Sunday, June 25, 2017

A Nerd in a Warrior Culture - Thirteen Chapters

A Bandit Accountant

Chapter Thirty-Two Minus Thirty-One

Chapter Root Two Squared

Chapter Pi, Roughly 

Chapter Two Pair

Chapter Full Hand

Chapter Half Dozen

Chapter Fourth Prime

Chapter Two Cubed

Chapter Three Quarters of Twelve

Chapter Binary Two

Chapter Red, Green, Yellow

Chapter Square Root of Gross

Chapter Baker's Dozen

Saturday, June 24, 2017

Being Geek in a Warrior Culture - Thirteenth Chapter

A Bandit Accountant

Chapter Baker's Dozen

Sunday, June 18, 2017

Not Even Not Zen 83: A Bandit Accountant, 13.6

A Bandit Accountant

Chapter Baker's Dozen

Scene Six: Geometry by Ropes

After five days of travel in these hills, Denario wrote in his journal, I have seen several examples of tally sticks and find them remarkably consistent. I have drawn examples here of the symbols used.

The split-stick method cannot accommodate a complicated transaction. Yesterday I saw that that one farmer owes his neighbor thirty-two chicks while he is owed six pigs from that neighbor in turn. Even for this simple record with just two entries, the hill folk cut two sticks. What's more, the symbols for some types of livestock can be similar to others. There is a parallel problem with the symbols for clan houses. Despite what the hermit told me, I suspect that cheating goes on.

Tally sticks do not record anything more than debts. For farmlands and water rights, the hill folk rely on oral histories, totems carved in stone, and warfare. Thefts of sheep between clan herds and between houses are common. I have been fired upon twice, each time when I was mistaken for an enemy shepherd. Both arrows missed of course or I would not be writing this entry. 

Everyone fights. Old women casually punch me on the shoulder to test my armor. Even the priests here fight over debts and territories. I was asked to adjudicate in the town of Double Bad on a border dispute between two churches. By popular reckoning, the local goddess is allowed two hundred ells distance from each spire of her church. (There are two, a north and a south spire.) The temple of the local god gets the pond, the well, and the lands west of the water. The border of the pond changed due to a snow melt years ago and the religious zealots on both sides have been fighting since. 

I saw that the goddess's church spires formed formed the two foci for an ellipse that defines the border of her holy grounds. When I drew an example for the mayor, he was glad to pass the problem to me. 

As Oggli accountants will know (most, anyway), the sum of the distances from any point on the ellipse to the two focal points is constant and it is known as the "major diameter." In this case, I knew it should be two hundred ells. The priests of both temples and many followers of both congregations came with me as I measured the bounds with ropes tied to the spires through the windows. They laid rocks and wooden totems along her holy border. There were surprises for everyone, as several private gardens turned out to be within the holy grounds and a church pagoda had to have a stone marker placed in it because it was not built precisely where it should have been.

Eventually, we came to the water. The priests were prepared for this. As it turns out, the goddess's lands now encompass about ten ells of marsh. That is not as far as the rival temple feared, so both holy men gave speeches, as planned, to say that the god had made a gift to the goddess. Then they laid down the largest marker stones in the watery border. A similar gift was made to the god from the goddess because lands once used by her congregation now clearly fell outside her border. 

As all accountants will appreciate, I made sure to get paid in advance. In this case, the priests were not too unhappy so I had the luck of getting fed and paid again afterward. The mayor carved a note on a block of wood for me. He does not have parchment, much less paper. But he composed a letter of transit much like the one I received in Pharts Bad. 

That letter has been useful, so I am glad to have another. 

Denario used the last of his day's ink to darken the lines in his drawing of the churches. He carefully cross-hatched the pond between the structures until the pen gave out. Then put the quill away, shut his journal, and closed his eyes. He pulled up a blanket as he leaned against the trunk of a fir tree to sleep.

The heavens hadn't gone completely dark yet but there was no question of extending the day with a campfire. He'd tried to start a blaze from pyrites he'd been given in Double Bad. He'd failed despite having been shown how to use them. Fire remained a mystery. And without a fire, someone had whispered, the raccoons and wolves would 'get him for sure.' Denario worried about the possibility but there wasn't much he could do. He'd heard a wolf or two howling but none had come close, at least not while he was making so much noise. He'd been troubled by no other beasts.

