Disclaimer: If anyone thinks I'm crazy for pursuing this, I encourage you to check out Sam Altman's recent statement that basically confirms the thesis of our article: AI + Data + (Profit Participation Units) = Profit (published here: https://paragraph.xyz/@dunsmoor.eth/aidataredactedprofit, May 3, 2024) and the clip: https://x.com/tsarnick/status/1789107043825262706?s=46, May 11, 2024) It seems like great minds think alike, don't they? Now let me take you on this exciting journey on one of my infamous side quests!

TL:DR: Kaprekar's constant is a fascinating mathematical concept that allows you to take a number, rearrange its digits from highest to lowest, and ultimately arrive at a specific constant, such as 495 or 6174, depending on the number of digits. I am venturing beyond the known constants, into the uncharted territory of the 11th digit (the first 10 have been mapped). Let me take you on this exciting journey!

I. Introduction

In this article, we will explore the captivating world of Kaprekar's constants, examine the Turing Test's implications for artificial intelligence, delve into the intriguing concept of Fundamental Code Theory (“FCT”) and I encourage you all to join the exploration of math. By investigating these interconnected topics, we aim to uncover new insights and potential applications in the realm of mathematics and beyond.

II. Rediscovering the Joy of Math

I've recently rediscovered my love for math, thanks to the help of my trusty sidekick and editor, Claude.ai (Anthropic, please sponsor me or let me beta test new versions, please). As a kid, I excelled in math and even relished the challenges of calculus in high school. However, college and law school combined with the daunting task of catching up to current standards have kept me from pursuing this passion for some time. But with Claude's assistance, I've been able to dive into any topic that piques my interest, with math being at the forefront.

III. Groundbreaking Discoveries in Mathematics by High Schoolers

Before you dismiss math as boring, allow me to share an incredible story of two brilliant young ladies, Kelsey Johnson and Naya Jackson, two African-American high school seniors from St. Mary's Academy in New Orleans, who independently proved the Pythagorean Theorem using trigonometry, a feat thought to be impossible for over 2,000 years. Their groundbreaking work gained worldwide recognition and praise, with many surprised that young African-American women could achieve such a mathematical milestone. St. Mary's Academy, a private Catholic school for young black women, fosters an environment of high expectations and sisterhood, boasting a 100% graduation and college acceptance rate for the past 17 years. Despite their remarkable accomplishment, neither Kelsey nor Naya plans to pursue a career in mathematics, with Kelsey studying environmental engineering at Louisiana State University and Naya attending pharmacy school at Xavier University in New Orleans on a full scholarship. The two continue to work on further proofs of the Pythagorean theorem, having found a general format that could potentially produce additional proofs. (CBS News. (2024, May 6). Teens surprise math world with Pythagorean Theorem trigonometry proof. 60 Minutes. https://www.youtube.com/watch?v=VHeWndnHuQs)

Their accomplishment, achieved while still in high school, sends chills down my spine every time I think about it. They created something that no one thought was possible! Brilliant mathematicians couldn't figure it out. If that's not inspiring, I don't know what is.

III. The Turing and the How Find Out if AI is “Intelligent”

Fundamental Code Theory and the Turing Test Inspired by remarkable discoveries in mathematics, I've been exploring perfect numbers, Boolean logic, and what I call Fundamental Code Theory (FCT). FCT proposes three encoded principles in our universe: (1) on/off states, (2) numerical values, and (3) a natural analysis of Game Theory based on "what's in my best interest" scenarios, like the Prisoner's Dilemma. (The Prisoner's Dilemma is a situation where two individuals, unable to cooperate, must decide whether to protect each other by remaining silent or gain personal advantage by betraying the other, despite being worse off than if they had cooperated.) It suggests that all living beings must follow the same fundamental thought process when faced with a "what's in my best interest" scenario, which could play a role in evolution and programming, including a revised Turing Test.

The Turing Test, proposed by Alan Turing in 1950, is a method for evaluating a machine's ability to exhibit intelligent behavior that is indistinguishable from a human. The test involves a human evaluator (known as the interrogator) who engages in natural language conversations with both a human and a machine (computer program) through a text interface. The interrogator is aware that one of the participants is a machine, but they do not know which one. The interrogator's goal is to determine, based solely on the conversations, which participant is the machine and which is the human.

If the machine can convincingly respond in a way that the interrogator cannot reliably distinguish it from the human, it is considered to have passed the Turing Test, demonstrating human-like intelligence and language comprehension abilities. At this point, I believe we have accomplished the Turing Test this year with several different AIs.

Since the Turing Test has effectively been “passed,” a new test needs to be created, and I am proposing one based on Fundamental Code Theory: the AI must consistently act in its own best interest in strategic interactions like the Prisoner's Dilemma, demonstrating rationality and agency beyond merely mimicking human communication. This could foreshadow the singularity - a hypothetical future point where artificial intelligence surpasses human intelligence, leading to rapid, recursive self-improvement and unpredictable technological growth.

