Understand the essence of the world from a different perspective.

Introduction: As AI gradually permeates every corner of life and traditional beliefs are constantly overturned by new ideas, do you ever feel confused about a world full of uncertainties? In this era of rapid change, how can we maintain rational and clear thinking?

The brand - new masterpiece The Logic of the World by Professor Ma Zhaoyuan from the Southern University of Science and Technology might offer you the answers. Professor Ma traces back to ancient Greek civilization to reveal how it influenced the way humans understand the world. Then he delves deep into the three crises in mathematics, showing you the uncertain nature behind the world's apparent certainty. He also explores the ways of human survival and speculation in the AI era, reconstructing our perception of the world from a modern scientific perspective.

It can be said that this book is not only a tribute to humanity's heroic journey of understanding the world but also a profound response to today's reality. Whether you're eager to break through the limitations of your thinking or curious about the essence of the world, opening this book will lead you to a top - level mindset for dealing with uncertainties and start a new journey of understanding the world.

(This article is excerpted from The Logic of the World)

Author: Ma Zhaoyuan

Publication date: September 2025

Publisher: Cheer Culture / Zhejiang Science and Technology Press

Before reading this book, please think about which of the following statements are correct:

· Human knowledge of nature is infinite.

· Natural phenomena can be predicted deterministically.

· Calculation and observation are consistent.

· There exists an objective world independent of human observation.

· Correct mathematical propositions will eventually be proven.

· Mathematical theories can ultimately achieve a grand unification.

· Physical theories can ultimately achieve a grand unification.

In the early days of my study of physics, I firmly believed that each of the above statements was an unquestionable truth, a self - evident common sense in the minds of every physics worker. This belief stemmed from my educational background before learning quantum mechanics. The classical scientific system had deeply penetrated into my cognitive system, forming the backdrop of all my knowledge, that is, the existence of an objective world independent of human observation.

Objective reality exists, and its existence is independent of human observation. However, as time passed and human scientific knowledge advanced, I began to realize that these views might not all be entirely correct.

Thinking about the World in the Ancient Greek Way

Since the 1920s and 1930s, many new discoveries and theories have emerged in the scientific community, challenging the traditional concept of objective reality. We've gradually realized that the processes of observation and cognition are inherently subjective, and the world we live in is full of uncertainties. This uncertainty is no longer an accidental phenomenon in the cognitive process but has a natural quality. Doubts about traditional concepts have prompted us to re - examine and re - define our understanding of the world. One of the core ideas of the new science that has emerged since the early 20th century is that uncertainty constitutes the boundary of human cognition. Only when we continuously explore and understand this uncertainty and transform it into relatively certain knowledge can our cognition expand. This process not only promotes the development of modern science but also deepens our understanding of the essence of the world. Accepting and exploring the uncertainty of this natural content is the necessary path for us to broaden our knowledge and enhance our understanding of the world. Therefore, in this book, based on the views of modern science, I've supplemented the knowledge related to classical rationality, expounded on what I believe are the basic characteristics of the modern scientific world view, and traced these characteristics back to the earliest stages of Western philosophical thought to show that they are the accidental products of history rather than inevitable outcomes. This is the real purpose of elaborating on early philosophical thoughts in this book.

Ancient Greek civilization holds a unique position in history. It not only shaped the way we understand the world but also laid the foundation for philosophy, science, and art. There is an indispensable tendency in the scientific spirit originating from ancient Greece, which is to bravely face the unclear and regard it as the driving force and signpost for further exploration. Putting aside this belief, as Schrödinger wrote in Nature and the Greeks: "The philosophy of the ancient Greeks still attracts us today because no other place in the world, either before or after them, has established such a highly developed, clear, and well - defined knowledge and speculation system."

Several ancient civilizations share a remarkable commonality: from their rise to prosperity, they took about a thousand years, then gradually stagnated, and were eventually replaced by new, more militarily powerful civilizations. For example, the ancient Egyptian civilization began to develop around 3200 BC and gradually declined from the 5th to the 4th century BC, and was finally conquered by the Kingdom of Macedon in 332 BC. Similar situations occurred in ancient India, ancient Babylon, and ancient China. These civilizations entered a mature and stable stage in about 2000 years, after which their development slowed down significantly, reaching a saturation point and then remaining relatively stagnant. Many archaeological studies have found that the living standards of humans in the late stages of these ancient civilizations were comparable to those before the Industrial Revolution. For instance, the per - capita calorie intake of the ancient Egyptians during the pyramid - building period was at the same level as that of the latter, including the consumption of meat, vegetables, bread, and beer; the per - capita lifespan, medical, and surgical levels of the ancient Egyptians were also similar to the general situation of humans before the Industrial Revolution. The philosophical thoughts, rational exploration, and empirical methods of ancient Greece laid the foundation for later scientific development. Ancient Greek scholars created a new way of understanding the world through observation, experimentation, and logical reasoning. This method was carried forward during the Renaissance and, with the assistance of industrial civilization, ultimately triggered the modern scientific revolution. This revolutionary change marked a new height in human understanding and utilization of nature and laid a solid foundation for the development of modern science and technology. From the development of many ancient civilizations, the emergence of science was not inevitable but accidental, and this accident first occurred in ancient Greece. John Burnet wrote in the preface of Early Greek Philosophy: "Science is 'thinking about the world in the Greek way,' which is an apt description of science. Therefore, it can be said that science has never existed except among those nations influenced by the Greeks."

