It also marks six full years since my very first post here on the blog. Yes, I've declared Pi Day of the Century -- March 14th, 2015, to be the ceremonial start date of this blog. But the chronological start date was July 22nd, 2014. I like celebrating both Pi Day and Pi Approximation Day -- including eating pie both days -- and so I celebrate both of them as launch dates for the blog.
This year, it is also National Hot Dog Day. It's always on a Wednesday in July -- usually it's the third Wednesday of the month, but for some reason this year the North American Meat Institute declared it to be the same as Pi Approximation Day. (Perhaps a Wednesday in the 16th-22nd range is preferred to one in the 15th-21st range.)
I celebrate both holidays today by eating a $1 Big Bite from 7-Eleven along with some pie. My pie of choice for Pi Approximation Day (or Casual Pi Day) is apple -- there's nothing more American than hot dogs, apple pie, and (the Fourth of) July.
Last year, I used the anniversary to create a FAQ about my blog and myself. I do the same this year -- and this year's FAQ is very different from last year's because I'm focusing on many coronavirus-related questions. As usual, let me include a table of contents for this FAQ:
1. Who am I? Am I a math teacher?
2. How will the coronavirus affect my current employment?
3. What is the Eleven Calendar?
4. What are some possible hybrid schedules?
5. What is the actual reopening plan in my old district?
6. Who is Laura Lemay, and why am I learning Java?
7. What's "Mocha music"?
8. Who is Rebecca Rapoport?
9. What is Shapelore?
10. Who is Ian Stewart, and why am we reading Chapter 11 today?
11. How will the coronavirus school plans affect this blog?
1. Who am I? Am I a math teacher?
I am David Walker. I'm trying to start a career as a math teacher, but I must admit that my career isn't off to as good a start as I'd like.
Four years ago was my first as a teacher at a charter middle school, but I left that classroom. By now, I fear that I won't be hired to teach this year at all. If I'm not hired, then I'll remain a substitute teacher. But this will make the launch of my teaching career that much more difficult.
By the way, in last year's FAQ I mentioned that my old charter school had but shut down due to financial mismanagement. Well, I found out recently that the leader of that school has pleaded guilty and now faces jail time. What I'd believed was carelessness has just become criminal.
I have absolutely nothing to do with my old school's financial problems. Still, I fear that having that school listed on my resume might raise a few eyebrows at schools that I apply to. I worry that my association with my old charter might cause other schools not to hire me.
So the answer to this question is no, I'm not currently a math teacher, but I'm hoping that I'll be one again soon.
2. How will the coronavirus affect my current employment?
I currently work as a substitute teacher in two districts here in Southern California. In my last post, I wrote that one of these districts has come up with a school reopening plan. But that was before Governor Newsom intervened.
Last Friday, he declared that all schools in counties on the coronavirus "watch list" must remain closed until such counties are removed from said watch list. Placement on the watch list depends on the number of coronavirus cases in the county as well as the availability of hospitals.
For obvious reasons, almost all urban and suburban counties are on the watch list -- indeed, the southernmost county not on the watch list is Kern County (Bakersfield, McFarland, etc.). This means that all schools south of Kern County will start the year with distance learning only.
So far, I've avoided naming the counties that my school is in, except to say that they are near the city of Los Angeles, and that they are in different counties. (This was two years ago, when a proposal to divide California into three states nearly made the ballot -- the new state lines would have followed county lines, and my two districts would have landed in different states.)
But since county lines are very relevant to the reopening plans, I might as well finally name the counties now. The district where I've been employed longer (my "old district," where I've worked almost the whole time I've had this blog, except for the time I left for the charter) is in LA County, and the other district (my "new district," where I've worked only since leaving that charter) is in Orange County.
I am currently a substitute teacher. Regular teachers will get paid for teaching online, and I've heard that some other school workers who get paid monthly will still receive a salary. But unfortunately, substitute teachers get paid by the gig -- as long as schools remain online only, the total amount of money I'll make will be $0.
And that's the problem -- no one knows how long my counties will remain on the watch list. I wouldn't be surprised if they're on the watch list the entire school year -- which would mean that my total income between now and next Pi Approximation Day will be $0. One might think that at least Orange County might have a better chance of reopening before LA County, if only because Orange County doesn't contain the big city of LA. But I've heard that no -- in fact, the virus is actually spreading more in Orange County than in LA County.
The school reopening issue is a contentious one. Many people, including parents, worry about the spread of the disease and would rather err on the side of caution. They want the schools to remain closed as long as virus is spreading. Others disagree -- they feel that the probability of an individual under 75 or 80 dying of the virus, rounded to the nearest percent, is 0% Thus they believe that schools and other businesses should remain open in order to avoid ruining the economy. (These two sides correspond roughly to political parties, but let's keep politics out of this.)
I'm going to state my biases up front -- I'm in favor of the schools reopening. It's not because I think that the likelihood of catching the virus is near 0% -- it's just right now, the only 0 I'm worried about is the zero after a $ sign, not the one before the % sign. And I'm biased in favor of the economy -- as in my personal bank account.
Don't get me wrong. I care deeply about our students and want them to remain safe -- let's not put them in any more risk than we have to. So my question is -- is there a way to keep our kids safe and for me, as a sub, to have an income greater than $0 over the upcoming year?
Over these past few months, I've been thinking about what a reopening plan should look like. I was waiting until today's FAQ to post it -- though I admit that I was thinking about this plan before Governor Newsom made his statement last Friday.
And my solution is simple -- the first step is the immediate adoption of the Eleven Calendar. (Note: this part is tongue-in-cheek. You may skip over this section and move ahead to the next section, which involves realistic solutions that don't involve changing the calendar.)
3. What is the Eleven Calendar?
The Eleven Calendar is my original contribution to Calendar Reform -- that is, the idea of replacing our current Gregorian Calendar with a different calendar. I mentioned the Eleven Calendar as part of last year's FAQ:
If you were to choose a number and invent a calendar based on that number, your calendar will probably not be original -- someone else would have already thought of your idea. Consider the neighbors of 11 -- 10 and 12. Well, there's already 12 months in our current Gregorian Calendar, while the ancient Egyptian calendar used 10 days per week ("decans"). And suppose you were to look at the prime neighbors of 11 -- 7 and 13. Of course, the Gregorian Calendar has seven days per week, while the International Fixed Calendar has 13 months per year.
Despite all of this, no existing calendar is based on 11. And so, I decided to create my own Eleven Calendar.
Suppose we want there to be eleven months per year. Then since a year contains 365 days, we divide 365/11 to obtain 33.18.... If we round this to 33 days, we notice that 33 is itself a multiple of 11. And so each 33-day month contains three weeks of 11 days each.
At this point last year, I started writing more about the monthly structure of the new calendar. But now I wish to focus more on the days and weeks in the calendar.
Only once on the blog did I mention what the school week would look like on the Eleven Calendar:
Finally we'll look at my own Eleven Calendar. Again, I like having six weekdays as this works well with block schedules. So there are now five days off from school.
But I don't propose having a five-day weekend. Instead, there will be four-day weekends -- and the fifth off day is used to break up the six-day week! So we have three days of school, a midweek break, three more school days, and then the four-day weekend.
I actually got the idea from another calendar -- the Triday Calendar:
https://www.hermetic.ch/cal_stud/ltc/ltc.htm
Currently most business run for five days out of seven and shut down for two. This 2-day interruption is inconvenient and reduces efficiency. On Friday afternoon employees and the business overall are winding down at the end of the week, and they require most of Monday morning to start up again. So the business is either not running or is running at half-pace for ½ + 2 + ½ = 3 days out of 7.
Businesses would be more efficient if they never shut down. Since employees (and employers) need time to lead their own lives a solution is for the business to run continuously without a break but to have only half the personnel at work on any given day. The Liberalia Triday Calendar accords well with such an arrangment, as will now be shown.
The simplest work scheme is to have two teams of personnel who work on alternating tridays, as follows
Here a "triday" refers to a three-day "week," but the actual cycle for workers consists of six days -- three days of work followed by three off days.
But now I'm trying to apply this idea to the coronavirus. We wish to divide the students into two shifts, with only one shift attending school on any given day. Then each class would be only half the size of a regular class, thereby allowing more space for social distancing.
How many school days would there be in a calendar year? Well, each student attends school for half the days, so we can just barely squeeze in 180 days. But that would mean that there's no room for holidays or summer break -- the most number of consecutive off-days is three. As much as students and teachers may like a three-day school week and a three-day weekend, they wouldn't want to lose summer or other breaks to pay for it.
When I first came up with this idea, I considered 180 days to be sacred (especially considering that many other countries have students attend more than 180 days). So I wish to come up with an idea similar to the Triday Calendar, with the following properties:
- More than half the days in the week are weekdays. (That way, the number of weekdays in a year is over 180, so that we can cut out the excess weekdays over 180 as vacation days.)
- There is a midweek day off.
- The midweek day off divides the workweek into two equal halves.
- The weekend is longer than a half-workweek.
There's a reason for the midweek off-day. Indeed, there were previous attempts to implement a calendar similar to this one -- the French and Russian Revolutionary Calendars. The French Calendar had a ten-day week, while the Russian Calendar had either five- or six-day weeks. But in both of these calendars, family members on different shifts might have different off-days, which was inconvenient for family life.
(Notice that even to this day, some French schools have a midweek day off, as I mentioned recently in another post. I wonder whether it's a relic of a ten-day week when a midweek off-day was needed.)