His everyday challenges came from people, not wild animals. The local hill men shot at him, haggled terrible bargains for his food, cursed him for worshiping strange gods, accused him of acting like a child, demanded that he get their tribal tattoos, and seemed disinterested in math, which they considered the concern of "lowland folk."

Sometimes Denario wondered why Master Winkel had never warned him how many people would try to kill an ordinary accountant. But actually he had, hadn't he? Winkel had lent him the guild log books. Those were full of the deaths of book keepers and accountants. Details had not been spared. Clients became murderous when crossed. That was the underlying lesson that Denario had failed to understand in Ziegeburg, he supposed. And the carnage wasn't limited to small towns. Large cities could be worse. Hadn't Winkel said that the reason he didn't work directly for the Marquis de Oggli was that he'd seen the marquis chop off the heads from his treasure room staff? Witnessing that event had made an impression.

Denario tried to sleep but although his body was tired, his mind was not. He'd gotten himself wound up about geometry. Making his proof to the mayor about the properties of ellipses had gotten him interested in proofs in general. That line of thought led him back to how three must always equal three and how there had to be a formal way to prove it. He wished again for a campfire.

Pine needles, he thought.

Hadn't he heard something in one of the small towns about using pine needles to start fires? Denario had given it a try before but that had been when the needles were damp from an afternoon rain. The ones he was lying on right now were so dry they crackled beneath him like a fire already.

His eyes opened. He turned to his travel pack and dug down to the bottom of it, where the pyrites had come to rest.

In a minute or two, he was ready. He had his bags pushed to the side and his blankets folded neatly behind them. The sun had gone down behind the hills but there was still enough light to see his hands and the fire-starters in them. He took a swipe, pyrite against pyrite. Nothing. There was no spark. He tried it again. He tried it twelve times.

He flopped onto the mat of needles in defeat. Then he sat for a while, head in hands, and tried to think of what he must be doing wrong. The man he'd bartered with in town had bashed one of the pyrites with a piece of flint. The blow had produced plenty of sparks. Denario didn't have flint. There were rocks all around him, though. He'd felt them against his back as he lay on the bed of pine needles.

“What does flint look like?” Denario murmured to himself. It was a dark stone. That's all he knew. But maybe he could look for dark rocks and hope. He started shifting piles of needles with the toes of his boots.

The first big rock he found was nearly white. It was some kind of milky quartz. He found other pieces like it all over the ground. He covered them over and kept looking.

A minute later, he rushed back.

It's not a touch on good flint but quartz works just fine, the fellow had said. Denario hadn't paid much attention. He'd figured that the pyrites were the secret to fire. He hadn't wanted any yokel advice. But now he dug through the pine needles until he found a fist-sized lump. It was a solid chunk of quartz. Parts of the rock were the color curdled milk but other parts of it were rosy, he judged. It was getting hard to tell in the darkening sky.

He didn't have much time before true night hit. He reared back and took a big swing.

When the quartz met the pyrite, there was an explosion of sparks. Denario gaped. Hot bits of pyrite flew everywhere. One of them settled on the dry pine needles and began to smolder.

“Ha!” he shouted. He began to giggle like a maniac. Fortunately, there was no one to hear him. His feet did a little dance. He crouched down low to the pine needles and smashed the quartz into the flint again.

“Fire! Fire!” One of the sparks landed on a bed of dry needles. The needles immediately began to burn. Excited, Denario knelt down and blew on the embers as he'd seen many of the Mundredi do when they wanted to encourage a flame. “Hah! Finally.”

The diameter of charring pine needles grew. In a minute, with carefully applied long, slow breaths, the embers expanded into a broad flame. Denario began to relax. He'd done it. He'd made a fire. Tonight he would be warm. Even better, he'd be able to see. He could get back to mathematics. He could work all night if he wanted. That was the best part.

He spotted his accounting bag. It was a little too close to the burning pile of pine needles for his comfort. He plucked it by the strap. After watching the fire for a moment, he gathered his other bags. He grabbed his blankets, bow, buckler, and spear.

