Chapter Red, Green, Yellow
Scene Two: Facts Discovered
“I thought you weren't any closer to figuring out Clumpi's system,” Hummel whispered, much too loudly for Denario's comfort. All of the mule drivers and book keepers had watched the confrontation with Burgher Dumm. Some of them had been keeping a close eye on Denario since. They probably wanted to overhear something to their advantage.
Outside, the clouds had fled. The sun climbed alone into a gray-blue sky. In the counting house, the shelves and stacks had been cast into shadow. Denario ordered the cargo doors opened to relieve his mood. It had taken him more than a day to notice that those doors existed because two boxes of turtle shells had been stacked in their way. Next to them five bales of raw wool also blocked the view. Denario had to help Hummel and the guard shift everything to get the place opened up. They discovered that lowest bale of fleece had gotten wet and started to go bad. But the reward for their work was plenty of light in the counting house. It made Denario feel better about his job.
That the large doors hadn't been used in a month, apparently, was depressing. It meant no caravan had brought in large barrows of supplies to the town for that long.
“I didn't even look at the tiles yesterday,” admitted Denario as he puzzled over how such a wealthy town could have gotten itself into such a dangerous situation. “But I'll start right now.”
The transactions with the muleteers had finished. Denario walked past the last mule driver and a fresh stack of otter furs on the way to the tile desk. The driver nodded to him. Denario nodded back rather absent-mindedly. Behind the trader, at the back desks where the scrolls and candles were kept, Keeper Senli had taken the opportunity to instruct Mistress Clumpi on the mechanics of penmanship. It wasn't easy. The quill was old and the ink was lumpy. Nevertheless, Olga and Senli entered records into a Tomaru scroll. Senli seemed to be a patient teacher, which was good considering the disposition of her student. Olga gave turtle-necked, hands-on-hips scowls to the marks she'd made on the page.
Denario didn't want to disturb the women, not yet, so he sat in front of the tiles at the edge of the bright sunlight. He made a quick recount of the colors and shapes of clay pieces. All of them had holes for stringing, of course, but most were square. A few had been cut into rectangles, probably also meant to be square. Others were flat discs. Still rarer types had been shaped into beads.
The beads were always black or red, never any other color. That was Denario's first clue.
“Hummel, did you talk to whoever made these tiles for Master Clumpi?”
“No, sir. I hear the man was just a farmer and part-time potter. He lives out of town, I think.”
“I'll bet Mistress Clumpi knows him.” It was odd that someone hadn't thought to talk to the potter responsible. That was a symptom of how this town worked. If a task wasn't convenient, it got put off. And certainly the burghers hadn't made it easy for Senli or Hummel to travel. A woman with a visible slavery tattoo had to worry about walking practically anywhere.
Denario had seen businesses in Oggli operate in a similar, lazy fashion. But unless those people were related to the marquis or some other noblemen, they didn't act that way for long. Instead, they went out of business. Master Winkel had listed those failed operations in his accounting logs along with the reasons he thought they'd gone bankrupt. Here in Phart's Bad, where there were no other mines, only one cobbler, one tailor, and not many farms, the only businesses that had to survive any competition were the caravans and the smiths.
It was no surprise that the Mundredi army got their best bronze spear points around here. The copper smiths had to be learning from one another and competing fiercely to acquire the best materials and techniques.
“Why aren't you moving the tiles, master?” asked Hummel. He wasn't even pretending to work. That was all right by Denario, though. He didn't want his book keepers doing fake work just to look busy when he was around.
“I'm counting the pieces again. I've got some ideas, given the numbers, but I don't want to disturb anything.”
In fact, Denario did move the tiles and strings. But he shifted them carefully, always restoring anything he'd displaced. Hummel watched for a while. But for a quiet man, he didn't have much patience. He soon turned his back and began to re-stack the otter pelts. Meanwhile, Denario kept a tally in the dirt of the various types of shapes and colors he encountered. In about two hours of careful work, he got to a point where he felt able to match the tile types to categories in the counting house inventory.
The basics fell together more or less at once. It started with a sense that the beads were operators instead of counters. From there, his guesses led logically to a series of vague conclusions that he couldn't prove. But he was sure he was generally right. When he felt himself getting confused about the details, he drew a chart:
black beads = addition
red beads = subtraction or sometimes a debt
disc tiles = multipliers
yellow square tiles = one
green square tiles = two
blue square tiles = four
“Mistress Clumpi?” he called. The old woman had finished her writing lesson. A friend of hers had come by with applesauce for lunch so she had just dug in. “Did your husband ever count by eights? Or maybe sixteens?”
“Sixteens, yes. He called them hexads.” She wiped her hands on her apron. “I don't know if he counted by them but he liked the number.”
“Hexads? I don't know that word. Maybe he invented his own term?”
“Yes.” Olga groaned for a moment as she got up off of her stool. She ambled toward Denario. “He liked the old tongue. A lot of his words came from that. But he shortened them when he used them in his math.”
“That could account for two of the three the missing colors.” Denario stared at his chart, which appeared to make sense. His guesses had been on the right track and he thought he could make another, too. “Did he compare hexads to tens and twelves?”
“He must have been very sharp.” In fact, the man must have been doing his accounting math in hexadecimal and translating it into decimal or duodecimal when talking to the caravan drivers, all of whom worked in base ten or twelve according to the slave book keepers. “Very sharp, indeed. He did all of the math in his head?”
“Bibbo couldn't write much.” She wrung her hands. Although she seemed encouraged, it was obvious that she felt confused by the line of questioning. She seemed a bit tired, too. Denario didn't feel he could offer her the rest of the day off but he wouldn't give her heavy work this afternoon.
He added to his chart,
red square tiles = eight
purple square tiles = sixteen
There were fewer purples than reds. Reviewing his results, he realized that he'd gotten ahead of himself. He hadn't even started to restore the system. But he was pretty sure he was on the right track about the basic scheme. Without these guesses, nothing else he did would matter anyway. He could puzzle out the state of the tiles on the strings with Olga in the afternoon. For the moment, he needed to come to a decision about whether the proportions of colors suggested connections to the inventory, signs for the traders, or tally marks – and the verdict seemed to be tally marks. A yellow tile didn’t indicate ‘one otter fur.’ It meant one of anything. All of the colors were numbers or operators and they were all part of a base sixteen accounting system.
“Do you need me?” asked Olga. “Only I want to get back to my sauce. And it looks like you already know what you're doing.”
“I've made a start. I'll need your help after lunch.” Denario smiled at her. “You see, I really need you. I can already tell there's a problem about these values if I'm right about your husband's method. And I'm pretty sure I understand the basic method.”
“So what's the problem?”
“Well, if no color belongs to any particular trader, how did Bibbo keep track of what account strings belonged to which trader? Did he say anything about that? Would you have any idea?"
She shook her head.
“And if each tile stands for a number, how did Bibbo know what kind of thing he was counting? How did he know someone had contributed sixteen bear skins but not sixteen pork bellies?”
“Maybe he just remembered.”
"That's what I'm afraid of," admitted Denario. It seemed all too likely.
Next: Chapter Eleven, Scene Three