Joel's Fantasy Economics

The Novels

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? Study economics?

Sociology 500, a Romance (Second Draft) -- The first book in the Economics 101 Trilogy.(On hold.)

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.

Saturday, April 8, 2017

Backup: Sociology 500, a Novel, ch 3 pt 9 -- Calculating Months in Skip Years

[JMR201704101934: edits -- forgotten structure.]

[Backup and edit history {replace}will eventually be{with}are{replace.} here: http://joel-rees-economics.blogspot.com/2017/04/backup-soc500-03-09-calculating-months-skip-years.html.]

[JMR201704101934: end-edits.]

[JMR201704082007: edits -- minor stuff.]

To which Professor Billings said, "Ted is being kind enough to loan it to the department." The department had had to {replace}scramble{with}scrounge{replace.} for the budget for the electricity, and we'll find out more about that later. The professor {replace}added{with}asked{replace.}, "Do you have the printout with you?"

[JMR201704082007: end-edits.]

[JMR201704081836: backup of http://joel-rees-economics.blogspot.com/2017/04/soc500-03-09-calculating-months-skip-years.html.]

TOC

Ted picked up the model of the solar system and demonstrated the orbit of their planet again. "We should focus the children's attention on the tilt of the earth, as Jack diagrammed. It would probably be good to review the reasons for the seasons."

Georgia asked, "When the north pole is tilted towards the sun, that's summer for us in the northern hemisphere, right?"

Professor Billings asked, "Anyone still not clear on that point? You don't want to find yourself in class, wondering which is which, with students looking at you and expecting you to know all the answers."

Jack asked, "Isn't the physics of the seasons obvious? I mean, we would expect to not even need that model in high school, right?"

Karen complained. "It's obvious to you. I'm still trying to figure it out. Is the sun that much closer to us in summer?"

"Yeah," Jack replied sarcastically. "A fraction of a percent makes that much difference."

"Jack, you'll confuse people." said Merill. "Karen, think of the sun against your car roof. At an angle, the light tends to reflect more."

Jack grumbled. "Maybe, maybe not."

"Okay," Karen said hesitantly. "I can see the angle being important. There was a teacher who explained it to us as distance when I was in elementary school, and I've been confused since then."

Ted said, "Well, it is partly distance, but the distance that is relevant is the distance through the atmosphere due to the angle, not the distance from the sun. But, more basically, like Merill says, the angle reduces the amount of sunlight that reaches the surface. And that's more important." And he drew a diagram on the chalkboard, of sunlight hitting their earth:

Karen still looked puzzled. "I'm not seeing it."

So Kristie stood up and said, "There's another way to draw that diagram that helped me." And she drew a second version of the diagram, using a polygon instead of a circle:

"It helped me see that the deeper angle reduces the amount of sunlight for the same amount of surface area." Then she picked up a textbook and held it in front of a window, rotating it to show the area being struck by sunlight. "Like this."

Karen thought a few moments and said, "Thanks, I think I can see that."

Kristie gave the chalk back to Ted and he started started writing out a chart on the chalkboard.

Dan grumbled. "You and Karel."

Kristie smiled as she sat down, and members of the class who knew our four protagonists laughed.

Karen continued after some thought, "I think I can probably draw diagrams like that in a class."

While Ted wrote, Professor Billings pointed out, "This kind of discussion often does much more than a lecture." He paused. "You may feel a little out of control, during the discussion, but I strongly urge you to learn to use this kind of discussion, in every grade you teach."

Ted turned around. "And if we can get the students to draw the diagrams and write the math on the board themselves, that works even better, right?"

"You've heard it before."

General laughter.

"So," Ted returned to the board, to the left of the chart he had been working on, and said, "if we can satisfy the students about the measured length of the solar year, we can tell them that the length of the year is three hundred fifty-two whole days and four hundred eighty-five six eighty-sixths of a day. But we probably want to show them decimal fractions, too:

1 year: 352 485/686 days (about 352.7070)

Carl asked, "How do we connect that with sevens?"