“Uh oh.” With all of his possessions in hand, he gazed upward at the dry pine tree. Flames from the pine needles on the floor beneath leaped to the lower branches. Denario suddenly realized that the needles, inches deep and dry almost all of the way to the ground, were too good a fuel. He saw no way to stop the burn.

Next: Chapter Fourteen, Scene One

Sunday, June 11, 2017

Not Even Not Zen 82: A Bandit Accountant, 13.5

A Bandit Accountant

Chapter Baker's Dozen

Scene Five: Accounting by Sticks

“Well now, that smells wonderful and awful at the same time,” said the hermit. He stood well away from Denario and scratched his armpit.

“Sorry, Mister, uh, Chains,” Denario replied. It was struggle to remember the hermit's name, particularly as it had the air of being made up. “The bag doesn't have enough compartments to keep everything separated. Sweet herbs have mixed with the savory. Do you want to trade?”

“Trade spice? Or food?”

“Anything, I think.”

The fellow that Denario assumed was some sort of hermit wore a pain brown tunic that had seen better days and probably better years and, in fact, probably better hermits as well. It looked like he was the last member of his church and had inherited the traditional garb. The brown burlap was cut too large but the sleeves were too short. The hemline didn't cover the man's knees. The holes, front and back, were badly patched.

The fellow wrinkled his nose often in the span of their brief conversation. He apparently didn't think much of Denario's smell, which was to be expected. At the Kaufmann's house, Denario had scrubbed himself down and changed his clothes. But when he'd lifted his mail shirt over his head, he'd been shocked to find bits of blood on the iron rings. And his back had felt wet. He was bleeding. Why? It took him a moment or two to work out the reason. Iron rings had pressed through the cheap farmer's shirt he'd been wearing. He needed a tougher shirt underneath.

As a result, Denario had chosen a heavy linen to protect him from his armor. It kept him warm beneath the mail and the leather hauberk. The linen kept him so warm, in fact, that he stank of sweat in a matter of minutes and kept on stinking more as he walked.

He wasn't planning to change out of his armor until he got to the creek. He hoped the other hill folks he met were as tolerant as the Kaufmanns. That wasn't likely, if Mr. Chains was a fair sample. He kept sniffing as if he couldn't believe how bad things smelled.

The hermit's eyebrows were really one eyebrow. His black and grey beard merged into his hair without a noticeable difference in color or thickness. His bare arms bristled with dark fur. He wore a holy symbol around his neck, a crescent of some sort. It was probably for a harvest god who Denario didn't recognize.

“We don't get many wizards through here, just one or two a year.” The man pointed blue stone coin to the chain around Denario's neck. It seemed as strange to him as his holy symbol was to Denario.

“I'm ...” Denario struggled to explain himself. “I'm something like that but I don't do magic except for numeromancy. That's magic with numbers.”

“Is that yer trade, then? Numbers?”

“Yes. I'm an accountant.”

At that, the hermit chuckled. “I've heard a song about an accountant.”

Denario thought about that for a moment. Even this fellow all alone, miles away from any city or town, had heard the Mundredi ballad. It seemed there would be no escape from it. Denario looked at his map. Then he looked at the stranger. Then he howled. He didn't know why he did it. The wail just burst out of him in a flood of loneliness and hopelessness.

“Oh,” said the hermit with a nod of understanding. “So that was ye, was it?”

“Hooooo,” Denario agreed, not quite able to speak.

“If it's any consolation, my neighbors know the whole thing to the end. And they said the song has a bit of numbers in it. They never knew numbers was so useful.”

Denario took a deep breath. He took another, slow one and started to feel better. Then he shook his map, which he realized was mostly imaginary, and tried to guess how long his march would take.

“What is this hill called? The one I'm on, I mean,” he asked.

“Yer on Crumbling Bluff. The next one yer facing is Knob.” Chains gestured with hairy fingers to east. “Then comes Brushfire, then Flint.”

“You seem to know quite a lot of geography.” Denario fumbled into his bag for the rod of graphite, antimony, and sulphur. That was his best instrument for drawing. What he found was a pen nub with some ink left in it. He used it to scribble the hill names onto his map.

“I gets around.”

“Would you happen to know where I can find No Map Creek?”

