1. Introduction
2. A Blog Omission
3. What I Still Remember About That Science Class
4. Reblogging About the Green Team
5. What Actually Happened with the Green Team
6. An Interesting Rapoport Problem
7. Cosmos Episode 13: "Seven Wonders of the New World"
8. Earth Day and the Coronavirus
9. Revisiting the Fourth Dimension Yet Again
10. Conclusion
3. What I Still Remember About That Science Class
4. Reblogging About the Green Team
5. What Actually Happened with the Green Team
6. An Interesting Rapoport Problem
7. Cosmos Episode 13: "Seven Wonders of the New World"
8. Earth Day and the Coronavirus
9. Revisiting the Fourth Dimension Yet Again
10. Conclusion
Introduction
Today is April 21st. Lately, I've been naming these posts after the special day or holiday on which I post them. But today falls right in between several holidays as observed on different calendars:
- Yesterday was Patriots' Day. It is celebrated mostly in New England -- especially Boston, with two special sporting events: the Boston Marathon and the 11AM Red Sox game. (Of course, due to the coronavirus, neither of those events are taking place today.) Because of this, spring break in this area is tied to Patriots' Day, not Easter. (Last year, Patriots' Day fell during Holy Week, but this is rare.)
- On the Hebrew Calendar, today is Holocaust Remembrance Day, although technically the holiday ended earlier this evening, at sunset. Through Cosmos, I've recently blogged about some Jewish scientists who were victimized by the Holocaust.
- On the Islamic Calendar, Ramadan starts later this week. The new moon is on Wednesday, but like all Muslim months, Ramadan will start with the sighting of the crescent. This might happen tomorrow evening in some time zones, but it's more likely to be Thursday night.
- And tomorrow is Earth Day. It will be the 50th anniversary of the second Earth Day, since the anniversary of the first Earth Day was a month ago, on March 21st.
Three years ago today, my old charter school held the culmination of the Green Team project. The reason it was on Earth Day Eve and not Earth Day itself was that the 22nd fell on a Saturday.
On the first Earth Day, I posted mainly about science, and I'll do the same in today's post. I think I'll begin with the story of a time I subbed in a science classroom, but never blogged about it until today.
A Blog Omission
It was four years ago this week when I interviewed for the position at my old charter school, and I was hired there by the end of April. Subbing, meanwhile, continued throughout May and the first few days in June.
Interestingly enough, during that last month of subbing, I had two multi-day assignments. One was during the second week in May, which I spent in a high school math class. I described it extensively on the blog. But the other long assignment, in a middle school science class during the week leading up to Memorial Day, has not been blogged.
Why didn't I mention this class on the blog? Well, that's an easy one -- at the time, I blogged about math classes and no other subbing, not even multi-day assignments. This was, after all, a math blog, and I was just hired as a math teacher. So why should I have bothered with that science class that had nothing to do with the math that I'd be teaching soon?
By now, you already know what ended up happening. At my new position at the charter school, I'd be expected to teach science in addition to math. And ironically, this middle school science class had more in common with what I'd need to teach three months later than that high school Geometry and Algebra II class.
Part of this is my own fault. I didn't need to be so stuck up about not blogging non-math classes. Even if I was subbing for a class of which there was no chance in the world that I'd be teaching soon (such as Spanish, considering that I don't speak it), blogging about it would have allowed me to reflect on other things, such as classroom management (which matters no matter what subject I'm teaching).
The other part falls on my new school. At the time I was hired as a math teacher, the thought was that a separate teacher would cover science -- indeed, such a teacher was there for the current 2015-16 school year. I suspect what happened was that she decided at the last minute not to return for the following 2016-17 school year, and no science teacher was found to replace her.
I have no idea when the administrators realized that I would need to cover science. I signed my contract in mid-June, and there was still no mention of any science class. Still, I wonder how things might have been different if I'd been informed of the possibility that I might have to teach science at the time I was hired.
For starters, I would have mentioned the full week of subbing science on the blog, as well as any other science classes I subbed for that May. Recall that there was a blogging challenge that year to post 30 times in May, so these science classes might have been something to blog about. It's doubtful that I would have described the science classes in full "A Day in the Life" format (since that wasn't part of the May blogging challenge), but at least I would have posted more details.
I also would have paid more attention to the science classes themselves. I could have looked at the walls for examples of science labs and other assignments, as well as check out the science texts to see what I'd be expected to teach (although the impending transition to NGSS standards might have affected any info I would've gleaned from the texts).
And I could have asked other science teachers for pointers. As I'd soon find out at the new school, the only other math/science teacher was at our sister charter (and she didn't teach eighth graders), so using other teachers as a resource would be difficult. On the other hand, while subbing for science, there were most likely two other science teachers right next door to me. And I'd be justified in asking them for help, especially at the school where I spent a full week teaching science (and even more so if I told them that I was a newly hired math teacher who might have science thrust upon me).
The idea, of course, is that if I could have done these things in May, I would have had a much better experience teaching science at the charter school in August. And perhaps with that better experience, I wouldn't have needed to leave the school when I did.
But of course, there was nothing I could do when I didn't know I'd be teaching science. As far as I know, during the week of May 23rd (when I was subbing science), the administrators at my new school hadn't the slightest inkling that their current science teacher wouldn't return the following year.
This is the reason why, ever since I left the old charter, I made a point to blog more about subbing in classes other than math, particularly middle school science classes, as well as days when I had to make key classroom management decisions. I want to keep a record of any ideas that might unexpectedly come in handy if I ever return to teach my own class someday.
What I Still Remember About That Science Class
Unfortunately, it's been four years since I subbed in that class. And I've subbed in hundreds of classrooms since that week. Thus I remember very little about the class. I don't even recall whether it was a sixth, seventh, or eighth grade class -- or perhaps different grade levels each period.
I do remember that some sort of written assignment (perhaps a lab) was due one day. The regular teacher told me not to collect any late assignments -- and I let the students know this. Still, one student tried to turn his assignment in late. I'd told him that if he gave he a late assignment, I'd just rip it up -- and I did. No, I didn't rip it up completely, but I left a huge half-tear in the packet, with a note to the teacher that I, the sub, intentionally ripped it because it was late. (It was up to the teacher to decide what to do about the late work.)
The main thing I do remember about this class relates to classroom management. There was an incident where several students appeared to bully a certain girl in one of the classes. I do recall that the girl was an immigrant (or the daughter of immigrants) -- but not from Mexico. I remember looking up the history of her last name and concluded that she was Ghanaian.
