Chapter Eighty-Two: A Mathematical Genius and a Historical Idiot

First, a quick word: cowpox is cowpox, and chickenpox is chickenpox. The two are different.

Cowpox, that is, smallpox, is a fierce viral infectious disease. Even now, if someone who has not been vaccinated against smallpox falls ill, there is still no truly effective treatment.

Chickenpox, on the other hand, is a benign, self-limiting contagious skin disease. It is a primary infection caused by the herpes zoster virus. The two are vastly different.

Not to mention modern medicine; even traditional Chinese medicine has dampness-clearing and detoxifying remedies: treatments made with mulberry leaves, chrysanthemum, burdock seed, apricot kernel, red peony root, isatis root, and the like.

The “cowpox” mentioned in the text was simply a confusion born of the Tang people not understanding the difference between chickenpox and cowpox. It was not smallpox.

——

“All right, stop reading. The accounts are fake.”

With a single sentence from Wu Ning, Qin Miaoniang was thoroughly startled. Fake? How did he know?

“Ning-ge... how does Ning-ge know they’re fake?”

She had checked these accounts several times. Even the old bookkeeper had not seen through them. How could Wu Ning decide they were false after hearing only a few pages of figures?

“Well...” Wu Ning really had no way to explain to Qin Miaoniang why they were fake.

Because the method he used to expose fraudulent accounts was something no one in this age could possibly understand.

He could only say, “The person who kept the books was very skilled. The purchases, sales, expenses, and balances all line up. You could say they are watertight.”

In any age, the most basic way to audit accounts is the same. Put plainly: people, money, and goods; production, supply, and sales.

In other words, for a shop or a company, if your sales minus profit, minus the cost of materials and labor, plus fixed assets, still balances out without any discrepancy, then the books are basically sound.

In fact, Qin Miaoniang audited them in exactly this way.

But there were simply too many things that could be falsified within it.

Take the purchase of materials, for example.

Using the Qin family’s cloth and garment shop as an example, the price from their suppliers was not fixed. The same silk could cost different amounts depending on the merchant and the time of purchase.

There was room to manipulate every slightly higher or lower figure.

Of course, for valuable fabrics like silk and gauze, the mistress of the house would keep a close eye on the price, so they were not easy to falsify.

But what about everything else?

A bundle of thread, a button, all those countless small consumables were inexpensive, bought from many sources, and came in many varieties. The head of the household could not possibly keep track of every single item.

And when auditing the books, it was impossible to inspect every expense from the ground up.

Truthfully, not only in the Tang Dynasty, but even in later ages, it is hard to trace the source of every tiny inflow and outflow.

Yet these expenses, though individually small, could not withstand the power of accumulation.

So even if Qin Miaoniang suspected someone had tampered with the minor purchases, there was nothing she could do. Even knowing it brought no solution; there was nowhere to start.

But Wu Ning did have a way.

You could record something bought for one coin as seven or eight, and cloth sold for fifty coins as thirty-four or forty.

However, the false figures you recorded were different from the real figures naturally produced. A professional auditor would know at a glance that it was counterfeit.

As Wu Ning put it, in this world, every thing, every truth, can be explained by mathematics.

Benford’s Law.

Benford’s Law states that among data drawn from real life, the numbers whose first digit is 1 occur with a probability of about thirty percent, roughly three times the expected one-ninth.

More generally, the larger the number, the less likely it is to appear as the leading digit.

That is to say, in a set of naturally generated data, the leading digit can be anything from 1 to 9: 18, 29, 98, 72.

If there are enough such unordered data points, one would naturally assume that the probability of each leading digit from 1 to 9 is one-ninth.

But in fact it is not. The probability of 1 appearing is about 30.1 percent, while 2 drops sharply to 17.6 percent, and so on. By the time you reach 9, the probability is only 4.6 percent.

It is a most interesting law. Not only can it be used to audit accounts, it applies to every aspect of life around us.

