Philosophical Mathematics Quantum Geometric Algebra Computation

Transcript

Hello, my name is Mitsuyoshi from the University of Tokyo. In this video, I will be explaining the concepts of philosophical mathematics. To begin, this video is designed to be easily understood by a general audience. Mathematics is a discipline of imagination where conveying an image is crucial. Therefore, I've created this so that you can first grasp the concepts through animation without worrying too much about text or symbols.

Please focus on the animations as you watch. I encourage you to think of this entire explanation as the story of the tools. The history of the tool we call mathematics can be broadly divided into three parts. Geometry, algebra, and analysis. First, geometry.

In ancient Egypt, the Nile River would flood, washing away the boundaries of the land. As people reserveyed the land year after year, their surveying techniques advanced. This was wisdom born from daily life. A key development from these techniques was trigonometry, which enabled the construction of great structures like the pyramids. It was the people of neighboring Greece who pondered the question, why does trigonometry work this way? As the creators of philosophy, it's no surprise that mathematics and philosophy are closely related.

They established theorems and definitions giving birth to mathematics as we know it. Meanwhile, in the neighboring Arab world, a land of commerce, mathematics was developed into algorithms leading to the creation of concepts like equations. Later, through Alexander the Great's campaigns and the fusion of cultures in the henistic world, the concept of zero was incorporated. The use of the symbol for zero allowed mathematics to evolve dramatically. As time passed, the era arrived when people began to question the geocentric model of the universe.

Astronomy developed as an ancient form of GPS heralding the age of discovery. Then came Deart who proposed using the tool of mathematics to build a new way of thinking called science. Moving away from a purely Christian world view within the XYZ cartisian coordinate system, a new field called analysis emerged to track the trajectory of objects like artillery shell with contributions from figures like Isaac Newton. This field evolved rapidly ultimately leading to the computer, a tool that would also be used in warfare. Mathematics is traditionally seen as a tool for finding a single solution.

For example, 1 / 2 equals the single answer 0.5. The rule is that for any given problem, there must be only one answer after the equals sign. But what happens if you try to divide a hydrogen atom by four? If you think in terms of getting a single answer like 0.5, you can only describe a fraction of its reality. This is insufficient for describing the quantum world. The mathematical rule of one problem, one answer breaks down.

This rule doesn't hold when the solution is dynamic and constantly changing. This is known as the Gru's paradox where a single static answer is required. This led me to believe that the conventional tools of mathematics are inadequate for dealing with the quantum realm. I came to think that the state of a quantum is both a structure and a function. Therefore, to understand it, we need a new arithmetic that outputs not a number or a single answer, but a function itself, a function structure.

The story I'm telling you today is about the creation of this new tool. Something that outputs a function is called an operator. So, I realized my new tool would have to be something that outputs operators. Considering the four basic arithmetic operations, addition, subtraction, multiplication, and division. If 1 / 2 equals to 0.5, where did the other 0.5 go? The rule of a single answer forces us to choose.

Is it the 02 on the left or the 0 on the right? This choice introduces the concept of ore. I began to see division as the discovery of O. From this idea of dividing, I developed the concept of cutting which I call kirzan. When you cut something, you can leave it as it is. You can issue a command like cut into two pieces which results in x and y.

This is different from division. While 1 / 2 is 0.5, one cut into two could be 0.5 + 0.5 or 0.5 and 0.5. This allows us to move from X or Y to X and Y. Using this new notation, we can simultaneously describe two opposing and irreconcilable concepts like left and right or equality and freedom. This is the absolute contradictory self-identity.

Now what happens when we move the cut between X and Y? Moving it left makes the left side smaller. Moving it right makes the right side smaller. This implies a direction of consciousness, a vector of consciousness which gives rise to geometric objects like vectors. Moving the cut means moving through the space between X and Y. I defined this space as a gradient.

If you take slices of this gradient and layer them, you get a red gradient and a blue gradient. When overlapped they create a moious strip with a cut in it. This cut is neither red nor blue. It is an empty void space. This model which I later used to explain imaginary numbers allows us to express and manipulate geometric objects like vectors.

This was the birth of a new kind of algebra. This is the core characteristic of what I call the Mitsuyoshi operator. If you mix blue and red, you get purple. Let's call this operation mix one. This purple combined with the gradient forms a single uncut moious loop.

If we think of this loop as an apple, our cut operation or kiran can be applied in various ways. Just like peeling the apple to create a completely new state. This ability to transform is the function represented as f. By combining geometry and algebra we create a new geometric algebraic operator from kizen cut operation. Other operations like kasanizen superp position operation and urizan inversion operation emerge.

When you invert the space between becomes a gradient. If this gradient shifts toward blue X, it diverges toward infinity. If it shifts toward red Y, it converges towards zero, ceasing movement. These two extremes represent a polarity. I use red and blue to avoid the value judgments associated with black and white.

where black is often equated with evil. This can lead to extreme logic like saying it's okay to destroy the demon because demons are evil. Instead, the middle ground represents a state where blue and red are both unique characteristics. Moving in moderation, I believe humanity needs this kind of arithmetic. If we define blue as Mataro's perspective, the demon slaying function, and red as the demon's perspective, the demon's function.