Often when bullying occurs, I can't tell who started it. It could be that the group was harassing the girl (perhaps because of her nationality). But it was also possible that the girl started it -- she started saying bad things about the others, and they became upset with her.
What did I do in that situation? Most likely, I said something like, "I don't care who started it, but I want all of you to stop it!" There were clear times when it was obvious that the girl was the victim -- for example, one day we watched some video about animals (which is why I suspect this was a seventh grade Life Sciences course), and one of the others remarked that the girl looks like one of the creatures from the video. But I also recall the girl insulting the others as well. The one thing I knew at the time was that I was three months away from starting at the charter school -- and the middle school kids I'd be seeing soon were likely to bully others, just as I was seeing right then.
What should I have done in that situation? As a sub, when it comes to classroom management, there are two types of conflicts that might occur -- student vs. teacher, and student vs. student. In the first situation, student vs. teacher, I'm directed in the lesson plans to give or collect some assignment or enforce some unpopular rule, and the students tell me that I'm wrong to collect the work or enforce the rule. This often led to arguments (and, unfortunately, yelling). I've found that one way to avoid arguments here is to be more subtle when enforcing the rules (that is, "pick my battles").
But if it's student vs. student, I should not be subtle when it comes to handling the situation -- I must be more emphatic. In this case, the kids want me to intervene, as opposed to the student vs. teacher situation when they want me to let them do whatever they want. And such intervention is even more necessary if it's student vs. students -- we have a single student on one side of the conflict and a group on the other, and I can't tell whether the single student is a jerk or a victim.
With that in mind, here's what I should have done: I begin by taking the side of the lone girl -- I treat her as a victim and tell the other students to leave her alone. But I warn her that I'll be monitoring the situation closely -- if at any point it appears that she's the aggressor rather than the victim, then I'll quickly side with the group against her.
One thing that might have helped -- especially considering that I'd see these kids all week -- is to speak with the girl in private. Unfortunately, I don't recall what the bell schedule was, with so much time having elapsed since the incident. Depending on the regular teacher's schedule, I might ask to see the student after class. But if this was, say, the last period of the day, she'd have wanted to go home and considered my keeping her after class to be a punishment (and hence refused to stay).
The best possible case was if her period was followed immediately by my conference period. Then she wouldn't have seen my keeping her as a punishment. (I could easily send her to her next class with a note that she was "helping out the sub.") During this time I have a heart-to-heart conversation by asking her, "Why do you think the other students bully (or don't like) you?" Then I can reassure her that I'll make every effort to protect her as long as she doesn't become the aggressor in return.
(Actually, I suspect that this week might have been part of SBAC testing -- the SBAC is often given in March or April in high schools but not until May in middle schools. Even though this was the year before the first California Science Test, the state math and ELA tests would have necessitated a block schedule that week. With a block schedule, her class was much more likely to be followed by a break than a conference period, so I wouldn't have been able to keep her.)
Assuming that this girl was indeed a seventh grader, she would have been a few months away from starting the eighth grade. There would be a few eighth grade girls at my new charter school who were often bullied, including one victim who then turned around and bullied a sixth grader herself. If I had written down (on the blog) the earlier bullying incident and learned how to handle it, perhaps I could have fared better with the bullies and victims in my new school. Maybe then the victim at my new school wouldn't have become a bully the next day -- and with better management and bully-handling skills, maybe I wouldn't have needed to leave the old school, even if I never completely figure out how to teach science properly.
Reblogging About the Green Team
Each time I make a science post, I keep referring to "Green Team" over and over again. So now you might ask, what exactly does this "Green Team" refer to?
Obviously, it refers to something that was supposed to happen at the old charter school. Let me go back and reblog parts of the November 2016 post where I first learned about the Green Team:
What Actually Happened with the Green Team
Obviously, the Green Team didn't go quite as planned. As I wrote above here, the success of the Green Team was dependent on other schools signing up for it -- and most likely, not enough schools signed up for it quickly.
The so-called "Pre-Assessment" was indeed just before winter break, but it wasn't formal -- it was just about four short questions about the students' habits (turning off lights and water, and so on).
The creator of the Green Team did visit us in January, but there was no science unit. Instead, she had the students fill out some information on the website, and two students would be randomly chosen to get T-shirts and have their pictures printed in the aforementioned newsletter. The winners turned out to be a sixth grade boy and a seventh grade girl.
And as for the science project/fair, that might have been close to starting right around the time that I left the school. I still had access to email, and saw that there would be a class visit to the LA County Arboretum on a certain Saturday in March -- a place where I once took a field trip as a young sixth grader as well.
(By the way, the Arboretum has made the news recently due to the coronavirus. It is one of the few places that has remained open during the outbreak. Meanwhile, Santa Anita Park for horse racing has been shut down, despite being in the same city -- Arcadia -- as the Arboretum.)
Thus it's possible that the Green Team science project proceeded as intended. But unfortunately, most of the action took place after I left the school.
The Green Team led me to make some questionable decisions regarding my teaching. First of all, November, when I first learned about the Green Team, was right around the time that I finally got printed teachers' editions of the Illinois State science texts (for Earth and Physical Sciences, though not for Life Science). Yet I didn't try then to start using these texts, because I thought that the Green Team would take care of my science curriculum.
Then in December, I submitted a lesson plan that reserved an entire day for the "Pre-Assessment" for the Green Team, namely the Tuesday (and penultimate day) before winter break. And this would lead to three problems. First, since the "Pre-Assessment" was just four questions, there was no real science pretest or lesson that day. Since I'd already told the students that there would be science that day, I quickly made up some science questions from the Study Island Unit 1 ("Pretest"). The students grew upset since it seemed that I was always giving them science "pretests" and without ever teaching any actual science.
The second problem was that one eighth grade girl had missed the previous week of school and tried to make up the math she'd missed. I told her not to worry about it -- there'd be no time to make it up due to the science pretest. And of course, that fizzled out, leaving her well-behind with her math (and her math grade).
And finally, it ruined my assignment for Wednesday, the last day before winter break. Because there was no real assignment on Tuesday due to the pretest fiasco, it led students to believe that there would be no work the entire week, so kids were playing around on Wednesday. One seventh grade girl would get in trouble that day for playing around with her phone. (Then again, the lesson I tried to give on Wednesday was a bad one anyway. I'd been inspired by previous days of subbing to assign a holiday graphing worksheet just before breaks, but this makes more sense in high schools when students are more comfortable with graphing, not in middle schools.)
