A Journey of Consciousness (I): The Pythagorean School, Part One

The Pythagorean school is a profound philosophical tradition that offers a distinctive way of observing and understanding the world. In Masonic historical materials, Pythagoras is revered as a source of the great relief—a fact that is certainly thought-provoking. Yet legend remains legend; its truth or falsehood lies beyond the scope of this discussion.

The core idea of the Pythagorean school is that “all things are number” (万物皆数), meaning that everything in the world is a manifestation of number—a concept that resonates with the idea of shu (数, number) among xiang (象, image), shu (数, number), and li (理, principle) in traditional Chinese Yi studies (易学).

However, the school's founders defined “number” rather narrowly, limiting it to integers; decimals had to be expressed as fractions. The most intuitive angle on this world is that everything has number: one apple, two apples—these are real integer manifestations. Even the number of apple seeds or the proportion of flesh can be quantified.

From a modern perspective, the flesh of an apple can be regarded as composed of molecules; in a sealed system, the amount of all matter remains constant, so the number of molecules is computable—precisely an entity that can be expressed as an integer.

When molecular units no longer suffice, we can subdivide further: if atoms do not apply, we may refine down to quark particles. Yet however finely we divide, all of them can be unified under a single unit for integer quantification. The final unit is unnameable; the Pythagorean school held that this most fundamental expression is always a numerical expression. The idea that “all things are number” means everything can be quantified and expressed through integer addition, subtraction, multiplication, and division. For example, 1.2 can be expressed as one and one-fifth—the concept of integer expression. Of course, in the early stage of the Pythagorean school, concepts such as atoms and quarks had not yet formed; they are mentioned here to help modern readers grasp their mode of thinking.

These tangible measurements are obvious. But what of intangible measurements—for instance, musical intervals? The Pythagorean school made important contributions in this domain. One day, Pythagoras passed a blacksmith's shop; the harmonious sound of the smith's hammering inspired him. By comparing the different sounds of hammers of different weights, he discovered the mathematical relations among various tones. He then experimented on strings and identified the relations of the octave, fifth, and fourth intervals. He concluded that harmonious musical relations are a kind of numerical relation.

The school further held that even intangible things are likewise manifestations of number. They firmly believed that the gods used number to govern all things in the world. Notably, this school did not care about the flow of energy or the process of material manifestation; they simply held that all things are number, and that number alone could express everything about them. This distinctive mode of thinking enabled the Pythagorean school to make outstanding contributions in mathematics and music.

For this reason, the school was keen on studying the relations among numbers and then applying those relations to magic or divination. Take amicable numbers: if for two numbers a and b, the sum of all proper divisors of a equals b, and the sum of all proper divisors of b equals a, then a and b are called a pair of amicable numbers.

Some readers may find this formulation headache-inducing; in fact, it simply says that two numbers, when you add up the divisors other than the number itself and get each other's value, can be called amicable. Amicable numbers express something that looks different on the surface, yet whose inner total effect is the same.

If one analyzes a human soul as, say, 220: 220 itself represents the person's manifest consciousness—the outward personality traits or way of engaging with the world. The factorization of 220 is 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. Since 220 represents the self, 220 itself is removed; the remaining numbers give the internal structure of that soul. Summing this inner soul structure yields: 1+2+4+5+10+11+20+22+44+55+110 = 284. Similarly, when 284 is factorized and 284 is removed, adding the remaining numbers yields 220. Such numbers are mutually amicable.

According to the mystical account, the soul's projection of 220 can coalesce into 284, and the soul projection of 284 can coalesce into 220; they possess perfect mutual affinity.

Then what role do amicable numbers play in mysticism? In Pythagoras's time there is no clear record of their application, but we can catch a glimpse through later practice. One application is to express the numbers 220 and 284 in some way and then apply them to two people. According to Pythagorean theory, numbers are closely linked with everything in the cosmos; thus, by employing the natural affinity of numbers, one can create affinity between the two people and thereby promote their relationship.

In Europe, people once believed deeply in the influence of amicable numbers. For example, young men and women would draw lots: if one drew 220 and the other 284, they were considered naturally fated and well suited for marriage. Thus, amicable numbers were once called “matchmaking numbers” (相亲数) in Europe. This belief stemmed from faith in the mystical power of numbers—the idea that combinations of numbers could influence one's destiny and emotions.

In sum, the magical application of amicable numbers lies chiefly in using their natural affinity to promote emotional bonds between people. Though this mode of application admits of no scientific explanation, it circulated widely in history and profoundly shaped people's ideas and behavior.

The Pythagorean school's research was not limited to amicable numbers; they also explored the relations between number and all things in the cosmos. They held that number is a form of existence beyond matter—the soul and skeleton of the universe.

They believed that by studying the relations of number, people could understand the mysteries of the cosmos and master its powers. This also influenced later Neoplatonism, and even the Christian view that mathematics is a discipline bestowed by God reflects a deep impact.

The Pythagorean school's influence on later ages is profound. Their research inspired generations of mathematicians, philosophers, and scientists; their thought has been deeply branded into the course of human civilization.

Yet the school was also much contested because of its mysticism and supernatural beliefs. In an age before science was born, people's understanding of the school was limited, giving rise to many misconceptions and superstitions.

Even so, the school's research still merits our reflection. The numerical relations and cosmology they proposed offer us a wholly new perspective on the world. Today, the study of numerical relations has become an important tool in many fields, and the Pythagorean school's thought continues to shape humanity's understanding of and exploration into the world.