New Year's Eve Post: My Favorite Lesson of 2020

Table of Contents

1. Introduction

2. Yule Blog Prompt #13: My Favorite Lesson of 2020...or One That Totally Flopped

3. Music: Guitar Chords for My December Songs

4. Completing the Slope Song

5. Karl Palmen's Weekend Rest Calendar

6. theAbysmal Eleven Calendar

7. Links to Other Challenge Participants

8. Conclusion

Introduction

Today is New Year's Eve, the last day of the year. For many people, 2020 was a sort of annus horribilis, a Murphy's year in which anything that could go wrong did go wrong. But the main reason for 2020 being such a horrible year was COVID-19 -- that is, coronavirus disease 2019.

Then again, the reason for the disease being numbered 2019 is that it was still that year when China reported the disease to the World Health Organization. Indeed, today's the first anniversary of that report -- New Year's Eve 2019. Still, because the disease didn't affect anyone outside of China until 2020, this is why many people consider 2020 to be Murphy's year rather than 2019.

Still, this New Year's Eve is worth celebrating. Because it's been one year since the virus was reported, it means that the first -- and presumably worst -- year of the pandemic is over. We now understand more about how to protect ourselves from the virus, and vaccines are beginning to be produced and released.

That's enough about the pandemic. It's time to continue the Yule Blog Challenge. And since today is the thirteenth day of winter break, let's proceed with the thirteenth prompt. (Yes, Shelli provided more than twelve prompts even though this is a 12-day challenge.)

Yule Blog Prompt #13: My Favorite Lesson of 2020...or One That Totally Flopped

This is an interesting one. My favorite lesson isn't an individual lesson at all -- in fact, it's something I did throughout the year, before and during the pandemic, and at different schools.

A few years ago, I came up with the idea of singing songs in the classroom. It was intended as a "brain break" of sorts, except that it's more like a "music break." Here's how it worked -- about halfway during the class period, I would start singing a song about math. Many of these songs came from Square One TV, an old math show that aired during the late 1980's and early 1990's. Some of these are parodies of common songs with the lyrics changed to math. And a few of them are original creations of my own.

When my long-term assignment began, I brought a guitar to leave in the classroom. Now music break is a regular feature of my class. I especially enjoy performing on hybrid days -- the 100-minute blocks can be tough on middle school students, and so a music break can be helpful. I usually chose one song to perform that week, since each class sees me only one hybrid block day per week.

Let me list the weekly songs that I've performed so far:

1. September 29th-October 2nd: "Count on It," Square One TV

2. October 6th-9th: "That's Math," Square One TV

3. October 13th-16th: "Wanna Be," Square One TV

4. October 20th-23rd: "Less Than Zero," Square One TV

5. October 27th-30th: "Ghost of a Chance," Square One TV

6. November 3rd-6th: "Vote," parody of "Do-Re-Mi"

7. November 9th-13th: "Whenever You Multiply," original song

8. November 17th-20th: "Solve It," original song

9. December 1st-4th: "Nine Nine Nine," Square One TV

10. December 8th-11th: "U-N-I-T Rate! Rate! Rate!" parody of UCLA fight song

11. December 14th-17th: "Rudolph the Statistician," parody of "Rudolph the Red-Nosed Reindeer"

The first three songs, "Count on It," "That's Math," and "Wanna Be," stress the importance of learning math to students' future goals. "Less Than Zero" was the first song that pertains to actual math content, as this song is an introduction to negative numbers (for Math 7).

"Ghost of a Chance" and "Vote" were chosen only because of the calendar -- those songs fit Halloween and Election Day respectively. "Whenever You Multiply" and "Solve It" are my first original songs during this long-term -- these songs describe multiplying/dividing signed numbers (for Math 7) and solving linear equations (for both Math 7 and Math 8). Then I returned to Square One TV with the song about the trick for multiplying by nine.

The purpose of all these songs isn't just to give students a break on block days -- it's to jog their memories when working on math problems. Thus when we're solving equations, I start singing "Solve It" to remind them which step is next. The next step might require them to multiply or divide both sides by a negative number, so then I immediately switch to "Whenever You Multiply." And if the number they must multiply both sides by is nine and the student struggles to remember the 9's times tables, it's time for me to switch to "Nine Nine Nine." So I might sing three songs to solve one problem!
The other part of today's prompt is a lesson "that totally flopped." Well, I can name one entire unit that totally flopped -- Math 8 Unit 3, on linear functions and slope. And part of the reason that it flopped is that I failed to sing an appropriate song during that unit.

I taught Unit 3 during the weeks of October 19th-November 6th. As you can see, one of the songs I performed that week was "Less Than Zero," which was for the benefit of my seventh graders. And the other two songs matched the calendar, not the content. At the time, if you had asked me to perform a slope song, I'd have told you that I didn't have a slope song to sing.

But here's the thing. When I was doing research for this Yule Blog Challenge -- that is, going back to blog posts from early this year to find three good things or decide what my favorite lesson from 2020 is, I rediscovered an original slope song that I had written!

The post was dated March 6th. It was the last day of a three-day assignment in a Math 8 class. While I did sing songs when subbing, I rarely wrote original songs for day-to-day subbing (since after all, I wouldn't know what math topic to write a song about). But since this was a multi-day assignment -- and the eighth graders were about to take their second trimester finals, I decided to write a song about one topic on that final, which was slope.

I wrote the song in my notebook. A week later, I took out my notebook to perform some Pi Day songs (even though it was an English class, it was Pi Day Eve and the regular teacher had several guitars in his classroom). I was almost home that day when I realized that I'd left the notebook in the classroom -- and you know what happened next. The pandemic struck, the schools closed, and I'd never return to that room again. (Even when the schools reopened, I didn't even try to retrieve the notebook -- I assumed that six months later, the book would have been thrown away by then.)

Over the summer, I created a new notebook of songs, using lyrics that I'd recorded on the blog. But by then, I'd completely forgotten the slope song. (If it had been a song that I'd performed several times, I would have remembered it, but I'd written it and sung it only once before the pandemic.)

And so by the time I reached the slope unit during my long-term in October, I didn't have a slope song in my notebook to sing. What's sad about this is that in my March 6th post, I wrote that it was just a short song, and that I would extend it the next time I taught slope. Well, that exact situation occurred just 7-8 months later, but I didn't perform the song at all, much less extend it. If I'd sung it, the eighth graders might have remembered slope better, and perhaps earned higher scores on the Unit 3 Test.

Thus singing marks my favorite lesson of 2020, and failure to sing marks my biggest flop. (Note: In my last post, I mentioned the Quizizz lesson during Unit 3 as one of the three good things of 2020. But on second thought, Quizizz was enjoyable, but it didn't raise Unit 3 scores that much. Since I need to count Unit 3 as my biggest flop rather than as a good thing, I went back and edited Tuesday's post.)

