Chapter 273 — The Summit of Arithmetic

Libationer Bashan dumped him at the gate of Six Harmonies Hall and turned on his heel, as though afraid Shen Mu might keep pestering him and drag him into the Celestial Sage Sect.

Shen Mu said sourly, "Sooner or later I will get you in."

The Imperial College of Six Harmonies Hall was presided over by Reverend Hongfa, a woman of great virtue and high repute, a Buddhist nun besides; she had taught and nurtured scholars here since the Grand Academy was first founded.

Shen Mu walked into Six Harmonies Hall. The hour was still early and no scholars had yet come for the lecture, but the reverend was already there, sweeping and wiping until the hall was spotless.

Only when the bell rang and the scholars filed in did Reverend Hongfa begin, unhurried: "Six harmonies -- which six? Heaven, earth, and the four quarters: that is the six harmonies. The Spirit Treasury of the Six Realms lies within our bodies, and to break through its wall you must first fix the position of the Six Harmonies Barrier. And how is that fixed? By calculation. Yesterday I told you to review the arts of the Six Harmonies. Did you review them?"

Shen Mu blinked and looked around the hall. There were a great many scholars attending -- more than thirty -- and among them Shen Wanyun, Yue Qinghong, Si Yunxiang and others.

Then he saw Ban Gongcuo.

Ban Gongcuo was not listening. His eyes were shut; he was trying to batter down his own barrier.

Reverend Hongfa went on, her speech somewhat slow: "A man standing on level ground can easily fix east, west, north, south, above and below -- but inside the human body, how does one fix east, west, north, south, above and below? We use your Primal Embryo Spirit Treasury to fix above and below: the crown of the spirit embryo's head is heaven, and what it stands upon is earth. Once above and below are fixed, we must fix east, west, north and south, and that requires the five luminaries of the Five Luminaries Spirit Treasury to set our bearings."

"You have all studied the Ten Mathematical Classics; the Ten Mathematical Classics serve to fix the five luminaries. And to derive from the five luminaries the points of the compass within the heaven and earth of the heart, one needs the Six Harmonies reckoning. Now let us take up page seventeen of the Six Harmonies Mathematical Classic: the meridian-returns-to-south algorithm."

...

Shen Mu looked this way and that, and suddenly someone poked him in the back with a finger. He turned; it was Si Yunxiang, Holy Maiden of the Celestial Sage Sect, her pearly teeth biting her red lip. "Last night," she whispered, "I saw the Sect Master drag three girls back to his room."

"Nothing of the sort!" Shen Mu denied flatly.

Si Yunxiang murmured, "One of them was the Seventh Princess."

Shen Mu's face flushed. "Holy Maiden, do not slander me and ruin my good name. Lend me your Six Harmonies Mathematical Classic -- it is my first time here and I have no book."

"Is the lecture hall a holy place, that whispering is permitted within it?"

Reverend Hongfa struck the desk and shouted, "You two, out! Stand in the corner!"

Si Yunxiang snatched up the Six Harmonies Mathematical Classic and went out of the hall with Shen Mu. The two leaned against the wall, and she handed him the book, saying with a smile, "The Sect Master is greedy for beauty -- take care you do not end up as Sect Master Li did."

Shen Mu opened the classic. It set out many formulas, methods extended from the Ten Mathematical Classics, for computing the precise bearings of east, west, north and south upon the basis of the five luminaries.

What Reverend Hongfa was lecturing on was page seventeen, the meridian-returns-to-south algorithm, which fixes the south; once south is fixed, east, west and north follow of themselves, and then a single line drawn above and below fixes the most exact position of the Six Harmonies Barrier within the body.

Every person is unique, and so the precise positions of each person's Five Luminaries Spirit Treasury differ; and since the Five Luminaries Spirit Treasury is precisely the foundation for determining the Six Realms Spirit Treasury, each person's Six Realms Spirit Treasury likewise lies somewhat differently. Hence the need for meticulous calculation, with no room for error.

Before long Shen Mu had read the Six Harmonies Mathematical Classic through. It used the quinary system of the five phases and the senary system of the six harmonies, requiring the quinary results of the five luminaries to be converted into senary before the reckoning could be worked out.

Shen Mu was dazed, and suddenly he thought of the Dutian Demon King's guidance.

The Dutian Demon King had once said that the octal system in the Supreme Mystery Mathematical Classic could be reckoned with the eight trigrams as a computing tool; and from that Shen Mu had seen the light and grasped the other computing tools in the Supreme Mystery Mathematical Classic -- the Taiji Eight Trigrams Diagram contained the binary of yin and yang, the quaternary of the four phases, and the octal of the eight trigrams.

But add the quinary of the five phases and the senary of the six harmonies, and the computing tool became complex indeed.

"Imperial Preceptor Jingping said that the four great spirit bodies are not the five phases; rather, each spirit body encompasses all five phases. That is to say, the four great spirit bodies -- Azure Dragon, White Tiger, Vermilion Bird, Black Tortoise -- are the four phases of the Taiji Eight Trigrams Diagram!"

A sudden clarity opened in Shen Mu's mind. The four phases: each phase encompasses the five phases, and different permutations and combinations of the five phases compose the phases!

In other words, reckoning in the quinary system of the five phases can yield the transformations of the four phases -- and thus one has a tool for computing five into four.

And the six harmonies: the four phases can fix east, west, north and south, while yin and yang fix above and below -- and thus one has a tool for computing the six harmonies.

"Which means I can very soon calculate the position of the wall of the Six Realms Spirit Treasury!"

Shen Mu returned the Six Harmonies Mathematical Classic to Si Yunxiang, stretched out both hands, pressed his right palm over his left, and drew them apart above and below. At once his threads of qi formed a strange Taiji pattern, embracing yin and yang, the four phases, and within the four phases the five phases.

Elated, Shen Mu drew his hands apart again, and layer upon layer of the Taiji five-phase patterns split open, each working its own reckoning, in perfect order.

Si Yunxiang watched the shifting patterns before him in astonishment and said hastily, "How are you calculating? It is not quite the same as what Reverend Hongfa teaches! Let me copy it, quick!"

Shen Mu calculated at flying speed, his mind divided between two uses, and told her what he had grasped.

Si Yunxiang's eyes grew brighter and brighter. She too was a woman of surpassing talent, and quickly grasped the wonder of it. "This method is good," she praised. "The method in the Six Harmonies Mathematical Classic is too cumbersome -- a month or two of calculation to reach a result, and easy to get wrong. With your method there can be no error at all, and at most an hour or two will do it!"

Shen Mu laughed. "Taiji, four phases, five phases, six harmonies, eight trigrams -- they are computing tools, made for reckoning."

Reading the Supreme Mystery Mathematical Classic now, he felt every knot untie itself, and his heart was light. Yet to master the teleportation divine ability, a single Supreme Mystery Mathematical Classic would probably not suffice.

Reverend Hongfa was still lecturing in the hall. Time passed, and at last Shen Mu was the first to fix the place of his own Six Realms Spirit Treasury -- somewhere in the dantian, bearing heaven and resting on earth.