Dan said, "Write the factors on the board, two times seven cubed."

Ted stopped, and he and many of the students turned to look at Dan.

"What? I didn't say I couldn't do any math at all, just not comfortable with some of it." Dan was grinning sheepishly.

More laughter, which Ted and Dan joined as Ted wrote out the factors on the board:

2 × 7 = 14, 14 × 7 = 98
98 × 7 = 686, 686 ÷ 2 = 343

Dan continued, "And we could work out the decimal fraction, to show how close it is to five sevenths. Should I work that out?"

Professor Billing smiled and held up a piece of chalk, which Dan took to a chalkboard at the side of the room, to show the long division for 5/7 and 485/686:

   0.714287             0.70699
-----------      -------------
7| 5.0000000     686| 485.0000000
   4.9                480.2
   10                 4.800
     07                 4.116
      30                  6840
28                  6174
   20                  6660
   14                  6174
60                  4860
        56
   40
       35
        50

And Dan sat down.

Carl pressed the question. "Is that the closest small fraction?"

Ted said, "Actually, I've got a chart of fractions that I printed up on the computer, where we can get a look at that question."

There were some complaints.

"Braggart."

And, "How come he's so lucky?"

Etc.

To which Professor Billings said, "Ted is being kind enough to loan it to the department." The department had had to scramble for the budget for the electricity, and we'll find out more about that later. The professor added, "Do you have the printout with you?"

"Yeah."

"I'll go get the overhead projector."

"I'll help you," Mark volunteered, and Mark followed the professor into the prep room as Ted went back to writing on the board.

Do you remember those heavy, hot, smelly, fragile overhead projectors we used to use, back in the 1950s and '60s? And big. That was what Mark and the professor emerged carrying. They set it up on a desk in front of a screen and plugged it into the wall to get the lamp warming up while Ted continued his explanation.

"We probably want to ask how many months in a year and show the division:"

1 ideal month: 352.7070 ÷ 12 = 29.39225 days

"Ideal month?" queried the professor.

"We can say it's some crazy professor's idea of a better month, but it isn't a real month."

"That explanation of ideal might work."

Ted continued, "Here's a question I think young kids will find interesting: If we used this exact length for the month, at what hour of the day on January 30th would it become February 1st?" And he showed them where he had written out the math for that, to the side of the still incomplete chart:

0.39225 * 24 = 9.414 hours
0.414 * 60 = 24.84 minutes
Before 9:25 A.M., January 30th.
After 9:25, February 1st.

While the other students absorbed that, he continued, "Then we can ask whether they would think it interesting for January thirtieth to suddenly turn into February first at about nine twenty five in the morning."

Jack suggested, "That's going to get some students excited, maybe too excited."

Dan chuckled. "It's the kind of thing Karel would say just as we split up for our specialty practice. Make sure we had plenty of time to think about it."

Kristie suggested, "Maybe you could save it until just before lunchtime? then the students would have lots of time to talk about it and forget their excitement."

Jack scratched his head. "Maybe, if you could get the timing right."

The professor was chuckling. He suggested, "Ted, let's look at your chart of fractions."

Ted dug a computer printout out of his books and handed it to the professor, who put it on the overhead projector's light stage.

: PRCH EMIT ;

: COMMA 44 PRCH ;
: COLON 58 PRCH ;

( No trailing space. )
: PSNUM ( number -- )
0 .R ;

: NUMERATORS ( count -- )
DUP 1+ 0 DO
   I PSNUM COLON SPACE
   I 1000 * OVER / PSNUM COMMA ( 1000 times I divided by count )
   SPACE LOOP
DROP ;

: FRACTIONS ( count -- )
CR
1+ 1 DO
   I PSNUM SPACE I NUMERATORS CR
LOOP ;

"What's this?"

"That's the program."