Music: Guitar Chords for My December Songs

I've added the "music" label to this post. Here on the blog, I usually discuss the actual chords that I play for my classroom songs, but I haven't done so since Thanksgiving. And so let's catch up with the songs that I performed this month.

Once again, I point out that tuning knob on my D string is broken -- it has been stuck at C. I've also tuned my B string down to A, so my guitar is currently tuned to EACGAE. Over Thanksgiving, I wrote that I was considering tuning the low A string down to G as well, which would give us EGCGAE. An extra string tuned to G would be helpful when playing songs in the key of G major.

But of all the songs I played in December, none were in the key of G. Therefore I kept the A string tuned to A. So all the chords listed below are still for the EACGAE tuning.

Let's start with "Nine Nine Nine." I played this song in the key of C major, using the following chords:

C: xx0030

F/A: x00201

A7: x01000

D7: xx2232

G7: xxx021

That week, I also played a few extra songs that weren't my unofficial song of the week. One of these was the Christmas song "Old Toy Trains," which used all the same chords as above. The other song was "Whodunnit," which was in the key of A minor. This chord is easy to play in this tuning:

Am: x00200

Since this song is about a murder mystery activity, I wanted to play the "DEAD" chord -- the notes A, D, and E played in some combination. Officially, this chord is known as Asus4. It sounded very eerie when I played it over E, using all six strings:

Asus4/E: 002200

For "U-N-I-T Rate! Rate Rate!" I actually played it in the key of D major. This was tricky, since the D string is the one whose tuning knob isn't working. The open string is like a C, and sounds pretty good as the root of a C major chord. But when I play the second fret to try to reproduce the original D, it sounds a bit off, and D chords played with that note as the root don't sound right.

This is why I've been sticking to C major using the EACGAE tuning for most other songs. To get our D chord, I masked the slightly off D by playing the chord over A:

D/A: x02002

G: xxx023

E7: 022120

A7: x01000

And for "Rudolph," I returned to C major. All the chords needed have already been listed, except for Am7, which can be played on open strings.

As soon as I finish that last week of the long-term, I plan on removing the guitar from the classroom -- and taking it directly to a Guitar Center to replace the D tuning knob. Then I'll finally return to the standard tuning, EADGBE. By the way, I've been devoting so many of these music posts to something called EDL scales -- an alternate way to fret (as opposed to tune) the guitar. It ultimately goes back to an old computer program, Mocha, that can be used to generate music.

I don't want to tie up this post with yet another discussion of EDL scales -- this post is also labeled "Calendar," and I want it to be my final Calendar Reform post for the holiday season (while I have all year to get back to EDL scales). I do wish to discuss what EDL scales mean for the guitar once I return to standard EADGBE tuning. (While nonstandard tuning and nonstandard fretting aren't necessarily related, I kept tying the two in past posts.)

All that's relevant now is that I've been using both 12EDL and 18EDL scales to create songs -- and while I said that I'd be using 18EDL moving forward, the slope song that I rediscovered was originally composed in 12EDL.

Completing the Slope Song

Here is the slope song that I just rediscovered from my March 6th post. I'll repost everything that I wrote back on March 6th -- the Mocha code that plays the song, an explanation of the 12EDL scale, and the lyrics.

https://www.haplessgenius.com/mocha/

10 N=8
20 FOR X=1 TO 35
30 READ A,T
40 SOUND 261-N*A,T
50 NEXT X
60 DATA 10,4,12,2,8,2,9,4,11,1
70 DATA 12,2,11,1,7,2,8,2,11,4
80 DATA 9,6,10,2,7,2,6,1,7,1
90 DATA 6,4,7,4,7,4,9,16,8,4
100 DATA 12,4,7,4,8,4,8,2,8,2
110 DATA 12,2,9,2,10,6,9,2,6,4
120 DATA 6,4,6,4,8,3,7,1,6,16

As usual, click on Sound before you RUN the program. Here are the scale and the notes used:

12EDL scale:
Degree  Note
12         white A
11         lavender B (or Bb)
10         green C
9           white D
8           white E
7           red F#
6           white A

C-A-E-D-B-A-B-F#-E-B-D-C-F#-A'-F#-A'-F#-F#-D-E-A-F#-E-E-E-A-D-C-D-A'-A'-A'-E-F#-A'

Notice the notes "D-E-A-F#" in the middle of the song. This is actually part of the "Whodunnit" song that the pseudorandom generator produced. I decided to keep it anyway, since I'd changed these notes back in "Whodunnit" -- back then I changed low A to high A, but here I keep low A. Also, I keep F# here, but back then I changed F# to D (so that the notes D-E-A-D would appear in the middle of that murder mystery song).

Now let's add some lyrics. I just take the final hints that aide has already written on the board (plus my calculator comments for the sixth resolution) and then make it into song lyrics:

The Slope Song

Delta-y over delta-x,
Rise over run and,
y equals mx plus b.
Calculator,
Use it if you need, but,
Try in head just for me.

y minus y all over,
x minus x, and,
Keep, change, change, yes you see.
Calculator,
Use it if you need, but,
Try in head just for me.

Notice that more teachers are starting to use "delta" when teaching slope. Once again, as a young student I once tried to impress my Algebra I teacher by using delta in my homework, and now suddenly teachers are using delta for real. Meanwhile, "keep, change, change" is a mnemonic used to remember how to subtract integers (keep the first number, change the subtraction to addition, and finally change the sign of the second number). Since the slope formula requires subtraction in the numerator and denominator, "keep, change, change" is relevant here.

Of course, this is a fairly short song that I wrote in one night. If this were a full song to perform on the day that slope is actually taught (as opposed to just being reviewed and tested), a slope song should probably explain it all better. So the delta expression and "rise over run" equal the slope, while y = mx + b is the slope-intercept form, not just the slope. And of course, "y minus y" is really short for y_2 - y_1, which we'd really need to explain better. Perhaps one of these days I'll expand this into a full song that can be used to teach slope.

And that takes us back to the present. Well, "one of these days" means today. (Actually, "one of these days" should have occurred in October or November.)

My promise was not that I'd add more verses -- we can keep the two verses that are there. What I need to do is add extra lines to explain what it all means. So here is the completed song:

The Slope Song

Delta-y over delta-x,
Rise over run and,

y equals mx plus b.

Slope-intercept form, you see!

Calculator,
Use it if you need, but,
Try in head just for me.

y minus y all over,
x minus x, and,

Keep, change, change, yes you see.

That's how to subtract, you see!
Calculator,
Use it if you need, but,
Try in head just for me.

