Quantum Realms, Fuzzy Logic, and the Enigma of Prime Patterns

The world of science, although derived from axioms and ground-set rules, has a quite peculiar interplay that dances within itself. The quantum realm recently discovered has opened avenues not only for a new science branch but also for science itself.

As empires are built and crumble, we fail to see that not only the wideness of the wall secures them, but also the inside aspects such as economy and faith.

And of course, there’s a lot more to take into account when going towards the central figures. But for the sake of science, we will assume that there is a specific pattern. A green line in which, if the central figures of a city are found, the city is growing. Just like the habitable zone that allows our planet to sustain life.

Further, I would like to explain my view of faith as the 100% certainty that all odds are in favor. However, to transcend faith, we would require tangible proof which would let our reasoning take the steps from 100% possible to absolute truthfulness. A state in which, every time we stumble under the same starting conditions, we can fast-forward to the past result and instantly acknowledge it as true or false, or even in some cases, use the same reasoning or formulas for different starting conditions, but under the same conceptual background to skip some math.

Maybe the world of quantum represents a world in which we are forced to either find the true statement or keep looking for it.

Further, as I lack the studies of a university, I will use ChatGPT to help me formalize and bring those ideas to a whole new level of understanding. Therefore, please keep in mind that all that comes next (and what I write after all) is purely theoretical and no previous research or ground-based testing has been done.

I strongly believe however that the new road of science is only in its infant state, despite the results we have so far achieved. And what I find so great about it, is that reason and logic rule.

The most fundamental aspects of logic and reasoning which we have used with both algebra and geometry could be revived as insights into this domain. Now, however, they might be used only as starting arguments that allow for action/reaction/movement/dimensionality and many more to take shape in a new form.

Remember that the magic of storytelling should not be in the words, but in the story itself and how we decide to visualize it.

Part 1: Fuzzy Logic

Try to envision mathematical concepts as a background set of rules. Arrangements in which this fuzzy logic makes sense. Quantum mechanics is the whole of this world. A world that has segments that are either ordered by those rules or not. When a rule is not followed, the truthfulness of information kind of transcends into the realm of possibilities where they fade until they will eventually reappear. Higher-dimensional aspects are those that show us insights into where the state of the probability is. More clouds suggest a higher chance of rain. The mathematical rule has not been achieved yet. It's at a point where it is in the process of being completed. The full background shows us that it is not raining yet, even if it’s close.

Let us see how our little AI helper sums these up. (Of course, I will lend my understanding to each point with italicized text.)

1. Mathematical Concepts as Background Set Rules: Mathematics provides a set of rules and structures that help us model and understand the world. These rules can range from simple arithmetic to complex algebraic equations and beyond. The consistency and universality of mathematical principles make them a powerful tool for describing various phenomena.

   
   

2. Fuzzy Logic and Quantum Mechanics: Fuzzy logic deals with degrees of truth rather than absolute truth values. It's often employed in situations where information is imprecise or uncertain. Quantum mechanics, on the other hand, is a branch of physics that deals with the behavior of particles at the quantum level. The probabilistic nature of quantum mechanics introduces an element of uncertainty, and the concept of superposition allows particles to exist in multiple states simultaneously.

   
   

   Here, we could say that those clouds are seen by 2 cities. In one city it’s raining, while in the other, it’s not. Even if the clouds are the central figure of the statement, the space marks the difference between where this is true and where it isn’t. Just like 2 particles can influence each other despite the distance, but when change is made, how can we know who made the change if it wasn’t us?

   
   

3. Higher-Dimensional Spaces: In mathematics, higher-dimensional spaces extend beyond our familiar three-dimensional space. These spaces are often used to model complex systems or describe relationships involving more than three variables. The idea of higher dimensions is also explored in physics and string theory.

   
   

   Higher dimensions could simply be the newly opened avenues in which the probability fluctuates. Maybe dimensions are created and destroyed just like cells. Cells may depend on both internal and external variables when it comes to their destruction. Whereas dimensions are created and destroyed only by rules that result from a greater whole, the whole of summed parts. We could see them as being only externally dependent. Simply representing the “external” concept. Something beyond.

   
   

4. Probability and Quantum States: Quantum mechanics introduces the concept of probability into the description of physical systems. The behavior of particles is often described by wave functions that provide probabilities for different outcomes. Observations collapse these probabilities into definite states.

   
   

   By observing, you see the “present” which was “present” 0.001, no, 2 seconds, no, 5 seconds ago. I believe there is no known way yet that allows us to see the real slope of growth as it is dependent on multiple factors. Focusing on just some of them will never allow us to see the full picture of the past, but we can use it to gather information for the potential full picture of the future. Just like a pirate using his spyglass to view a castle. He can never be sure that the castle is 100% the same as when he spies at the door since he cannot see the whole castle.