OK, so let's say our calendar has n workdays, 1 day off, n workdays, and n + 1 days off. We then check for each value of n until we get one with more total workdays than off-days:
n = 1: This gives 1 day on, 1 day off, 1 day on, 2 days off. There are only 2/5 workdays -- too few.
n = 2: This gives 2 days on, 1 day off, 2 days on, 3 days off. There are 4/8 workdays -- exactly half, which is still too few, but we're getting closer!
n = 3: This gives 3 days on, 1 day off, 3 days on, 4 days off. There are 6/11 workdays -- this is enough, and of course, it's what I propose for the Eleven Calendar.
And so my original idea was to divide the school into 11 cohorts. Each cohort attends school only six of the 11 days, and so only six cohorts attend school each day, which allows for social distancing.
Of course, this is quite complex. The reason is because students attend more than half the week, in order to squeeze 180 school days into the calendar year.
But in the coronavirus era, it's permissible for students to attend fewer than 180 days -- the idea being that students have online education the other days. Since students have a combination of online and in-person classes, this is often referred to as a hybrid schedule.
The simplest way to make a hybrid schedule on the Eleven Calendar is to have two shifts -- one of them attends school for the first five days, the other attends school the next five days, and then both shifts have the eleventh day off.
I've labeled the days of the Eleven Calendar week in various ways. The easiest is simply to number them from 1 to 11. In some posts, I labeled the first three days "Friday," "Saturday," and "Sunday" -- the three Abrahamic Sabbaths. Then the remaining days are labeled Fourday through Elevenday.
(For those of you who are curious, today, Pi Approximation Day, is Friday, the first day of the week.)
Since the USA is a majority Christian nation, we'd expect American schools to choose Sunday as the common day off. Schools in the Middle East might choose Friday as the day off, while Israel might select Saturday.
For the rest of this post, let's follow the American plan. One shift attends school from Fourday until Eightday, and the second shift goes Nineday, Tenday, Elevenday, Friday, Saturday. Both shifts are off on Sunday, the Christian Sabbath.
Five-Day Hybrid: Fri. Sat. Sun. 4 5 6 7 8 9 10 11
Shift A x x x x x
Shift B x x x x x
OK, so students attend school five days and are off for six days, but what about teachers? In theory, teachers could work both shifts, but then they'd be working 10 out of 11 days. But if we instead have teachers only work one shift, then we'd need twice as many teachers -- at a time when school budgets are being cut due to falling tax revenues.
So instead, let's divide the school into three shifts. Students will attend one of the three shifts, while teachers work two of the three shifts.
On the Eleven Calendar, each shift will be three days. Then three shifts add up to nine days, so we can have two common days off for everyone. One of these days is Sunday, the Christian Sabbath. We will follow American tradition and let the other common day off be Saturday, the Jewish Sabbath.
This means that the first shift attends Fourday through Sixday, the second shift Sevenday through Nineday, and the third shift Tenday, Elevenday, Friday:
3-Day Hybrid #1: Fri. Sat. Sun. 4 5 6 7 8 9 10 11
Shift A x x x
Shift B x x x
Shift C x x x
It's also possible for the three shifts to attend every third day instead. So the first shift attends Fourday, Sevenday, Tenday, the second shift Fiveday, Eightday, Elevenday, and the third shift Sixday, Nineday, Friday:
3-Day Hybrid #3: Fri. Sat. Sun. 4 5 6 7 8 9 10 11
Shift A x x x
Shift B x x x
Shift C x x x
Here the numbering of these hybrid plans as #1 and #3 is intentional -- the 3 in #3 stands for "every third day" or "three days apart," while the 1 in #1 implies that the school days are "one day apart" (that is, consecutive).
Is it possible for there to be a 3-Day Hybrid #2? I'm sympathetic for a schedule with classes two days apart here. After all, recall that these are hybrid schedules in that students are supposed to have distance learning between the in-person days. If the school days are two days apart, then the students can go online on the in-between days.
With 3-Day Hybrid #1, all the online days must be before or after the in-person part of the week. And with 3-Day Hybrid #3, the two days off in between school days might cause students to slack off -- consider the reason that teachers are loath to give tests on Mondays. The #2 schedule seems to be just right -- enough time for distance learning, less time to slacking off.
Here's a possible #2 schedule: the first shift works Fiveday, Sevenday, Nineday, the second works Sixday, Eightday, Tenday, and the third works Elevenday, Saturday, Fourday:
3-Day Hybrid #2: Fri. Sat. Sun. 4 5 6 7 8 9 10 11
Shift A x x x
Shift B x x x
Shift C x x x
Note that instead of Saturday off, this plan now has the two off-days be Friday (the Islamic Sabbath) and Sunday (the Christian Sabbath). It's a great schedule for a school which has a significant number of both Christians and Muslims (and such schools exist here in Southern California). The third shift crosses both Sabbaths, but doesn't have school on either Sabbath (except the Jewish one of course).
It's also possible to make a 5-Day Hybrid #2 as well. I didn't take the time to write it out, since I assume that with no more than two off-days in a row, no one would want it. (The two-day stretch of off days would be Sunday and whichever of Saturday, Fourday is an off day for your shift.)
While I claim that Hybrid #2 is most student-friendly, neither #2 nor #3 are teacher-friendly, if we assume that teachers work two of the three shifts. For #2, any teacher who works Shift C and one of the other two shifts will make the workdays be very much spread out. The same is true for #3 for a teacher whose two shifts are A and C.
Hybrid #1 is the most teacher-friendly. Shifts A and C would have the teachers go 3 on, 2 off, 3 on, 3 off (very much like my original Eleven Calendar week). If we combine Shift B with one of the other shifts, then teachers work six straight days. While teachers might wish that there was a day off in the middle of the six-day week, at least they get a five-day weekend.
All of these plans assume that we're switching to the Eleven Calendar. I already know that this isn't really going to happen. So now let's see what these hybrids look like on our real seven-day calendar.
4. What are some possible hybrid schedules?
The Five-Day Hybrid is easy to figure out -- one shift simply attends school for one week while the other shift attends the following week. The weekends don't change, and so teachers end up working a regular school week and year, switching between the two cohorts of students week by week.
The other hybrids where students attend every second or third day are a bit more complex. It's possible to do this naively -- number the days of the school year from 1 to 180. Then if there are two shifts, have one shift attend odd days and the other attend even days. And if there are three shifts, then have one shift attend Days 1, 4, 7, ... 178, the second attend Days 2, 5, 8, ..., 179 and the third attend on the multiples of three.
Here I assume that teachers work two of the three shifts. (Notice that during the year I was at the old charter school, I blogged on Days 1, 2, 4, 5, 7, 8, and so on -- all the non-multiples of three. Thus I was unwittingly following this hybrid schedule for blogging, years before the pandemic.)
The problem with these hybrids is that they don't readily correspond to the day of the week. Indeed, a student might attend class on Monday, Wednesday, Friday one week and Tuesday, Thursday the next, or Monday, Thursday the first week and Tuesday, Friday the second. And of course, this happens because the number of weekdays, five, isn't a multiple of two or three.
To fix this, we can consider Saturday to be a workday, with Sunday (the Christian Sabbath) as the only day off. (In the Middle East, Friday can be the only off-day, while in Israel, Saturday can be the only day off.)
Using Sunday as the Sabbath, this results in the following hybrid schedules:
3-Day Hybrid #1: M Tu W Th F Sa
Shift A x x x
Shift B x x x
3-Day Hybrid #2: M Tu W Th F Sa
Shift A x x x
Shift B x x x
2-Day Hybrid #1: M Tu W Th F Sa
Shift A x x
Shift B x x
Shift C x x
2-Day Hybrid #2: Sa M Tu W Th F
Shift A x x
Shift B x x
Shift C x x
2-Day Hybrid #3: M Tu W Th F Sa
Shift A x x
Shift B x x
Shift C x x
Since Christianity is the majority religion in the USA, this follows the Sunday Sabbath. But Jewish families can still choose shifts that avoid Saturday, while Muslims can choose to avoid Friday.
Under the 2-Day Hybrid Plans, students attend one shift (two days per week) and the teachers have in-person instruction for two shifts (four days per week). Under the 3-Day Hybrid Plans, we don't expect teachers to work both shifts (six days per week) -- but then again, we don't expect districts to hire more teachers (with budget cuts due to falling revenues). Thus I expect that students will be called upon to attend school two, not three, days per week under a hybrid plan.
Some people might wonder whether it's worth including Saturday as a school day. Well, the mod 3 schedule provides 60 school days per student. By including Saturday, it's possible to extend the number of school days to 70, as follows.
A typical school year has 38 weeks, not counting weeks when school is completely closed (summer, Thanksgiving week, winter break, spring break) but including short weeks with 3-/4-day weekends.
Let's assume that schools are closed for the federal holidays of Labor Day, Columbus Day, Veterans Day, MLK Day, Presidents' Day, and Memorial Day. But if these holidays are on a Mondays, then we expect schools to close on nearby days in order to keep the shifts equal. For example, on 2-Day Hybrid #2, we expect schools to close Monday-Wednesday during those holidays. (This also works for Veterans Day, since November 11th is on a Wednesday this year.)
On 2-Day Hybrid #3, we can also close Monday-Wednesday, but Friday-Monday might be better, especially since the Friday before certain holidays are already observed in some districts. (For example, Friday before Labor Day is California Admissions Day in the LAUSD, Friday before Presidents' Day is Lincoln's Birthday in my new district, and my old district takes both Good Friday and Easter Monday off -- spring break is separate from Easter there.)