For example: the length of rivers, the area of lakes, population, physical and chemical constants, per-capita income in each city, how many people hooked up in a day, how many confessed their love, how many huskies tore apart their homes...

You can make the books look perfectly balanced, flawless to the last detail, and even make the sources of income and expenditure impossible to trace.

But fake is fake, and it differs fundamentally from naturally generated raw data.

As long as Wu Ning counted whether the probabilities of digits 1 through 9 followed Benford’s Law, that would be enough. No matter how balanced the books looked, it would be useless.

But he could not explain any of this to Qin Miaoniang. How could she know what Benford’s Law was?

And even if Wu Ning told her, whether Qin Miaoniang would believe it was another matter entirely.

So Wu Ning simply stopped explaining and said flatly, “The books are fake. There’s a problem with your accountant.”

Qin Miaoniang: “...”

“But the Qin family’s accountant, Uncle Sun... he has been in my household service for more than thirty years. That seems unlikely.”

“Then it’s even more certain!” Wu Ning was all the more confident.

“Only someone who is not an old bookkeeper of decades could have made the accounts so perfect that you can’t find a single flaw.”

“Investigate him. He’s definitely got a problem.”

When Qin Miaoniang heard that, she was truly troubled. How was she supposed to investigate? Just because Wu Ning said so, should she go and question her family’s bookkeeper?

“Ah!”

Wu Ning let out a long sigh, thinking, my foolish girl, you really shouldn’t be in business. Do I have to teach you even this?

“Ordinary bookkeepers, even if they make false records, will still keep the original books.”

“In other words, there are definitely two ledgers. One is for you to see, and one is kept by him, for constant cross-checking so he can avoid mistakes or deal with unexpected situations.”

“So...” He shook Qin Miaoniang’s fake ledger. “You don’t need to care what’s written in this one. Just find the small ledger.”

“But...” Qin Miaoniang still wore a deeply furrowed brow. “Uncle Sun is not going to hand me the real books himself. How am I supposed to check?”

“Forget it.”

Wu Ning was utterly speechless. This girl was already beyond saving.

“Leave it to me.”

——

When he returned to Fourth Uncle’s house, Fourth Uncle happened to be there today as well.

After thinking it over, Wu Ning told him about the Qin family bookkeeper’s fraud.

In Wu Ning’s mind, there was no need to make a fuss. If the Patrol Guard Battalion or the yamen stepped in and seized that Sun fellow, a little intimidation should be enough to make him cough up the real books.

But as soon as Fourth Uncle heard it, he laughed.

“Why make it so troublesome?”

To Fourth Uncle, Wu Ning’s method already counted as troublesome.

“Ninth Young Master doesn’t know this?”

“All you need to do is check the paper shop, see how much paper the Qin family’s cloth store bought, and compare it with the paper used up in the books. If they don’t match, just ask Bookkeeper Sun for the rest. If he can’t produce it, wouldn’t everything be clear?”

“Ah... ah?”

Wu Ning had not understood. “That can be checked like that?”

When Wu Changlu heard this, he could not help but laugh.

“Ninth Young Master really doesn’t know? The paper used for ledgers is not something you can buy just anywhere. To prevent forgery, the paper used for account books is not ordinary paper. It has a special texture.”

“And that kind of paper cannot be sold just anywhere. In the city, only one government-run paper shop carries it. Moreover, every purchase is recorded. A quick check will tell you everything.”

“There’s such a thing?” Wu Ning was dumbfounded.

Fine. He really knew nothing about history.

“But what if Bookkeeper Sun doesn’t use ledger paper?”

“He won’t!” Wu Changlu waved a hand. “Such bookkeepers are registered with the yamen, too. The authorities are afraid merchants will use fake accounts to evade taxes, so no other paper shops will sell to bookkeepers.”

“If he buys paper, even if it isn’t ledger paper, he can only get it from the one government-run shop.”

“...”

For the first time, Wu Ning felt he had underestimated the people of this era.

So they had anti-counterfeiting measures too, and rather sophisticated ones at that.

.