“Never heard of it.”

Denario sighed. As he dropped the pen nub back into his bag, he realized he had at least a week's worth of foot travel left. But that wasn't so bad. He liked having the time to think and write about math. His armor and equipment didn't bother him as much as they had a month ago. He closed his eyelids and rested. After a minute, he decided to ignore the hermit Chains as politely as he could. It had been a long morning.

When he opened his eyes, though, the hermit was sitting on the ground near his feet. Denario closed his eyes one more time but it bothered him to be rude. Despite his concerns about not carrying food for two, he offered to share his lunch.

Chains hopped to his feet. It was what he'd been waiting for. Fortunately, he was content with hunks of cheese.

Now that he'd gotten the idea that Denario was some sort of priest of numbers, Chains gave him a lecture on his use of tally sticks at his old job. The hermit had kept accounts on sticks for all of his life. Some of that time had been spent in a temple where he'd helped keep the records. Carved sticks represented the only advanced math known to Mister Chains. In the hermit's opinion, all other forms of accounting were trickery. He didn't trust things that were written down. Words could be changed. A stick, he felt sure, could not be faked.

“But accounting isn't ...” Denario restrained himself. He made a gift of his last sausage as he reconsidered his words. He'd been about to say that accounting did not include split debtor sticks. Winkel would have proudly stated that. It's what every accountant in Oggli would have told a country bumpkin like this one. Accounts were complicated things, written down or, in rare cases, recorded and manipulated mechanically.

“Tell me,” he said as he tried to shift the clock-gears of his mind with mixed success. His emotions went thunk, chunk, what would others say? He plunged on. “When you split a tally stick, how do you tell who is the banker and who is the debtor?”

“If ye mean who does the owing, that's easy.” Chains wiggled his butt happily into his patch of ground beneath Denario's rock. He cuddled his sausage in both hands. “Ye make a cut near the bottom of the stick. That takes a special knife with teeth.”

“A saw?”

“That's the name. Just a little saw and a little cut only halfway through the wood. Then when ye make the split of the tally, one half of the account is shorter than the other. See? The longer part is called the stock. The stock goes to the lender. The shorter part is called the foil. That goes to them what owes.”

“The debtors. So the debtor gets the short side, which fits into the long one exactly at the notch. Don't debtors try to cheat by losing their sticks?”

“They do. I can see that you're wise for a young man. Many folks try tricks like that. But the tally stick is full of the tribe markings, clan markings, and house markings. The lender side gets the clan and house marks of them that owes.”

“Ah, I see. And the short stick has marks for who they need to pay.”

“God marks, too,” Chains said in hushed tones. “Signs of them gods what will take revenge on cheaters. That's the important thing.”

His fanatically-wide eyes alarmed Denario enough that he had to glance away for a moment. Chains seemed to be a man with complete faith in the gods. It gave intensity to his alone-in-the-world strangeness. After a pause to sniff the sausage in his cupped hands, the hermit pushed his face up against his palms and ravaged the meat. He drove flecks of pork by-products into his beard.

After their lunch was finished, the hermit mentioned that he knew where there was safe water. Denario needed to fill his canteens, so he packed up and followed Chains about two hundred yards downhill to a muddy spring that Denario would never have known existed. It was surrounded by bushes and underbrush.

Inside the canopy of juniper and maple boughs, the tent-sized oasis was dark as dusk. Denario couldn't have found the water by himself even knowing it was there. The pool had collected in rocky cleft at the base of a two-year sapling.

Although it didn't look good, the water tasted fine. Denario patiently filled his bottles to capacity.

“I've been thinking about your tally stick system,” he ventured.

The hermit smiled. His eyes glowed like distant moons in the shade of the hollow.

“The carved debts are very nearly money. Do you know money?”

“Like ... carved pieces of copper? Or gold?”

“Yes, like that. They can transfer from person to person easily. That's an advantage of money. But the tally sticks come close. They mark how many sheep or goats are owed ...”

“Or pigs!”

“Or pigs or other things, yes. But the debt has to stay in the same house or same clan. It can pass from father to son but not to anyone outside outside the clan.”

“Not outside the house,” grunted Chains. “Debts are personal.”