The 2-Day Hybrid #1 schedule is the trickiest for holidays -- how does Shift B, which attends school on Wednesdays and Thursdays only, observe Monday holidays? (The opposite is true for Veterans Day -- it's perfect for Shift B but not the other two shifts.)
And of course, all three 2-Day Hybrids suffer another problem -- if one day is a holiday, then there is only one day of school that week. Most districts try to avoid one-day weeks. (Recall the problems in New York seven months ago when they tried to have school on Monday, December 23rd.) But there's not much else to do if there's school two days a week and one of those days is a holiday.
Anyway, dropping six days for these holidays means that there are now 38 * 2 - 6 or 70 days of school for each shift of students, and 140 days of in-person instruction for teachers.
What should we do about Professional Development Days -- those days when only teachers go to work, but not students? Well, if school is out Monday-Wednesday for a holiday, then that Tuesday and Wednesday can be PD days. (Teachers who are off Tuesday or Wednesday attend the other day as a PD day, while those whose scheduled day off is Monday would observe the holiday on Tuesday and then attend the Wednesday PD.) This means that all scheduled PD days are moved to the nearest holiday -- for example, districts that usually have a PD near the start of second semester can hold it on the Tuesday or Wednesday after MLK Day instead.
In California, Columbus Day isn't observed as a holiday -- incidentally, both of my districts have scheduled a PD on Columbus Day instead. Instead of Columbus Day, my old district can observe Easter weekend as the sixth holiday (as explained above), while my new district might observe Yom Kippur as the sixth holiday. (This year, Rosh Hashanah is on a Saturday, so observant Jews should be already avoiding it as the Sabbath anyway. But Yom Kippur is on a Monday, so it should follow the pattern for the other Monday holidays. Then the Columbus Day PD is switched to the Tuesday or Wednesday after Yom Kippur.)
Unfortunately, there are still some problems with the holidays here. For example, the 2-Day Hybrid #2 schedule is written so that Saturday is the first day of the week. But since students return from winter break the first week in January, it means that the first day back is Saturday, January 2nd. I've heard of schools that start on January 2nd before (in New York, for example), but for that day to be Saturday is especially awkward. Other problems on any of the three plans occur with spring break -- schools that take the week after Easter would have school on Good Friday, those that take the week before Easter would have school on Easter Monday, and it's possible on either plan to have school on Holy Saturday.
There might be weird situations regarding Labor Day and the first day of school, or Memorial Day and the last day of school. Both of my districts have just one week of school left after Memorial Day, so this means that under 2-Day Hybrid #2, those on Shift C would have its last day of school on the Saturday (finals week, presumably) before Memorial Day, while those on the other shifts have their finals on the Thursday or Friday after the holiday. (Starting and ending school one week later would avoid these problems with finals.)
Let's assume that schools have figured out how to handle the holidays, and they've come up with a 70-day schedule for students and a 140-day schedule for teachers. Earlier, I heard a rumor that the budget cuts will be so severe that teachers might need to take furlough days (just as they did after the Great Recession). So a 140-day teacher schedule (plus maybe a few days for PD, as I just explained above) could mean as many as 40 furlough days for teachers.
Some of those savings could be used to hire an extra teacher or two (but not much more than that), if one is needed to ensure enough teachers on all the shifts. Indeed, this would be my best chance to be hired as a teacher next year. (It's either that or have two shifts under the 3-Day Plans, but again, I know there's not enough money for either of those.)
On the other hand, if I remain as a sub, the hybrid schedule would allow for there to be plenty of days for me to sub. The fear, of course, is that virus cases increase, districts will still close completely until the threat has subsided. I'd definitely be willing to sub on Saturdays, as listed above, in order to make up for the days lost when the districts are completely shut down by a virus surge.
When I came up with these hybrid plans, there were a few things I forgot to consider. First of all, California requires the school year to be 180 days -- counting both online and in-person days, it must be possible to count out 180 days. Thus we couldn't have, say a 2-Day Hybrid #2 plan with an online day in between, since that's only three total days per week. Indeed, for any of the hybrid plans that includes Saturday as one of the days, we must ask whether Saturday counts towards 180 or not.
There's also a minute requirement -- each day, online or in-person, must be at least 240 minutes. In fact, I remember exactly when this requirement began. I was a young fifth grader, and our school had minimum days that were exactly four hours in length. Thus officially, we weren't allowed to have recess on those days or we'd fall below the state requirement. So instead, we had "P.E.," written in scare quotes, on our schedule. That "P.E." time was unstructured, so in reality it was recess. Since then, my old elementary school has extended the minimum day by ten minutes and then placed a recess of ten minutes on the schedule.
(I once read of another California district where it wasn't the minimum day that fell below 240 -- it was the weekly Early Out Wednesday/whatever that fell below 240. When the state found out, it was declared that none of those days counted, and kids were forced to make it up over the summer -- one day for each Wednesday that was under 240. This infuriated teachers, students, and parents.)
Now we can see how important those numbers 180 and 240 are. So let's look at the actual reopening plan for my district and see how it meets the 180-day and 240-minute requirements.
What is the actual reopening plan in my old district?
Last week, my old district declared that there will be four stages to reopening. Stage 1 is fully online, while Stage 4 will be in person.
Stage 3 is a hybrid schedule as described earlier. Not only will it match the 180-day calendar, but it will match the district's block schedule as well. You see, some of the schools in the district have an all-classes day on Monday, odd blocks on Tuesday/Thursday, and even blocks Wednesday/Friday. So this is how the hybrid schedule will go -- one shift is Tuesday, Thursday, and the second shift is Wednesday, Friday. All classes are online on Mondays. So for the most part, this matches the 2-Day Hybrid #2 plan above, except that there is no Saturday, Monday shift.
One good thing about making Monday the online day is that it avoids the problem with Monday holidays -- simply skip the online Monday that week. Only Veterans Day on Wednesday will cause a problem with the Stage 3 plan (and chances are we won't be anywhere near Stage 3 by November in the first place).
Stage 2 is an interesting level. It's a bit like Stage 3, except instead of attending full-length classes, students attend 30 minutes of required "office hours" for each class. These office hours are on the same days as the in-person days in Stage 3 -- either Tuesday/Thursday or Wednesday/Friday. This district is one of the few that has proposed anything like Stage 2.
The district has also discussed something else I haven't thought much about -- what to do about passing periods. If high school students have six periods per day, that's six opportunities to pass the virus to others. Of course, our schools have block schedules where students only have three classes each day -- but that only works when they have the other three classes the next day.
So our district solves the problem by implementing another type of block schedule -- the 4 x 4 plan. I wrote about this on the blog four years ago, when I was trying to explain what block schedules are:
I first heard of the 4 x 4 plan back when I was in high school. Our school opened up a satellite campus for students who were deficient in credits. I found out that students were able to catch up because the satellite campus had a 4 x 4 Block Schedule.
Under the 4 x 4 plan, a whole year's material is completed in a semester. This means that each semester on a traditional schedule is like a quarter under 4 x 4. Students must take finals at the end of every quarter under 4 x 4, just as they take semester finals on a traditional schedule. And each quarter on a traditional schedule is like a quaver under 4 x 4. Sometimes teachers only mark grades of "D" or "F" on the quaver progress report on the traditional schedule, but under 4 x 4, every student must get a grade every quaver.
OK, so our district will have four quarters and three classes per quarter (so it's actually the 4 x 3 plan and not 4 x 4). Thus students only need to attend three classes in Stages 2 and 3, reducing the number of people who meet together and possibly pass the virus.
Therefore the school year will be 180 days no matter what. And whether it's online or in-person, the three classes will be for 80 minutes each (less breaks), so it's 240 minutes per morning. In all stages, students have the option to meet teachers online or in person (depending on the stage) after lunch.
So there are four quarters and four stages -- and it's tempting to map each stage to a quarter, so we'd assume that schools will be fully online in Stage 1 until mid-October, then Stage 2 office hours meet the rest of the calendar year, and so on.
But it's virus conditions that will determine the stages, not the quarters. In particular, Governor Newsom's order implies that the district must be in Stage 1 until LA County is removed from the watch list. It's likely that the county won't be removed from the list at all this year, and so the district will be stuck in Stage 1 the entire school year.
I wonder what role we substitutes will play in each of these stages. Of course, subs will have no job in Stage 1 and can work in Stage 4. The assumption so far in this post is that subs can work during the Stage 3 hybrid schedule.
This leaves only the Stage 2 office hours. I guess it's possible that subs can see the students for 30 minutes each on those days -- have them sign in so the regular teacher knows who attended. But it's also possible for the district to say that if the teacher is sick, office hours are cancelled -- so as far as subs are concerned, Stage 2 would be just like Stage 1, with nothing for us to do.
I know that as long as LA County is on the watch list, Stage 4 and likely 3 are impossible. I wonder whether it's possible to have Stage 2 office hours if the numbers are trending in the right direction, even if they're not quite low enough to remove the county from the watch list. (Of course, this question becomes moot if subs can't work during Stage 2 anyway.)
So far I haven't said anything about my new district in Orange County. That district is scheduled to have a board meeting tomorrow night to discuss reopening plans. It might come up with something similar to my old district, but with some differences. In particular, the Stage 3 hybrid in my old district was influenced by its block schedule. But my new district doesn't have a block schedule, and so any possible hybrid schedule may look completely different.
