On the Application and Improvement of Modern Astronomy and Traditional Numerology (Part One)

First published on the WeChat public account "Daoist Yinfu Culture," 2020-08-25. Illustrations omitted.

As is well known, in traditional Chinese arts of calculation, Qimen Dunjia has the issue of setting the board via the intercalary method; Ziwei Doushu and Qizheng Siyu have the issue of fixing the Life Palace; the Four Pillars of Bazi have the question of when to switch the year and month pillars; and Da Liu Ren and Jin Kou Jue have the issue of changing the monthly general. All of these trace back to astronomy.

This article will explain these topics as simply and accessibly as possible, steering clear of jargon. In this series we will discuss many major pitfalls and debatable questions left by the tradition.

Because the Earth both revolves around the Sun and rotates on its axis, one might think that one year of orbital motion would be straightforward — but the tilt of the Earth's axis complicates things.

Taking the Earth as the center, the plane formed by the relative motion of the Earth and the Sun constitutes the ecliptic plane. What must be emphasized is that this ecliptic is the apparent path of the Sun relative to the Earth.

The Earth also rotates. Taking the axis of rotation as the center, the celestial bodies all revolve around a common point; the plane this forms is the celestial equator.

Because the Earth's axis of rotation is tilted, the ecliptic and the equator do not coincide. The circle traced by the ecliptic and the plane of the equator form an angle known as the obliquity of the ecliptic (ecliptic–equatorial angle).

When gazing up at the night sky, human beings sought to describe the motion of celestial bodies by projecting the sky onto a plane. Since the sky moves while the Earth is fixed, a relative frame of reference within the sky is needed for description.

Thus the choice of reference system determines whether one adopts the ecliptic or the equatorial framework — corresponding respectively to the Earth's revolution and rotation.

Since humans mainly settled away from the equatorial and polar regions, where the influence of sunlight is most pronounced, the changes of the four seasons are clearly felt. If we divide the year by season, four easily observed extreme points emerge.

First come the vernal and autumnal equinoxes, at which the lengths of day and night are exactly equal. If we further find the moments of longest and shortest solar shadow, we can locate the winter and summer solstices.

Once these four extreme points are found, dividing the year equally into twenty-four solar terms forms the ecliptic system. This system actually reflects the relative positional changes between the Sun and the Earth, so it is also called the tropical zodiac (tropical ecliptic).

The word "tropical" means that after a year, the Sun returns to the same position; this cycle is called the tropical year.

But this division has a problem: the Earth's orbital speed around the Sun varies. Therefore there are two schemes for the solar terms: equal division by time, and equal division by space.

China's earliest method divided the year into twenty-four equal parts by time, beginning from the winter solstice point — this is the mean-solar-term method (pingqi). After the Ming dynasty, spatial equal-division was adopted: each 15 degrees of the Sun's motion is converted into one solar term — this is the true-solar-term method (dingqi).

For a long time, including up to the present, the true-solar-term method has been used to set solar terms; it reflects the Sun's real position in real time.

In late Ming and later numerological traditions — whether Four Pillars Bazi or Qimen and Ziwei — the stems-and-branches calculation almost always uses the true-solar-term method for determining the switch of the monthly branch at a solar-term change. But here there is a major pitfall.

In Western esoteric systems, although the twenty-four solar terms are not used, the twelve zodiac constellations are. In early ancient Greece, the vernal equinox lay exactly at 0° of Aries; the summer solstice was in Cancer, the autumnal equinox in Libra, and the winter solstice in Capricorn. Using the actual constellations in the sky as reference points is also called the sidereal zodiac.

Later, in the era of Ptolemy of ancient Greece (roughly contemporary with China's Eastern Han dynasty), Ptolemy, basing himself on the geocentric model, adopted the Tetrabiblos house system for astrology and began using the tropical zodiac.

What must be emphasized here is that although the ancient Chinese used solar shadows — that is, the tropical zodiac system — they also used the Big Dipper and the Twenty-Eight Mansions as reference points in the sky, employing the celestial equator system.

As the saying goes, "When the Northern Dipper points north, all under Heaven is in winter." The ancient Chinese used this as a metaphor for the Dipper commanding the four seasons. Because Wenchang lies before the Dipper, and the Dipper is the Emperor's chariot, it was also said that all decrees and proclamations were governed by Wenchang.

This is also why Wenchang is most closely associated with scholarly and official success. In ancient times, studying for the examinations and entering officialdom was the principal path to fulfilling one's life, and was most closely tied to literary fortune and rank. Moreover, because it precedes Kuixing — the star that heads the list — it bears even stronger symbolism for success in the imperial examinations.

It must be noted that whenever the ecliptic — especially the tropical ecliptic — is used in the arts of calculation, one inevitably encounters the effect of precession.

Around the second century BC, Hipparchus discovered the existence of precession and believed it advanced one degree every one hundred years.

In ancient China the discovery came somewhat later: Yu Xi of the Eastern Jin discovered the phenomenon of precession, and after doing so estimated one degree every fifty years — somewhat more accurate than Hipparchus.

By the Sixteen Kingdoms period under Later Qin (384–417 AD), Jiang Ji discovered that atmospheric refraction causes a difference between a body's true and apparent positions. In the West it was not until the sixteenth century that the Danish astronomer Tycho Brahe discovered and explained atmospheric refraction.

Here there is a point of cultural difference between East and West: the definition of precession.

