The Novels

Sociology 500, a Romance (Second Draft) -- The first book in the Economics 101 Trilogy.
Karel and Dan, former American football teammates and now graduate students, meet fellow graduate students Kristie and Bobbie, and the four form a steady study group.

Economics 101, a Novel (Rough Draft) -- My first sustained attempt at a novel, two-thirds finished in rough draft, and heading a little too far south.
What would you do if you and your study partner, with whom you had been seriously discussing marriage, suddenly found yourselves all alone together on a desert island?

Featured Post

Sociology 500, a Romance, ch 1 pt 1 -- Introducing Bobbie

TOC Well, let's meet Roberta Whitmer. Bobbie entered the anthropology department office and looked around. Near the receptionis...

Wednesday, March 29, 2017

Sociology 500, a Novel, ch 3 pt 8 -- Calendar Math (I know you really want to read this. ;-)

Previous

You said you wanted to see my notes on their calendar, didn't you? But my notes are boring.

By coincidence, that Monday morning in Dan and Kristie's overview of physical science education topics, they were discussing teaching about skip years. We'll pick up a little after Professor Billings's lesson began.



The professor posed this question: "Many students will find the subject of skip years interesting on the last day of January or the first of February in a skip year. But when it's a regular day of a regular year, how can we get students interested in the length of the year?"

Bess thought out loud. "Models of the solar system are generally good for raising interest."

"Like this one?" The professor took a solar system model out from under his desk and demonstrated rotating the planets a bit. "What does it tell the students about skip years?" he asked, and set it on the lab table beside his lectern.

Kristie responded, "I guess that many students won't draw a connection without help?"

"Well?"

Merill suggested, "If someone has a birthday that falls on January 30th, that could also motivate interest. You could raise the question of whether or when to count January 30th birthdays on skip years."

Some of the students nodded.

Dan commented, "But I'd guess it's going to have to be something related to either astronomy or the calendar."

"How about the math?" Professor Billings suggested. "Do you think young students would find that interesting?"

Merill's response was fast. "No way!"

Ted's response was a little more positive. "Maybe. Sometimes math that seems to break rules is interesting to children. Skip years being exceptions in a cyclic series, they might be presented as breaking rules."

"Okay, who agrees with Merill," and he paused as some students raised their hands, "and who agrees with Ted?" and he paused again as other students raised theirs. Dan and Kristie raised their hands both ways.

"Kristie, can't you and Dan make up your minds?"

"It's not a binary question." Kristie said, and the professor nodded.

Dan said, "My buddy Karel used to entertain the football team with oddball math, but he had a sense for it that's a little unusual."

"So what do you think?"

"I learned some of his tricks, but the math sure doesn't come natural to me. I think I might use it in class sometimes, but not as much as Karel could."

The professor chuckled. "I guess I need to try harder to get you guys to really dig into the math. The more you guys are interested, the more your students will be."

"Would asking why skip years happen also help?" Kristie asked.

"Kids are often interested in reasons," the professor encouraged.

Merill laughed. "My little sister once asked me why someone couldn't have just passed a law to make all the years the same."

"There's a possibly good approach, asking why just making a law wouldn't work."

"Why not?" asked Karen. "I mean, isn't it just like π, numbers somebody made up?"

Yes, I'm translating that. The character was not π, and it was not pronounced as in "pie". Strangely enough, however, one of their words for "pie" did have the same pronunciation as the name of the constant. More than coincidence, maybe?

Against the general chorus of groans and cat-calls, Dan said, "Take it easy on Karen. I think more than half of us have at sometime in our college lives had the same question."

"Thank you, Karen and Dan. You're both welcome to a maple cookie for your contributions today."

Professor Billings liked to encourage various kinds of independent thinking with lab-baked sweetbreads.

And now you're wondering that they have maple in their world. Well, the tree and its leaves look a lot like the maple, and its sap serves pretty much the same as the sap of maple serves us. The flavor is slightly different -- we might think someone had mixed in a little chocolate or cinnamon, depending on the variety.

You ask how either you or I could taste their maple, considering the distances between their planet and ours?

Good question. Back to the lesson.

There were still complaints. Jack was among those complaining: "But we're college students. Surely we all should know by now that the ratio of the radius of a circle to its circumference is a physical property of the real world, not a product of the whimsy of lawyers and legislators."