I already wrote a month ago what I should have done here -- I should have taught science and acted as if there was no Green Team. Plan a curriculum as described (Physical Science for eighth grade, Life Science for seventh, Preferred Integrated for sixth) and just ignore Green Team activities until they actually begin. Don't include the Green Team in lesson plans until I'm completely sure that I have material for Green Team lessons.
An Interesting Rapoport Problem
There are no Geometry problems on the Rapoport calendar this week. But these days, I've been blogging Rapoport problems anyway, mainly because it's the only math I've been doing lately. (When it's not a Geometry problem, I bury it deeper in my post, as opposed to Geometry problems that I include right at the top of the post.)
Today on her Daily Epsilon of Math 2020, Rebecca Rapoport writes:
The number of subsets of {1, 2, ..., 6} that contain no consecutive numbers.
Before we begin, don't forget that sets (and thus subsets) can contain 0 or 1 element -- and of course, every such set fails to contain two numbers (much less any two consecutive numbers). Thus we already know seven subsets that work -- the empty set, {1}, {2}, {3}, {4}, {5}, and {6}.
It's easy to see that any subset with four or more elements won't work. And so all that remains are to check the subsets with 2-3 elements. There are only 6 choose 2 + 6 choose 3 = 15 + 20 = 35 such subsets, so it wouldn't take that long to check all of them.
But if we did that, we wouldn't learn as much as if we looked for patterns instead. Let's define:
f (n) = the number of subsets of {1, ..., n} that contain no consecutive numbers.
Then our goal now is to find f (6). There are two initial cases here:
f (0) = 1 (the empty set)
f (1) = 2 (the empty set and {1})
So f (2) is the first non-trivial case here. We know that f (2) is at least 2, since the two sets in f (1) work for f (2) as well. And likewise f (3) is at least as great as f (2), since any set in for f (2) works for f (3) as well. Since we're looking for patterns, let's write this as:
f (2) = f (1) +
f (3) = f (2) +
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
Looking at f (2) again, we wish to include the new element 2. There are two sets from f (1) we have so far, empty and {1}. We can't adjoin 2 to the set {1} since the new set {1, 2} contains consecutive numbers, but we can adjoin it to the empty set to obtain {2}. We adjoined 2 to the empty set -- which, if you recall, is the only set in f (0). So we have:
f (2) = f (1) + f (0)
f (3) = f (2) +
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
Looking at f (3) again, we wish to include the new element 3. There are three sets from f (1) we have so far, empty,{1}, and {2}. We can't adjoin 3 to the set {2} since the new set {2, 3} contains consecutive numbers, but we can adjoin it to the empty set to obtain {3} and to the set {1} to obtain the new set {1, 3}. We adjoined 2 to the empty set and to {1} -- which, if you recall, are the only two sets in f (1). So we have:
f (2) = f (1) + f (0)
f (3) = f (2) + f (1)
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
And by now the pattern is obvious. To find f (4), we start with the sets in f (3) and then adjoin 4 to each of the previous sets that don't contain a 3, which are exactly the sets in f (2). And we do the same with 5 and 6:
f (2) = f (1) + f (0)
f (3) = f (2) + f (1)
f (4) = f (3) + f (2)
f (5) = f (4) + f (3)
f (6) = f (5) + f (4)
That's right -- the values of f (n) are simply the Fibonacci numbers! And since f (0) is the second Fibonacci number and f (1) is the third Fibonacci number, f (6) must be the eighth Fibonacci number, which is 21. And of course, today's date is the 21st.
Cosmos Episode 13: "Seven Wonders of the New World"
Here is a summary of Cosmos Episode 13, "Seven Wonders of the New World":
For starters, I would have mentioned the full week of subbing science on the blog, as well as any other science classes I subbed for that May. Recall that there was a blogging challenge that year to post 30 times in May, so these science classes might have been something to blog about. It's doubtful that I would have described the science classes in full "A Day in the Life" format (since that wasn't part of the May blogging challenge), but at least I would have posted more details.
I also would have paid more attention to the science classes themselves. I could have looked at the walls for examples of science labs and other assignments, as well as check out the science texts to see what I'd be expected to teach (although the impending transition to NGSS standards might have affected any info I would've gleaned from the texts).
And I could have asked other science teachers for pointers. As I'd soon find out at the new school, the only other math/science teacher was at our sister charter (and she didn't teach eighth graders), so using other teachers as a resource would be difficult. On the other hand, while subbing for science, there were most likely two other science teachers right next door to me. And I'd be justified in asking them for help, especially at the school where I spent a full week teaching science (and even more so if I told them that I was a newly hired math teacher who might have science thrust upon me).
The idea, of course, is that if I could have done these things in May, I would have had a much better experience teaching science at the charter school in August. And perhaps with that better experience, I wouldn't have needed to leave the school when I did.
But of course, there was nothing I could do when I didn't know I'd be teaching science. As far as I know, during the week of May 23rd (when I was subbing science), the administrators at my new school hadn't the slightest inkling that their current science teacher wouldn't return the following year.
This is the reason why, ever since I left the old charter, I made a point to blog more about subbing in classes other than math, particularly middle school science classes, as well as days when I had to make key classroom management decisions. I want to keep a record of any ideas that might unexpectedly come in handy if I ever return to teach my own class someday.
What I Still Remember About That Science Class
Unfortunately, it's been four years since I subbed in that class. And I've subbed in hundreds of classrooms since that week. Thus I remember very little about the class. I don't even recall whether it was a sixth, seventh, or eighth grade class -- or perhaps different grade levels each period.
I do remember that some sort of written assignment (perhaps a lab) was due one day. The regular teacher told me not to collect any late assignments -- and I let the students know this. Still, one student tried to turn his assignment in late. I'd told him that if he gave he a late assignment, I'd just rip it up -- and I did. No, I didn't rip it up completely, but I left a huge half-tear in the packet, with a note to the teacher that I, the sub, intentionally ripped it because it was late. (It was up to the teacher to decide what to do about the late work.)
The main thing I do remember about this class relates to classroom management. There was an incident where several students appeared to bully a certain girl in one of the classes. I do recall that the girl was an immigrant (or the daughter of immigrants) -- but not from Mexico. I remember looking up the history of her last name and concluded that she was Ghanaian.
