To uncover nature’s secrets of nature, we must first establish how to observe it.

The study of mathematics begins with finding motifs through the observation of nature. The components of nature each reveal their unique properties through these motifs. To be a subject of study in mathematics, it must be represented as an image; and to become an image, motifs must be identified through observation. Those who meticulously observe living organisms, identify motifs, and illustrate them as images are known as biologists.

Once we have found a motif, now we need to find a pattern, which is a group of motifs. However, nature does not easily reveal its patterns. That is why mathematicians devised numbers and letters. People usually think that numbers are tools for counting, and symbols are tools for setting up equations. However, it is not as simple as we think. If each observed pattern could be assigned a number or letter, the patterns, which are the collection of motifs, become clearly defined. In other words, numbers and letters serve as mathematical tools that play an important role in identifying patterns within motifs. If we identify the patterns in nature, we can understand its structure. Patterns are relational expressions woven from numbers and symbols, and these form chemical formulas. The structure of nature is a fractal shape.

To uncover the secrets of nature, it is important to understand the structure of nature, represented by fractals.

Chemists are people who name visible forms through chemical formulas. However, there are countless things in this world that possess names, even though they lack physical forms. Mathematicians are the people who continually strive to assign names to things without forms. Merely discovering patterns does not mean we have fully grasped the secrets of nature. Within nature's patterns, countless other patterns exist, and, at the same time, patterns also collapse. People need a higher level of awareness to perceive these elements clearly at a glance. Moreover, we must also consider the aspect of time since patterns are confined within the spaces of nature.

To find the regularities of nature, one must be able to understand space as it moves with time. Unlike the static concept of patterns, regularity possesses continuity that unfolds over time. So, how exactly can we find the regularities of nature? How can we uncover the hidden order within the seemingly irregular, non-linear structures of the world of physics? Living organisms all strive to maintain their complete form. To do so, they must possess some kind of internal force and hidden laws. The world that physicists deal with is this kind of chaos.

The observation of nature and drawing it, followed by assigning numbers and letters, does not always guarantee the discovery of patterns. Furthermore, even if a pattern is discovered, it is not always possible to definitively say that the pattern represents the essence of the phenomenon. Since patterns and pattern collapses occur simultaneously in the nature we live in, we must be able to recognize patterns and pattern collapses at a glance to understand the essence of phenomena.

For example, when we look at the surface of a lake, we can observe that gentle ripples appear in a regular pattern. However, when a leaf suddenly falls onto the surface, concentric waves spread out from that point. The introduction of a new pattern causes the original ripple pattern to collapse. If the wind begins to blow here as well, the pattern collapse will continue, making it increasingly difficult to discern any rules. If patterns and pattern collapses can occur in something as simple as ripples, how many patterns and pattern collapses might be happening within living organisms?

Even if biologists and chemists have depicted the forms of nature as images, it is very rare for patterns to be readily apparent. It is dangerous to conclude that a pattern does not exist simply because it is not visible. Nature possesses a mathematical structure of higher dimensions that is difficult for human senses and reason to grasp.

If a pattern is not easily visible, we should examine the image by attaching letters or numbers. Mathematics is the study that uncovers the secrets of nature. Numbers and letters are the tools of mathematicians for uncovering the secrets of nature, that is, finding patterns. As the saying goes, “The use of letters made mathematics convenient, and the concept of speed made mathematics great.” In this way, numbers and letters serve as tools for mathematicians to uncover the secrets of nature, forming the foundation of idealism.