The classroom became quiet. The professor waited a moment and then asked, "Okay, who is willing to admit that you really aren't quite sure of either of these questions?"

A few hands hesitantly drifted up, almost as if without the will of their owners.

"Thanks for being honest." He continued, "If you couldn't look it up, how many of you would be unable to calculate an accurate value of π?" He paused. More students started raising their hands. Then he asked, "And how many of you would not be confident of being able to design a proper experiment to measure the length of the year?"

More hands were raised. He continued, "... especially since outer space has no reasonable way to set down a signpost that says, 'This is where we were this time last year.'?"

Jack was looking rebellious, but everyone around him had raised their hands.

"And now, how many of you think this discussion is interesting? Are we all awake enough to review the math?"

Many in the class nodded in partial understanding.

Kristie commented, "Asking questions in a way that asks children to think is generally pretty good for keeping the students awake, right?"

"You've heard me say that before, too. Good. Now we've talked a little about some lead-ins, how about the explanations? Who thinks they have an approach to the math?"

"Start with the shifting seasons?" Mark suggested.

"Who has ever seen a season shift?" the professor asked.

No one had.

Jack said, "Well, I really think we should start with demonstrating how to tell when a year has passed."

"Do tell." The professor motioned Jack forward.

Jack stood up at the chalkboard and drew a diagram showing their planet in orbit around their sun, showing the four positions of maximum and minimum tilt with the seasons labeled. For simplicity's sake, he avoided using the terms that would translate as equinox and solstice:


Chalkboard. Yes, they had calcium-rich minerals in abundance, and they made large boards to write on with the chalk. And, yes Jack used colored chalk.

"There you go," he said. "Standard stuff."

"And the kids really understand it?" the professor asked.

"Sure, well enough."

"How do you explain the part about marking the start position in outer space?"

"Oh. Yeah. We tell them we are counting the minutes from noon on the longest day of the year to noon on the longest day of the next year."

"And if the students understand how hard that is?"

"Most of the kids who will understand what the marker question means will have dads or moms who have already explained the precession of the equinoxes. Those who haven't will probably take the question for granted, and that should be okay for this level of lesson. Any oddballs, we can invite to help us make a class experiment."

"Good enough. Especially that last part about making experiments. Thank you. Do you want an oatmeal cookie?"

He grinned. "Thanks, but I take so many home, my wife has started baking cookies for me to bring. I actually have some oatmeal raisin cookies to share today." Jack sat down.

Oats. Wheat. Not quite the same, but closer to wheat than to rice. Oh. And they have a grain quite similar to rice, as well. And the raisins were a dried fruit that would be hard to say was not a grape, or maybe a cross between a grape and a currant.

"Okay, let's compare recipes after class," the professor laughed. "So where do we go from here?"

Mirium had a suggestion. "Some students won't really be familiar with the calendar, and reviewing a little will probably keep them listening. We should explain about how many weeks there are in a year, with how many left-over days, and how there is one less left over in skip years."

"Why not explain the varying number of days in the months, and the reason January may be twenty-nine or thirty days? We could talk about that." Merill countered.

"Wouldn't days in the week be simpler as a starting point?" Mirium responded.

"True, the weeks look simpler, but is simpler always simpler?" the professor asked.

The students all thought for a moment, then Ted spoke up. "Sometimes I've found it harder to get kids to talk about the simpler approach. Especially if they think they've heard it before. Simple sometimes means boring, uhm, because simple doesn't necessarily offer many features for them to get a grip on, to manipulate the ideas. I think we need to prepare multiple approaches."

"Thank you, Ted. I think there's an almond-flake doughnut in the box today."

And lot's of students said, "Yum!"

The almond seems to be an important form factor for nuts in many worlds.

Doughnuts? ... Uhm, yeah. Someone in their country had dropped a ring of sweet pastry batter into a pot of hot oil and discovered that it made an interesting way to cook sweetbreads.

"Okay, let's walk through both. Mirium, could you go first on the number of weeks?"

She nodded and stood.

"And, Merill, either you or Ted could do the days in the months?"

"I'll let Ted. I think he's brought something interesting."

Ted agreed to do the months, and Mirium went to the chalkboard.

"How many days this year?" Mirium asked.

Several students responded. "Three hundred fifty-three."

Mirium wrote the number on the chalkboard as she asked, "How many days in a week?"