Again, it all goes back to my bank account. In some ways, I wouldn't mind if the four stages were to correspond to quarters, so that Stage 2 (with subs, hopefully) really can start in mid-October and I can earn something greater than $0.
But this goes to show how low my standards have gone. When the schools first closed in March, the closures were announced to be only two or three weeks. I actually found this closure welcome -- I worked for two districts with different spring breaks, and I feared that while one district was on break, I'd keep getting calls from the other district, so that I wouldn't get a break. (Indeed, I was considering turning down some subbing calls so that I could get some semblance of a spring break!)
Then the closures were extended until the start of May. So then I said to myself, OK, I can still earn paychecks for hours work in May -- due to how paychecks work in the two counties, I'd get these checks at different times. Then these checks might get me through most of the summer.
Then the closures were extended until for the rest of the year. So then I told myself, OK, this year is a bust, but at least I can earn regular paychecks in the new school year.
And now I'm settling for reopening in October. And, of course, there's a good chance that my counties will still be on the watch list then, forcing the schools to stay online even longer.
I wonder what it will take for my districts to reopen. No, Governor Newsom never said that a coronavirus vaccine is needed for reopening. But I fear that while smaller rural counties will be able to reopen without a vaccine, nothing short of a vaccine will be able to get the numbers in big-city counties like LA and Orange low enough for removal from the watch list.
At the start of the pandemic, it was suggested that a vaccine might be 12-18 months away. If we split the difference and call it 15 months, and start the clock from Pi Day when the schools first closed, then that takes us to Tau Day of next year. This would allow teachers and students to get vaccinated next summer, and we can have a regular 2021-22 school year.
But 12-18 months is actually the minimum time required for a vaccine. Indeed, coronaviruses are notoriously resistance to vaccines. It might be more like 12-18 years without a vaccine -- and there's no guarantee that one will ever be found. I could live long enough to die of old age, and someone else might die of the coronavirus that same day! (This week, Oxford scientists have announced progress towards a vaccine.)
And of course, not even a vaccine will guarantee the end of the pandemic. There exist, for various reasons, many vaccine skeptics who don't take annual flu shots and hence won't take any vaccine for the coronavirus. The name Bill Gates has been tied to vaccine conspiracy theories, and so even those who do take annual flu shots might avoid a Bill Gates-produced vaccine.
We need to be thinking in terms of periods longer than a year. Earlier in this post, I mentioned the period of time I call a quaver, or half a quarter (named after a British musical eighth note). I also use musical names for periods longer than a year -- I call two years a breve (a double whole note) and four years a longa (a quadruple whole note). So it's possible that a vaccine might be a breve away, or even a longa away from now.
I first came up with dividing my life into breves and longae when I was in college. I noticed that I had first enrolled in my new high school on November 3rd, 1995, was transferred to a Chemistry class (and ultimately to the magnet program) on November 3rd, 1997 (exactly one breve later), and started my first day of work at the UCLA library on November 3rd, 1999 (exactly one longa later).
Thus I divided my life into breves and longae, beginning with November 1995. Indeed, I've given names to these time periods:
1. Nov. 1995-1999: The High School Longa
a. Nov. 1995-1997: The Academy Breve
b. Nov. 1997-1999: The Magnet Breve
2. Nov. 1999-2003: The Bruin Longa
a. Nov. 1999-2001: The Undeclared Breve
b. Nov. 2001-2003: The Math Major Breve
3. Nov. 2003-2007: The Between Longa
a. Nov. 2003-2005: The Gap Breve
b. Nov. 2005-2007: The Local Library Breve
4. Nov. 2007-2011: The Preliminary Longa
a. Nov. 2007-2009: The Preliminary Start Breve
b. Nov. 2009-2011: The Preliminary End Breve
5. Nov. 2011-2015: The Clear Longa
a. Nov. 2011-2013: The Clear Start Breve
b. Nov. 2013-2015: The Clear End Breve
6. Nov. 2015-2019: The Teaching Longa
a. Nov. 2015-2017: The Charter Breve
b. Nov. 2017-2019: The Two County Breve
I actually announced the end of the fifth longa here on the blog. But I made no mention of the end of the sixth longa at all, until today.
Breves and longae have significance outside of my life. Longae are especially important on the Julian and Gregorian Calendars since Leap Days occur approximately once per longa -- about four months after the start of the longa. (Breves occasionally occur on Reform Calendars with 8-10 days per week, since 730 is closer to a multiple of these week lengths than 365 is.)
Presidential elections occur once per longa. Congressional elections occur once per breve, with Election Day about halfway through each breve.
The Summer Olympics usually occur once per longa, while each breve contains either a Summer or Winter Olympics. Even with Tokyo delayed until next year, there's still time for these Games to occur before the end of the current breve.
The longae are named after what diploma I was trying to earn at the time -- high school, college, preliminary credential, or clear credential. Unlike the first breve and longa, my major life events didn't always happen on November 3rd, so the names are approximate. For example, the California BTSA program to clear my credential takes two years -- that is, one breve. But that time doesn't line up with any of the breves listed above -- it does fit fully in the fifth longa. Meanwhile, I was only at the charter school for under a year, but it does fit fully in Breve 6A.
But what shall we call the current seventh longa and breve? It's clear that the virus is defining my current life and career. If a vaccine does appear at the 12-18 month mark, then the pandemic would be confined to the current breve:
7. Nov. 2019-2023: The ??? Longa
a. Nov. 2019-2021: The Coronavirus Breve
but it's more likely that no vaccine will be developed until the end of the longa:
7. Nov. 2019-2023: The Coronavirus Longa
Here's my rather dire prediction. We will have a vaccine by Tau Day -- but not next Tau Day, but Tau Day of the Century. That's June 28th, 2031 -- just before the 12-18 year prediction that I made earlier (but it's better late than never)
According to this prediction, if we're too afraid to have the Tokyo Games next year without a vaccine, then we might as well cancel the 2028 Games -- scheduled for right here in LA.
And if we can't open schools in LA or Orange County without a vaccine, it means that students who just finished kindergarten will be vaccinated in time for their senior year. In other words, they'll spend all of Grades 1-11 online.
And as for me, it means that my total income from now until 2031 will be $0. It means that I will die, not of the coronavirus, but of starvation.
It means that I shouldn't think in terms of the Coronavirus Breve or the Coronavirus Longa, but of the Coronavirus Decade of the '20's. This means that the coronavirus will define the decade -- thus making those "New Decade Resolutions" I posted in January 2020 look stale anyway.
Here are some resolutions that might require changing in the Coronavirus Decade:
5. "We treat the ones born in 1955 like heroes." One of those heroes was supposed to be Bill Gates, the creator of Microsoft Word. But I might not wish to emphasize the name Bill Gates due to the vaccine conspiracy theories. Instead, I may emphasize the other '55'ers, Jobs and Bernays-Lee. Also, this rule was intended to keep kids off of technology during class so that they can learn enough math to build new forms of technology. But I'm not sure how well that will work out when online learning rules the day, even on the days when students are in the classroom.
8. "We sing to help us remember procedures." Even though I enjoy singing songs to my classes, I might need to tone them down a little during the coronavirus, since a singing class may expel extra water droplets and spread the virus. I'll continue to sing my math songs, but songs about procedures (which I never got around to writing anyway) are unnecessary. Instead, I should use non-singing methods, such as praise and "teacher look," to remind students what they should be doing.
9. "We attend every single second of class." Attendance might be awkward during the coronavirus decade, even on days when students attend class in person. Hand-washing will be important, and students might need multiple restroom trips during class in order to keep their hands clean.
Again, I reiterate that I do wish to keep our students safe. But how can I keep them safe and continue to earn money during the upcoming breve, longa, or decade?
Recall that when I first began this blog, I was a math tutor -- it was a way for me to earn money during the fifth longa, when I was too busy with BTSA to work as a sub. I've heard that some families are considering hiring teachers to be tutors. A return to tutoring isn't ideal, but again, if the choice is between tutoring and making $0, I'll have to choose the former.
And of course, if all else fails, it could me that the only way for me to make any money is to leave the field of education altogether.
Who is Laura Lemay, and why am I learning Java?
Laura Lemay is the author of an online book about the Java computer language. Here's a link to her online text:
http://101.lv/learn/Java/index.htm
If the schools are shut down for an extended period of time -- and it becomes impossible for subs like me to get work -- then I must seriously consider looking for a job other than teaching.
The cliche response to someone who can't get a job is "learn to code." Well, that's exactly what I'm trying to do here. I chose Java because it's currently the language taught in AP Computer Science -- if AP considers Java to be a language worth learning, then I do as well. I assume this means that there are coding jobs out there where Java is the language of choice.
I've currently involved myself in a number of summer projects that I'm describing on the blog. The most important of these by far is my learning Java project.
So far, I've read the first ten Lemay lessons, and thus I'm ready for Lesson 11 now. Here's the link to today's lesson:
http://101.lv/learn/Java/ch11.htm
Lesson 11 of Laura Lemay's Teach Yourself Java in 21 Days! is called "More Animation, Images, and Sound," and here's how this chapter begins:
Animation is fun and easy to do in Java, but there's only so much you can do with the built-in Java methods for lines and fonts and colors. For really interesting animation, you have to provide your own images for each frame of the animation-and having sounds is nice, as well. Today you'll do more with animation, incorporating images and sounds into Java applets.
We begin with learning how to retrieve images. Lemay writes about the method getImage():
If getImage() can't find the file indicated, it returns null. drawImage() on a null image will simply draw nothing. Using a null image in other ways will probably cause an error.