“Yes.” Denario didn't want to upset the hermit with strange ideas. Anyway, Chains was right. Debts were personal things. Master Winkel had never been comfortable with the way they were passed around like money in Oggli.

As they strolled out of the wooded area that surrounded the spring, Denario ventured, “Do people try to cheat with the tally sticks?”

“How?” The hermit raised his furry eyebrows. They formed an arch through the middle of his forehead.

“If a debtor loses his half ...”

“He's pretending.”

“This time I mean if he really loses it, maybe in a fire. Then he needs to keep it secret. Doesn't he? If the lender knew he'd lost his half, the lender would cheat by adding more marks.” Denario hesitated. The hermit had crouched his shoulders. He looked uncomfortable with the idea. “Unless the gods stepped in, of course.”

“Yes!” Chains stood straighter. “The gods can help. Yer wise for a young man. Did ye really leave a wounded man on the ground and rush to help yer captain?”

“Eh?” It took Denario a moment to realize that the hermit was referring to the humorous ballad he'd heard. “Yes, something like that.”

“Wicked of the man to come back at ye after ye let him live.”

Denario touched the scar on his head. The hermit's gaze rose to it.

“I'm not much of a fighter,” Denario admitted. “I didn't think much about it. Most of my life, I've thought about math.”

“How ken ye say ye think about math when ye know nothin' much about tally sticks?” Chains wailed.

The hermit followed Denario for almost two miles. He kept describing tally sticks and quizzing Denario on what he'd just said. It made Denario worry that he'd made a serious mistake in feeding the man. In his travel bag he kept no more than a few days' worth of food. If he had to supply nourishment for a fellow drifter, they'd both go hungry by the dinner after next.

Fortunately, Mister Chains disappeared in the late afternoon.

He'd been marching behind the accountant. Both men had fallen silent. Denario had twice proved that he understood the spacing of symbols on local tally sticks. There seemed to be nothing more to learn. As they reached a furrow of land between two hills, Denario heard a rustle in the brush. He stopped and turned to ask Chains what it was. But there was no sign of the hermit. Up the hill they'd left, a grove of poplar and juniper trees stood. Chains could have been hiding there but Denario couldn't figure out why he'd bother.

The accountant spent a few minutes making sure that his unwanted guest hadn't fallen down and hurt himself. He pushed aside weeds with his bow and his spear. No one seemed to be lying on the ground. In a few minutes, he decided that Chains must have wandered away a while ago without saying goodbye.

When Denario turned back on track, he marched only a few yards before he managed to startle a ring-necked peasant. Its body was brown and white and its head, above the white ring, was as green as the grass. It hunched down to hide rather than take flight. He grabbed his bow and tried to string it. But he failed the strength test again. He lost his grip. The recurved end of the bow sprung back and smacked him in the eye. His bowstring flew up in the air. A second later, Denario tripped while grabbing for the falling string.

When he arose, oddly enough, he discovered that the pheasant had fluttered only a few feet away. He lunged after it. But his swipe with the bow missed. He tripped again. The bird took off and kept going.

He resolved to find more work as a math teacher. He wasn’t ready to live as a hunter.

Next: Chapter Thirteen, Scene Six

Sunday, June 4, 2017

Not Even Not Zen 81: A Bandit Accountant, 13.4

A Bandit Accountant

Chapter Baker's Dozen

Scene Four: Journal Entry; Looking for a Creek

Denario wrote in his journal, 6,452 steps since breakfast. I’m exhausted. And I’ve been terrorized by a huge animal with antlers, called a ‘deer’ by the locals but it must have been three times the size reported. Then a pair of rabbits charged me and drove me upslope for half a mile. Other accountants never mentioned things like this in their journals.

At least the mountains aren’t as noisy as the farms. Coming out of Zeigeburg, I prayed to the gods to strike down every songbird. There aren’t many in the cities. In the wilds, they’re everywhere and they never shut up. Sometimes I wonder why no gods answer my prayers. Doesn’t the singing annoy them too? 

I’m getting better at hiking. Except for tree branches. They grow at the exact height of my right eye. At least, they have on several occasions.


