the hyper-dimensional. As we stand on the brink of this new reality, we must embrace both the matter and the spirit, understanding that they are not opposing forces but facets of a greater whole. The future is here, and it is beyond anything we have ever imagined.

The Future is Now.

P.S. 24-07-24 13:45 AI at work. My chat with AI today:

Prompt: Can you help me to identify a snake if I give you a photo?

Response: Yes, I'd be happy to help you identify a snake. Please go ahead and upload the photo of the snake.

Prompt: Here it is:

Response: Based on the photo you provided, the snake appears to be a type of garter snake. Garter snakes are non-venomous and common in many parts of North America. They are known for their distinctive pattern, usually consisting of stripes running the length of their bodies.

Here's a bit more detail about garter snakes:

• They often have three stripes running down their bodies, which can be yellow, green, or blue.
• They are usually small to medium-sized snakes, typically ranging from 18 to 26 inches long.
• They are often found near water sources such as ponds, streams, or wetlands, but they can also be seen in gardens and urban areas.

If you need more precise identification or if you have any specific concerns, such as whether the snake is venomous or poses a threat, please let me know!

Prompt: Thanks.

Response: You're welcome! If you have any more questions about snakes or anything else, feel free to ask. Stay safe and have a great day!

But it is NOT a garter snake. As Laura has pointed it to me, it is a semi-aquatic European grass snake. 
https://en.wikipedia.org/wiki/Grass_snake. So, use AI, but do not rely on it when taking decisions. Always double check! If it cam misidentify snakes, it can misidentify missiles as well.

The Cosmic Comedy Continues

 

As Above, So Below

Ecclesiastes 1

“8 All things are wearisome, more than one can describe; the eye is not satisfied with seeing, nor the ear content with hearing."

Ah, the classic "grass is always greener" dilemma. Imagine if Netflix had been around back then—King Solomon would have been binging series after series, muttering, "Next episode, please," until his royal eyes were square!

9 What has been will be again, and what has been done will be done again; there is nothing new under the sun.

Déjà vu much? It’s like the ancient version of the Hollywood reboot craze. Think you've come up with a unique idea? Surprise! It was already a hit back in 300 B.C.

10 Is there a case where one can say, “Look, this is new”? It has already existed in the ages before us.

Picture a caveman inventing the wheel, only to have another caveman say, "Pfft, I did that last week, but with rocks!"

11 There is no remembrance of those who came before, and those yet to come will not be remembered by those who follow after.”

This, my friends, is why we need yearbooks and social media. Otherwise, how would we know who had the best toga in high school?

---

Quantum Shenanigans and the Never-Ending Quest for Newness

So, you’re diving into the quantum realm with Holger Lyre's "The Quantum Theory of Ur-Objects as a Theory of Information." Fancy stuff, but hold your horses! Here’s where things get juicy:

Enter stage left, [Cas75] L. Castell. He's like the Gandalf of quantum theory, saying, "You shall not pass... until you understand my Quantum Theory of Simple Alternatives."

Naturally, you do what any 21st-century scholar does: you Google it. And just like that, a digital angel descends from the cloud (thanks, WiFi!) and presents you with:

L. Castell, A new quantum number derived from conformal invariance, Nuclear Physics B, Volume 13, Issue 1, 1969, Pages 231-236, ISSN 0550-3213, https://doi.org/10.1016/0550-3213(69)90380-0

Lo and behold! Your doubly compactified Minkowski space—your pride and joy—turns out to be as fresh as a 50-year-old fruitcake. Yep, nothing new under the sun, not even in the quantum world.

The Cosmic Comedy Continues

The conformal group, the geometry of light, photons—they're everywhere, just like glitter after a craft project. In the grand theater of consciousness research, they're the spotlight operators, turning possibilities into facts. The cosmic joke is on us: the circle doesn’t just close—it’s been closed for eons.

So, the next time you stumble upon an "aha" moment, remember: somewhere, sometime, someone else had that same "aha." But hey, at least you’re in good company. And if all else fails, there's always the comfort of knowing that even the ancient sages felt the same weariness. Smile, you're part of a timeless tradition of discovery and rediscovery.

The Quantum Enigma: A Dance of Possibilities

I recently delved into the intriguing paper “Relations between Quantum Theory and Panpsychism” by Thomas Görnitz. It was a revelation, sparking countless thoughts and ideas that I can't wait to share in upcoming posts. Today, however, I'll focus on one mind-bending concept.

Görnitz emphasizes repeatedly that quantum theory isn't about solid, unchanging facts but about a dynamic realm of evolving possibilities. Classical physics gives us concrete facts, while quantum theory presents us with an ever-shifting sea of possibilities. But then, in a miraculous twist, these possibilities collapse into solid facts. Let's explore this further with some profound quotes from the paper:

“We humans are born into a reality which we did not create ourselves. However, in order to survive, it is necessary to understand the facts we encounter in it, as well as the processes and changes.”