But hold on a minute -- where am I supposed to get these images from? I downloaded Java a few months ago when I began this project. Are these images built-in to my Java compiler?
Well, let's look at the first listing and see what happens when I try it on my compiler:
Listing 11.1. The Ladybug applet.
1:import java.awt.Graphics;
2:import java.awt.Image;
3:
4:public class LadyBug extends java.applet.Applet {
5:
6: Image bugimg;
7:
8: public void init() {
9: bugimg = getImage(getCodeBase(),
10: "images/ladybug.gif");
11: }
12:
13: public void paint(Graphics g) {
14: g.drawImage(bugimg, 10, 10,this);
15: }
16:}
And of course there's no ladybug on my screen. Earlier, Lemay warns us that if the method can't find the image, it will return null and draw nothing. So my compiler returns null and draws nothing.Later on, she writes about a Neko cat applet and gives the following note:
The Neko images, as well as the source code for this applet, are available on the CD.
Oh, so that's my problem. While I'm reading this as an online text, Lemay originally published this text in print form -- and the print book had an accompanying CD. Since I don't have a print copy of the text, I don't have the CD -- so I can't run any of the programs in this lesson.
I guess it's just as well, since today's my Pi Approximation FAQ Day. So I might as well skip large parts of this lesson, even though they sound interesting. One of the listings involves scaling the ladybug up or down (that is, performing a dilation on the ladybug). And another listing also tells us how to add sound to the applet -- but of course, I can't access the sound files either.
The only listing that doesn't require a CD is the last listing. Here we learn about how to reduce the "flicker" that's prominent in many Java animations. Lemay writes:
Yesterday you learned two simple ways to reduce flickering in Java animation. Although you learned specifically about animation using drawing, flicker can also result from animation using images. In addition to the two flicker-reducing methods described yesterday, there is one other way to reduce flicker: double-buffering.
With double-buffering, you create a second surface (offscreen, so to speak), do all your painting to that offscreen surface, and then draw the whole surface at once onto the actual applet (and onto the screen) at the end-rather than drawing to the applet's actual graphics surface. Because all the work actually goes on behind the scenes, there's no opportunity for interim parts of the drawing process to appear accidentally and disrupt the smoothness of the animation.
(By "yesterday," Lemay means "in our last lesson." She assumes that we're reading one lesson per day, but I'm a whole lot slower than that here on the blog.)
Here is the listing:
Listing 11.5. Checkers revisited, with double-buffering.
1: import java.awt.Graphics;
2: import java.awt.Color;
3: import java.awt.Image;
4:
5: public class Checkers3 extends java.applet.Applet implements Runnable {
6:
7: Thread runner;
8: int xpos;
9: int ux1,ux2;
10: Image offscreenImg;
11: Graphics offscreenG;
12:
13: public void init() {
14: offscreenImg = createImage(this.size().width, this.size().height);
15: offscreenG = offscreenImg.getGraphics();
16: }
17:
18: public void start() {
19: if (runner == null); {
20: runner = new Thread(this);
21: runner.start();
22: }
23: }
24:
25: public void stop() {
26: if (runner != null) {
27: runner.stop();
28: runner = null;
29: }
30: }
31:
32: public void run() {
33: setBackground(Color.blue);
34: while (true) {
35: for (xpos = 5; xpos <= 105; xpos+=4) {
36: if (xpos == 5) ux2 = size().width;
37: else ux2 = xpos + 90;
38: repaint();
39: try { Thread.sleep(100); }
40: catch (InterruptedException e) { }
41: if (ux1 == 0) ux1 = xpos;
42: }
43: xpos = 5;
44: }
45: }
46:
47: public void update(Graphics g) {
48: g.clipRect(ux1, 5, ux2 - ux1, 95);
49: paint(g);
50: }
51:
52: public void paint(Graphics g) {
53: // Draw background
54: offscreenG.setColor(Color.black);
55: offscreenG.fillRect(0,0,100,100);
56: offscreenG.setColor(Color.white);
57: offscreenG.fillRect(100,0,100,100);
58:
59: // Draw checker
60: offscreenG.setColor(Color.red);
61: offscreenG.fillOval(xpos,5,90,90);
62:
63: g.drawImage(offscreenImg,0,0,this);
64:
65: // reset the drawing area
66: ux1 = ux2 = 0;
67: }
68:
69: public void destroy() {
70: offscreenG.dispose();
71: }
72: }
Ah, it works! The flicker is indeed reduced, but the author tells us that this is more complicated as it requires us to keep track of the hidden surface in some of the methods:First, add the instance variables for the offscreen image and its graphics context.
Second, add an init method to initialize the offscreen buffer.
Third, modify the paint() method to draw to the offscreen buffer instead of to the main graphics buffer.
Finally, in the applet's destroy() method we'll explicitly dispose of the graphics context stored in offscreenG.
If the schools remain closed, then I'll continue to study Lemay's Java text on my own and keep track of my progress on the blog. If I reach the end of the text and the schools still haven't yet opened, then I will start applying to non-teaching positions which involve coding in the Java that I've learned.
What's "Mocha music"?
In many recent posts, I refer to something called "Mocha music." This is a good time to explain what Mocha music actually means.
When I was a young child in the 1980's, I had a computer that I could program in BASIC. This old computer had a SOUND command that could play 255 different tones. But these 255 tones don't correspond to the 88 keys of a piano. For years, it was a mystery as to how SOUND could be used to make music. Another command, PLAY, is used to make music instead, since PLAY's notes actually do correspond to piano keys.
Last year, I found an emulator for my old BASIC computer, called Mocha:
When we click on the "Sound" box on the left side of the screen, Mocha can play sounds, including those generated by the SOUND command. So finally, I could solve the SOUND mystery and figure out how the Sounds correspond to computer notes.
I discovered that SOUND is based on something called EDL, equal divisions of length. We can imagine that we have strings of different lengths -- as in a string instrument or inside a piano. The ratio of the lengths determine their sound -- for example, if two strings are in a 2/1 ratio, then the longer string sounds an octave lower than the shorter string.
The key number for SOUND is 261, the "Bridge" (or end of the string). Mocha labels the Sounds from 1 (low) to 255, so we subtract these numbers from 261 to get a Degree ranging from 260 (long string) to 6 (short string). The ratios between the Degrees determine the intervals. I found out that the Degrees corresponding to powers of 2 (8, 16, 32, 64, 128, 256) sound as E's on a piano, with Degree 128 being the E just above middle C (that is, E4).
Let's say we were to play the following two notes on Mocha:
10 SOUND 51,8
20 SOUND 86,8
The second number 8 indicates a half note, since 8 is half of 16 (the whole note). But we want to focus on the first numbers here, which indicate the pitches (tones).
We first convert the Sounds to Degrees. Since 261 - 51 = 210, the first note is Degree 210. The Degree of the second note is 261 - 86 = 175. Now the ratio between these two Degrees is 210/175, which reduces to 6/5. This is the interval of a minor third, so the two notes are a minor third apart. As it turns out, the two notes sounds as G and Bb -- "rugu G" and "rugugu Bb."
Let's try another example:
30 SOUND 144,8
40 SOUND 196,8
Warning -- we don't attempt to find the ratio 196/144 (which is 49/36 by the way). We only find the ratios of Degrees, not Sounds. The Degrees are 261 - 144 = 117 and 261 - 196 = 65. Thus the interval between the notes is 117/65 = 9/5, a minor seventh. (Using Degrees instead of sounds makes a big difference, since 49/36 would be an acute fourth or tritone, not a minor seventh.) The names of the two notes played by Mocha are "thu F" and "thugu Eb."
Where do all these strange color names like "gu/green" and "thu" come from? Actually, they refer to Kite's color notation, and the colors tell us which primes appear in the Degree:
- white: primes 2 or 3 only
- green: prime 5
- red: prime 7
- lavender: prime 11
- thu: prime 13
- su: prime 17
- inu: prime 19
Kite's color notation also uses colors such as yellow, blue, and so on. But these are "otonal" colors, while EDL scales/lengths of string are based on "utonal" colors only.
The website where Kite explains his color notation is here:
https://en.xen.wiki/w/Color_notation
Actually, here's another link where Kite's color notation is explained:
https://en.xen.wiki/w/Color_notation
Actually, here's another link where Kite's color notation is explained:
Of course, the whole purpose of this is to compose music. When I was at the old charter school, I used to compose my own math songs for the class, but this was before I discovered that there was a Mocha emulator. Now that I know about Mocha, I can generate random music on Mocha and then make new songs.
In fact, this is one of my summer projects -- to go back and reorganize my old songs. I've been mostly just reblogging the lyrics, but I'll go back and post simple tunes for some of the songs as well.
By the way, you might notice that I'm not using Java to compose these songs. Deep down, I was hoping that since sound is one of the topics in today's Laura Lemay chapter, perhaps she'd teach us how to do everything above in Java instead of BASIC. But instead, Lemay only tells us how to include sounds from files into our applets -- and just as I don't have access to the CD containing images, I can't access any of these sounds either.
Then again, how would I play any of these songs in an actual classroom (if I ever get back there)? It may be possible to play some Mocha music if the school computers can access Mocha. But in general, I'd like to play some of these songs on my guitar. In fact, in previous posts, I started thinking about how we might refret a guitar so that it plays 18EDL music (that is, by spacing the frets equally apart, 1/18 of the string length, so that it really is an "equal division of length").
Unfortunately, my current guitar is broken. After leaving the old charter school, the tuning knob on one of the strings, the D string, doesn't turn properly. I can tune the string down, but not up.