Everyone answered seven, and Mirium wrote:
353 days ÷ 7 days per week =
and paused.

"Seven times five is thirty-five," Georgia said.

"Fifty, remainder three."
353 days ÷ 7 says per week = 50 rem 3,
or 50 weeks and 3 days
"Fifty and three sevenths, or ..." Jack recalled his sevenths. "50.428571, repeating from the four."

"Too many decimals," Georgia suggested.

"Maybe," replied Professor Billings. "But you want to be sensitive to the class. Some classes, some days, details can keep the students awake instead of put them to sleep. Some days, your plan may even require details."

Mirium continued, "Is next year a skip year?" General noises of agreement. "How many days?" And she continued the exchange while she wrote.
352 ÷ 7 = 50 rem 2, or 50 2/7, or 50.285714
"What does two sevenths mean?" she asked.

"Two days out of a week," Georgia volunteered.

"Okay," Mirium continued, "in seven years, how many skip years do we have?"

"Two," in chorus.

"How many non-skip years?"

"Five."

"How many days in seven years?"

"Don't forget to give the slow students a little time to see the answers if they can." the professor reminded them. "Even if you have to wait a minute, try to keep them answering in their own heads."

And the exchange continued while Mirium wrote on the board:
352 days/yr × 2 yrs + 353 days/yr × 5 yrs
704 + 1765 = 2469 days in seven years, usually
"Okay, how many weeks?"

Georgia suggested, "Divide by seven."

"Seven what?" Mirium asked. "Seven years?"

"Seven days in a week," Georgia replied again.

And Mirium wrote on the board,
2469 days in 7 years ÷ 7 days/week
   = 352 weeks 5 days in 7 years
"Again, how many weeks in a regular year?"

Karen answered, "Three fifty-three divided by seven is fifty with three days left over. Fifty weeks and three days."

"How many in a skip year?"

Georgia answered, "Three fifty-two divided by seven is fifty with two days left over. But, just one day less, so, of course fifty weeks with just two days left over."

Bess spoke up. "I've always wondered, is there a reason that the number of weeks in seven years is the same as the number of days in a skip year?"

"Good question. Anyone?"

Ted raised his hand.

"Ted?"

Ted said, "If we had, for example, 366 days in a regular year, and 365 in skip years, the numbers would be similar."

Merill worked the math on some scratch paper, reading it out loud. "Three sixty-six times five plus three sixty-five times two is twenty-five sixty. Divide that by seven and we get three hundred sixty-five and five days. Wait. Of course. There are five years that have one more day than the short year, so of course it's the shorter number plus the extra days. It's because there are seven years in the cycle and seven days in the week."

Professor Billings laughed. "Okay, Merill, if you'll put that on the board, you can have the apple fritter in the box."

Apples, yes, they had several fruit trees that produced fruit with flesh and skin like apples. Some varieties were naturally tinged with a cinnamon-like flavor. Some tasted slightly like persimmon.

(Oh. They had a persimmon-like fruit, too. And you are asking again how we would know about the tastes of these. X^)

"Can I skip Ted's theoretical years from some science fiction planet and just do real years?"

"Sure."

So Merill put his work on the chalkboard, carefully organized:
Whole weeks per year: 50
( 50 wks/yr × 7 days/wk × 7 years ) ÷ 7 years
   == 350 days/yr

( 50 wks/yr × 7 days/wk × 7 years ) ÷ 7 days/wk
   == 350 wks in 7 years

leftover days --
2 days in 2 years, and 3 days in five years:
   2 days/yr × 2 yrs/cycle + 3 days/yr × 5 yrs/cycle
   4 + 15 or 19 days in seven years

or, leftover days --
2 days in 7 years, and 1 more in five years:
   2 days/yr × 7 yrs/cycle + 1 day/yr × 5 yrs/cycle
   14 + 5 or 19 days in seven years

19 days/cycle ÷ 7 days/wk == 2 wks 5 days,
   or 2 5/7 weeks/cycle

19 days/cycle ÷ 7 yrs/cycle == 2 5/7 days/yr     
"Which is just to show that dividing by seven is dividing by seven, I guess. Since we have seven years in the small cycle of years, and we have seven days in a week, there are numbers that will appear the same."

The professor asked, "Do you think you could explain that to elementary school children?"

