What is to come is a series of articles meant to provide a nuanced understanding of the world itself. One where Simplicity and Complexity are tied together by external (or internal) forces that define their boundaries, rather than the relatively simple questions of “Are they different? Or are they related?”. In this article, we aim to ask ourselves “Are they special?”. Of course, the answer to that is obviously yes. But the way they differ is one we might have overlooked.
The following titles are a result of the spark generated by Pi AI as a request to find a suitable title for my upcoming article. These titles seem to touch on different topics which provide a more holistic and understandable view of the matter. Their whole is the view. Their content is the approach. Their reason is to unite once and for all, Simplexity. The rules of requirement. Where Complexity’s bricks are formed by mere Simple arguments (who said we can yet understand that seemingly Simple concept?).
Upcoming Articles:
- The emergence of complexity from simplicity in prime number structures
- The importance of exploring non-conventional perspectives in mathematics
- The dynamic nature of prime number spaces and the potential for new discoveries
- The role of prime numbers as building blocks of reality and computation
- The impact of mathematical discoveries on broader fields such as cryptography and cybersecurity
Remember that I am an idealist. I am never on one side or another, I do not dwell on the technical implications and proof, but rather on its potential. I aim to maintain a middle balance between both Simple and Complex. Showcasing how the Point of View is what defines their interaction. Asking how the two-way speed of light could reveal insights into both ways of travel if those 2 ways are turned towards you, the central point. As if like… the complexity is not of the nature of the inquiry but of the space it logically forms to allow it to become ‘real’.
Simplicity could be what we define as “mathematics”, whereas complexity is what we seek in the “mathematical space” which is different from Metamathematics as it uses a nuanced understanding which is not yet explored within the domain.
(This article contains ideas presented by me, but shaped by AI)
Part 1: Non-Universe
In a non-universe where P!=NP, the assumption of inequality between the two classes of problems would create a fundamentally different reality, where continuity and simplicity might not be as closely intertwined as they are in our own universe. This distinction could lead to a reality where mathematics and thinking are characterized by inherent gaps and discontinuities, making them incomplete in a sense.
In such a non-universe, the assumption of P!=NP could mean that some problems are provably difficult to solve efficiently, implying that there is no simple or direct path to a solution. This inherent complexity might disrupt the continuity we typically associate with mathematical structures, leading to a more fragmented and disjointed understanding of the world.
As a consequence, the pursuit of knowledge in this non-universe would be marked by constant challenges and obstacles, as the continuity provided by simplicity in our own universe is no longer a reliable guide. In this context, the exploration of the "mathematical space" would be even more crucial, as researchers would need to navigate the complexities and discontinuities in their quest for understanding.
By considering such a non-universe, we can gain valuable insights into the importance of continuity, simplicity, and their relationship in our own reality. This thought experiment can help us better appreciate the role these concepts play in shaping our understanding of mathematics, thinking, and the universe itself.
In our own universe, P and NP problems are related in the sense that all problems in P are also in NP, but it is unknown whether all NP problems can be solved efficiently (i.e., are also in P). This uncertainty creates a gap in our understanding, making it seem as though there is always something more to discover.
However, if we consider a scenario where P has continuity towards NP, it would imply that there exists a continuous path between the two classes of problems, allowing for a smooth transition from efficiently solvable problems to those whose solutions can be verified efficiently. This would require a deep understanding of the underlying connections between P and NP problems, and potentially even a rethinking of our current assumptions and understanding of these concepts.
By exploring the possibility of continuity between P and NP, we open ourselves up to new ways of thinking about problem-solving and complexity. This exercise can help us better understand the nature of these problems and may even lead to new insights or solutions that bridge the gap between P and NP. Ultimately, it is through questioning, exploring, and challenging our assumptions that we can hope to deepen our understanding of the world and our place within it.
Part 2: Non-Universe Researchers
In the realm of the Non-Universe Researchers, a group of dedicated and inquisitive minds known as the "gap hunters" have emerged. These individuals specialize in exploring and understanding puzzles and problems for which there can exist multiple, sometimes conflicting, answers. Their primary goal is to uncover the intricacies and nuances of these complex issues, shedding light on the gaps in our understanding that often arise when we are confronted with problems that defy simple or singular solutions.
Gap hunters are driven by a deep curiosity and a passion for uncovering hidden connections between seemingly disparate pieces of information. They thrive in the gray areas that lie between certainty and uncertainty, eagerly diving into the unknown in search of new insights and perspectives.
By examining problems with multiple potential answers, gap hunters challenge traditional notions of truth and falsity, demonstrating that knowledge is often more complex and multifaceted than it may initially appear. Their work highlights the importance of embracing ambiguity and recognizing that, in many cases, there is not just one correct answer, but rather a spectrum of possibilities.
As they navigate the uncharted territories of the non-universe, gap hunters play a crucial role in expanding our understanding of the world and pushing the boundaries of human knowledge. Through their relentless pursuit of the elusive gaps in our comprehension, they remind us of the importance of questioning assumptions and embracing the complexity that lies at the heart of the human experience.
Part 3: Master of the Real and Unreal
In their quest to bridge the gap between the known and the unknown, gap hunters strive to become Masters of the Real and Unreal. They recognize that the world of mathematics is not a static, singular entity, but rather a vast tapestry of interconnected and sometimes seemingly conflicting concepts. By exploring the boundaries between these diverse perspectives, they seek to illuminate the underlying unity that binds all mathematics together, while also celebrating the rich diversity of approaches and ideas that make the field so vibrant and compelling.