Thus the note played by the string gradually became flatter. For a while, the note played by the string was at least a third-tone -- nearly a semitone -- too flat. In Kite's color notation, if the correct tuning of the string is white D, it became tuned to red C# instead.
I tried tuning all the other strings so that they were in tune with the flattened D string. But this meant that they were no longer in tune with the outside world. In fact, last Christmas I watched a holiday special, Grandma Got Run Over by a Reindeer. I had the sheet music for the title song, and I tried playing my guitar along with the song during the special. But my guitar wasn't in tune -- the show played the song in the key of E major, while my guitar was more like Eb major.
I was so upset that I tried to tune my D string back to D -- but instead, I made it worse. My D string is now about a whole tone too flat, sounding more like a C.
Afterward, I remembered that there was a guitar shop near one of the schools where I sub. I was thinking about going in to replace the tuning knob one day -- perhaps around the last day of school, and definitely by next Christmas. But you already know what happened -- the coronavirus shut everything down before I had a chance to go in.
It's also possible for me to tune all the strings down a whole tone -- and instead of a tuning knob, I could get a capo and place it at the second fret to recover the original tuning. But I'm tired of having an out-of-tune guitar -- in fact, I used to have perfect pitch, where I could hear a note and identify which note it is. But my out-of-tune guitar corrupted my perfect pitch -- if a note sounded like my D string, I'd want to identify it as D, when in reality it was a C# (or even a C).
Notice that I can kill two birds with one stone here -- I might find a retuning so that my D string can play as the C that it's stuck at, and also anticipate a retuning that fits with Mocha music and a possible 18EDL refretting (that is, whenever I can reach a guitar store again).
In a previous post, I mentioned several possible 18EDL tunings. Unfortunately, all of those tunings involving keeping the D string as D. Here's a possible retuning:
EACGAE
I like to keep as many strings tuned to standard tuning as possible. This tuning keeps four of the six strings -- in addition to the broken D string, the B string is tuned down to A. With four strings tuned correctly, I hope that I'll be able to regain perfect pitch.
In the tunings that I've mentioned earlier, all the open strings are assumed to be white. But for this tuning, the C and G strings are green while the rest are white. (Or if you prefer, keep the C and G white and tune the other strings yellow, which is equivalent.) Using this tuning, the open strings form a just A minor 7th chord (Am7/E).
Here are the notes playable in EACGAE if C and G are green and the rest white:
wa E | su E#, wa F#, gu G, ru G#
wa A | su A#, wa B, gu C, ru C#
gu G | sugu G#, gu A, gugu Bb, rugu B
gu C | sugu C#, gu D, gugu Eb, rugu E
wa A | su A#, wa B, gu C, ru C#
wa E | su E#, wa F#, gu G, ru G#
I'm not quite sure how this tuning will play out in practice, though. For example, it's easy to see how to play a C major chord (xx0030), but A minor chord is tricky. The strings are tuned to Am7 and we'd like to get rid of the G to make it Am. But the A at the second fret on that string is green A, while the open strings are white A. It might sound better just to play Am7 instead of Am. Likewise, an Em chord would need to be played as Em7 (022020).
Meanwhile, G major would be playable except that there aren't quite enough open strings. Instead, we must settle for G/B (x22023) or G/D (xx2023), or perhaps a G6 (322020) or Gadd9 chord (323003, but the add9 here is 20/9 instead of the usual 9/4). While D major isn't playable, there is a playable D7 chord (as xx2232).
(If we prefer all the strings to be white, we might try EABEAE -- one of the tunings I mentioned in a previous post, though it wasn't preferred. But if I tune my D string down to B, then I won't be able to tune it back up to C, since I can only tune it down and not up. I don't wish to commit to this tuning, especially since only three strings would match standard tuning rather than four.)
Although my summer project is to write math music from my old charter school -- whether just lyrics, Mocha version, or EACGAE guitar version -- I'll wait until my next post to continue.
So instead, let's just code a pi song based on 16EDL, similar to the song we played for Tau Day:
NEW
10 N=16
20 FOR X=1 TO 32
30 READ A
40 SOUND 261-N*(17-A),4
50 NEXT X
60 DATA 3,1,4,1,5,9,2,6,5,3
70 DATA 5,8,9,7,9,3,2,3,8,4
80 DATA 6,2,6,4,3,3,8,3,2,7
90 DATA 9,5
10 N=16
20 FOR X=1 TO 32
30 READ A
40 SOUND 261-N*(17-A),4
50 NEXT X
60 DATA 3,1,4,1,5,9,2,6,5,3
70 DATA 5,8,9,7,9,3,2,3,8,4
80 DATA 6,2,6,4,3,3,8,3,2,7
90 DATA 9,5
As is traditional, I stop just before the first zero. Then digits 1-9 map to Degrees 16 down to 8, with the lowest note played on E (line 10, N=16). We can change the value of N to any value from 1 to 16 to change the key.
Here's an actual song converted to 12EDL, a simpler EDL scale, the Sailor Pi theme song:
NEW
10 N=13
20 FOR X=1 TO 26
30 READ D,T
40 SOUND 261-N*D,T
50 NEXT X
60 DATA 8,4,8,2,9,4,9,2,10,4,11,4,9,12
70 DATA 9,4,9,2,10,4,10,2,11,4,12,4,10,12
80 DATA 12,4,12,2,10,4,10,2,8,4,6,4,7,12
90 DATA 8,4,9,4,10,2,11,6,12,16
Only the main verse is coded here. The "bridge" part -- which is instrumental in both the original Sailor Moon and Lizzie's Sailor Pi song -- is too hard for me to code without sheet music.
Here are the lyrics for the first verse -- the part which we coded above:
Fighting fractions by moonlight
Perplexing people by daylight
Reading Shakespeare at midnight
She is the one named Sailor Pi.
Speaking of Bizzie Lizzie, today's a great day to post lyrics after all -- the lyrics to her "Digit Connection," a parody of "Rainbow Connection," which I posted on the blog 2 1/2 years ago:
THE DIGIT CONNECTION
Copyright 1998 by Elizabeth Landau, aka Bizzie Lizzie
1st Verse:
Why are there so many debates about pi?
And what's on the other side?
Pi is a ratio of random proportions.
Its digits have nothing to hide.
So we've been told and some choose to believe it,
But I know they're wrong, wait and see!
Someday we'll find it, the digit connection,
Mathematicians, logicians, and me.
2nd Verse:
Who said that everything has some sort of pattern,
Consisting of nothing but math.
Somebody thought of that, and someone believed it.
Now we're all caught in its wrath....
What's so hypnotic in something chaotic,
And what do we think we might see?
Someday we'll find it, the digit connection,
The optimists, the theorists, and me.
All of us under its spell,
We know it must be math-e-magic...
3rd Verse:
Have you been half asleep? And have you heard voices?
I've heard them calling my name.
Is this the sweet sound that calls the young sailors,
The voice might be one and the same....
I've heard it too many times to ignore it,
Irrational, random, and free.
Someday we'll find it, the digit connection,
The lovers, the dreamers, and me.
3.1415926535 dot, dot, dot!
Bizzie Lizzie also had an "American Pi" song, but there's just one problem. I copied down the lyrics from her old website just before that site disappeared -- into my notebook. That's right -- the notebook that I took out on Pi Day Eve to sing to the class I subbed that day, and just left in the classroom. And because of the coronavirus closure, I can never access that notebook again. In fact, it was the loss of that notebook that encouraged me to start this project in the first place -- all I have to do is reread my Summer 2020 posts and I'll have lyrics to any song I wish to sing in class.
It's so frustrating -- I had plenty of chances to post the lyrics to this blog, but I never did, because I told myself that I'd always have that notebook, so I didn't need to blog it! And Liz now has her own website where she posted lyrics to "American Pi," but they aren't the old lyrics that she originally wrote as a teenager -- the lyrics I like the best! (In fact, her new lyrics are one verse too short to fit the original Don McLean song.)
Well, let me post the lyrics to her old song about the constant e -- and I had to create some of the lyrics myself because I'd never written those lyrics before either. Most likely I'll have to do the same and add one more verse to her "American Pi" song, maybe by next Pi Day.
Bizzie Lizzie's e song was a parody of "Sugar, Sugar," by the Archies. I think I recall the refrain:
e (2.718)
Ah, number number (281828)
You are my natural log,
And you got me calculating.
e (2.718)
Ah, number number (281828)
You are my derivative,
And you got me calculating.
But alas, I can't remember the rest of the song. Well, since it's e Day, let me supply extra lines. Some of these lines are from my faint memories of Landau's original song -- I made up all the lines that I couldn't remember.
1st Verse:
I just can't believe the loveliness of graphing you.
I can't believe you're more than two.
I just can't believe the loveliness of graphing you.
I can't believe you're more than two. (to Refrain)
2nd Verse:
I just can't believe your digits go forever now.
As long as a number can be.
I just can't believe your digits go forever now.
As long as you're the number e. (to Bridge)
Bridge:
Put a little cash in the bank, money.
Put a little cash in the bank, baby.
I'll make more next year, yeah, yeah, yeah!
Put a little cash in the bank.
100% interest on my money.
Compound it continuously, baby.
I'm gonna take the limit now, yeah, yeah, yeah!
My cash is multiplied by you, e. (to Refrain)
The bridge is mostly mine -- Landau didn't mention anything about money in her song. I chose to include money since it rhymes with the original Archies lyrics ("honey") as well as retell the story of Jacob Bernoulli's discovery of this constant.