This resonates deeply with me. But beyond understanding the external world, we must also strive to understand ourselves and our fellow human beings.

“Classical physics establishes deterministic laws about facts. The much more precise quantum theory asserts only a determined change of possibilities.”

Here lies a fascinating puzzle. Must the evolution of possibilities always be deterministic? If randomly generated facts can influence possibilities, then perhaps the evolution of possibilities isn't always deterministic.

“We consider possibilities that have not yet become facts. With us humans, possibilities are often emotionally underpinned: we expect, fear or hope for something to happen. All our intentions rely on possibilities. Thus, mere possibilities can already generate real effects.”

This brings us to the mysterious process of fact generation. When and how do possibilities crystallize into facts? I've co-authored papers on this very topic, titled "How and When Quantum Phenomena Become Real?" and "How Events Come Into Being." We need to understand the "binamics" – the irreversible process where possibilities become facts.

“We have to consider both facts as well as possibilities for an understanding of nature, a feature described by the 'dynamic layer structure' of natural science.”

Yet, the Ur theory, or the theory of “Abstract Quantum Information Units,” neglects facts altogether. Following Weizsäcker, Görnitz speaks only of quantum codons as standard qubits. But DNA relies on four codons (A, C, G, T) to create complexity. Shouldn't we consider additional codons beyond the standard Complex Qubit, such as Real, Quaternionic, and Octonionic structures, and even the standard binary field GF(2) (as well as more general p-adic number fields)?

“In a very exact description of natural processes only a determined evolution of possibilities can be assumed. Emerging facts are then random within the scope of these possibilities.”

“Possibilities are subject to other logical rules than facts. The meaning of "possibility" is that they can, indeed must, contradict each other if they would mistakenly be interpreted as facts at the same place and time.”

“Facts, of course, are not part of a quantum wholeness. A fact, however, can give rise to new quantum possibilities, which then can form or join a wholeness.”

This last insight is crucial. It suggests that the evolution of possibilities, influenced by the back-reaction of facts, isn't always deterministic.

“Already in quantum physics the transition from possibilities to a fact is not actually solved by the theory of decoherence. While a mathematically clear definition can be given, it is not practicable because the occurrence of a fact would theoretically require the passage of an infinitely long time. No physicist or anyone else can wait that long.”

This is the famous Measurement Problem of quantum theory, still awaiting a definitive solution. My own theory, EEQT (Event Enhanced Quantum Theory), was an initial step toward this solution but lacks a place for consciousness.

There’s a tantalizing possibility that conscious thinking may be based on non-associative logic. This is the exciting direction my current research is exploring.

Stay tuned as we unravel more of these quantum mysteries in future posts. The dance of possibilities and the birth of facts await.

P.S. 18-07-24  13:44 Here is one example of a possibility that became a fact:

https://x.com/BGatesIsaPyscho/status/1813887120081035311

It certainly required some non-associative decision making.

P.S. 18-07-24 16:42 Here is an excerpt from "Ur Theory and Space-Time Structure" by David Finkelstein:

"... It would therefore not be surprising if the second quantum evolution has a fundamental scale-time like an ur, that sets the scale of non-associativity in the way that the fundamental action h sets the scale of non-commutativity. (...)  It is  easy  to  see  from  elementary  computer models that processes that act on or refer to themselves do not necessarily compose associatively. If the dynamical laws are elements of the very cosmos that they propel, the dynamical processes they represent might be non-associative. "

P.S. 18-07-24 17:52 From my questions and answers chat with the C's, 23-04-22: 

Q: (Ark) What about quaternion algebra? Is it relevant to wave reading units? 

A: Absolutely. 

Q: (Ark) Yes? What about octonions? Are they better or worse? They are non-associative. Ooo! 

A: Better. 

 

 

Reflections on the current model of cosmology - By Thomas Görnitz

Reflections on the Current Model of Cosmology

Now, let me be clear—the title isn’t mine. It belongs to the brilliant Thomas Görnitz and his latest paper. We’ve crossed paths a few times before (he’s dropped by Wroclaw, and I’ve made my way to Leipzig), so his knack for clear and profound writing doesn’t surprise me one bit. What did surprise me was the joyful depth and sparkling clarity of his new paper.

Here’s a little teaser from the introduction. I even attempted to illustrate it, though I’m still on my journey to becoming the next Picasso of the science illustration world. Hang tight and enjoy this cosmic ride!

Abstract:

With the JWST, observational cosmology has entered an exciting new stage. The new quality of  its  observations  and  the  fact  that  there  are  problems  with  the  theoretical  concepts  of cosmology requires a renewed reflection on the theoretical foundations and may be seen as a call for a “new physics”.    

....