Often when bullying occurs, I can't tell who started it. It could be that the group was harassing the girl (perhaps because of her nationality). But it was also possible that the girl started it -- she started saying bad things about the others, and they became upset with her.
What did I do in that situation? Most likely, I said something like, "I don't care who started it, but I want all of you to stop it!" There were clear times when it was obvious that the girl was the victim -- for example, one day we watched some video about animals (which is why I suspect this was a seventh grade Life Sciences course), and one of the others remarked that the girl looks like one of the creatures from the video. But I also recall the girl insulting the others as well. The one thing I knew at the time was that I was three months away from starting at the charter school -- and the middle school kids I'd be seeing soon were likely to bully others, just as I was seeing right then.
What should I have done in that situation? As a sub, when it comes to classroom management, there are two types of conflicts that might occur -- student vs. teacher, and student vs. student. In the first situation, student vs. teacher, I'm directed in the lesson plans to give or collect some assignment or enforce some unpopular rule, and the students tell me that I'm wrong to collect the work or enforce the rule. This often led to arguments (and, unfortunately, yelling). I've found that one way to avoid arguments here is to be more subtle when enforcing the rules (that is, "pick my battles").
But if it's student vs. student, I should not be subtle when it comes to handling the situation -- I must be more emphatic. In this case, the kids want me to intervene, as opposed to the student vs. teacher situation when they want me to let them do whatever they want. And such intervention is even more necessary if it's student vs. students -- we have a single student on one side of the conflict and a group on the other, and I can't tell whether the single student is a jerk or a victim.
With that in mind, here's what I should have done: I begin by taking the side of the lone girl -- I treat her as a victim and tell the other students to leave her alone. But I warn her that I'll be monitoring the situation closely -- if at any point it appears that she's the aggressor rather than the victim, then I'll quickly side with the group against her.
One thing that might have helped -- especially considering that I'd see these kids all week -- is to speak with the girl in private. Unfortunately, I don't recall what the bell schedule was, with so much time having elapsed since the incident. Depending on the regular teacher's schedule, I might ask to see the student after class. But if this was, say, the last period of the day, she'd have wanted to go home and considered my keeping her after class to be a punishment (and hence refused to stay).
The best possible case was if her period was followed immediately by my conference period. Then she wouldn't have seen my keeping her as a punishment. (I could easily send her to her next class with a note that she was "helping out the sub.") During this time I have a heart-to-heart conversation by asking her, "Why do you think the other students bully (or don't like) you?" Then I can reassure her that I'll make every effort to protect her as long as she doesn't become the aggressor in return.
(Actually, I suspect that this week might have been part of SBAC testing -- the SBAC is often given in March or April in high schools but not until May in middle schools. Even though this was the year before the first California Science Test, the state math and ELA tests would have necessitated a block schedule that week. With a block schedule, her class was much more likely to be followed by a break than a conference period, so I wouldn't have been able to keep her.)
Assuming that this girl was indeed a seventh grader, she would have been a few months away from starting the eighth grade. There would be a few eighth grade girls at my new charter school who were often bullied, including one victim who then turned around and bullied a sixth grader herself. If I had written down (on the blog) the earlier bullying incident and learned how to handle it, perhaps I could have fared better with the bullies and victims in my new school. Maybe then the victim at my new school wouldn't have become a bully the next day -- and with better management and bully-handling skills, maybe I wouldn't have needed to leave the old school, even if I never completely figure out how to teach science properly.
Reblogging About the Green Team
Each time I make a science post, I keep referring to "Green Team" over and over again. So now you might ask, what exactly does this "Green Team" refer to?
Obviously, it refers to something that was supposed to happen at the old charter school. Let me go back and reblog parts of the November 2016 post where I first learned about the Green Team:
So what exactly is this Green Team, anyway? Here is a quote from the brochure:
"Let's Move Nation & Beyond's" Green Team Program is designed to engage students and their families; school faculty, administration and leadership; and the broader community on the importance of energy conservation topics. It will focus on campus-wide awareness, direct education to children, and Green Team leader development."
As I wrote earlier, I met with the leader of the Green Team this afternoon. She tells me a little more about how this program will work:
-- There will be a monthly newsletter for all students K-8 informing them about ways they can help their families save energy and water. We're hoping that the first newsletter will be December 1st.
-- The next step is to introduce this unit in science with a Pre-Assessment. This Pre-Assessment should be given just before winter break.
-- In January, the science unit will begin in earnest. Students can bring in copies of their energy and water bills. By the end of the unit, we're hoping that students have implemented enough saving tips to see a noticeable reduction in their bills. The grade with the largest reduction can win prizes, which could be anything from a classroom pizza party to even some sort of field trip.
-- There will also be a science project or fair associated with this unit. If everything goes right, the projects will be completed by Earth Day, which is Saturday, April 22nd.
In order for this to work out, as the Green Team leader explains, there should be at least ten schools participating in the program. So far, five schools have signed on, counting my own. All of these schools are either charters, like my own, or small private schools. Unfortunately, our sister charter can't be included, because it's not actually within the Los Angeles city limits and thus isn't served by the LA Department of Water and Power (one of the sponsors of the program).
Originally, the Green Team program was intended for Grades 5-7. But it's awkward to include sixth and seventh grade at a middle school but not eighth, so now it's extended to eighth grade as well.
On the other hand, fifth grade usually isn't included at most middle schools. But we're a K-8 school, and so we can include fifth grade all we want. I've spoken with our fifth grade teacher on our PD day, and she's enthusiastic about the program as well. After all, even the fifth grade class has only the Illinois State text and thus the science is limited to only the STEM projects. Both of us know that both fifth and eighth grades have NGSS tests in May, so let's include both grades as this could be the only science they'll see. I might even drop by our school on Wednesday and let the fifth grade teacher know what I learned today -- since, if you recall, she'll be at the school that day to decorate!
As I said earlier, I definitely look forward to working with the Green Team in my room. I hope that it will help my students out with science -- and even save them a little money.
Obviously, the Green Team didn't go quite as planned. As I wrote above here, the success of the Green Team was dependent on other schools signing up for it -- and most likely, not enough schools signed up for it quickly.
The so-called "Pre-Assessment" was indeed just before winter break, but it wasn't formal -- it was just about four short questions about the students' habits (turning off lights and water, and so on).
The creator of the Green Team did visit us in January, but there was no science unit. Instead, she had the students fill out some information on the website, and two students would be randomly chosen to get T-shirts and have their pictures printed in the aforementioned newsletter. The winners turned out to be a sixth grade boy and a seventh grade girl.