"Maybe. It'd take a lot more thought than this, I think."

"Good enough for now?"

No one could think of questions, so Merill sat down and Mirium continued. "Now, is it always going to be like this?" she asked. "Is every seven year cycle going to be the same?"

"This is where you are going to start to lose students." the professor warned.

Turning to the professor, she asked, "Then, should I just finish the math out myself?"

Mark suggested, "Would that also depend on the class?"

"What do you all think?"

Ted suggested, "Would it be a good idea to work on the months now?"

No one had a complaint, so Ted stood up and Mirium sat down.




Patience. We're getting there.


Previous TOC Next




[Backup and edit history will be here: http://joel-rees-economics.blogspot.com/2017/04/backup-soc500-03-08-calendar-math.html.]



[Chapter 3 part 8 is original to the second draft, and is not found in the first draft. Chronologically, it would come in chapter five of the first draft: http://free-is-not-free.blogspot.com/2016/05/economics-101-novel-ch05-first-semester.html.]

Monday, March 13, 2017

Backup: Sociology 500, a Novel, ch 3 pt 7 -- Family Games and Calendars

[JMR201704261021: edits -- long month interval.]

But they have two moons. Did I mention that? The smaller moon orbits their earth in just under seven and an eighth days, and their larger moon orbits it in about twenty-eight and seven eighths days. About forty-nine and a half lunar weeks a year and about twelve and {replace}two fifths{with}a fifth{replace.} lunar months each year.

[JMR201704261021: end-edits]

[JMR201703240947: edits -- 1st draft location ]

[Chapter 3 part 7 is original to the second draft, and is not found in the first draft.{add} Chronologically, it would come in chapter five of the first draft: http://free-is-not-free.blogspot.com/2016/05/economics-101-novel-ch05-first-semester.html.{add.}] 

[JMR201703240947: end-edits. ]


[JMR201703132032: edits -- Specifying the leap years more completely. ]

But it isn't exact, of course. They have to {add}further {add.}adjust that {replace}again{with}down a day{replace.} every 98 years and then {replace}once again|with}up one day{replace.} every 343 years. Already too much detail, and you're falling asleep?

[JMR201703132032: end-edits. ]

[JMR201703132032: edits -- before burning helium. ]

Bobbie said, "Everyone's behind. Even the teachers are behind. We may need to cut back on the socializing this week.{add} And right before conference week.{add.}"

--------

Their fifth planet is a water ice planet about twice the size of ours. I don't have whether it has a rocky core or not in my notes, but I assume it does. It has seas of methane and continents of water ice. At some future time, {replace}when{with}well before{replace.} their sun begins to burn helium, that planet is destined to become habitable by life such as our own{replace}, b{with}. B{replace.}ut it now serves to harbor a different sort of life. It shines blue in their skies and is named after a god of the sea from their mythology, more similar to Ægir than to Neptune, if my notes are correct.

[JMR201703132032: end-edits. ]


[JMR201703132020: backup of http://joel-rees-economics.blogspot.com/2017/03/soc500-03-07-family-games-calendars.html -- for fifth planet.]

Previous



On Sunday, our four protagonists were at Bobbie and Kristie's apartment playing a game similar to Pit with some of their roommates and home evening brothers. Joel was there, too, but Dan and Karel did not ask him about Kelly.

If you are not familiar with Pit, the game they were playing used a deck of cards which was divided into commodities. Pit, in it's more common form, uses cards representing commodities like wheat, rye, corn, barley, flax, and such. The object of the game is to semi-randomly trade cards with other players until someone gets all the cards of one commodity, at which point that person rigs the bell or calls out, "Corner!", and wins the round.

Or something like that.

Since trading is not done by turn, but any time a player is ready, at any point in time there are several players calling out the number of cards they want to trade. It's a very noisy game.

Which doesn't really have much to do with the plot of the story at this point. It's enough that you know they were playing the sort of game that you might play as a family.

After the fifth round, Kristie said, "I think this will be my last round for the night. I've got to get my books out and study. Would anyone care to help me with some education theory?"

Karel joined Kristie in the living room, and the two of them spread their books out on the floor. After two more rounds, Dan and Bobbie dropped out of the Pit game to join them, as well.

Michelle called out "Party poopers!" as they left the kitchen table amid laughter and jokes.