Okay, it isn't exactly the program code he showed. Although the colon and semicolon were similar, most of the characters did not look much like our Latin-based alphabet. And I've translated it into symbols derived from English.

But the postfix grammar was surprisingly similar to the language Forth.

Maybe not so surprising, if we consider what a progressive definition grammar would naturally look like.

I made sure the translation would run in most Forth interpreters, if you are interested in trying it out. It definitely works in gforth, which is relatively easy to get for most PCs and for Android phones. Probably the easiest way to get it on a MSWindows PC is to go to the Cygwin site and install that, then use Cygwin's installer to get gforth. Android's Play Store has it, and, if you are using a Linux OS, it is probably in the packages.

(It also runs in my bif-c interpreter, but that is not easy to get if you aren't into compiling things yourself.)

In our world, it would have been a few more years before Forth became somewhat available, but we'll hear more about that later.

Professor Billings moved the printout down on the staging table to show the chart:

9 fractions
1 0: 0, 1: 1000,
2 0: 0, 1: 500, 2: 1000,
3 0: 0, 1: 333, 2: 666, 3: 1000,
4 0: 0, 1: 250, 2: 500, 3: 750, 4: 1000,
5 0: 0, 1: 200, 2: 400, 3: 600, 4: 800, 5: 1000,
6 0: 0, 1: 166, 2: 333, 3: 500, 4: 666, 5: 833, 6: 1000,
7 0: 0, 1: 142, 2: 285, 3: 428, 4: 571, 5: 714, 6: 857, 7: 1000,
8 0: 0, 1: 125, 2: 250, 3: 375, 4: 500, 5: 625, 6: 750, 7: 875, 8: 1000,
9 0: 0, 1: 111, 2: 222, 3: 333, 4: 444, 5: 555, 6: 666, 7: 777, 8: 888, 9: 1000,

He used a pen to trace through the listing. "Okay, these are the first three digits to the right of the decimal point, right?"

"Right. So we can see that 0.714 in the fives column of the sevens row is about the closest fraction less than ten."

Jack was still doubtful. "But seven tenths is closer than five sevenths."

"Well," Carl spoke up again, "When somebody way back there in our history first set up our modern calendar, he wouldn't have even had mechanical calculators, and the numbering system wasn't always base ten. And it took several centuries to get the length of the year accurately measured, didn't it?"

While the rest of the class talked about this, Ted finished his chart on the chalkboard.

"What's this?" Professor Billings asked, as he slid the listing across the stage table so the class could see it:

7 showmonths

0 0: 30 (30, 29.392 )
0 1: 29 (59, 58.784 )
0 2: 30 (89, 88.177 )
0 3: 29 (118, 117.569 )
0 4: 29 (147, 146.961 )
0 5: 30 (177, 176.353 )
0 6: 29 (206, 205.746 )
0 7: 30 (236, 235.138 )
0 8: 29 (265, 264.530 )
0 9: 29 (294, 293.922 )
0 10: 30 (324, 323.315 )
0 11: 29 (353, 352.707 )

1 0: 30 (383, 382.099 )
1 1: 29 (412, 411.491 )
1 2: 29 (441, 440.884 )
1 3: 30 (471, 470.276 )
1 4: 29 (500, 499.668 )
1 5: 30 (530, 529.060 )
1 6: 29 (559, 558.453 )
1 7: 29 (588, 587.845 )
1 8: 30 (618, 617.237 )
1 9: 29 (647, 646.629 )
1 10: 30 (677, 676.022 )
1 11: 29 (706, 705.414 )

2 0: 29 (735, 734.806 )
2 1: 30 (765, 764.198 )
2 2: 29 (794, 793.591 )
2 3: 29 (823, 822.983 )
2 4: 30 (853, 852.375 )
2 5: 29 (882, 881.767 )
2 6: 30 (912, 911.160 )
2 7: 29 (941, 940.552 )
2 8: 29 (970, 969.944 )
2 9: 30 (1000, 999.336 )
2 10: 29 (1029, 1028.729 )
2 11: 30 (1059, 1058.121 )