And as for the science project/fair, that might have been close to starting right around the time that I left the school. I still had access to email, and saw that there would be a class visit to the LA County Arboretum on a certain Saturday in March -- a place where I once took a field trip as a young sixth grader as well.
(By the way, the Arboretum has made the news recently due to the coronavirus. It is one of the few places that has remained open during the outbreak. Meanwhile, Santa Anita Park for horse racing has been shut down, despite being in the same city -- Arcadia -- as the Arboretum.)
Thus it's possible that the Green Team science project proceeded as intended. But unfortunately, most of the action took place after I left the school.
The Green Team led me to make some questionable decisions regarding my teaching. First of all, November, when I first learned about the Green Team, was right around the time that I finally got printed teachers' editions of the Illinois State science texts (for Earth and Physical Sciences, though not for Life Science). Yet I didn't try then to start using these texts, because I thought that the Green Team would take care of my science curriculum.
Then in December, I submitted a lesson plan that reserved an entire day for the "Pre-Assessment" for the Green Team, namely the Tuesday (and penultimate day) before winter break. And this would lead to three problems. First, since the "Pre-Assessment" was just four questions, there was no real science pretest or lesson that day. Since I'd already told the students that there would be science that day, I quickly made up some science questions from the Study Island Unit 1 ("Pretest"). The students grew upset since it seemed that I was always giving them science "pretests" and without ever teaching any actual science.
The second problem was that one eighth grade girl had missed the previous week of school and tried to make up the math she'd missed. I told her not to worry about it -- there'd be no time to make it up due to the science pretest. And of course, that fizzled out, leaving her well-behind with her math (and her math grade).
And finally, it ruined my assignment for Wednesday, the last day before winter break. Because there was no real assignment on Tuesday due to the pretest fiasco, it led students to believe that there would be no work the entire week, so kids were playing around on Wednesday. One seventh grade girl would get in trouble that day for playing around with her phone. (Then again, the lesson I tried to give on Wednesday was a bad one anyway. I'd been inspired by previous days of subbing to assign a holiday graphing worksheet just before breaks, but this makes more sense in high schools when students are more comfortable with graphing, not in middle schools.)
I already wrote a month ago what I should have done here -- I should have taught science and acted as if there was no Green Team. Plan a curriculum as described (Physical Science for eighth grade, Life Science for seventh, Preferred Integrated for sixth) and just ignore Green Team activities until they actually begin. Don't include the Green Team in lesson plans until I'm completely sure that I have material for Green Team lessons.
An Interesting Rapoport Problem
There are no Geometry problems on the Rapoport calendar this week. But these days, I've been blogging Rapoport problems anyway, mainly because it's the only math I've been doing lately. (When it's not a Geometry problem, I bury it deeper in my post, as opposed to Geometry problems that I include right at the top of the post.)
Today on her Daily Epsilon of Math 2020, Rebecca Rapoport writes:
The number of subsets of {1, 2, ..., 6} that contain no consecutive numbers.
Before we begin, don't forget that sets (and thus subsets) can contain 0 or 1 element -- and of course, every such set fails to contain two numbers (much less any two consecutive numbers). Thus we already know seven subsets that work -- the empty set, {1}, {2}, {3}, {4}, {5}, and {6}.
It's easy to see that any subset with four or more elements won't work. And so all that remains are to check the subsets with 2-3 elements. There are only 6 choose 2 + 6 choose 3 = 15 + 20 = 35 such subsets, so it wouldn't take that long to check all of them.
But if we did that, we wouldn't learn as much as if we looked for patterns instead. Let's define:
f (n) = the number of subsets of {1, ..., n} that contain no consecutive numbers.
Then our goal now is to find f (6). There are two initial cases here:
f (0) = 1 (the empty set)
f (1) = 2 (the empty set and {1})
So f (2) is the first non-trivial case here. We know that f (2) is at least 2, since the two sets in f (1) work for f (2) as well. And likewise f (3) is at least as great as f (2), since any set in for f (2) works for f (3) as well. Since we're looking for patterns, let's write this as:
f (2) = f (1) +
f (3) = f (2) +
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
Looking at f (2) again, we wish to include the new element 2. There are two sets from f (1) we have so far, empty and {1}. We can't adjoin 2 to the set {1} since the new set {1, 2} contains consecutive numbers, but we can adjoin it to the empty set to obtain {2}. We adjoined 2 to the empty set -- which, if you recall, is the only set in f (0). So we have:
f (2) = f (1) + f (0)
f (3) = f (2) +
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
Looking at f (3) again, we wish to include the new element 3. There are three sets from f (1) we have so far, empty,{1}, and {2}. We can't adjoin 3 to the set {2} since the new set {2, 3} contains consecutive numbers, but we can adjoin it to the empty set to obtain {3} and to the set {1} to obtain the new set {1, 3}. We adjoined 2 to the empty set and to {1} -- which, if you recall, are the only two sets in f (1). So we have:
f (2) = f (1) + f (0)
f (3) = f (2) + f (1)
f (4) = f (3) +
f (5) = f (4) +
f (6) = f (5) +
And by now the pattern is obvious. To find f (4), we start with the sets in f (3) and then adjoin 4 to each of the previous sets that don't contain a 3, which are exactly the sets in f (2). And we do the same with 5 and 6:
f (2) = f (1) + f (0)
f (3) = f (2) + f (1)
f (4) = f (3) + f (2)
f (5) = f (4) + f (3)
f (6) = f (5) + f (4)
That's right -- the values of f (n) are simply the Fibonacci numbers! And since f (0) is the second Fibonacci number and f (1) is the third Fibonacci number, f (6) must be the eighth Fibonacci number, which is 21. And of course, today's date is the 21st.
Cosmos Episode 13: "Seven Wonders of the New World"
Here is a summary of Cosmos Episode 13, "Seven Wonders of the New World":
- Carl Sagan, the first Cosmos host, was drawn to science at the 1939 World's Fair in New York.
- That World's Fair was where television was first introduced.
- A young Neil DeGrasse Tyson visited that same World's Fair a quarter century later.
- The fair presented a vision of the future filled with higher technology, such as computers.
- There were also models of spacecraft that could be used for both exploration and warfare.
- Now imagine what the New York World's Fair would look like in the year 2039
- A young girl named Nguyen (no, not Fawn) is seen contemplating about her future.
- A new colossal building, made from carbon dioxide, is at the entrance to the World's Fair.