"Are you guys as far behind as I am?" Kristie asked, as they joined her and Karel in the living room.

Karel said, "We're not behind. I'm sure a week will be enough time to finish this and do the reports, too."

Bobbie said, "Everyone's behind. Even the teachers are behind. We may need to cut back on the socializing this week."

Dan said, "Who talked me into coming back for post-graduate work? Remind me not to trust your suggestions next time, Karel. This is hard work."

And they all laughed and got to work, comparing notes, sharing ideas, and otherwise digging in to their assignments..

After about another half hour, the home evening brothers said they had homework and bid everyone goodnight.

A short time later, when Bobbie and Kristie's roommates had retired to their rooms, Dan leaned back and asked, "So, did Joel say anything about his partner on the folk dance team when you guys were at the dance on Friday?"

"Well, yes, he did." Kristie looked up. "Why do you ask?"

Bobbie also looked up. "Dan, didn't you say you were working with someone on the folk dance team on your ward's activities committee?"

"Really, we shouldn't be talking about this." Karel did not look up.

"So, can we infer that there is mutual interest?" Bobbie wasn't going to let the question go without an answer.

Dan said, "Yeah, ..."

And Karel said, "What is and what we should infer are two separate things. I say we keep our hands out of it."

Kristie agreed. "We really shouldn't be messing with other people's relationships."

Dan and Bobbie grinned at each other and Bobbie said, "For now."

During another break a little later, Bobbie asked Karel, "That woman I thought I saw watching us from the stacks on Tuesday, have you talked to her since?"

"Haven't seen her. I'm wondering if she's avoiding the cafeteria when I'm likely to be there."

"What happened?"

"No idea."

Maybe a half an hour later, Dan pushed his books back and said, "I'm beat. Just not focusing on the homework any more. Can we look at the rest of this tomorrow, maybe at lunch?"

Kristie looked up and nodded sleepily. "I think I'm about ready to stop for the night. Karel, did you say we could all eat at the dorm cafeteria if you showed them your residence pass?"

"Yeah, ..."

"That's a great idea," Bobbie said. "I'm done for the night. Let's let this stuff sit, and we can all focus better tomorrow."

"Okay. I'm probably done for the night, too. It's late on the Sabbath, and we're getting close to curfew anyway."



Days of the week. We hardly bother thinking about them.

But there are other ways to organize a year than in seven day weeks. Come to think of it, a month might not be roughly a twelfth of the year and a week might not be roughly a quarter of a month. Etc.

Might not be. But the world of this novel does have a calendar similar to ours. It even has some historical disagreement about whether the Sabbath was the first day of the week or the last. We don't need to know all the specifics, but we might be more comfortable talking about time if we have a bit of an overview.

Uhm, lemmesee. Where did I put those notes? Oh, here they are. 353 days per year in about five years out of seven and 352 in the other two. So they have two skip years out of seven where we have one leap year out of four.

But it isn't exact, of course. They have to adjust that again every 98 years and then once again every 343 years. Already too much detail, and you're falling asleep?

But they have two moons. Did I mention that? The smaller moon orbits their earth in just under seven and an eighth days, and their larger moon orbits it in about twenty-eight and seven eighths days. About forty-nine and a half lunar weeks a year and about twelve and two fifths lunar months each year.

So their week is really a small month, so to speak. But they set the calendar week to exactly seven days. On the other hand, their calendar big month shifts between twenty-nine and thirty days.

God has different ideas about celestial mechanics, that don't obey our mortal ideals. It's not the sort of mortal clockwork we like to make. So we use various tricks to adjust our calendars to God's.

(While I'm talking about it, the two moons look about the same size in the sky. And they are about the same size in the sky as their sun. And every century or so, they end up with the two moons and their sun nicely in a line, giving a double full eclipse. Partial double eclipses are more common, of course. And I'm really putting you to sleep now.)

Now, I'll admit it, I've been fudging on the days of the week and using the names from our world. In their world, in their language, things line up differently, even though they have named the days of the week after some old, funky, northern mythology. With the two moons and one sun and six planets visible to their naked eye, we might expect nine day weeks. But the period of the inner moon wins on the weeks, while the number twelve is close enough for their months.

Confusing? That's why I've been using our names for the days of the week and our names of the months, and I'll continue to do so. Let me look at my notes again, and tell you how the days of the week actually line up for them. And we'll see if your eyes glaze over.