If the schools remain closed, I'll probably continue this project through the fall. Even after I finish all the songs I played at the old charter school, there are several other songs I sang while subbing, especially during the year from Pi Day 2019 to Pi Day 2020.
Rebecca Rapoport is the author of Your Daily Epsilon of Math calendar. In most years, she produces a calendar that provides a math problem. The answer to each question is the date. I will post the Rapoport questions for each day that I blog. Traditionally I would post only her Geometry questions, but ever since the schools closed, I've been posting non-Geometry as well.
The question for July 22nd this year is:
Among 150 people, the smallest x such that at least x people were born on the same day of the week.
Well, since there are 11 days in a week, we divide 150 by 11 to get 13+ -- oops! Sometimes I think too much in terms of the Eleven Calendar.
Let's try this again. Since there are 7 days in a week, we divide 150 by 7 to get 21+. In other words, if there are only 21 people born on each day of the week, then there are only 147 people total. In order to get to 150, at least three days of the week must have a 22nd person born that day.
Therefore the number guaranteed to be born on at some day of the week is 22 -- and of course, today's date is the 22nd. This is a generalization of the Pigeonhole Principle, if we place n + 1 pigeons into n pigeonholes, at least one pigeonhole must contain 2 pigeons. And if we place mn + 1 pigeons into n pigeonholes, at least one pigeonhole must contain m + 1 pigeons. For today's problem, m is 21 and n is 7.
Let's do one more problem from later this week, since it's an actual Geometry problem:
If GE is 12, what is FC?
(Here is the given info from the diagram: In Square ABCD, the diagonals intersect at E, F is chosen on
This is a very tricky problem -- indeed, it took me some time to figure it out. This is the sort of problem that begins with an "angle chase" -- that is, finding the values of some angles.
We notice that Ray AF bisects Angle DAC. Now Angle DAB is obviously 90 since it is one of the angles of a square. Then Angle DAC must be 45 since the symmetry diagonal of any kite (including a square, where both diagonals are symmetric diagonals) bisects two angles of the kite. Then Angle DAF must be 22.5, as is FAC (same as EAG), since Ray AF bisects DAC.
Now Angle AEG is 90, since the diagonals of a kite (including a square) are perpendicular, and Angle ADF is also right as it's the angle of a square. Thus Triangles DAF and EAG are similar by AA~.
And we know exactly what the scale factor of this similarity is. In these triangles, the longer leg DA corresponds to the longer leg AE. But AE is also the leg of Triangle DAE -- which we already know is a 45-45-90 triangle (since DAE is the same as DAC) with DA as its hypotenuse. Thus DA is exactly sqrt(2) times as long as AE, thereby making sqrt(2) the scale factor of the similarity.
Since shorter leg FD corresponds to shorter leg GE, we know that FD = GE * sqrt(2). We're given that GE = 12, and so FD = 12sqrt(2).
Now let's get back to the angle chase. In right triangle AEG, E is the right angle and EAG is 22.5, and so the other acute angle EGA must be 67.5 degrees. Since Angles EGA and DGF are vertical angles, we conclude that DGF is 67.5 degrees as well.
Now in Triangle DGF, we know that Angle GDF is 45 (for the same reason as DAC -- the diagonal of a square bisects two angles of the square). Since the angles of a triangle add up to 180, we find that the last angle DFG of the triangle is 180 - 45 - 67.5 = 67.5 degrees.
So Triangle DGF has two base angles both of measure 67.5 degrees. Then by Converse Isosceles Triangle Theorem, the legs FD and GD are also congruent. Since FD = 12sqrt(2), we conclude that GD is also 12sqrt(2) as well.
By the Betweenness Theorem, ED = EG + GD = 12 + 12sqrt(2). Now in Triangle CDE, we see that ED is the leg of a 45-45-90 triangle with CD as its hypotenuse. Since ED = 12 + 12sqrt(2), we find that CD is exactly sqrt(2) times as long. Thus CD = (12 + 12sqrt(2))sqrt(2) = 12sqrt(2) + 24.
By the Betweenness Theorem again, CD = FD + FC. We know that CD = 12sqrt(2) + 24 and FD is known to be 12sqrt(2). Therefore FC, the side we're asked to find, must be 24. The desired length is 24 -- and of course, this problem is for Friday the 24th.
Even though we've completed the problem, notice that Triangle ADF is a 22.5-67.5-90 triangle with shorter leg 12sqrt(2) and longer leg 12sqrt(2) + 24 -- exactly 1 + sqrt(2) times as long. Thus we conclude that tan(22.5) = 1/(1 + sqrt(2)) = 1 - sqrt(2), and tan(67.5) = 1 + sqrt(2). These are exact trig values that we just found using pure Geometry, without need for any half-angle trig formulas at all.
If the schools remain closed, I'll continue posting both Geometry and non-Geometry problems from the Rapoport calendar. Once the schools reopen, I'll return to posting only her Geometry problems.
What is Shapelore?
When we teach Geometry, sometimes I fear that students will struggle over the vocabulary. This includes not just longer words/phrases such as "Alternate Interior Angles" and "Reflexive Property," but even the shorter words for the trig functions "sine," "cosine," and "tangent." More often than not, these confusing words come from complex Greek and Latin roots.
And so this project seeks to replace some of these words with roots that come from Old English. It was inspired by the Anglish website, where Anglish is the language we get by removing all Greek and Latin words from our language, leaving behind pure English:
https://anglish.miraheze.org/wiki/Main_Leaf
https://anglish.miraheze.org/wiki/The_Anglish_Wiki:Goals_of_Anglish
(Hey, that's interesting -- the Miraheze website is celebrating its fifth birthday today, since as this blog is celebrating its sixth birthday today.)
In fact, the name "Shapelore" is itself in Anglish -- here -lore refers to something that is studied, so it's the Anglish equivalent of the Greek suffix "-ology":
https://anglish.miraheze.org/wiki/Shapelore
In Shapelore, "Alternate Interior" becomes Otherside Inside and "Reflexive Property" becomes Selfsame Law. I've decided to keep some words as simple even if they are from Latin or Greek -- for example, most people know what a "square" is, so I keep it even though the word is from Latin. I'm also keeping the word "angle," also from Latin. The Anglish website proposes nook for "angle," but I'd rather keep "angle." Thus I refer to this as "Plain English" instead of "Pure English" or Anglish.
The new names for the trigonometric functions are wheelex for "cosine," wheelwhy for "sine," and wheelslope for "tangent." The wheel part indicates that these are the wheel (or circular) functions. So instead of tan(67.5) = 1 + sqrt(2), we'd write ws(67.5) = 1 + sqrt(2). The word "root" is Old English and I already said I'm keeping "square," so sqrt doesn't change, but tan becomes ws, wheelslope.
So far, I've been translating the U of Chicago Geometry text into Plain English. In 1991, the University of Chicago School Mathematics Project published a series of secondary mathematics texts. I was able to purchase both the Algebra I and Geometry texts for two dollars each at a local public library. One thing I discovered was that the U of Chicago Geometry text is based on the same transformations that appear in the Common Core Standards -- even though the U of Chicago published the text nearly two decades before the advent of the Core.
I'll return to Shapelore in my next post. Right now we're in the middle of Chapter 14, the chapter on trigonometry and vectors. If the schools remain closed, that I might skip to the lessons that would have been covered if the schools had been open (that is, Chapter 1 early in the school year, Chapter 12 later on, and so on).
Instead, let me use this section for my annual Pi Approximation Day YouTube video sample:
1. Draw Curiosity
Notice that this video, from four years ago, actually acknowledges Pi Approximation Day.
2. Converge to Diverge
In this video from two years ago, the speaker attempts to approximate pi just as Archimedes did it -- using a regular 96-gon.
3. Sharon Serano
Well, I already gave ten facts about pi, and so this video is twice as good.
4. TheOdd1sOut
This video is specifically listed as a "Vi Hart rebuttal."
5. Michael Blake
I like the idea of using music to teach math, so here's a favorite, Michael Blake's "What Pi Sounds Like." I tried to find a way to incorporate songs such as this one into the classroom.
6. Coding Challenge #140
Today is Pi Approximation Day, and so this video is all about approximating pi.
7. Ki & Ka
This is a brand new video for this year.
7. Math Without Borders
This is another video that uses the Archimedes method of approximating pi.
8. Sen Zen
This is yet another video that uses the Archimedes method of approximating pi.
9. Mathematics Online
10. Stand-Up Math
This video uses the Leibniz series, but all work is done by hand.
11. Think Twice
This video uses a Monte Carlo approximation technique. I attempted to do something similar using Java in an earlier post.
Who is Ian Stewart, and why am we reading Chapter 11 today?
Ian Stewart is a prolific mathematics author from Great Britain. I've mentioned his book Calculating the Cosmos sporadically on the blog before, but one of my summer projects is to read it from cover to cover and write about it on the blog.
In my last post, we read Chapter 9, so we ought to read Chapter 10 today. But this time, I'm skipping ahead to Chapter 11. That's because I already covered Chapter 11 in my November 14th post (back when I was jumping around in the book), and so I'd rather just cut-and-paste that post today. (I did the same thing with my Tau Day post and Chapter 6.)
And besides -- I already wrote about the Eleven Calendar and Chapter 11 of Laura Lemay's book, so I might as well continue the elevens with Chapter 11 of Stewart. (Eleven is half of 22 -- today's date -- but then again, Half-Pi or Lambda Approximation Day was eleven days ago.)