Denario had spent two days on foot from Ziegeburg to Hogsburg. He'd spent four days chasing armed warriors in the hills. He'd seen thirteen sunrises with a quarter of the Mundredi army as he patrolled the countryside. Finally, he'd worked for three weeks and two days more in Pharts Bad to solve their book keeping problems.

Time had slipped by. A journey that would have taken him eight or nine days by coach had grown to over a month. Worse, he hadn't made much progress. On the map, he'd moved south and east and that was good. But he'd covered no more than the equivalent of two days' coach travel along the Riggle Kill. He'd spent much of his time earning food.

This morning's march out of the magic of Tree Stump brought him another two hills eastward in the chain. But the rises were small and close together. Most of his progress had been vertical. It wouldn’t look like much when charted. He perched on a fat rock to consult his maps after his noon meal. Unfortunately, his most recent, hand-drawn map was largely guesswork. He fretted about how little he knew of the lands between him and No Map Creek.

The Kaufmanns, because they were such nice people, had tried to help him find the creek. Among their half-dozen magical knick-knacks was a scrying bowl. Hadewig could make it imitate a crystal ball by filling it with holy water. As long as the surface was perfectly calm, she could see distant places with it.

“There's no creek,” she told him.

“There's got to be one.” He pointed to the blank areas in his map. “Vir said it was in here somewhere in the hills between the Mundredi and Kilmun territories.”

“That's the chief of the Mundredi, Vir de Acker?”

Denario nodded.

“Well, he ought to know. If the water originates along the eastern border of his lands, it must be on the edge of West Valley. But there's no stream that shows up there. Every time I try to look at where it should be, the bowl goes all wobbly.”

They kept at it for an hour. Then, to prove that she knew what she was doing, Hadewig took a the spare drawing compass from Denario. It was the one he hadn't unpacked since he'd left home. She used it to tune her bowl to Denario's counting house in Oggli. After about a minute of work, she let Denario see. Sure enough, he could spy down on two of the rooms and a hallway in his home. He felt like he had a view of the place from the rafters except the clarity of vision was better. The walls didn't get in the way as much as they would have in real life. The magic of the bowl let him see through the top two or three feet of each interior wall if he concentrated.

In Oggli, everyone had left for the morning already. They hadn't been gone long. There were unwashed dishes sitting next to the kitchen tub, which was half full of water. A plate of food had been left to dry for at least a day. There were papers and parchments strewn about. Some of books were missing from bookshelves. Scrolls were missing from their slots but most of them had been laid out on the desks and pinned down with survey weights and stones. Good.

The counting house had seen a busy morning, apparently. Clothes had been tossed about, some of them positively kicked from the apprentices’ bedroom into the hall. But Denario had been gone for all winter and, after that much time, he was relieved things didn't look worse. Maybe the cleaning chores had gone downhill a bit but that wasn't so bad. It was a sign of strength, for sure, that there was enough work to be done to make Curo drag everyone from the counting house, even Mark and Guilder.

“But still no sign of No Map Creek,” Hadewig had said after she tried again.

She and Jake had given Denario a pouch of cooking herbs before he left. They told him about their neighbors on the lesser hills and advised him to barter for dinner whenever he could. They also mentioned that he might meet a few magical deer, mostly gold in color, and some werewolves, nearly black.

“Are you saying to watch out for wolves?”

“No. These are bigger than wolves. But you won't see them. The moon won't be right for days. You should always make sure to talk with the locals as you go along, though.”

“Of course.” He'd been planning to do that anyway. But how could he bring up the subject of 'have you or any of your friends turned into wolves?'

“Oh, I almost forgot,” said Hadewig. She reached up to a jar on her top shelf. “I've got one last herb for your pouch.”

She handed him a few sprigs of dark green leaves with dried, purple flowers. Denario recognized it from the apothecary on South Street in Oggli and from the Poisoner in Ziegeburg, too. This was wolfsbane. The way the dark green stem curled, he felt sure this was the magical variety. Hadewig's father probably supplied it to the wizards. Now Hadewig made room in his spice pouch and tucked in the sprigs. She pulled the leather drawstring shut with a smile.

That was why, in the middle of the day as he studied his map, he kept his spice pouch open by his side.

Next: Chapter Thirteen, Scene Five