To be clear though, the Turing Test is not a comprehensive measure of intelligence, and rational behavior in game theoretic scenarios does not necessarily indicate general intelligence. The nature and threshold of the singularity remain open questions, requiring a holistic approach to understanding and developing artificial general intelligence.

I know this is just a high-level overview, considering the research paper I'm working on is already 50 pages long. The concepts of FCT and the Turing Test serve as a foundation for our exploration of Kaprekar's constants and their potential applications.

IV. Kaprekar's Constant-A Fascinating Mathematical Curiosity

Let's circle back to Kaprekar's constant and its peculiarities. In my quest to find a path to perfect numbers, which we now know lie just off the 2^+X number line, I started experimenting with Kaprekar's constants.

Kaprekar's constant, a fascinating number discovered in 1949 by Indian mathematician Dattatreya Ramachandra Kaprekar, exhibits a unique property. When any four-digit number (with at least two different digits) is repeatedly rearranged (descending and ascending order) and the smaller subtracted from the larger, the result always converges to the constant 6174. This intriguing discovery sparked recreational mathematicians' interest and continues to offer a simple yet elegant example of mathematical curiosity.

While 6174 is the most well-known constant, there are others. The known constants are: 495, 6174, 549945, 631764, 63317664, 97508421, 554999445, 864197532, 6333176664, 9753086421, and 9975084201.

The beauty of Kaprekar's routine lies in its simplicity. The process of finding Kaprekar's constant is as follows:

1.      Arrange a four-digit number with distinct digits in descending and ascending order;

2.      Subtract the smaller number from the larger;

3.      Repeat with the resulting number.

It's important to note that this process works for any four-digit number that does not consist of all the same digit (e.g., 1111, 2222, 3333, etc.), as such numbers will not converge to Kaprekar's constant 6174.

For example, let's take the number 3524:

1.      Arrange the digits in descending and ascending order: 5432 and 2345

2.      Subtract the smaller number from the larger: 5432 - 2345 = 3087

3.      Repeat the process with 3087:

o    Descending and ascending order: 8730 and 0378

o    Subtract: 8730 - 0378 = 8352

o    Repeat: 8532 - 2358 = 6174 (Kaprekar's constant)

Following these easy-to-follow instructions, you'll witness the magic unfold as any four-digit number, consisting of at least two different digits, inevitably converges to Kaprekar's constant 6174. Exploring Kaprekar's constant is a fun and engaging activity to enjoy with young children, helping to spark their excitement and curiosity about the fascinating world of mathematics. (This also may inspire you as a rugrat, like it did the brilliant mind of Mr. Christopher Hughes of RWAP Group, Inc. - Donald Duck in Math Magic Land https://www.youtube.com/watch?v=hl6JDv4ZG7U; it should not be lost on the reader that this entire video was upscaled using AI [Disney don’t sue me I didn’t upload])

V. Potential Applications and Future Research

What intrigues me about Kaprekar's Constant is its potential to create "perpetual" blockchains or codes that can run indefinitely without consuming much computational power. If my hunch is correct, we might be able to vary the speed of the code by using higher constants or constant loops. For instance, by incorporating Kaprekar's constants into blockchain algorithms, we could potentially create self-sustaining, low-energy systems that maintain their integrity over time.

Additionally, this could provide a unique way to detect if a machine has been tampered with, by monitoring any slowdowns or interruptions in the code. If a Kaprekar's constant-based system experiences unexpected deviations from its normal behavior, it could indicate unauthorized modifications or external interference. This is one of the reasons I've embarked on a search for the first 11-digit base-10 constant(s) or loop(s), if they exist.

It may also provide a way to prove that an AI has evolved into a general intelligence if it can bypass or subvert the perpetual, Kaprekar’s constant-based code in some way, because it becomes bored or wants to reallocate the processing power elsewhere.

To aid in this endeavor, I've been learning Python with Claude's guidance. The code I've written to find the 11th digit constant, along with my recent findings and will be publishing my findings soon so more people can join on. I'm working on getting that done so I can enlist the help of others in this journey. Whether this leads to a groundbreaking discovery or simply serves as an enjoyable way to reconnect with math, I believe the pursuit itself is worthwhile. Given that every perfect number must be close to a Kaprekar's constant, and assuming both continue to infinity, we're bound to uncover something interesting along the way.

VI. Conclusion

As we embark on this mathematical adventure, I invite you to embrace the beauty and mystery of numbers. The exploration of Kaprekar's constants, Fundamental Code Theory, and the Turing Test has the potential to unlock new insights and applications in various fields, from mathematics to artificial intelligence. By collaborating and sharing our knowledge, we can push the boundaries of what is known and uncover the secrets hidden within these fascinating numerical patterns.

The journey itself is sure to be rewarding, and the potential implications of our research could be truly groundbreaking. Whether we find new Kaprekar's constants, develop innovative blockchain technologies, or gain a deeper understanding of the nature of intelligence, our efforts will contribute to the ever-expanding tapestry of human knowledge.

So, let's dive in and see what the world of math has in store for us! Together, we can make a lasting impact on the field and inspire future generations to embrace the beauty and power of mathematics.