3 0: 29 (1088, 1087.513 )
3 1: 29 (1117, 1116.905 )
3 2: 30 (1147, 1146.298 )
3 3: 29 (1176, 1175.690 )
3 4: 30 (1206, 1205.082 )
3 5: 29 (1235, 1234.474 )
3 6: 29 (1264, 1263.867 )
3 7: 30 (1294, 1293.259 )
3 8: 29 (1323, 1322.651 )
3 9: 30 (1353, 1352.043 )
3 10: 29 (1382, 1381.436 )
3 11: 29 (1411, 1410.828 )

4 0: 30 (1441, 1440.220 )
4 1: 29 (1470, 1469.612 )
4 2: 30 (1500, 1499.005 )
4 3: 29 (1529, 1528.397 )
4 4: 29 (1558, 1557.789 )
4 5: 30 (1588, 1587.181 )
4 6: 29 (1617, 1616.574 )
4 7: 29 (1646, 1645.966 )
4 8: 30 (1676, 1675.358 )
4 9: 29 (1705, 1704.750 )
4 10: 30 (1735, 1734.143 )
4 11: 29 (1764, 1763.535 )

5 0: 29 (1793, 1792.927 )
5 1: 30 (1823, 1822.319 )
5 2: 29 (1852, 1851.712 )
5 3: 30 (1882, 1881.104 )
5 4: 29 (1911, 1910.496 )
5 5: 29 (1940, 1939.888 )
5 6: 30 (1970, 1969.281 )
5 7: 29 (1999, 1998.673 )
5 8: 30 (2029, 2028.065 )
5 9: 29 (2058, 2057.457 )
5 10: 29 (2087, 2086.850 )
5 11: 30 (2117, 2116.242 )

6 0: 29 (2146, 2145.634 )
6 1: 30 (2176, 2175.026 )
6 2: 29 (2205, 2204.419 )
6 3: 29 (2234, 2233.811 )
6 4: 30 (2264, 2263.203 )
6 5: 29 (2293, 2292.595 )
6 6: 29 (2322, 2321.988 )
6 7: 30 (2352, 2351.380 )
6 8: 29 (2381, 2380.772 )
6 9: 30 (2411, 2410.164 )
6 10: 29 (2440, 2439.557 )
6 11: 29 (2469, 2468.949 )
ok

"I calculated out a chart to show how the lengths of months would mesh with the lengths of days cumulatively across seven years. It might be useful for demonstrating how variable a calendar would be if we didn't use something like skip years. Typing it up for a duplicator would be a lot of work. But you can see how the first year in that chart looks a lot like the calendar we use."

The professor moved the chart back up to year zero and let the students look it over. Then he asked, "How hard would it be to go to 700 years, so we could get a look at the entire cycle?"

"Waste of paper and ink, I'd say. Also, I'd have to fix part of the program that can only calculate to a bit more than thirty thousand days."

"Oh. So even a hundred years is going to be too many, then?"

"If I don't fix it."

"Well, it would be nice to pass this table out to everyone. Anyone want to type it up for the duplicator?"

Xerography was still too expensive to substitute for stencil or spirits duplicators, so copying out material like this still required a lot of manual labor. Georgia and Karen volunteered to type it up.

And this chapter is getting a bit long, so I'm going to arbitrarily end it here so you and I can take a break.

TOC

[Backup and edit history will eventually be here: http://joel-rees-economics.blogspot.com/2017/04/backup-soc500-03-09-calculating-skip-years.]

[Chapter 3 part 9 is original to the second draft, and is not found in the first draft. Chronologically, it would be placed in chapter five of the first draft: http://free-is-not-free.blogspot.com/2016/05/economics-101-novel-ch05-first-semester.html.]
[JMR201704081836: end-backup.]