The innermost planet is named after a corollary of Tewes, or Hermes, or Mercury -- a sort of messenger god in one of their predecessor civilizations.

The second, as I mentioned elsewhere, is named after a goddess of beauty and love, corollary to Venus, or maybe Frigg.

They live on their third planet, as do we. It is just a little larger than ours and, relative to their sun, in roughly the same sort of habitable zone, with similar water-carbon biology. In their time, the world they live on is a blue planet, with high water content and more surface sea than continent, again, similar to ours. And they call it a cognate of "earth", which should be of no surprise.

Big, wet clod of dirt.

Like our fifth planet, the fourth planet in their system never properly formed. The debris from the failed planet was the source of both of their moons. But there are, in the mix of asteroids, two minor planets roughly the size of their larger moon, orbiting each other. Fortunately, those two minor planets are in a stable mutual orbit around their sun that doesn't come too close to their earth, nor to their fifth full planet.

These two minor planets have fairly low albedo, and are not always visible to the naked eye on their planet. So they are sometimes called ghost twins. The common names of these two planets might be considered corollary to Freyr and Freyja.

Their fifth planet is a water ice planet about twice the size of ours. I don't have whether it has a rocky core or not in my notes, but I assume it does. It has seas of methane and continents of water ice. At some future time, when their sun begins to burn helium, that planet is destined to become habitable by life such as our own, but it now serves to harbor a different sort of life. It shines blue in their skies and is named after a god of the sea from their mythology, more similar to Ægir than to Neptune, if my notes are correct.

Their sixth planet is a gas giant with rings, similar to our Saturn. The rings are quite large, in breadth, thickness, and diameter, and are sometimes visible to the naked eye from their earth, depending on the relative angles of rotation and such. The coloring of the sixth planet in their skies varies from red to brown to violet, depending on the weather there more than on the weather of their earth. It is named after an agricultural god, but there is greater parallel to Gefjon than to Saturn.

And of course they don't see their earth in their sky, so there you have their five planets visible to the naked eye for them.

There are two more minor planets and two more full planets that they have discovered with the aid of telescopes at the time of this story, but those never entered into their historical calendars. And talking about history that is lost to them will only confuse things more. (A previous civilization whose records are lost to them now had not only telescopes but space travel.)

Both of their moons have two common names. For many purposes they are called, simply, Fastmoon and Slowmoon. But the near moon is also called after a cat god, and the far after an elephant god.


So, the days of their week: Sunday, Slowmoonday, Ægisday, Gefnday, Freyday, Tewesday or Tewsday, and Vensday. At least, that's the most popular assignment in their language at the time of our story. And I don't need to remind you that the real pronunciation is quite different.

So, you'll forgive me if I just use the names of the days of the week you are familiar with? And you'll let me skip the discussion of the names of the months and just use the months we are familiar with, as well?

Thank you. It's easier this way, I assure you.



Oh, while I'm talking about numbers, they have five fingers on each hand. This probably has something to do with most of their cultures standardizing on decimal math just like in our world. They have had other bases in common use. The tally, base two, base five, base seven, base thirty-five, and base forty-nine were each historically popular for a time in certain cultures, but that's going too far afield.

Uggh. Ninety-eight year centuries. But that was a different period, in a different culture, not the one of the present story. Sort of.

Previous TOC Next



[Backup and edit history here: http://joel-rees-economics.blogspot.com/2017/03/backup-soc500-03-07-family-games-calendars.html.]



[Chapter 3 part 7 is original to the second draft, and is not found in the first draft.]
[JMR201703132020: end-backup] 

Sociology 500, a Novel, ch 3 pt 7 -- Family Games and Calendars

Previous



On Sunday, our four protagonists were at Bobbie and Kristie's apartment playing a game similar to Pit with some of their roommates and home evening brothers. Joel was there, too, but Dan and Karel did not ask him about Kelly.

If you are not familiar with Pit, the game they were playing used a deck of cards which was divided into commodities. Pit, in it's more common form, uses cards representing commodities like wheat, rye, corn, barley, flax, and such. The object of the game is to semi-randomly trade cards with other players until someone gets all the cards of one commodity, at which point that person rigs the bell or calls out, "Corner!", and wins the round.

Or something like that.

