Jun's Blog

Let’s explore the theme: “This world is constituted by order.”

1. Human Evolution and the Dawn of Mathematical Thinking

Over an immense period, approximately 7 to 5 million years ago, humanity achieved bipedalism. This freed our hands, leading to the development of the cerebral cortex as we harnessed intelligence and tools. This development is thought to have enabled more rational cognitive abilities, forming the basis of mathematical thinking. The origin and evolution of bipedalism remain a fascinating mystery, with various ongoing studies and hypotheses proposed.

2. Characteristics of Mathematical Thinking and “Realization”

Mathematical thinking and behavior refer to the process of receiving information from the external world, making logical and rational judgments, and acting upon them. Humanity’s intellectual curiosity and unceasing efforts to improve things lead to new understandings and insights – what can be called uniquely human “realization” or “epiphany.”

Neuroscientist Walter Freeman theorized the dynamics of the entire brain based on complex systems theory, explaining how a vast number of brain cells function to produce complex cognitive activities. His theory describes how individual neurons or parts of the brain do not unilaterally control other parts. Instead, self-organization emerges as they mutually influence each other, much like a chorus. This self-organization process is believed to be the source from which the brain integrates new information and generates unexpected “realizations” or insights.

Thinking is the process by which the brain processes information and makes judgments within the confines of time and space. However, this mathematical thinking has its limits and cannot fully explain fundamental questions like “the beginning of the world.” For example, it’s difficult to derive clear answers to questions like “Did God create the world’s mechanisms?” or “Is God an eternal being?” solely through empirically verifiable mathematical approaches. These questions require philosophical considerations that extend beyond the realm of science.

3. Limitations of Mathematical Thinking and Physical Constraints

Humans currently rely heavily on a cognitive process that makes mathematical judgments based on causality within the framework of time and space. Ultimately, concepts such as time, space, and mathematics can be interpreted as frameworks that humans create or use to understand the world.

For example, an infinite regression image on a television screen might be considered mathematically endless. However, this is not the case in the real physical world. Due to phenomena like light diffraction, slight distortions in the monitor, and the fundamental constraint that matter is composed of atoms, it’s impossible to generate an infinitely clear image. Because a perfect monitor cannot be created at the atomic level, we reach a physical limit where further subdivision is impossible at a certain point, and the infinite repetition stops. This suggests that our mathematical concepts (infinity) do not necessarily apply directly to the real physical world. Human mathematical understanding is merely a conceptual framework, and the real world is always accompanied by physical constraints. This serves as a concrete example demonstrating the limits of mathematical thinking.

For humans, what is visible might feel like the truth, but in the vast universe, it is not necessarily the sole truth. Human perception is a repetition of seeing, communicating, comparing, and judging, and it has a beginning and an end. However, concepts like infinity and eternity – a world without beginning or end – are difficult for finite human thought to fully grasp. In philosophy, there has long been a debate, stemming from Plato’s theory of Forms (perfect ideals) versus the real world (imperfect phenomena), regarding which is more essential.

4. Order in Chaos and New Understanding

In recent years, new understandings have emerged. It has become clear that order exists even within what appears to be chaos. Mathematician Ichiro Tsuda has researched the mathematical structures hidden behind self-organization phenomena, explaining that an “attractor” (a basin of attraction) representing “order” exists behind complex phenomena like convection. He interprets chaos as a state where order and disorder are inextricably intertwined.

Furthermore, the universal validity of fundamental laws of physics like the law of conservation of energy, and the suggestion of multidimensional space in theoretical physics such as string theory, can also be considered indicators of underlying order in the world.

Leaving aside essentialist arguments like Plato’s Forms, what current scientific knowledge can tell us is that the edges of the universe, where light cannot reach, might appear as a “nothingness” to direct human perception. However, if we consider multidimensional space and other forms of existence, it also sparks the imagination that this world might be eternally “something” and not “nothing,” without beginning or end.

Currently, many scientific and philosophical questions remain unanswered, such as the beginning and end of the universe, the behavior of multidimensional space, and the fundamental nature of existence. Even with the possibilities of a multidimensional world and quantum theory, the current scientific consensus is that we cannot definitively state “this world exists eternally.” However, if this world is eternal in some sense, then its very permanence could be evidence that some kind of order prevails throughout this world, and that essential order exists even within phenomena that appear chaotic. Perhaps the very laws and structures present in this world are the source that makes us feel “order.”