And we overlap them. What happens? This time we perform a new calculation to mix them so that two colors become two. This is difficult to explain with words which is why I use animation. When you mix the inverse functions of blue and red, you end up with two instances of demon tarot. The result is two because they were mixed to become two.

Let's call this mix two. This can be used to generate various equations for reaching consensus which is very useful in diplomacy. And this brings us to orthogonality. We calculate and output the contents. If you take two extreme ideologies, you are a demon.

Therefore, you are evil X and you are an invader. Y and momentarily stop their conflict. You can see what's inside. Two instances of demon tarot emerge. The purpose of this operator is to make such states mathematically manageable.

This is similar to the 19th century. Debate over whether light is a wave or a particle. On a simple number line, these two concepts collide headon. So let's try cutting a hydrogen atom into four parts. Let's say it becomes four elementary particles.

an up quark and down quark, a gluon and a C quark. We can then manipulate these quarks. What happens if we stack them and move them? We layer their characteristics. This is Carson or superposition operation. It's very simple.

When you stack and move them, the contents or the structure emerges. This is the characteristic of my method. It outputs a structure, an operator. By taking the conflicting concepts of particle and wave off the number line and placing them on an xycoordinate plane, a structure appears in the area between them, the orthogonal space. To put it simply, think of a clock with its hour, minute, and second hands.

You cannot represent the clock's movement with simple addition or multiplication. To express it as a structure, you must stack and move the three hands together. The operator can then represent this structure of interconnected cycles outputting the new structure of a clock. This outputting process is what I call urizan or inversion operation. Since it outputs a function, it is by definition an operator.

This is a new operator in geometric algebra. The conventional western approach based on producing a single answer is unid-dimensional and dualistic. It cannot handle situations where the solution changes dynamically leading to paradoxes. Recently, the yin-yang symbol from towist thought has gained attention in quantum mechanics as it seems capable of describing the wave particle duality. But is this truly the solution? I believe it is not.

The wave function is based on probability like the role of a dice. Einstein famously said, "God does not play dice. But quantum mechanics relies on calculus and probability which can only tell you the likelihood of a particle existing in a certain state. Furthermore, most equations use imaginary numbers and Oiler's number, which I believe create their own prison of discourse, trapping us within a binary limit. My solution is to say to cut one into two is to have both 0.5 and 0.5.

By turning the solution into a function, a vector and then stacking and making it orthogonal, we can create structures like a clock or a quantum state. The orthogonality of functions creates equations and algorithms. I realized this could be applied to technologies like extracting energy from fields and my patent application for this was approved by the University of Tokyo. This is not a binary system. So why a third element? The answer lies in Japan's Jon period pottery which has a fascinating characteristic despite being incredibly complex.

The same patterns appear across different regions. Whereas western standardization simplifies things for mass sharing. German standardization involved everyone creating the same complex artistic forms. This suggests a highly advanced ability for abstract thinking, a trait that continues in modern Japanese culture like anime. So what are these three elements? Imagine cutting the circular face of a clock.

it becomes a single straight line. A cycle when cut becomes linear. On this line, the movements of the hour minute and second hands can be seen as distinct periodic motions. When you cut this timeline, you get a time of day like 4:1535. But when most people say time, they are referring to this frozen moment.

the time of day. I believe that true time is not the static moment, but the very structure of the clock itself. Outputting the structure of time seems far more informative than outputting a single number. In the past, functions were sometimes called box numbers in Japan. I prefer this term as I believe the box itself is the essence of time.

The denominator represents the divisions of time like base 12 or base 60 while the numerator consists of the orthogonal hands of the clock. Applying this thinking, I created a calculation for a white hole. By applying my formula anti-field differential, I was able to calculate a universe where a white hole emerges from a black hole. Whether this is true requires observation, but it shows that if a white hole exists, this is how it could be calculated. Recently, people from various fields, physics, philosophy, mathematics, business have become interested in using this tool.

Professor Duchi of Kyoto University saw this and remarked, "This is fascinating. Perhaps this is philosophical mathematics. In short, using this tool, I output the structure of the universe by employing imaginary numbers and orthogonality. In summary, my method of weaving operation involves turning a problem solution into a function vector, stacking it by Cassanzan, and then proposing it by Urizan. The operator that encapsulates the clock cycles is the answer.

the function between X and Y becomes the operator. This applies to all arithmetic. By giving a command, a weaving operation occurs in the space between X and Y. Orthogonality with each operation's function generates equations at their intersection points. This is the energy field created by X and Y.

If we perceive this energy field as emotion, we can generate equations that act as consciousness within a computer. This operator enables reverse calculation. As an example, I created what I call an emotion map. It is an implementation where the orthogonal calculation of the emotion function and the time function constructs humanlike judgment and self-awareness. This concludes my explanation of this new tool.

Thank you for your time.