When we seriously examine ancient Greece, we'll find that the mathematical knowledge we learned in middle school, including plane geometry and algebra, as well as most of the physics knowledge, were already known in ancient Greece and were written into works and textbooks. When we talk about the Earth, we've already assumed it's spherical, while the ancient Chinese said "the sky is round and the earth is square." So how was it discovered that the Earth is spherical, and how did people prove it? The ancient Greeks first observed the changes in the brightness of Venus on different days and inferred that Venus was reflecting sunlight. Due to the difference in distance, it appeared brighter or dimmer on Earth. They speculated that the moon was also reflecting sunlight. When the Earth moved between the sun and the moon, it would block the sunlight, so the waxing and waning of the moon were caused by the Earth's shadow. Since only the shadow of a spherical object is always round, they deduced that the Earth must be spherical. The ancient Greeks even measured the diameter of the Earth, and the measurement error was no more than 10%.

The Austrian philosopher and classical scholar Theodor Gomperz said in Greek Thinkers: "Almost all of our intellectual education originated from the Greeks. To free ourselves from their overwhelming influence, we must first thoroughly understand these origins." Ancient Greece was indeed a special existence. Ancient Greek civilization not only shaped ancient Rome but also gave birth to Christianity within the framework of Roman civilization. Christianity is one of the few religions based on logical rules. Its in - depth discussion of logical issues provided a philosophical foundation for later scientific development.

Compared with other civilizations, ancient Greek civilization formed a complete logical system, which enabled knowledge to be stably accumulated and passed down. In ancient civilizations without a logical system, it was difficult for knowledge to have stable precipitation. Such ancient civilizations often encountered bottlenecks after developing to a certain stage. As the population of the civilization grew, it was difficult to reach a consensus on different views and ideas. Old knowledge was forgotten and rediscovered repeatedly, resulting in the inability to stably accumulate knowledge. The logic developed by the ancient Greeks allowed knowledge to be precipitated and accumulated. Through the efforts of generations, relatively correct knowledge was screened out and accumulated, laying the foundation for the explosion of civilization. About 2000 years after ancient Greek civilization, science exploded within the Christian world, which was closely related to Christianity inheriting the logical spirit of ancient Greece, that is, a strict way of thinking. This way of thinking provided theoretical support for the development of scientific methods, promoting in - depth human understanding of nature and rapid technological progress.

Modern Science Originates from Classical Logic

In this book, I refer to the logic before the 1930s as classical logic, also known as classical logic. This logical system is based on determinism, emphasizing the belief in clear thinking, and within this framework, it constructs the traditional cognitive system, including how to acquire new knowledge and how to conduct meaningful discussions and proofs within the assumed scope of the knowledge system.

Based on the classical logic of ancient Greece, people developed knowledge in basic fields such as mathematics and physics, which has now become common knowledge in education. However, with the development of modern mathematics, people began to seriously reflect on the reliability of this mathematical certainty. For example, seemingly simple concepts in arithmetic, such as the common - sense content of 1 + 1 = 2, are something we've been dogmatically instilled with since childhood. But if we think deeply, what exactly does "1" represent? If we add "1 chair" and "1 table," we get 2 pieces of furniture, but this is not equal to "2 chairs." What exactly does this addition operation represent? Is there a clear definition of the equal sign in this process? In the binary system of Boolean algebra, 1+1 = 10 also holds. This flexibility suggests that the foundation of arithmetic and the construction of the knowledge system are not immutable but have a subjective flavor.

When learning calculus, we come across the concepts of "infinity" and "infinitesimal." What exactly do these concepts mean? We often use them without thinking in practical applications. When Newton established calculus, he also directly adopted these concepts, although he realized that this was not a strict mathematical proof but just a practical tool. This practice laid the groundwork for the second crisis in mathematics.

It wasn't until around 1880 that Georg Cantor seriously studied the exact meanings of "infinity" and "infinitesimal," which solved this problem but triggered the third crisis in mathematics and even led to a later mathematical revolution. These historical events show that even for the most basic mathematical concepts, strict scrutiny and reconstruction are needed to ensure the stability and development of the knowledge system. Through this critical reflection and logical analysis, we can understand the structure of knowledge more deeply and promote the progress of science.