In modern astronomy, the famous westward drift of the vernal equinox was explained in Ptolemaic terms with the ecliptic as the primary frame: all celestial bodies were thought to advance eastward along the ecliptic. Even when Western astronomy was introduced into China, this same explanation was still employed.

A bit of background is needed here. In order to achieve their goal of spreading the faith through knowledge, Western missionaries did not introduce the latest Western astronomical research. The astronomy they transmitted was Tycho's minor-wheel system — which can broadly be understood as celestial bodies riding on one wheel after another. This bore a strong resemblance to the multi-layered-heaven tradition in ancient Chinese culture, making it convenient for correlational missionary work.

More importantly, the new Western theories of the time were not yet fully mature. The Tychean system was only relatively more accurate in certain calculations of eclipse times. Historically, many accounts claimed that Western astronomical precision of the era was so high that it stunned the Chinese.

But in fact this was not the case. When the missionary Matteo Ricci demonstrated the precision of the Western calendar, he did so by selectively deleting the eclipse records from the Chongzhen calendar reform period.

And a strange phenomenon occurred at the time. Anyone familiar with the astronomical development of the period would find that Western astronomical calculations themselves were sometimes imprecise, yet in the missionaries' reports to the Chinese court, every single calculation was perfectly accurate.

Actually, this is because in the mid-to-late Kangxi reign, after the missionaries gained posts at the Imperial Astronomical Bureau, they intensified the falsification of data: whenever reporting eclipse predictions, they simply copied earlier forecast values, not fully recording the actual observations.

During the Kangxi era, the missionary Ferdinand Verbiest also stated that this kind of opportunity should be fully exploited, made good use of, for the work of evangelization.

So although some of the computational algorithms within the Tycho astronomical system did represent genuine advances, the actual precision was far from as exaggerated as claimed.

This is also why many people at the time opposed the Tycho computational system — not out of mere conservatism, but because the missionaries of the day deliberately overstated its accuracy.

In ancient China, precession was explained with the equator as the primary frame: the ecliptic plane was thought to slide westward along the equator. This was in fact the correct understanding, but the introduction of Western astronomy afterwards led to considerable conceptual confusion.

Because of this confusion, China's astronomical calculators were thoroughly baffled. Especially from 1723 to 1840, when China closed itself off from the outside world, most of the systems used were those introduced by the Western missionaries. What deserves attention is that this also had a major impact on the arts of calculation, creating many pitfalls — to be mentioned later when the opportunity arises.

Even during the period of isolation, China still produced talent. A calculator named An Qingqiao emerged, conducting independent research in a closed environment, thoroughly refuting the Ptolemaic system, and proposing an explanation and conclusions identical to those of modern astronomy.

Combining this with the ancient saying that "the Way of Heaven turns to the left," An Qingqiao argued that this refers precisely to the ecliptic axis itself rotating counterclockwise while also revolving around the polar axis. He not only reached the correct conclusion that the ecliptic moves eastward relative to the equator, but went further to deny Tycho's minor-wheel system altogether, regarding it as a concept with no real existence.

So even though Chinese astronomical theory in the Ming–Qing period was indeed relatively behind that of the West, from the standpoint of practical application in the arts of calculation, the actual gap was not as large as one might imagine — not large enough, in fact, to overthrow the traditional algorithms.

A typical case: although modern high-precision astronomical algorithms can determine the exact positions of celestial bodies — for instance, the Swiss Ephemeris and similar tools — this higher precision does not actually solve the fundamental problems.

Most of the problems and contradictions do not lie in precision, but in the macro-level methodology.

The most typical example is the Four Pillars Bazi system, which usually takes one double-hour (shichen) as one unit. Errors at a term change only affect whether the month pillar should switch to the next; across the more than four thousand double-hours in a year, the precision impact amounts to only twelve such cases.

So the conceptual framework and the overall approach matter most. During the Qing isolation period, erroneous foundational astronomical knowledge also brought disorder to the practice of the arts of calculation and led much research astray.

One of the most typical cases: among the many case records left by the legendary Song-dynasty Da Liu Ren master Shao Gongyanhe, if one reverse-engineers by time, it turns out that the method of fixing the monthly branch used in the calculations was the true-solar-term method — yet in the Song dynasty, the mean-solar-term method was actually in use.

There are only two possibilities: either Shao Yanhe's cases were largely forged, or, sometime from the late Ming to the mid-Qing, someone revised them.

If we consider the latter possibility — that these cases are genuine — then we must consider how Shao Gongyanhe was able to make accurate divinations in the first place.

More importantly, there were many legendary masters in the Song dynasty, and the calendars available to them could only have employed the mean-solar-term method. Could the mean method truly have been superior?

The matter is far from simple — I will leave this as a cliffhanger for a future article.

At this point some may wonder: the true-solar-term method seems perfectly reasonable, since it reflects in real time the Sun's angular position on the ecliptic. What could be wrong with using it today?

People in the Ming and Qing thought so too — but in fact this is a major pitfall. The Sun's position is only a reflection of the Earth's revolution; the Earth also rotates, that is, there is the celestial equator. From the standpoint of astrology and the arts of calculation, considering only the ecliptic is very one-sided, neglecting the existence of the celestial equator.

In the next article, we will discuss the establishment of the center point in astrology, and the evolution of combined ecliptic–equatorial applications in the arts of calculation, so as to gain insight and food for thought.