- In the Pavilion of the Searchers, famous scientists are virtually brought to life.
- In the Pavilion of the Fourth Dimension (time), you can go anywhere on the Cosmic Calendar.
- "Saco," who lived half a billion years ago, was the last common ancestor of nearly all animals.
- Botanists discover a plant, otherwise green, that turns red if a landmine is nearby.
- They breed a new poplar tree that converts dangerous TCE gases into harmless chloride.
- In the Pavilion of the Lost Worlds, you can revisit civilizations that disappeared millennia ago.
- The Nok lived in ancient Nigeria, and the Indus Valley flourished, but little is known of them.
- In the Pavilion of Worlds Still to Come, you can see the depths of the solar system and beyond.
- It is like an Encyclopedia Galactica listing the distant worlds and their survival probability.
- Our survival probability is only 50% per 100 years, unless we embrace our position on the Tree of Life and learn to respect nature and the world around us.
These last two episodes of Cosmos are timed perfectly with Earth Day. In Episode 12, Tyson talked about the sixth mass extinction event -- the Anthropocene extinction -- and stressed that it's caused by humans ruining the environment. That episode was a warning that unless we change our habits now, we will lose thousands of species.
Episode 13, in contrast, gives a reason for optimism. The timeline imagined by the little girl Nguyen shows carbon dioxide levels finally returning to their pre-industrial levels, for example. Tyson expresses the hope that we humans will realize the error of our ways and ultimately change our habits in order to protect our environment. This optimism is, of course, the reason that Earth Day was created fifty years ago.
The Worlds' Fairs are used in this episode since the fairs in years past were where futuristic forms of technology were first introduced. Tyson mentions that he himself, as a young child, was inspired by the 1964 fair, as was the original host Carl Sagan at the 1939 fair. Thus the girl Nguyen represents a future scientist who is likewise drawn to save the environment by what she sees at the 2039 fair -- exactly one century after Sagan's fair.
It's possible that I could have taught some of these ideas at the old charter school. Once again, some of these ideas fit with the Green Team that was supposed to start in March three years ago. No, the Green Team Science Fair wouldn't have been anywhere near as extravagant as any of the Worlds' Fairs were or will be.
But our fair could have at least inspired our students to think about their ecological futures. Perhaps some of our students might go on to solve the major environmental problems of today.
Earth Day and the Coronavirus
A month ago, I mentioned that some tips for protecting our environment (throwing stuff away keeps our landfills from overflowing), are at odds with tips for protecting our health during the coronavirus (throwing stuff away gets rid of germs more easily). As I promised, I'm posting some links discussing what to do about protecting the environment during the virus outbreak:
https://www.theverge.com/2020/4/2/21204094/plastic-bag-ban-reusable-grocery-coronavirus-covid-19
With grocery stores being one of the few places still open during COVID-19 lockdowns, disposable plastic bags are making a comeback as some people fear that reusable bags could spread the disease. Before the pandemic, a growing number of governments banned single-use plastic bags in an effort to cut down on waste. But as the novel coronavirus has spread around the globe, people have gotten leery about coming in close contact with other people and their possessions, including reusable bags. On March 31st, New Hampshire became the first state in the US to temporarily ban reusable bags during the pandemic.
The following Scientific American link, published in time for Earth Day, discusses how air pollution makes us more susceptible to the virus:
https://blogs.scientificamerican.com/observations/air-pollution-covid-19-and-earth-day/
On the other hand, the World Economic Forum notes that due to the coronavirus lockdowns, fewer people are traveling -- and this has a positive effect on our environment:
https://www.weforum.org/agenda/2020/04/coronavirus-lockdowns-air-pollution
Revisiting the Fourth Dimension Yet Again
Three year ago, on April 21st, 2017, the Green Team Fair should have occurred, but unfortunately, I'll never know whether there really was a fair or not. I'd already left my old school back then?
What did I blog that day? I wrote about the fourth dimension again, this time from the perspective of Eugenia Cheng (and referred back to Rudy Rucker as well). Since Neil DeGrasse Tyson briefly mentioned the fourth dimension in this last episode, let me reblog the fourth dimension from Cheng:
Chapter 12 of Eugenia Cheng's Beyond Infinity is "Infinite Dimensions." She begins:
"Would you like to be able to travel in time? It sounds exciting, but it also sounds terrifying because of the dire consequences if you even slight interfere with your own past."
In this chapter, Cheng writes about the concept of infinitely many dimensions. But this is tricky as it's difficult to imagine what it means for a world to have four dimensions, much less infinitely many.
Last year at around this time (between Round It Up to Pi Day and April Fool's Day 2016), I was blogging about Rudy Rucker's The Fourth Dimension: Toward a Geometry of Higher Reality. As the title implies, this book discusses the fourth dimension. Cheng writes about the fourth dimension as well, albeit en route to even higher dimensions.
By the way, last year I mentioned Rucker's other book -- Infinity and the Mind. That's right -- it's yet another book about infinity. We can see how Rucker and Cheng apparently both love infinity and higher dimensions. Clearly I share that love as well, since I keep blogging about their books.
Let's get back to Eugenia Cheng. Anyway, Cheng begins by describing several examples of one-, two-, and three-dimensional objects. A line is one-dimensional, but so is a circle, since someone living on a circle can only go one way or the other, just like on a line. (This is why we often refer to a circle as S^1.) Likewise, a plane and a sphere are both two-dimensional. In both cases we need a pair of coordinates to specify our location, but even on a plane, we can use circular (polar) coordinates. Of course, our ordinary space is three-dimensional.
One example of a possible fourth dimension is time. She writes:
"If you find this hard to understand, you can imagine time as a fourth dimension. This is a valid and in fact powerful way to think of time, put to great use in theoretical physics, but it is just one way of thinking of a fourth dimension, not the only way."
Rucker also mentions time as an example of a fourth dimension. Cheng also gives color as a possible fourth dimension, where you're only in the same place as something if you're the same color. Again, Rucker gives the same example in his book.
According to Cheng, dimensions should be independent. So when she gives her location as "4 miles east, 2 miles north, and sqrt(18) miles northeast," only two of those dimensions are independent. So she doesn't need to provide a northeast coordinate.
Cheng proceeds:
"As my research is in higher-dimensional category theory, I spend a lot of time talking to people about dimensions, both formally and informally."