Since trading is not done by turn, but any time a player is ready, at any point in time there are several players calling out the number of cards they want to trade. It's a very noisy game.

Which doesn't really have much to do with the plot of the story at this point. It's enough that you know they were playing the sort of game that you might play as a family.

After the fifth round, Kristie said, "I think this will be my last round for the night. I've got to get my books out and study. Would anyone care to help me with some education theory?"

Karel joined Kristie in the living room, and the two of them spread their books out on the floor. After two more rounds, Dan and Bobbie dropped out of the Pit game to join them, as well.

Michelle called out "Party poopers!" as they left the kitchen table amid laughter and jokes.

"Are you guys as far behind as I am?" Kristie asked, as they joined her and Karel in the living room.

Karel said, "We're not behind. I'm sure a week will be enough time to finish this and do the reports, too."

Bobbie said, "Everyone's behind. Even the teachers are behind. We may need to cut back on the socializing this week. And right before conference week."

Dan said, "Who talked me into coming back for post-graduate work? Remind me not to trust your suggestions next time, Karel. This is hard work."

And they all laughed and got to work, comparing notes, sharing ideas, and otherwise digging in to their assignments..

After about another half hour, the home evening brothers said they had homework and bid everyone goodnight.

A short time later, when Bobbie and Kristie's roommates had retired to their rooms, Dan leaned back and asked, "So, did Joel say anything about his partner on the folk dance team when you guys were at the dance on Friday?"

"Well, yes, he did." Kristie looked up. "Why do you ask?"

Bobbie also looked up. "Dan, didn't you say you were working with someone on the folk dance team on your ward's activities committee?"

"Really, we shouldn't be talking about this." Karel did not look up.

"So, can we infer that there is mutual interest?" Bobbie wasn't going to let the question go without an answer.

Dan said, "Yeah, ..."

And Karel said, "What is and what we should infer are two separate things. I say we keep our hands out of it."

Kristie agreed. "We really shouldn't be messing with other people's relationships."

Dan and Bobbie grinned at each other and Bobbie said, "For now."

During another break a little later, Bobbie asked Karel, "That woman I thought I saw watching us from the stacks on Tuesday, have you talked to her since?"

"Haven't seen her. I'm wondering if she's avoiding the cafeteria when I'm likely to be there."

"What happened?"

"No idea."

Maybe a half an hour later, Dan pushed his books back and said, "I'm beat. Just not focusing on the homework any more. Can we look at the rest of this tomorrow, maybe at lunch?"

Kristie looked up and nodded sleepily. "I think I'm about ready to stop for the night. Karel, did you say we could all eat at the dorm cafeteria if you showed them your residence pass?"

"Yeah, ..."

"That's a great idea," Bobbie said. "I'm done for the night. Let's let this stuff sit, and we can all focus better tomorrow."

"Okay. I'm probably done for the night, too. It's late on the Sabbath, and we're getting close to curfew anyway."



Days of the week. We hardly bother thinking about them.

But there are other ways to organize a year than in seven day weeks. Come to think of it, a month might not be roughly a twelfth of the year and a week might not be roughly a quarter of a month. Etc.

Might not be. But the world of this novel does have a calendar similar to ours. It even has some historical disagreement about whether the Sabbath was the first day of the week or the last. We don't need to know all the specifics, but we might be more comfortable talking about time if we have a bit of an overview.

Uhm, lemmesee. Where did I put those notes? Oh, here they are. 353 days per year in about five years out of seven and 352 in the other two. So they have two skip years out of seven where we have one leap year out of four.

But it isn't exact, of course. They have to further adjust that down a day every 98 years and then up one day every 343 years. Already too much detail, and you're falling asleep?

But they have two moons. Did I mention that? The smaller moon orbits their earth in just under seven and an eighth days, and their larger moon orbits it in about twenty-eight and seven eighths days. About forty-nine and a half lunar weeks a year and about twelve and a fifth lunar months each year.

So their week is really a small month, so to speak. But they set the calendar week to exactly seven days. On the other hand, their calendar big month shifts between twenty-nine and thirty days.

God has different ideas about celestial mechanics, that don't obey our mortal ideals. It's not the sort of mortal clockwork we like to make. So we use various tricks to adjust our calendars to God's.

(While I'm talking about it, the two moons look about the same size in the sky. And they are about the same size in the sky as their sun. And every century or so, they end up with the two moons and their sun nicely in a line, giving a double full eclipse. Partial double eclipses are more common, of course. And I'm really putting you to sleep now.)