To get Mocha to play the extra line, add Line 95 as a repeat of Line 90:

95 DATA 6,4,7,4,7,4,9,16,8,4

Karl Palmen's Weekend Rest Calendar

Let's continue this year's Calendar Reform posts with a new calendar I found on Calendar Wiki. The creator of this calendar is Karl Palmen -- a prolific calendar inventor.

https://calendars.wikia.org/wiki/Weekend_Rest_Calendar

The Weekend Rest Calendar is inspired by a tear-off calendar that normally displays one day per page but puts both weekend days on the same page. Such a calendar has 'dates' that consist of either one weekday or a whole weekend. Then we can have 12 months each of 26 'dates', except the last month, which has 27 'dates' in a common year and 28 'dates' in a leap year. Then leap years need occur only once every 15 or 16 years, because a common year starting on Saturday has 53 weekends and so 366 days.

OK, so on this calendar, six "dates" cover seven sunrises/sunsets. One date covers both Saturday and Sunday, since Palmen's tear-off calendar combines weekends on the same page.

Whenever I see a new calendar, I always try comparing it to previous Calendar Reforms. There actually exists another calendar where six days cover seven sunrises/sunsets -- the 28-Hour Day. There used to be a website for the 28-Hour Day, but it no longer exists. There is now an XKCD comic on the 28-Hour Day, but I don't link to it because it mentions an inappropriate joke. You can just find it on Google.

While neither XKCD nor the old 28-Hour website mentions a calendar to go with it, the Weekend Rest Calendar fits well with he 28-Hour Day. In both cases six "dates" cover seven days -- the difference is that Palmen has five 24- and one 48-hour "date," while XKCD has six 28-hour dates.

But forget the 28-Hour Day. There's something else I find interesting about the Weekend Rest Calendar, and that's the Leap Day rule:

The calendar uses the simplest accurate such cycle, which is the 62-year cycle with 4 leap years (17+17+17+11)

The numbers 11, 17, and 62 should look familiar. There's another calendar that has uses 11-, 17-, and 62-year cycles -- the Andrew Usher Calendar that I posted back on Leap Day (February 29th).

While I enjoy my Eleven Calendar, I know that in reality, it will never be adopted by the public. It's unlikely that any week other than seven days will be used, since the religious connection to the 7-day week is so strong (even though I've found ways to place religious holidays on my calendar).

I believe that the only Calendar Reform that has a chance of being adopted is the Usher Calendar. This calendar has two parts -- an invisible Leap Week and an visible Leap Day Calendar. The big change is that the Leap Day cycle is modified so that it fits the Leap Weeks -- and the cycles used in this calendar are 11, 17, and 62 years.

In fact, I wonder whether it's possible to align the Usher and Palmen Calendars. We might notice that Palmen's Leap Days (December 28ths) occur in years that start on Wednesday. In the Usher calendar, 366-day years starting on Wednesday have a special property -- such years have both a Leap Day (February 29th) and a Leap Week (Week 1 -- normal weeks are numbered 2-53). And so I referred to such years as Double Leap Years. (Years starting on Thursday always contain Leap Week, but the dates are wrong if they were to contain a Leap Day as well. In fact, Usher created his Leap Day rule for the express purpose of avoid having any year starting on Thursday contain a Leap Day.)

And so it would be nice if we could align the calendars so that Usher's Double Leap Years are the same as Palmen's December 28th years. But there is one problem -- Palmen's "Rata Die" epoch:

and the Rata Die epoch of Monday 1 January 1 CE in the Proleptic Gregorian calendar.

OK, so the year 1 in Palmer's Calendar starts on a Monday. Since every cycle is 62 years long, this means that the years 63, 125, 187,..., 1923, 1985, 2047,..., all start on Monday. Now let's check the dates on the Gregorian Calendar:

January 1st, 1985, was a Tuesday.

January 1st, 2047, will be a Tuesday.

January 1st, 2109, will be a Tuesday.

January 1st, 2171, will be a Tuesday.

and every 62nd year after that, up to the year 2419, falls on a Tuesday. The last time one of Palmer's cycles started on a Monday was 1923.

There's a reason for this. The Gregorian and 62-Year Calendars differ by about one day every 1771 years, and so every date after the year 1771 figures to be one day off. The only reason this makes any difference is that I want the transition to the Usher Calendar to be a smooth transition -- switching calendars in a year when both calendars match. But most of the time, the Gregorian and Palmer Calendars are one day off (and so would Usher, if we were to make Usher and Palmer match.).

In particular, the Double Leap Years I mentioned in my February 29th post are exactly one year before the Palmer December 28th years. That's because the "years beginning on Wednesday" are one year off.

It's possible to make the transition in Gregorian February 29th years starting on Monday. These years often match because January 1st falls after the Palmen 366-Day year (starting on Saturday) yet before the Gregorian February 29th. The next such year is 2024 -- after that it's 2052.

Notice that if we end up aligning Usher Double Leap Years to Palmen's December 28th years, then yes, these years will match, but not necessarily other years. On the Usher Calendar, 366-Day years can start on any day except Thursday, but Palmer long years start only on Wednesday and Saturday. But in the long run, the two calendars are equivalent.

I'm actually upset that I didn't come up with this idea before Palmen did. Indeed, the fact that no Palmen year can start on a Sunday reminds me of the fact that the Rose Parade and Rose Bowl game can never occur on Sunday. In such years, the parade and game occur on Monday, January 2nd. (But on the Palmen Calendar, dates span the entire weekend, and so January 1st would be both Saturday and Sunday in such years. So just have the parade and game on Saturday.)

Meanwhile, I was also fascinated with the Jewish Calendar. It turns out that the Jewish New Year can never fall on Sunday. In particular, neither Rosh Hashanah nor Yom Kippur can fall on the day before or the day after the Jewish Sabbath. To avoid this, the second and third months of the year can have either 29 or 30 days -- whichever results in Rosh Hashanah falling on a legal day. (Since Hanukkah falls near the end of the third month, it means that the date of the eighth night can differ by one day.)

So the equivalent in our calendar would be for every Saturday, January 1st to be followed by February 29th, so that the next January 1st is on a Monday. That is, we fiddle with the Leap Day so that the Rose Parade and Rose Bowl can always fall on January 1st, yet never on Sunday. (Notice that on this version of the calendar, since January 1st can never be Sunday, then January 2nd can never be Monday, and January 3rd can never be Tuesday, and likewise every date has one day it can never fall on.) It only remains when the extra Leap Days must occur, since only doing them in years starting on Saturday means that Leap Day is only once every six years, which isn't enough.

And this is essentially want the Palmen Weekend Rest Calendar does -- except, of course, weekends share a single date. And Palmen figured out how often the additional Leap Days need to occur -- namely four times every 62 years.