There's a saying in the market that "the end of physics is philosophy, and the end of philosophy is theology." However, in the past 100 years, the view in the scientific community is that the greatest contribution of philosophy to science in the past 100 years is no contribution. - Just don't cause trouble. We separated more than 100 years ago, and we each do our own thing. Wittgenstein further promoted the complete separation of the two. In the 1920s and 1930s, Wittgenstein "ended" the classical philosophical metaphysical tradition but at the same time inspired new philosophical schools. He deeply influenced the Vienna Circle, and the Vienna Circle established the rules of the scientific profession, that is, we can only study "testable facts under valid statements." Any scientific statement must be a statement that conforms to logical rules and is preferably a statement that can be expressed in a mathematical way. This is the basic requirement for the statement style of all scientific papers: it must be a valid statement.

A scientific statement must construct a testable fact. Only when the truth or falsehood of a fact can be tested can a statement or a hypothesis become a scientific proposition that can be studied and develop into a so - called scientific paper. No matter what you study, you must follow these rules and abide by scientific norms during the research process: how to put forward a hypothesis, how to conduct a proof, how to design an experiment, and how to draw a conclusion. Only testable facts within this scope are scientific. Those that cannot be carried out according to these rules are not scientific propositions and do not need to be labeled as "scientific" or "unscientific." People can put forward various other ideas or views, but if they cannot construct a testable fact, they do not belong to the scientific category. From this perspective, in modern science, mathematics emphasizes instrumentality, and physics emphasizes application and practice. Under such simple norms, mathematics constructs tools through rationality, systematically sorts out and expresses the ideas in our minds, and makes valid statements; physics connects these ideas with nature, forms the first "interface," and presents testable facts.

In universities, when training doctoral students, teachers constantly train them to learn the rules of the profession, just like a blacksmith training an apprentice. No matter what craft you learn, you must first learn the rules. The same goes for science. The scope and interests of research can be broad, but there are very clear rules, which were initially established by the Vienna Circle. Before that, there were many different scientists and various schools, but no one established the rules of science until the founding of the Vienna Circle.

Uncertainty Provides Us with a New Way of Thinking

This book will introduce the three crises in mathematics, which have shifted our attitude towards knowledge from the pursuit of certainty to the acceptance of uncertainty. The first crisis in mathematics refers to the Pythagorean crisis regarding irrational numbers. The second crisis stems from the study of "infinitesimals" - what exactly is infinity? The third crisis stems from set theory. Around 1900, Bertrand Russell pointed out the fundamental difficulties in set theory. This difficulty has not been completely resolved to this day. This has actually reshaped our perception of mathematics and even made us question the entire theoretical framework, forcing us to carefully consider whether mathematics itself is a stable and reliable tool. This crisis has not ended yet, and its impact on future cognition continues and is still being hotly debated.

In the 1930s, Gödel's incompleteness theorems pushed the third crisis in mathematics to a climax. This theorem is almost the most important proof in human history and can be said to be the most important event in the history of human cognition. Within the framework of Gödel's incompleteness theorems, we can discuss how to construct an ideal system because Gödel's incompleteness theorems tell us that any finite and describable system has flaws. For example, can we construct an ideal voting mechanism? Voting has been around since ancient Greece. After more than 2000 years, have we found a voting method that satisfies everyone? The fact is that no matter what we do, our election rules are necessarily finite, so we cannot avoid Gödel's incompleteness theorems. In 1951, the mathematician Kenneth Arrow proved Arrow's impossibility theorem. Within the framework of Gödel's incompleteness theorems, this means that it is impossible for people to design a free, fair, and non - dictatorial election method that can fully reflect public opinion through finite rules.

Alan Turing inherited Gödel's ideas and truly carried them forward and implemented them. We can see Gödel's influence in many of Turing's important works. Turing's impact on modern technology is obvious. All modern computers today, including quantum computers, are built based on the principle of the Turing machine. The Turing machine has become the foundation of artificial intelligence (AI) and all modern computer hardware. In his well - known paper published in 1936, Turing elaborated on the design of a universal computing device and pointed out that its core purpose was to prove Gödel's incompleteness theorems. For this purpose, he conceived a machine that could automatically perform calculations, which later became widely known as the Turing machine.

Turing proved that there is no difference between computer instructions and data. All instruction sequences or physical laws can be regarded as the data of a Turing machine. Von Neumann used this principle to establish the modern computer architecture, ensuring that the output of the computer is equivalent to the result of a universal Turing machine. In this architecture, both instructions and data are regarded as information stored in the computer, and there is no essential difference between them. The concept of the Turing machine forms the basis of modern computers. No matter how the form of the computer changes, whether it's a wearable device, a smartphone, or a cloud computing center, they can all be regarded as equivalent Turing machines.

In the 1936 paper, in addition to designing the Turing machine and laying the physical foundation for today's artificial intelligence, Turing also pointed out the limitations of the Turing machine and proved the undecidability of the halting problem, providing a computational - theoretical counterpart to Gödel's incompleteness theorems. This characteristic of the Turing machine made later researchers realize that although the Turing machine is very useful, it is not omnipotent. This inspired people to explore the limitations of machines and artificial intelligence and understand that there are tasks they cannot complete. In other words, no matter what the knowledge system is, as long as it is computable, it is different from human cognition. Some abilities in human cognition may exceed the scope that algorithms can handle. This also means that computability and completeness are essentially incompatible.