Friday, April 7, 2017

Sociology 500, a Novel, ch 3 pt 9 -- Calculating Months in Skip Years

TOC

1 year: 352 485/686 days (about 352.7070)

2 × 7 = 14, 14 × 7 = 98
98 × 7 = 686, 686 ÷ 2 = 343

   0.714287             0.70699
-----------      -------------
7| 5.0000000     686| 485.0000000
   4.9                480.2
   10                 4.800
     07                 4.116
      30                  6840
28                  6174
   20                  6660
   14                  6174
60                  4860
        56
   40
       35
        50

And Dan sat down.

Carl pressed the question. "Is that the closest small fraction?"

Ted said, "Actually, I've got a chart of fractions that I printed up on the computer, where we can get a look at that question."

There were some complaints.

"Braggart."

And, "How come he's so lucky?"

Etc.

To which Professor Billings said, "Ted is being kind enough to loan it to the department." The department had had to scrounge for the budget for the electricity, and we'll find out more about that later. The professor asked, "Do you have the printout with you?"

"Yeah."

"I'll go get the overhead projector."

"I'll help you," Mark volunteered, and Mark followed the professor into the prep room as Ted went back to writing on the board.

Do you remember those heavy, hot, smelly, fragile overhead projectors we used to use, back in the 1950s and '60s? And big. That was what Mark and the professor emerged carrying. They set it up on a desk in front of a screen and plugged it into the wall to get the lamp warming up while Ted continued his explanation.

"We probably want to ask how many months in a year and show the division:"

1 ideal month: 352.7070 ÷ 12 = 29.39225 days

0.39225 * 24 = 9.414 hours
0.414 * 60 = 24.84 minutes
Before 9:25 A.M., January 30th.
After 9:25, February 1st.

And this chapter is getting a bit long, so I'm going to arbitrarily end it here so you and I can take a break.

TOC

[Backup and edit history are here: http://joel-rees-economics.blogspot.com/2017/04/backup-soc500-03-09-calculating-months-skip-years.html.]

Wednesday, April 5, 2017

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

[JMR201704052226: edits -- Taking care of some clumsy points.]

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 {replace}partway through{with}a little after{replace.} Professor Billings's lesson{add} began{add.}.

----------

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

{add}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?

<add.}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."

----------

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

----------

"Okay, let's compare {replace}cookies{with}recipes{replace.} after class{replace}.{with}," the professor laughed. "{relace.}So where do we go from here?"

----------

"{replace>H{with}Again, h{replace.}ow many weeks in a regular year?"

----------

Georgia answered, "Three fifty-two divided by seven is fifty with two days left over. {replace}Wait. J{with}But, j{replace.}ust one day less, so, of course fifty weeks with just two days left over."

----------

"Good question. Anyone?{replace} {with}

Ted raised his hand.

{replace.}Ted?"

----------

{add>The professor asked, {add.}"Do you think you could explain that to elementary school children?"

----------

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

----------

{replace}Mirium turned{with}Turning{replace.} to the professor{replace}.{with}, she asked,{replace.} "Then, should I just finish the math out myself?"{delete} she asked.{delete.}

[JMR201704052226: end-edits ]

[JMR201704052217: backup of http://joel-rees-economics.blogspot.com/2017/03/soc500-03-08-calendar-math.html.]

TOC

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 partway through Professor Billings's lesson.

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?"

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 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 cookies after class. 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

"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. Wait. 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?"

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."

"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 Mirium continued. "Now, is it always going to be like this?" Mirium 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.

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

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.

TOC

[Backup and edit history will be here: http://joel-rees-economics.blogspot.com/2017/03/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.]
[JMR201704052217: end-backup]

Wednesday, March 29, 2017

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

TOC

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

352 ÷ 7 = 50 rem 2, or 50 2/7, or 50.285714

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.

TOC

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

TOC

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.

TOC

[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

TOC

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.

TOC

[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.]

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Sociology 500, a Novel, ch 3 pt 9 -- Calculating Months in Skip Years

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

Monday, March 13, 2017

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

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