It might be interesting to have a version of the Usher Calendar with Leap Days only in years starting on Saturday or Wednesday, matching the Palmen Calendar (but with dates numbered normally, not with combined weekends). Leap Weeks occur either in years starting on Thursday, or Double Leap Years starting on Wednesday. This works, though it's no longer the calendar described by Andrew Usher. I point out that this simpler leap rule might be easier to motivate. -- I already used football to motivate the Usher Calendar in my February 29th post, so we can use football again (the Rose Bowl) to motivate the new leap rule. (Notice that unlike the other Usher holidays, New Year's Day really has to be January 1st and can't be fixed to a day of the week. But we can at least make New Year's Day avoid Sunday.)

Then again, while the Usher Calendar is the only Calendar Reform that could actually happen, I've always put more thought into my Eleven Calendar. But is the Eleven Calendar really my invention?

theAbysmal Eleven Calendar

I've read about theAbysmal Calendar a few years ago -- officially, this calendar began on December 21st, 2012 (the Mayan "end of the world") with the year zero.

While the main version of theAbysmal Calendar is a 13-month calendar, the author has posted several versions of his calendar. And it's come to my attention that there's even an 11-month version:

https://calendars.wikia.org/wiki/TheAbysmal_Calendar

https://decolonizingtime.wordpress.com/time-lab/theabysmal-2/363-day-calendars/

This particular calendar is a recent discovery, and to my knowledge, is the first with 11 months of 33 days.

And now I'm wondering, what the...? I've always thought that my Eleven Calendar was original, and now this guy claims that his calendar is the first 11-month calendar? (I use masculine pronouns here since, face it, most Calendar Reformers are male. I do acknowledge the Primavera Calendar, named for its female creator. And of course Wendy Krieger helped me with my Eleven Calendar as well.)

I announced my calendar on January 1st, 2016. The blog entries at theAbysmal are undated (how ironic for a calendar blog), so I can't be sure when his Eleven Calendar was created. I did check the edit history at Calendar Wiki and noticed that the edit mentioning an 11-month calendar was made just earlier this month. So it's likely that theAbysmal 11-month calendar is less than a year old.

I admit that theAbysmal Calendar was one of my inspirations. But at the time Wendy and I were working on the Eleven Calendar, there was no 11-month Calendar at theAbysmal website. Hence I was able to claim my Eleven Calendar as original.

Unlike most versions of theAbysmal Calendar that start at the winter solstice, his 11-month Calendar starts on the summer solstice, June 22nd:

The 363-day Calendar begins on June 22 (21), on or about the Northern Solstice.

He states that the two blank days are September 7th and April 5th, in addition to Leap Day, which occurs at the end of the year on June 21st. In the simplest version, theAbysmal Leap Day occurs four months after Gregorian Leap Day (and so the blank day moves up to April 4th in such years). The author hasn't developed a full Leap Day rule for any of his calendars, though he states that he's considering a 128-year cycle.

The following link shows a full version of his 11-month (and other) calendars:

https://decolonizingtime.wordpress.com/time-lab/symmetry-of-the-year/calendar-building-iv/

This author likes to begin counting with zero, and so the months are numbered 0-10, and the dates within each month are numbered 0-32. He refers to the 11 months of the year as "elevonths" (as in 11 months, of course) and the three 11-week thirds of the year as "terms" (so the sports seasons that I described in previous posts are actually terms).

I could align my Eleven Calendar with theAbysmal 11-month calendar, just as we aligned the Usher and Palmen Weekend Rest Calendars. But then I'd be conceding that theAbysmal is the originator of the Eleven Calendar, even though my calendar predates his by over four years.

Here's what I'm going to do. In my December 27th post, I mentioned a version of the Eleven Calendar that starts in the summer, on July 1st -- and that was weeks after theAbysmal edited Calendar Wiki to announce his 11-month calendar. Therefore, I acknowledge theAbysmal as the creator of the 11-month calendar that begins in summer, and align the holidays I mentioned in that post to his calendar. (I edited that post as well, to remove mention of anything that contradicts theAbysmal Elevonth Calendar.)

Note that theAbysmal doesn't state what the days or months are named, so here I go. The months will be named from July-May, so that each month overlaps the Gregorian month of the same name. The months will be numbered 0-10, as stated by theAbysmal. The days of the week will be named Zeroday up to Tenday, again in accordance with theAbysmal's numbering conventions.

And theAbysmal emphasizes the symmetry inherent in his calendar. It's possible to set up a six-day school week as detailed in previous posts, but do it symmetrically. Twoday-Fourday are school days, with Fiveday as the midweek day off. Sixday-Eightday are school days, and then the weekend lasts from Nineday to Oneday.

The Christian Sabbath can be Oneday since the Bible states that the first day of the week is the holiest for Christians. (Yes, the week starts on Zeroday, but the Bible mentions 1, not 0.) Then Zeroday becomes the Jewish Sabbath and Tenday the Muslim Sabbath. (I was considering making Nineday -- the penultimate day of the week -- be the Muslim Sabbath, but I also want Muslims to have a day of preparation for the Sabbath on Nineday.)

The two blank days, September 7th and April 5th (or 4th), can be Assumption and Easter, and vacation weeks can be set near those weeks. As for Christmas, the winter solstice is the middle day of the year, and so in the name of symmetry, we can place Christmas on that day, and take the entire week off for winter break. But notice that these three vacation weeks don't divide the year equally into three equal terms as defined by theAbysmal. I'll leave it open for now whether it's better to divide the year equally or around the religious holidays. 

Holidays can be placed on the same day of the month each year, as previously stated. But the Fourth of July (which now means day 4 of month 0) is now a Fourday, which is a school day. But the date corresponding to Gregorian July 4th is now (00/12), a Oneday, so Americans might choose to place all holidays on the 12th of the month. Note that theAbysmal is Canadian, and so he might wish to place holidays on the 9th of the month, corresponding to Gregorian July 1st, Canada Day. (Then 01/09 would be the new Civic Day, 02/09 the new Labor Day, and so on.)

Notice that 03/00 corresponds to September 30th, and 03/32 is November 1st. Thus October 1st-31st line up in both calendars (except that October is now month 3 -- here I make no attempt to match up the Latin month names). Pi Day 03/14 becomes October 14th, which falls on Threeday, a school day.

One more thing about this calendar is that since it starts in the summer, students can advance to the next grade at the start of month 0 and leave it at the end of month 10. In fact, the months 0-10 can then be used for school pacing, particularly for a curriculum like APEX. Month 0 can be used for introductory activities, and then Unit 1 is taught in month 1, Unit 2 in month 2, and so on. If Christmas is on the winter solstice and winter break is the middle week of month 5, then the APEX Unit 5 (which is a semester final) can be given the first week of month 5. After winter break, the third week of month 5 another introductory week to get back into the flow of things, and then Unit 6 starts in month 6, leading up to the Unit 10 final in month 10. (This all presumes that we use winter break to divide the year into semesters, rather into the trimesters/terms mentioned by theAbysmal.)