I already knew that category theory is Cheng's specialty from her first book, How to Bake Pi. So of course she finds a way to discuss category theory in her new book as well. Indeed, the next chapter of her book, Chapter 13, is titled "Infinite-Dimensional Categories."
And just as in her first book, Cheng likes to give food analogies. She writes that in order to make French macaroons, she needs to decide how much icing sugar, caster sugar, and ground almonds to include in the recipe, so that's three "dimensions" to consider. The oven temperature is the fourth dimension, and the fifth through ninth dimensions are all temporal -- how long to whisk the whites, fold the batter, pipe the circles, let them stand, and finally bake them.
She continues:
"You might think that this is all very well, but is there ever a need to study those higher-dimensional spaces? Do we even need to know that they're there?"
Her answer is an emphatic "yes" -- we use seven dimensions every time we move our arms. Two of these are shoulder movement and two more are wrist movement. The remaining three dimensions are all angles -- the elbow angle, the angle the hand is facing, and the upper arm angle. She points out that as humans we don't think about all of these dimensions, but if we were to program a robotic arm, we must consider all of them.
But Cheng admits:
"Thinking about higher-dimensional space is difficult. That's why there are whole branches of math devoted to it."
Now Cheng provides several examples of improperly reducing dimensions. The dominant example is when filling out surveys that ask, "Do you prefer socializing in large groups or one-to-one?" as if one can't like both equally or hate both equally. She adds that for years, people thought of politics as being one-dimensional (left-wing or right-wing) when two dimensions represent them better. Thus she provides the following link to a two-dimensional political survey:
http://www.politicalcompass.org
She wraps up the chapter with the following:
"Sometimes when I'm doing a 'pros and cons' type evaluation of a situation, I discover that the criteria are too difficult to separate out. For example, you might be thinking about short-term benefits and long-term benefits."
In other words, there are too many variables to consider -- and sometimes we can't even tell how to divide the criteria into separate variables! And so this is a job for -- infinitely many dimensions. As Cheng points out, "No wonder decisions are difficult."
Conclusion
Even though this was Neil DeGrasse Tyson's last episode of Cosmos, we're not done with it yet. We missed the first two episodes, and so I'll recap those as soon as they air on FOX, which should be at some point this summer.
I wish that Tyson would give us a 14th episode on the one scientific issue that's on everyone's mind right now -- the coronavirus. But recall that these episodes were produced last year (and were delayed due to allegations against Tyson), so there's no way there could be a coronavirus episode. I did find a link to a YouTube podcast where Tyson discusses the virus and the environment, so this is the best we can do for now:
Speaking of podcasts, I never did blog about the traditionalists' podcast I mentioned in my last post, since I wanted this post to be about Earth Day and science. Unfortunately, I didn't avoid politics completely, since much of the environmental debate is political.
With Cosmos done for now, I'll be making plans for computer/coding in my next post.
Meanwhile, I notice that another math blogger, Vi Hart, made a cororavirus-related video:
Episode 13, in contrast, gives a reason for optimism. The timeline imagined by the little girl Nguyen shows carbon dioxide levels finally returning to their pre-industrial levels, for example. Tyson expresses the hope that we humans will realize the error of our ways and ultimately change our habits in order to protect our environment. This optimism is, of course, the reason that Earth Day was created fifty years ago.
The Worlds' Fairs are used in this episode since the fairs in years past were where futuristic forms of technology were first introduced. Tyson mentions that he himself, as a young child, was inspired by the 1964 fair, as was the original host Carl Sagan at the 1939 fair. Thus the girl Nguyen represents a future scientist who is likewise drawn to save the environment by what she sees at the 2039 fair -- exactly one century after Sagan's fair.
It's possible that I could have taught some of these ideas at the old charter school. Once again, some of these ideas fit with the Green Team that was supposed to start in March three years ago. No, the Green Team Science Fair wouldn't have been anywhere near as extravagant as any of the Worlds' Fairs were or will be.
But our fair could have at least inspired our students to think about their ecological futures. Perhaps some of our students might go on to solve the major environmental problems of today.
Earth Day and the Coronavirus
A month ago, I mentioned that some tips for protecting our environment (throwing stuff away keeps our landfills from overflowing), are at odds with tips for protecting our health during the coronavirus (throwing stuff away gets rid of germs more easily). As I promised, I'm posting some links discussing what to do about protecting the environment during the virus outbreak:
https://www.theverge.com/2020/4/2/21204094/plastic-bag-ban-reusable-grocery-coronavirus-covid-19
With grocery stores being one of the few places still open during COVID-19 lockdowns, disposable plastic bags are making a comeback as some people fear that reusable bags could spread the disease. Before the pandemic, a growing number of governments banned single-use plastic bags in an effort to cut down on waste. But as the novel coronavirus has spread around the globe, people have gotten leery about coming in close contact with other people and their possessions, including reusable bags. On March 31st, New Hampshire became the first state in the US to temporarily ban reusable bags during the pandemic.
Like pretty much everything else right now, reusable bags should probably be handled more carefully to minimize the risk of transmitting disease to other people. At the same time, there has been no evidence so far that using reusable grocery bags have been responsible for spreading the novel coronavirus.
But protecting public health doesn’t have to be at odds with efforts to stem the flood of plastics filling landfills and collecting in the ocean, environmental advocates say. “If stores, particularly workers, want to keep themselves as safe as possible and limit the bags coming in because they don’t know if people wash them, certainly a temporary pause on that, I think that’s understandable,” Ivy Schlegel, a senior research specialist for Greenpeace USA, says. But that “pause” shouldn’t be permanent, says Schlegel. She has followed the plastics industry’s history of fighting environmental reforms by claiming that reusable bags are unsanitary. She sees the industry seizing the opportunity now to push its own agenda.
The following Scientific American link, published in time for Earth Day, discusses how air pollution makes us more susceptible to the virus:
https://blogs.scientificamerican.com/observations/air-pollution-covid-19-and-earth-day/
Fifty years ago, on April 22, 1970, millions took to the streets on the first Earth Day, demanding clean air and environmental protection. Massive citizen participation, some 10 percent of the U.S. population at the time, led to the Clean Air Act, and other landmark environmental protection laws.
Because COVID-19 attacks our lungs, air pollution makes us more vulnerable to the virus. It’s no surprise that COVID-19 deaths are high in places with poor air quality. Recent research from Harvard University documents this well. In fact, the study’s findings, the researchers noted, “underscore the importance of continuing to enforce existing air pollution regulations to protect human health both during and after the COVID-19 crisis.” So why are we doing the opposite?