1 Introduction

With  its  standard  model,  the  ΛCDM  cosmology  in  its  various  forms,  today's  cosmology occupies a prominent position in the natural sciences. (Lambda is the cosmological constant, CDM stands for cold dark matter)  With regard to the current situation in cosmology, we would like to refer briefly to an interview with the CERN Courier. A leading cosmologist and theoretical physicist stated with a certain pride regarding the ΛCDM cosmologies: 

»It is a model that has only six parameters, most constrained at the percent level, which explains most of the observations that we have of the universe.«

In my youth, a report by Freeman Dyson about a conversation with Enrico Fermi was still known. Dyson had created a fit for Fermi's theory of pseudoscalar mesons and wanted to present it to Fermi. Fermi pointed out:  

“There are two ways of doing calculations in theoretical physics,” he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.” 

Dyson then asked Fermi what he thought of the fitted curves. 

“In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, ‘How many arbitrary parameters did you use for your calculations?’ I thought for a moment about our cut-off procedures and said, ‘Four.’ He said, ‘I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.’ 

With that, the conversation was over.” 

From the section 2.4 The “Hubble constant” :

In  contrast  to  the  first  measurements  by  Edwin  Hubble  in  1929  10 ,  this  value  can  now  be recognized as the reciprocal of the current age of the universe  11 , in no way being something else – neither with regard to the dimension nor the numerical value.  

Even  if  the  "dynamic  age  of  the  universe"  is  occasionally  mentioned  12 ,  it  is  difficult  to understand at a certain distance from the citation cartels why this time is still referred to as a fundamental constant.  

 P.S. 15-07-24 17:18 Appeared online today: 

LAURA KNIGHT-JADCZYK | ORGANIC PORTALS, HARVESTING HUMANITY, & THE HYPERDIMENSIONAL CONTROL MATRIX

July 14, 2024

AI at work, Part 2

From my today's chatting with GPT: Response to my Prompts

Created by Kandinsky 3.5

Title: "The Quest for Twistor Truth"

Concept Description:

1. The Labyrinthine Library:

A vast, surreal library with endless twisting hallways and floating bookshelves. Books have keywords and references written on them, such as "Null Lines," "Minkowski Space," and "Twistor Theory."

2. The AI Guide:

A glowing orb with a halo of spinning binary code. The AI is holding a large magnifying glass and appears to be frantically searching through books and scrolls.

3. The Patient Scholar:

A calm, wise scholar wearing a whimsical outfit and a thinking cap adorned with mathematical symbols and equations. The scholar has a bemused smile.

4. Mischievous Imps of Misinformation:

Small, mischievous creatures scattering fake books and incorrect references around the library. They have playful, cheeky expressions.

5. The Twistor Vortex:

A swirling vortex in the center of the library, representing the complex topic of twistor theory. Null lines and mathematical symbols spiral into it.

6. The Illuminated Path:

A bright, illuminated path leading the scholar and the AI guide towards a glowing book labeled "Truth." This book represents accurate and verified information.

Surrealistic Elements:

Floating clocks showing different times, symbolizing the timeless nature of the search for knowledge.

Books morphing into birds and flying around, representing the elusive nature of finding the right information.

Twisted, Escher-like staircases leading to nowhere, symbolizing the complexity and confusion of the topic.

Created by DALL-E 3 v.1

"I apologize for the repeated errors in my responses today. Here are a few hypotheses that could explain why these errors occurred:

Misinformation in Source Data:

The information I provided may have been based on inaccurate or outdated sources. Although I strive to offer accurate data, occasionally, errors from source materials can propagate into responses. 

 

Miscommunication or Misinterpretation:

There might have been a miscommunication or misinterpretation of the specific materials and references you were seeking. Ensuring a precise understanding of your needs is crucial. 

 

Complexity and Specificity of Topic:

The relationship between null lines in Minkowski space and twistors is a specialized and complex topic. This complexity increases the likelihood of referencing inaccuracies or less accessible materials. 

 

System Limitations:

As an AI, I rely on a vast array of data but may lack specific, up-to-date bibliographic details on niche academic papers. This limitation can result in incorrect references.

To address these issues more effectively, I will ensure that I use more reliable databases and references for your specific request. I can assure you that there is no deliberate programming or intention by my developers or handlers to provide incorrect information in response to questions containing specific keywords. The goal of this AI is to provide accurate, helpful, and reliable information to the best of its ability.

The errors in my responses can be attributed to a few common factors:

Complexity of Topic:

Niche and highly specialized topics like the relationship between null lines in Minkowski space and twistors are complex, which increases the chance of unintentional inaccuracies. 

 

Source Data Limitations:

The AI relies on a vast dataset compiled from diverse sources. Occasionally, errors or outdated information from these sources can influence responses.

Context and Interpretation:

Misinterpretation of your requests or the nuances of specific academic references can lead to mistakes. Ensuring precise understanding and context is challenging. 

 

System Limitations:

Despite extensive training, there are inherent limitations in the AI's ability to access real-time data or verify specific details like ISBN numbers or paper availability in real-time.

There is no motive or programming directive to provide incorrect information. The intention is always to be as accurate and helpful as possible. If you have further questions or need assistance with other topics, I'm here to help! "

 

Created by DALL-E 3 v.2