All that's left is the year numbering. We know that theAbysmal uses 0 to name the year that started on December 21st, 2012, but he doesn't name the years in his Elevonth Calendar. I think it's better to let year 0 start on June 22nd, 2012, so that both this and the other Abysmal Calendars can use the same rules for Leap Days.

Once we acknowlege that theAbysmal created the Elevonth Calendar that starts in summer, then I remain the originator of the Eleven Calendar that starts in March. 

Links to Other Challenge Participants

Today I link to Anne Agostinelli -- again, she doesn't actually mention Yule Blog, but she's linked to right there on Shelli's blog, so that's close enough:

http://53degreeshift.blogspot.com/2020/12/we-are-not-martyrs-we-are-not-trees.html

She mentions teaching both middle school and fifth grade:

Now, finally, I have come full circle back to the school where I began my career. My then-AP is now our principal and the vibe is back to the magic that prioritized kids and their families back in the good old days. I learned so much from my pit stops along the way, and I needed them to grow within and beyond my career, but I'm so happy to be "home" where I will finish my career.

And she has her own opinion of what's missing from teaching in 2020:

We are in a strange time in education, and too many districts are showing how little they value us by ignoring the global pandemic that is raging around us. Classroom teachers are omitted from the narrative, while we are the ones doing the actual work of nurturing youth through this challenging time.

Conclusion

Well, this concludes my last post for 2020. My final task this year will be to tear up the paper New Year's glasses that I wore twelve months ago, as a symbolic end of this annus horribilis. May we all have a much better year in 2021.

Cold Moon Post: 3 Good Things from 2020

Table of Contents

1. Introduction

2. Yule Blog Prompt #11: 3 Good Things from 2020

3. A Nine-Month Calendar Reform for 2020

4. Sports and Christian Holidays on the Eleven Calendar

5. Calculating the Cosmos Chapter 13: Alien Worlds

6. Links to Other Challenge Participants

7. Conclusion

Introduction

Tonight is the full moon. The full moon at this time of year is often referred to as the "Cold Moon" or the "Long Nights Moon," named for its proximity to the winter solstice.

Two months ago, there was a Blue Moon on Halloween -- the second full moon of October. On lunar calendars such as the Islamic, Jewish, or Chinese Calendars, every month contains exactly one full moon and so there are no Blue Moons. On solar calendars such as our Gregorian Calendar, blue moons can and do occur.

That's enough about full moons. It's time to continue the Yule Blog Challenge. And since today is the eleventh day of winter break, let's proceed with the eleventh prompt.

Yule Blog Prompt #11: 3 Good Things from 2020

This one is tricky -- the task is to find good things that happened during a pandemic. To find three things from 2020, let's divide the year into three equal parts and find something good from each part. The three parts of the year, after all, correspond to different stages of the pandemic:

January-April: The coronavirus is a little problem.

May-August: The coronavirus is a big problem.

September-December: The coronavirus is a problem with a solution.

So let's dive in. One good thing that happened to me from January-April concerns subbing in one of my districts -- specifically the one in LA County. Even though I've worked for this district for several years, I rarely received calls from that district.

That changed in the 2019-2020 school year. I started getting calls at least once a week -- and sometimes several calls in a week. This started in September 2019 and continued into early 2020. Indeed, it marked the most calls I've received from this district in a school year, despite the virus closure.

As it turned out, most of these calls were for English classes. But on March 9th, I subbed in a high school math class. It was a Monday, and so all classes met that day. One of the classes was Calculus BC and another class was Statistics. The other three classes were all Algebra I.

I definitely enjoyed subbing that day. I've never taken high school Stats (though I do remember some things I learned in a college Stats course at UCLA), and while I passed Calculus BC with a score of 5, I don't remember studying parametric equations much at all. Thus during those classes, I was learning almost as much as the students were. In the Algebra I classes, I gave the students some tricks to help them graph quadratic functions. And so this day of subbing -- along with all the assignments I had in my old district this year -- comprise the first good thing of 2020.

The next day, I also subbed in my old district, in an English class I'd covered a few times before. Then I had a multi-day assignment in another English class in my main Orange County district, which lasted from March 11th-13th. And we all know what happened next.

One good thing that happened to me from May-August concerns what I did instead of subbing while all the schools were closed. I took the time to learn a new computer language -- Java, the language of the AP Computer Science exam.

I began my study of Java at the start of May. My textbook was an online text by Laura Lemay, and I even kept track of my progress right here on the blog. The highlight of my study was on July 6th, when I reached the graphics lesson. After I read this chapter, I even wrote a short applet using the graphics I learned -- a Monte Carlo simulation to estimate the value of pi.

I proceeded very slowly through Lemay's text, so I didn't get very far past the graphics lesson. And I did read other books during the long break, including Ian Stewart's Calculating the Cosmos. And so all the books I read this summer -- especially Lemay's Java text -- comprise the second good thing of 2020.

One good thing that happened to me from September-December is obvious -- the schools reopened, and I landed a long-term assignment in a middle school math class. I've written extensively about this long-term several times during the Yule Blog Challenge.

I began the long-term assignment with APEX Unit 2 in both seventh and eighth grades. The Math 7 unit was on adding/subtracting signed numbers and the Math 8 unit was an introduction to functions. Most students in both grades seemed to understand the information well. My long-term overall comprises the third good thing of 2020.

A Nine-Month Calendar Reform for 2020

Let's get back to Calendar Reform. Earlier, I suggested a nine-month calendar with the months April, May, and June removed, since there were no sports played in spring 2020 during the pandemic. It was during those months when it was easy for me to lose track of "COVID-19 time." March seemed to drag on forever until finally it was July and sports resumed.

Here's a link to a possible nine-month Calendar Reform: the Modern Calendar:

https://calendars.wikia.org/wiki/Modern_Calendar

On this calendar, the nine months have 40 days each. Here February, June, and December are the months that are dropped. Actually, since 40 * 9 is only 360, a five- or six-day period called December is placed at the end of the year.

Since 40 is a multiple of eight, the Modern Calendar has eight-day weeks. The extra day is placed between Friday and Saturday and is called "Remday." All weekends are three-day weekends, and so all holidays are placed on Remdays.

On my COVID-19 version of the Modern Calendar, the extra day of the week should be the Muslim Sabbath, and so there would be two Fridays ("Thank God It's Friday," the last day of the workweek, and "Thank Allah It's Friday," the Muslim Sabbath and first day of the weekend) instead of Remday. We might even wish to let Monday be the first day of the week, so that TAI Friday becomes the sixth day, Saturday the seventh day, and Sunday the eighth day of the week.