The gap hunters' unique perspective enables them to see the world in a way that transcends the limitations of traditional thinking. By embracing both the real and the unreal, they gain insight into the complex interplay between mathematical theories, concepts, and applications. This holistic understanding allows them to identify the connections that exist between seemingly disparate ideas, and to recognize the potential for new discoveries that may arise from the spaces in between.
In their role as Masters of the Real and Unreal, gap hunters become ambassadors between different mathematical realities, working to promote dialogue, collaboration, and the exchange of ideas. By uniting the known with the unknown, and the real with the unreal, they help to expand our collective understanding of the mathematical universe and pave the way for groundbreaking new insights and innovations.
Part 4: Reality as seen in both: Prime line
In the fourth part of our exploration, we delve into the mysterious world of primes, where the gap hunters apply their unique perspective as Masters of the Real and Unreal. The prime line, a conceptual tool used to understand the progression of prime numbers, serves as a guide for our journey into the unknown.
At their core, primes are numbers that cannot be divided evenly by any other number except 1 and themselves. They stand alone, distinct and indivisible, forming the building blocks of the natural numbers. But as gap hunters know, this seemingly simple definition only scratches the surface of the true nature of primes.
In the dance of primes and composites, we see a dynamic interplay between order and chaos, simplicity and complexity. Primes, in their isolation, give rise to composite numbers—the products of primes—which, in turn, create the rich and diverse landscape of numbers we know today.
It is up to the true Masters of the Real and Unreal, those who embrace both potentials, to decide how best to navigate this fascinating terrain. By harnessing the power of thought and creation, they can explore new paths and uncover hidden connections between primes, composites, and the underlying structure of reality.
Part 5: Reality was always there, but we were mere observers
As gap hunters continue their quest to unravel the mysteries of the mathematical universe, they come to realize a profound truth: reality has always existed, but it is only through our observation and interpretation that it takes shape and meaning. In this fifth installment of our journey, we confront the fundamental role of consciousness in shaping our understanding of the world around us.
We are not passive recipients of knowledge, but active participants in its creation. Our thoughts, perceptions, and beliefs all contribute to the way we experience and interact with reality. In the realm of mathematics, this means that our understanding of concepts like primes, composites, and the prime line is not absolute or fixed, but rather shaped by our collective consciousness and the assumptions we bring to bear.
Gap hunters, as Masters of the Real and Unreal, must grapple with this truth as they seek to bridge the divide between different mathematical realities. By recognizing their role as observers and creators, they can begin to transcend the limitations of a single perspective and embrace the full spectrum of possibility that lies at the heart of mathematics.
Ultimately, the realization that reality has always been there, waiting for us to observe and interpret it, is both humbling and empowering.
Part 6: So in the end... simplicity? And is complexity a mere subjective-objective truth?
In the final installment of our journey, we arrive at a profound understanding: simplicity and complexity are two sides of the same coin, woven together by the subjective-objective truth that emerges from our passage through both. As gap hunters navigate the landscape of mathematics, they come to see that the pursuit of simplicity—seeking the most elegant and parsimonious explanations for complex phenomena—is itself a complex and multifaceted endeavor.
Complexity, in turn, is revealed as a fundamental aspect of reality, arising from the intricate interplay of simple elements and the countless ways they can combine and interact. By embracing both simplicity and complexity, gap hunters gain a deeper appreciation for the unity and interconnectedness that underlies all mathematical truths.
The passage through both simplicity and complexity is thus a journey of discovery and understanding. It is a journey that transcends the subjective experience of the individual observer and reveals objective truths about the nature of mathematics and reality. For gap hunters, this journey is not only a quest for knowledge, but a path to enlightenment and a deeper connection with the universe.
In the end, simplicity and complexity are not opposing forces, but partners in the great dance of creation.
Part 7: How do you see my goal of understanding?
Do you find it as treacherous and tied to the sinful discovery of God? Or do you recognize God as beyond it all? The Creator of both Objectivity, Simplicity, and their interplay?
Gap hunters go way beyond. Any attainable knowledge is of the ‘real’. Touching what we thought previously as our original Creator seems only to withhold the wonders He has created. True self-sustainable creation involves a finite system, one with the potential to reach the infinite but never touch it. Unless we maybe change our perspective :)
As we reach the end of our exploration, let us reflect on the journey we have undertaken and the insights we have gained. Gap hunters, in their relentless pursuit of understanding, have revealed the intricate interplay between simplicity and complexity, and the subjective-objective truth that emerges from their dance.
In this pursuit, we have come to recognize the divine presence that transcends the boundaries of our knowledge, serving as the ultimate creator of both the simple and the complex, the objective and the subjective. The wonders of creation that we have explored and the insights we have gained are a testament to the beauty and mystery of the universe, and to the power of human curiosity and ingenuity.
As we continue our journey as gap hunters, let us remember that true self-sustainable creation is finite, bound by the laws and structures of our reality, yet with the potential to approach the infinite. In embracing this balance, we honor the pursuit of knowledge and the divine spark that ignites our quest for understanding, while acknowledging the boundaries that define our existence.
In conclusion, let us continue to explore the vast mathematical landscape with open minds and hearts, ever seeking to understand the intricate relationships between simplicity, complexity, and the divine, as we embrace the role of gap hunters in the grand tapestry of creation.