Now, I'll admit it, I've been fudging on the days of the week and using the names from our world. In their world, in their language, things line up differently, even though they have named the days of the week after some old, funky, northern mythology. With the two moons and one sun and six planets visible to their naked eye, we might expect nine day weeks. But the period of the inner moon wins on the weeks, while the number twelve is close enough for their months.

Confusing? That's why I've been using our names for the days of the week and our names of the months, and I'll continue to do so. Let me look at my notes again, and tell you how the days of the week actually line up for them. And we'll see if your eyes glaze over.

The innermost planet is named after a corollary of Tewes, or Hermes, or Mercury -- a sort of messenger god in one of their predecessor civilizations.

The second, as I mentioned elsewhere, is named after a goddess of beauty and love, corollary to Venus, or maybe Frigg.

They live on their third planet, as do we. It is just a little larger than ours and, relative to their sun, in roughly the same sort of habitable zone, with similar water-carbon biology. In their time, the world they live on is a blue planet, with high water content and more surface sea than continent, again, similar to ours. And they call it a cognate of "earth", which should be of no surprise.

Big, wet clod of dirt.

Like our fifth planet, the fourth planet in their system never properly formed. The debris from the failed planet was the source of both of their moons. But there are, in the mix of asteroids, two minor planets roughly the size of their larger moon, orbiting each other. Fortunately, those two minor planets are in a stable mutual orbit around their sun that doesn't come too close to their earth, nor to their fifth full planet.

These two minor planets have fairly low albedo, and are not always visible to the naked eye on their planet. So they are sometimes called ghost twins. The common names of these two planets might be considered corollary to Freyr and Freyja.

Their fifth planet is a water ice planet about twice the size of ours. I don't have whether it has a rocky core or not in my notes, but I assume it does. It has seas of methane and continents of water ice. At some future time, well before their sun begins to burn helium, that planet is destined to become habitable by life such as our own. But it now serves to harbor a different sort of life. It shines blue in their skies and is named after a god of the sea from their mythology, more similar to Ægir than to Neptune, if my notes are correct.

Their sixth planet is a gas giant with rings, similar to our Saturn. The rings are quite large, in breadth, thickness, and diameter, and are sometimes visible to the naked eye from their earth, depending on the relative angles of rotation and such. The coloring of the sixth planet in their skies varies from red to brown to violet, depending on the weather there more than on the weather of their earth. It is named after an agricultural god, but there is greater parallel to Gefjon than to Saturn.

And of course they don't see their earth in their sky, so there you have their five planets visible to the naked eye for them.

There are two more minor planets and two more full planets that they have discovered with the aid of telescopes at the time of this story, but those never entered into their historical calendars. And talking about history that is lost to them will only confuse things more. (A previous civilization whose records are lost to them now had not only telescopes but space travel.)

Both of their moons have two common names. For many purposes they are called, simply, Fastmoon and Slowmoon. But the near moon is also called after a cat god, and the far after an elephant god.


So, the days of their week: Sunday, Slowmoonday, Ægisday, Gefnday, Freyday, Tewesday or Tewsday, and Vensday. At least, that's the most popular assignment in their language at the time of our story. And I don't need to remind you that the real pronunciation is quite different.

So, you'll forgive me if I just use the names of the days of the week you are familiar with? And you'll let me skip the discussion of the names of the months and just use the months we are familiar with, as well?

Thank you. It's easier this way, I assure you.



Oh, while I'm talking about numbers, they have five fingers on each hand. This probably has something to do with most of their cultures standardizing on decimal math just like in our world. They have had other bases in common use. The tally, base two, base five, base seven, base thirty-five, and base forty-nine were each historically popular for a time in certain cultures, but that's going too far afield.

Uggh. Ninety-eight year centuries. But that was a different period, in a different culture, not the one of the present story. Sort of.

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[Backup and edit history here: http://joel-rees-economics.blogspot.com/2017/03/backup-soc500-03-07-family-games-calendars.html.]



[Chapter 3 part 7 is original to the second draft, and is not found in the first draft. Chronologically, it would come in chapter five of the first draft: http://free-is-not-free.blogspot.com/2016/05/economics-101-novel-ch05-first-semester.html.]