As for the months, we wish to skip April, May, June, so that the nine 40-day months are named from January-March and July-December. But what should we name the final five or six days, if December is already taken as one of the 40-day months?

Moreover, by dropping February and June, the Modern Calendar linked to above restores the original Latin names of September-November as the 7th-9th months, as well as December as a (miniature) tenth month of sorts. But if we skip April-June, then September becomes the sixth month. It's desirable, if we have to change September so that it's no longer the ninth month, at least to let it be the seventh month to match its Latin name.

One way to solve both problems is to place the extra five-six days between March and July. This short month becomes the new fourth month, so that July is the fifth month and September the seventh, as suggested by Latin, and December is a full 40 days. A good name for this new month is "May," since it actually lines up with the first five days of Gregorian May, assuming January 1st is the same in both calendars. (In years with a February 29th, such as 2020, the mini-month of May spans April 30th-May 5th, so they don't exactly line up in 2020, even though the stated goal of this calendar is to match the 2020 sports calendar.)

In the original Modern Calendar with December as the short month, it's stated that this December becomes a special holiday period, with Christmas on December 1st. On my version of the calendar with May as the short month, this May can also be a special holiday period. May 1st can remain May Day (or International Labour Day), and May 5th can remain Cinco de Mayo. This is the same as Children's Day in Japan -- and indeed, this mini-month of May lines up very nicely with Japanese Golden Week.

OK, but our goal is to place sports on this calendar. And the original idea is to place the sports in the same named months as they occurred in 2020. Using this rule, here are when the regular seasons of the four major sports take place:

NFL: September-December (we won't use exact dates here, but focus mainly on Sundays)

MLB: July 23rd-September 27th

NBA: December 22nd (2020 start date)-August 15th (2020 play-in game)

NHL: January 13th (2021 start date)-August 9th (2020 last qualifying game)

But note what impact these changes have. The NFL season is expanded from its original pre-pandemic length -- even though it remains at four months, these four months now have 40 days each, which includes 20 Sundays. The NFL was already eying lengthening the season to 17-18 games anyway -- with 20 Sundays, there's enough time for 18 games with two bye weeks. And there's even more rest built in since consecutive Sundays are now eight days apart instead of seven.

The NBA and NHL remain close to their usual lengths. Before the pandemic, their seasons spanned about six months or half the year. On this new calendar, the NBA, starting in December, is slightly longer at about five (out of nine, not counting short May) months and the NHL, starting in January, is slightly shorter at four months.

But it's baseball that gets the short end of the stick. In 2020, baseball played only 60 games -- the only major sport not to play even half of its usual season. Even with July, August, and September having 40 days instead of 30-31, the season is still much shorter than usual. It might be better to let baseball have the entire months of July, August, and September rather than wait until July 23rd. With 15 weeks in these three months and assuming baseball is played 6-7 out of eight days per week, there is enough time for around 100 games.

One concern in the NBA and NHL in 2020 is that football is the most popular spectator sport by far -- any other sport scheduled against an NFL game ends up suffering in the ratings. This has always been a problem for baseball, since unlike the other sports, MLB's biggest games -- the September division races and October playoff games -- are played during football season. In 2020, the NBA and NHL had to suffer this as well, with their playoff games scheduled during football season -- and indeed, both sports had their lowest ever postseason ratings. A few years ago, baseball changed its World Series schedule to avoid the big football nights of Thursday and Monday, and this year, the NBA and NHL had to do the same with their respective Finals.

One reason for football's popularity is that it has the shortest season, and so even a single regular season game matters more than a playoff game in MLB, NBA, or NHL, unless it's Game 7. (Another reason for NFL's dominance is fantasy football -- it causes fans to be interested in teams other than their favorite team, whereas with the other sports, fans don't watch unless their team is playing.) In other words, football has the perfect season length, while the other sports' seasons are too long.

And so not only would baseball object to my calendar due to its shorter season, but so would basketball and hockey, if I permanently set their playoffs against the NFL's regular season. Again, when I first came up with this idea, I thought that sports would resume in May. Then baseball would have had just a slightly shorter season, and the NBA and NHL playoffs would still end before football begins.

If I really wanted a sports schedule that fits the nine-month calendar, I'd instead accept that football -- at four Gregorian months, or one-third of the year -- has the perfect season length. Then I'd shorten all other sports so that all seasons are one-third of the year (that is, three of the nine full-length months):

NBA/NHL: January-March

MLB: July-September

NFL: October-December

The month before the regular season starts is the preseason, and the month after is the postseason. This allows fans' eyeballs to move on to the next sport based on their team's position in the standings. In September, fans of baseball teams still in contention can watch baseball while fans of last place teams move on to the NFL preseason. In October, fans of playoff teams watch baseball while fans of teams not in the playoffs watch the NFL regular season. In November, all fans watch football. In December, fans start looking ahead to preseason NBA/NHL if their football teams are out of contention, and so on.

But while football season is still one-third of the year, there are now only 15 Sundays in this range, so there aren't enough weeks to play 16 games. One solution is that, as Thursdays are already established as a football night, more games can be played on Thursdays. We wouldn't want to make players play Sunday-Thursday-Sunday with just three days off in between the games, so instead, teams play several Thursday games in a row. Then only twice in a season do they have just three off days -- from Sunday to the first Thursday game, and from the last Thursday game to Sunday. All other weeks they have seven off days between games -- an extra day, to compensate for the lack of a bye week.

As I mentioned earlier, there will be about 100 baseball games per regular season. Basketball and hockey, if they play 3-4 times per eight-day week, will end up with a 50-game season.

On the original Modern Calendar with a short December, basketball can start on that December 1st, since Christmas is always a big NBA day. Hockey might wish to wait until January 1st -- New Year's Day (with the Winter Classic) is the bigger holiday in the NHL. In my version of the calendar with a short May, this might be baseball's opening week.

OK, that's all I wish to say about the nine-month, eight-day calendar. It's not my favorite calendar -- again, when I first came up with this sports idea, I was hoping sports would resume in May so that the resulting virus-inspired calendar would be the Eleven Calendar. So now I must ask, what would the sports schedule look like on the Eleven Calendar?

Sports and Christian Holidays on the Eleven Calendar

I still like the idea of dividing the calendar into three parts. Notice that I already divided the year into thirds when I responded to the Yule Blog challenge, and I did the same with the nine-month calendar. I point out that we can also do the same with the 12-month Gregorian Calendar -- football season can remain September-December, but now NBA/NHL is January-April and baseball is May-August.