   
   

5. Incomplete Mathematical Concepts: The notion that certain mathematical concepts are not yet complete suggests ongoing exploration and discovery. In fields like pure mathematics, researchers are continuously working on extending existing theories, proving new theorems, and exploring the boundaries of mathematical knowledge.

   
   

   In the end, we might get to a new science, a new understanding which we will call “true science” and for those that come next will be just… science.

Part 2: A State of Chaos

There is so much information. So many weights and counterweights to take into consideration. What has to remain and what has to be scratched off? Oh God… I feel like my head is going to explode—theoretically, of course. The point of no return, when the force of rejection will simply become stronger than the pull, is too far ahead. But then… we wouldn’t wish for a blackhole to appear either. How can we balance this play? What does it MEAN to be in balance yet, not be dead?

We know (or theorize) that life could resemble the turning gears of change. Without change, everything is static. No good, no bad could happen further. But then, if life is always pulling up the rope of change, balance is surely broken. If we were to counterweight life, we would arrive at death. What else could happen here so that we will ever grow? Could life be its own domain? Could life be so inextricably different from death that it never touches it? Could life and death, and their impossibility to touch each other, be both enveloped into a both-enveloping sphere?

So many questions, so few answers. “But how? And why?” - and this just makes it worse.

Let’s turn our glare towards the prime numbers and something interesting ChatGPT explained to me.

”The distribution of prime numbers is a fascinating topic in number theory. Primes are often considered the "building blocks" of natural numbers, and their distribution on the number line has been a subject of extensive study.

While primes themselves may seem somewhat irregular (as they have no divisors other than 1 and themselves), the overall pattern of their distribution exhibits some regularities. There are well-known results and conjectures related to the distribution of primes, such as the Prime Number Theorem, which describes the asymptotic distribution of primes among the natural numbers.” - ChatGPT.

Part 3: When will this stop?

“The overall pattern… exhibits some regularities.”

Down below, I would like to place some patterns I randomly found a while ago when playing with primes.

Now if you are to ask me what is going on in those pictures, I will ask you in return for better equipment. I will check the patterns and think that I see something. After days, weeks, or months, I would simply take a break from all the patterning and turn back to rational thinking in the hope that this time, the patterns that come into my mind support my claims.

And this is how I deal with primes in a nutshell. No fuzzy logic. No fuzzy math (only to the point where logic and reason seem to hold tight to the primes). Only admiring and thinking about what could this great picture of art mean. Could we have discovered order itself? If yes, then how would we explain it? How can we understand its meaning? How can we communicate with/using it?

Sadly, my job is not a full-time researcher. No matter how much I involve myself in the field there will always be someone ahead of me.

Someone who will say:

The Riemann zeta function is a mathematical function that plays a crucial role in number theory and complex analysis. It is named after the German mathematician Bernhard Riemann, who first defined and studied it.

The Riemann zeta function is defined for complex numbers �(kind of S and C combined symbol)s with real part greater than 1 by the infinite series:

�(�)=1�+2−�+3−�+4−�+…ζ(s)=1s+2−s+3−s+4−s+…

This series converges when the real part of �s is greater than 1. The series can be analytically continued to other values of �s (except for �=1s=1, where it has a simple pole), providing a way to define the zeta function in a larger domain.

One of the most famous properties of the Riemann zeta function is its connection to the distribution of prime numbers. In particular, the zeta function is closely related to the Prime Number Theorem, which describes the asymptotic distribution of prime numbers. - ChatGPT

You are telling me that you found a function that correctly jumps at each prime number occurrence, yet, you have no idea why it does that. Now you try looking into those domains and dimensions that you had no idea even existed. Exploring a land of the unknown where all your beliefs shatter, only to force you to connect them once again if you want it to make sense. And that is… MARVELOUS.

We, as humankind, are insignificant. Yet, here we are. Closer and closer to the power of understanding dimensionality. This pursuit of knowledge seems like it must be our happiest years. When in the meantime, some place their ideas into new smart ways for crypto. Others pray that today will be our happy day. Others are simply lost due to psychological or physical warfare.

If knowledge is what we say defines us, it sure seems we never met our parents.

I hope you all stay safe and healthy. It is a very foggy world out there. And our lanterns seem to shine only ourselves. Take care of your loved ones, of yourself, and of course, of your knowledge.

“If she is cherished, one is exalted; if she is embraced, one is honored. But if you refuse to listen to her when she calls, when you pay no attention when she stretches out her hand, so too, will she ignore you when you most need her, in times of distress and trouble. How much better to get wisdom than gold, to get insight rather than silver!” - Eternalised