On the other hand, the World Economic Forum notes that due to the coronavirus lockdowns, fewer people are traveling -- and this has a positive effect on our environment:
https://www.weforum.org/agenda/2020/04/coronavirus-lockdowns-air-pollution
The COVID-19 pandemic has caused industrial activity to shut down and cancelled flights and other journeys, slashing greenhouse gas emissions and air pollution around the world. If there is something positive to take from this terrible crisis, it could be that it’s offered a taste of the air we might breathe in a low-carbon future.
The World Health Organisation (WHO) estimates that about 3 million people die each year from ailments caused by air pollution, and that more than 80% of people living in urban areas are exposed to air quality levels that exceed safe limits. The situation is worse in low-income countries, where 98% of cities fail to meet WHO air quality standards.
Revisiting the Fourth Dimension Yet Again
Three year ago, on April 21st, 2017, the Green Team Fair should have occurred, but unfortunately, I'll never know whether there really was a fair or not. I'd already left my old school back then?
What did I blog that day? I wrote about the fourth dimension again, this time from the perspective of Eugenia Cheng (and referred back to Rudy Rucker as well). Since Neil DeGrasse Tyson briefly mentioned the fourth dimension in this last episode, let me reblog the fourth dimension from Cheng:
Chapter 12 of Eugenia Cheng's Beyond Infinity is "Infinite Dimensions." She begins:
"Would you like to be able to travel in time? It sounds exciting, but it also sounds terrifying because of the dire consequences if you even slight interfere with your own past."
In this chapter, Cheng writes about the concept of infinitely many dimensions. But this is tricky as it's difficult to imagine what it means for a world to have four dimensions, much less infinitely many.
Last year at around this time (between Round It Up to Pi Day and April Fool's Day 2016), I was blogging about Rudy Rucker's The Fourth Dimension: Toward a Geometry of Higher Reality. As the title implies, this book discusses the fourth dimension. Cheng writes about the fourth dimension as well, albeit en route to even higher dimensions.
By the way, last year I mentioned Rucker's other book -- Infinity and the Mind. That's right -- it's yet another book about infinity. We can see how Rucker and Cheng apparently both love infinity and higher dimensions. Clearly I share that love as well, since I keep blogging about their books.
Let's get back to Eugenia Cheng. Anyway, Cheng begins by describing several examples of one-, two-, and three-dimensional objects. A line is one-dimensional, but so is a circle, since someone living on a circle can only go one way or the other, just like on a line. (This is why we often refer to a circle as S^1.) Likewise, a plane and a sphere are both two-dimensional. In both cases we need a pair of coordinates to specify our location, but even on a plane, we can use circular (polar) coordinates. Of course, our ordinary space is three-dimensional.
One example of a possible fourth dimension is time. She writes:
"If you find this hard to understand, you can imagine time as a fourth dimension. This is a valid and in fact powerful way to think of time, put to great use in theoretical physics, but it is just one way of thinking of a fourth dimension, not the only way."
Rucker also mentions time as an example of a fourth dimension. Cheng also gives color as a possible fourth dimension, where you're only in the same place as something if you're the same color. Again, Rucker gives the same example in his book.
According to Cheng, dimensions should be independent. So when she gives her location as "4 miles east, 2 miles north, and sqrt(18) miles northeast," only two of those dimensions are independent. So she doesn't need to provide a northeast coordinate.
Cheng proceeds:
"As my research is in higher-dimensional category theory, I spend a lot of time talking to people about dimensions, both formally and informally."
I already knew that category theory is Cheng's specialty from her first book, How to Bake Pi. So of course she finds a way to discuss category theory in her new book as well. Indeed, the next chapter of her book, Chapter 13, is titled "Infinite-Dimensional Categories."
And just as in her first book, Cheng likes to give food analogies. She writes that in order to make French macaroons, she needs to decide how much icing sugar, caster sugar, and ground almonds to include in the recipe, so that's three "dimensions" to consider. The oven temperature is the fourth dimension, and the fifth through ninth dimensions are all temporal -- how long to whisk the whites, fold the batter, pipe the circles, let them stand, and finally bake them.
She continues:
"You might think that this is all very well, but is there ever a need to study those higher-dimensional spaces? Do we even need to know that they're there?"
Her answer is an emphatic "yes" -- we use seven dimensions every time we move our arms. Two of these are shoulder movement and two more are wrist movement. The remaining three dimensions are all angles -- the elbow angle, the angle the hand is facing, and the upper arm angle. She points out that as humans we don't think about all of these dimensions, but if we were to program a robotic arm, we must consider all of them.
But Cheng admits:
"Thinking about higher-dimensional space is difficult. That's why there are whole branches of math devoted to it."
Now Cheng provides several examples of improperly reducing dimensions. The dominant example is when filling out surveys that ask, "Do you prefer socializing in large groups or one-to-one?" as if one can't like both equally or hate both equally. She adds that for years, people thought of politics as being one-dimensional (left-wing or right-wing) when two dimensions represent them better. Thus she provides the following link to a two-dimensional political survey:
http://www.politicalcompass.org
She wraps up the chapter with the following:
"Sometimes when I'm doing a 'pros and cons' type evaluation of a situation, I discover that the criteria are too difficult to separate out. For example, you might be thinking about short-term benefits and long-term benefits."
In other words, there are too many variables to consider -- and sometimes we can't even tell how to divide the criteria into separate variables! And so this is a job for -- infinitely many dimensions. As Cheng points out, "No wonder decisions are difficult."
Conclusion
Even though this was Neil DeGrasse Tyson's last episode of Cosmos, we're not done with it yet. We missed the first two episodes, and so I'll recap those as soon as they air on FOX, which should be at some point this summer.
I wish that Tyson would give us a 14th episode on the one scientific issue that's on everyone's mind right now -- the coronavirus. But recall that these episodes were produced last year (and were delayed due to allegations against Tyson), so there's no way there could be a coronavirus episode. I did find a link to a YouTube podcast where Tyson discusses the virus and the environment, so this is the best we can do for now:
Speaking of podcasts, I never did blog about the traditionalists' podcast I mentioned in my last post, since I wanted this post to be about Earth Day and science. Unfortunately, I didn't avoid politics completely, since much of the environmental debate is political.
With Cosmos done for now, I'll be making plans for computer/coding in my next post.
Meanwhile, I notice that another math blogger, Vi Hart, made a cororavirus-related video:
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