In the Eleven Calendar, we can't easily divide the eleven months into thirds. But recall that I already defined three holidays that indeed trisect the year -- Christmas, Easter, and Assumption. So we have:

NBA/NHL: Christmas-Easter

MLB: Easter-Assumption

NFL: Assumption-Christmas

The NBA, of course, would be thrilled to start on Christmas, while the NHL might prefer to start a few days later. Once again, I expect there to be 50 NBA/NHL games each and 100 MLB games.

But the NFL will have the most problems with this schedule. The week is eleven days long, and each third of the year has eleven weeks. So there are only 11 Sundays available for football.

Once again, the solution will be to have more midweek games. Since Sunday is the third day of the week, we might choose Eightday or Nineday. Recall that Eightday was an alternate day for the Christian Sabbath, while Nineday might have more of a "Thursday" feel to it (as Tenday is the last day of the workweek).

Perhaps Sevenday, as the midweek day off, might be a suitable day for football. There would be three days off if a team plays both Sunday and the following Sevenday (similar to Sunday-Thursday in the Gregorian Calendar), while there are six days off between Sevenday and the following Sunday (like Sunday-Sunday in the Gregorian Calendar). So playing Sunday-Sevenday-Sunday isn't impossible -- and after all, a team wouldn't need to play every Sevenday. If this is still too tough, then teams can be scheduled on two Sevendays in a row without playing on the intervening Sunday. There will be less need for bye weeks since the majority of the time, there would be ten days off between games.

By the way, I was also thinking about placing other religious holidays on the Eleven Calendar. For example, if there's an Easter on my calendar (April 25th), then when does Lent begin? Lent usually begins on Ash Wednesday, but there is no Wednesday in the Eleven Calendar. It's also said to begin 40 days before Easter, but Ash Wednesday is actually 46 days before Easter. The usual explanation is that when counting the days of Lent, Sundays don't actually count.

We could count Lent the same way in my calendar -- 40 non-Sundays. Notice that in my calendar, this is easy -- there is one Sunday and ten non-Sundays per week, so 40 non-Sundays is four weeks. This takes us back to March 14th. We might start Lent on that Sunday itself, or perhaps the next day, which is a Fourday, March 15th. (The Orthodox start Lent on a Monday as well -- Clean Monday -- but they count the 40 days differently.)

Indeed, we might count backwards from Christmas to Advent the same way -- 40 weekdays plus four Sundays before Christmas, which takes us to October 25th. This is Veteran's Day on my calendar (and reminds us of Martinmas -- an old definition for the start of Advent). Or if we prefer, we might start Advent just two Sundays before Christmas, on November 14th. (This is December 3rd Gregorian -- the latest possible start of Advent.)

It's convenient to use this same method to other holidays before Easter as well. Before Lent, we have Quinquagesima, Sexagesima, Septuagesima Sunday. These names are Latin for 50, 60, 70, but as usual they are misnomers -- Septuagesima is only nine weeks (or 63 days) before Easter. We can use exclusive counting (weekdays only, no Sundays) and count back five, six, seven weeks before Easter so that all of these are Sundays. So we reach March 3rd, January 25th, January 14th for these days. (Notice that moving back into January also means skipping over the blank days -- so my Septuagesima ends up being 79-80 days before Easter. Maybe I shouldn't complain about the real Septuagesima being only 63 days before Easter after all.)

After Easter, we have Pentecost Sunday, so-named because it's 50 days after Easter. So we count five weeks after Easter to obtain June 14th. Ascension is said to be 40 days after Easter -- usually it's a Thursday, but if we count four weeks after Easter, we can force Ascension to be on Sunday, June 3rd.

When are the Twelve Days of Christmas (you know, the twelve days which inspired the 12-Day Twitter and Blogger challenges)? Sometimes they are said to be December 25th-January 5th, and other times they are said to be December 26th-January 6th (excluding Christmas Day but including Epiphany).

Well, on our calendar, let's place Epiphany on another Sunday, December 14th. Then our Twelve Days of Christmas can include both Sundays and the ten days in between, December 3rd-14th. But for Candlemas, which is 40 days after Christmas, we'll return to excluding Sundays and count it as four weeks after Christmas, January 14th.

(Hey -- so we're including Sundays to count Epiphany but excluding them to count Candlemas. But compare that to how Christians actually count these holidays -- exclusive counting is used to mark January 6th as 12 days after Christmas, but inclusive counting is used to mark February 2nd as 40 days after Christmas!)

Also, notice that Candlemas (the last day counting forward from Christmas) and Septugesima (the first day counting backward from Easter) fall on the same day, January 14th. This can sometimes happen on the current calendar -- in 2021, Septuagesima is on January 31st, two days before Candlemas. (Hey, that allows me to avoid the 79-80 day problem with Septuagesima -- just call it Candlemas and drop the name Septuagesima altogether.)

Calculating the Cosmos Chapter 13: Alien Worlds

Earlier in this post, I mentioned reading Ian Stewart's book as one of the "good things" I did during this past summer. I started summarizing his book here on the blog, but then abruptly stopped when the schools reopened and my long-term subbing began. I even typed up a summary for Chapter 13, but then left it in drafts and never posted it.

I also watched Neil DeGrasse Tyson's Cosmos on National Geographic last spring, but I missed an episode and didn't watch it until just two weeks ago when it aired on FOX. Both the missing episode and the chapter I summarized in drafts are on the same topic -- life outside the solar system.

Since I finally summarized the last Tyson episode on December 15th, I'll finally post the chapter that's been stuck in drafts all these months. (I'll still wait until next summer to continue with Chapter 14.)

Chapter 13 of Ian Stewart's Calculating the Cosmos is called "Alien Worlds." As usual, it begins with a quote:

"Alien astronomers could have scrutinized Earth for more than a billion years without detecting any radio signals, despite the fact that our world is the poster child for habitability."

-- Seth Shostak, Klingon Worlds

And the proper chapter begins:

"It's long been an article of faith among science fiction writers that the universe is littered with planets."

Today's chapter is all about planets -- and more specifically, the possibility that life exists on planets outside our solar system. After all, the universe contains countless stars and dust particles:

"It would be strange if there were some forbidden intermediate size range, and even stranger if it happened to coincide with the typical sizes of planets. Indirect arguments are all very well, but the elephant in the room was notable by its absence."

In other worlds, if there are so many planets teeming with life out there, where are they? A Russian-American astronomer, Otto Struve, noticed that the motion of the sun is influenced by the gravity of the planets that orbit it.

Here Stewart includes his first picture -- the motion of the sun relative to the center of mass of the solar system, 1960-2025. Indeed, during these 65 years the sun moves around the center at least two or three times:

"The overall movement is about three times the Sun's radius. Struve's technique of Doppler spectroscopy led to the first confirmed exoplanet sighting in 1992, by Aleksander Wolszczan and Dale Frail."