Before I cut-and-paste, this is a great time for me to acknowledge the Google Doodle from two days ago -- of Dilhan Eryurt, a Turkish astrophysicist. She was featured on Monday, not because it was her birth or death day, but to celebrate the 51st anniversary of the moon landing.
OK, so now the cut-and-paste begins below:
Chapter 11 of Ian Stewart's Calculating the Cosmos: How Mathematics Unveils the Universe is called "Great Balls of Fire." Chapters in this book begin with a quote:
"We may determine the forms of planets, their distances, and their motions -- but we can never know anything of their chemical composition." -- Auguste Comte, The Positive Philosophy.
This chapter is all about, well, the chemical composition of planets and stars. (I've heard of Comte before -- he is the originator of the 13-Month Calendar Reform. He named his calendar after the philosophy mentioned above -- the Positivist Calendar.) Stewart begins:
"With twenty-twenty hindsight it's easy to poke fun at poor Comte, but in 1835 it was inconceivable that we could ever find out what a planet is made of, let alone a star."
And the author tells us how we did finally figure out what celestial bodies are made of:
"By combining observations with mathematical models, scientists have inferred detailed answers to all of these questions, even though visiting a star with today's technology is virtually impossible. Let along tunneling inside one. The discovery that rubbished Comte's example was an accident."
Stewart begins with the story of Joseph Fraunhofer, a glassmaker's apprentice. He inadvertently discovered a spectroscope which can measure wavelengths. Using his spectroscope, he could compare the wavelengths in a star's spectrum to that produced by a chemical element:
"Fraunhofer applied this idea to Sirius, thereby observing the first stellar spectrum. Looking at other stars, he noticed that they had different spectra."
The astronomer Jules Janssen then sought the chemistry of the sun's chromosphere -- as opposed to the part of the sun that we see, the photosphere:
"The chromosphere is so faint that it can be observed only during a total eclipse, when it has a reddish hue."
He and Norman Lockyer eventually discovered a new element in the periodic table -- helium, named after the Greek word for "sun":
"We see it in the Sun because the Sun isn't just made of it, along with a lot of hydrogen and lots of other elements in lesser amounts: it makes it...from hydrogen."
At this point, Stewart discusses other stars and their classification. Each class is assigned a letter based on its temperature:
"Stars are also given a luminosity class, mostly written as a Roman numeral, so this scheme has two parameters, corresponding roughly to temperature and luminosity. Class O stars, for instance, have a surface temperature in excess of 30,000 K, appear blue to the eye, have mass at least 16 times that of the Sun, show weak hydrogen lines, and are very rare."
The author tells us that our own sun is classified as a G2 star. The vast majority of all stars are in Class M -- the coolest and smallest. He displays a scatter plot of known stars with their temperatures and magnitude (or brightness) known as the Hertzsprung-Russell diagram:
"The most prominent features are a cluster of bright, coolish giants and supergiants at top right, a curvy diagonal 'main sequence' from hot and bright to cool and dim, and a sparse cluster of hot, dim white dwarfs at bottom left. The study of stellar spectra went beyond butterfly collecting when scientists started using them to work out how stars produce their light and other radiation."
At this point Stewart discusses how stars make their energy. He begins by discussing "deuterium," which is a type (isotope) of hydrogen that contains a proton and a neutron in its nucleus:
"After about four seconds the deuterium nucleus fuses with another proton to make an isotope of helium, helium-3: quite a lot more energy is released."
But eventually, the energy will run out:
"This takes hundreds of billions of years for slow-burning red dwarfs, 10 billion years or so for stars like the Sun, and a few million years for hot, massive O-type stars."
Our sun will become a red giant in about five billion years. Other larger stars have a different fate:
"The core of the star can end up as a white dwarf or a black dwarf, which is a white dwarf that has lost so much energy that it stops shining."
Another possibility is a black hole -- but Stewart saves that for a later chapter. Instead, he discusses the origin of the heavier elements which we are made of. In short, we're stardust -- it was discovered by Fred Hoyle:
"He published a lengthy analysis of reaction routes leading to all elements up to iron. The older the galaxy, the richer its brew of elements."
Some elements also formed by supernovas, or exploding stars. The author tells us that this theory doesn't account for how much of the element lithium there is in the universe:
"Some scientists think this is a minor error that can probably be fixed up by finding new pathways or new scenarios for lithium formation."
This error appears with the heavier elements as well, leading some scientists to fudge the numbers:
"I'm not suggesting anyone deliberately does this kind of thing, but selective reporting like this is natural, and it's happened elsewhere in science."
One element of particular concern is carbon, since we're carbon-based lifeforms. According to Hoyle, there shouldn't be enough carbon in the universe to make us:
"Unless...the energy of carbon is very close to the combined energies of beryllium-8 and helium. This is a nuclear resonance, and it led Hoyle to predict a then unknown state of carbon at an energy 7.6 MeV above the lowest energy state."
Stewart warns the reader against concluding that the universe has been "fine-tuned" for life:
"But we shouldn't confuse outcomes with causes, and imagine that the purpose of the universe is to make humans. One reason I've mentioned this (aside from a distaste for exaggerated fine-tuning claims) is that the whole story has been made irrelevant by the discovery of a new way for stars to make carbon."
In this theory, the carbon comes from young stars, not supernovas. At this point, Stewart now switches to a discussion of sunspots, and whether sunspots cause climate change. In particular, minimal sunspot activity sometimes coincides with lower temperatures on earth:
"So did a previous period of low sunspot activity, the Dalton minimum (1790-1830), which includes the famous 'year without a summer' of 1816, but the low temperatures that year resulted from a huge volcanic explosion, Mount Tambora in Sumbawa, Indonesia."
Later scientists continued to study sunspots and their effects:
"Horace Babcock modelled the dynamics of the Sun's magnetic field in its outermost layers, relating the sunspot cycle to periodic reversals of the solar dynamo."
The author tells us how the sun's magnetic field indeed causes sunspots:
"The result is a long-period oscillation in the average size of the field during a cycle, and when it dies down few sunspots appear anywhere."
Now Stewart moves on to finding the distance to the stars. The history of calculating long distances -- just like many chapters we just read in his Story of Mathematics -- goes back a few millennia:
"In the sixth century BC the ancient Greek philosopher and mathematician Thales estimated the height of an Egyptian pyramid using geometry, by measuring its shadow and his own."
And of course, this type of question shows up in the similarity chapters of Geometry texts. We learn that from the distance from the earth to the sun, we can calculate the distance to the stars by observing them six months apart -- a technique known as parallax:
"The star's distance is approximately proportional to the parallax, and a parallax of one second of arc corresponds to about 3.26 light years."
This unit is now known as the parsec, or parallax arcsecond. At this point, Stewart tells us the story of an American astronomer, Henrietta Leavitt:
"In the 1920's Pickering hired her as a human 'computer,' carrying out the repetitive task of measuring and cataloguing the luminosities of stars in the Harvard College Observatory's collection of photographic plates. Most stars have the same apparent brightness all the time, but some, which naturally arouse special interest among astronomers, are variable: their apparent brightness increases and decreases in a regular periodic pattern."
Some such variable stars are known as Cepheids. She discovered a formula to calculate their brightness, thus giving a new meaning to "Twinkle, Twinkle Little Star":
"And those results then extended to all Cepheids, using the formula relating the period to the intrinsic brightness. Cepheids were the long-sought standard candle."
Stewart concludes the chapter by relating brightness of stars to their distance:
"Each step involved a mixture of observations, theory, and mathematical inference: numbers, geometry, statistics, optics, astrophysics. But the final step -- a truly giant one -- was yet to come."
I'll return to Chapter 10 in my next post. If the schools remain closed, then we'll continue reading the Stewart book until we complete its last chapter.
11. How will the coronavirus school plans affect this blog?
This year, my plans were to follow the calendar of my new district (the one in Orange County). This switch has absolutely nothing to do with the coronavirus -- and indeed, I made that decision long before the pandemic began. I liked my old district calendar because it allowed me to cover Chapter 7 of the Geometry text before winter break, and this year, my new district planned to change to a similar calendar.
But now, of course, the coronavirus has changed everything. So instead, I'll follow the same pattern that I've been following since the schools closed on Pi Day -- post once or twice a week as long as the schools are online only (Stage 1). Once the schools reopen (Stages 2-4), then I'll post one Geometry lesson for each day that students are physically present on campus.
I haven't decided how this will work, given the 4 x 4 block schedule possibilities. Keep in mind that I wish to follow my new district, and they won't release plans until tomorrow night's meeting. So my blogging schedule may become clearer after tomorrow night.
When the schools first closed in March, I had no idea that most people would still be afraid to open them in August. The state declared on Monday that no high school sports will begin until either December or January, suggested that the schools themselves may remain closed until at least then.
Then again, I had no idea that states and cities would still, in July, be breaking daily records in for the number of coronavirus cases. The future is definitely uncertain.
I reiterate that I do want students, teachers, and staff members to remain safe these days. It's not that I don't care about the health of others -- or even myself. It's just that I don't want to wait years, breves, longae, or decades for my next paycheck. Many people are suffering, not just subs. And it will be difficult for me to find work -- in education or otherwise -- unless the schools reopen. (Again, if I do get a job outside of education, I'll no longer post to this blog.) That's the main thing that will be on my mind over the next few months, during these tough times of uncertainty.
And so I wish everyone a Happy Pi Approximation Day.
No comments:
Post a Comment