At this point the author writes about some possible exoplanets orbiting Alpha Centauri, one of the closest stars to the sun -- but the findings are mostly likely false. Since the book has been published, two exoplanets orbiting Proxima Centauri have been discovered and confirmed.

"Initially the only worlds that could be observed were 'hot Jupiters': massive planets very close to their stars."

Another way to spot exoplanets is to observe how the star gets dimmer as a planet crosses it:

"As the planet begins its transit, it starts to block some of the light from the star. Once the entire disc of the planet lies within that of the star, the light output levels off, and remains roughly constant until the planet approaches the other edge of the star."

Now Stewart includes two diagrams. The first is a simple model of how the star's light output becomes dimmer when a planet transits. Assuming the star emits the same amount of light at each point, and that planet blocks all of it, the light curve remains flat while the whole of the planet blocks the light. In practice these assumptions are not quite correct, and more realistic models are used.

In his second diagram, the author shows a graph of the actual light curve of the 1 June 2006 exoplanet transit of the 10x8 R-magnitude star XO-1 by the Jupiter-sized planet XO-1b. Solid dots are 5-point averages of magnitudes from images shown by small dots. The line is a fitted model.

Scientists learn much information about the planet using this transit method:

"It sometimes tells us about the chemical composition of the planet's atmosphere, by comparing the star's spectrum with light reflected from the planet. NASA chose the transit method for its Kepler telescope -- a photometer that measures light levels with exquisite accuracy."

With this telescope, over a thousand exoplanets have been discovered:

"For example, the star systems Kepler-25, Kepler-27, Kepler-30, Kepler-31 and Kepler-33 all have at least two planets in 2:1 resonance."

Two German-Swiss astronomers, Michael Hippke and Daniel Angerhausen, have been searching for exoasteroids, but not by using a simple transit method:

"Instead, Hippke and Angerhausen use a statistical approach, like wandering through a game reserve counting lion tracks."

And this is shown in two of Stewart's next graphs. On the left are the combined light curves for a million transits, showing small dips at the Trojan points L4 and L5 (marked). These are not statistically significant. On the right, "folded" data show a statistically significant dip, indicating the existence of Trojan asteroids there.

Of course, even if many planets exist, do any of them have intelligent life? The most famous astronomer who considered this question was Frank Drake. (By the way, Frank Drake is still alive -- he celebrated his 90th birthday a few months ago.)

"He was trying to isolate the important factors that scientists should focus on. His equation has flaws, if you take it literally, but thinking about them provides insight into the likelihood of alien civilizations and the possibility that we could detect their signals."

It helps that life is known to adapt to the prevailing conditions:

"Even on Earth, living creatures occupy an astonishing variety of habitats: deep in the oceans, high in the atmosphere, in swamps, in deserts, in boiling springs, beneath the Antarctic ice, and even three kilometres underground."

Still, the hunt for habitable planets focuses on those where liquid water can exist -- planets that are neither too close nor too far from its star, where it is neither too hot nor too cold:

"In between, the temperature is 'just right,' and inevitably this region has acquired the nickname 'Goldilocks zone.'"

Actually, in our solar system Mars is in the Goldilocks zone, and indeed the red planet may once have had liquid water billions of years ago, before it froze:

"Mostly, it stays that way. Distance from the primary, then, isn't the only criterion. The concept of a habitable zone provides a simple, comprehensible guideline, but guidelines aren't rigid."

There is a picture of the red planet here. Dark streaks in Garni crater, on Mars, are caused by liquid water that melts and refreezes every year.

The Kepler telescope has discovered at least one potentially habitable planet -- Kepler 62f, orbiting the star Kepler-62:

"Other confirmed exoplanets that resemble Earth include Gliese 667Cc and 832c, and Kepler 62e, 452b, and 283c."

Proxima Centauri b, discovered a few months after this book was published, would also be included on this list. It's also possible that life can exist elsewhere in our our solar system:

"If life exists elsewhere in the solar system, where is it most likely to be? As far as we know, the only inhabited planet in the Sun's habitable zone is the Earth, so at first sight the answer has to be 'nowhere.'"

But there's an outside chance that life may exist on moons such as Titan, a satellite of Saturn:

"Its diameter is half again as big as the Moon's, and unlike any other moon in the solar system it has a dense atmosphere."

But our water-based biology won't work on Titan, which is too cold for liquid water:

"Our cells are surrounded by a membrane formed from phospholipids -- compounds of carbon, hydrogen, oxygen, and phosphorus."

Instead, Titanian biology would be completely different from terrestrial biology. Here on our planet, there are several "universals" that many species have:

"One sign of a universal is that it has evolved several times independently on Earth. For example, flight has evolved in insects, birds, and bats, by independent routes."

On the other hand, a trait specific to the conditions of our planet is called a "parochial." For example, DNA is probably a parochial:

"If we encountered aliens who had developed a spacefaring civilization, but didn't have DNA, it would be daft to insist that they're not alive. I said 'specify' rather than 'define' because it's not clear that defining life makes sense."

And indeed, the author has come up with his own thought experiment -- Nimbus is a moon similar to Titan and harbors life:

"The original description had much more detail, such as evolutionary history and social structure. Nimbus, as we envisaged it, is an exomoon with a dense atmosphere of methane and ammonia."

In this story, silicon-based life forms developed on Nimbus. These organisms are similar to our computers (or robots) and reproduce like a cellular automaton, similar to the mathematical games created by John von Neumann (and later on by John Conway). Each automaton have three parents:

"One parent stamps a copy of its builder circuit on to bare rock. Later, another passes, notices the stamped circuit, and adds a copy of its copier. Finally, a third parent contributes a copy of its data."

Admitting that such alien organisms are unlikely, Stewart concludes the chapter as follows:

"But they illustrate the rich variety of new possibilities that might evolve on worlds very different from ours."

Links to Other Challenge Participants

I link to Kim Charlton, a middle school teacher who also responds to the "3 Good Things" prompt:

http://logicalpoetry.blogspot.com/2020/12/3-good-things-from-2020.html

One of her "3 Good Things" also started before the pandemic:

We got a puppy! We got her back in February and she has been absolutely amazing during the pandemic. I am NOT a dog person, I was attacked by a Rottweiler at a very young age and have a lot of anxiety around dogs. But my husband did a lot of research and got us a corgi. She's small dog who doesn't jump on us or drool too much. She's super cute and snuggles with me all the time.

I always enjoy reading middle school blogs since I'm working in one now, and so Charlton's blog is one I'll be watching for in the near future.

Conclusion

I have one more calendar to discuss, and I will in my next post. I usually don't post this often during Calendar Reform week (the week between Christmas and New Year's) -- but then again, I haven't had a Yule Blog Challenge to inspire me to post this off.