I have decided to move my files from GitHub to this site. Why? Well, there are two main reasons.
First, GitHub is not really designed for hosting documents. It is a great tool for version control and collaboration, but not for publishing content. It's great that it is free, but I feel a bit guilty to use it to get around Google Drive quotas.
Second, GitHub pages are updated slowly and sometimes not at all. Pages are reformatted from Markdown to HTML. This has been running slowly. It usually takes minutes, but today it hasn't updated at all.
Look at the blog pages - currently under development - for new materials.
The main theme of the 1982 movie Conan the Barbarian revolves around the Enigma of Steel. Conan must answer the Enigma of Steel or he will be cast out of Valhalla by Crom. In the beginning of the film, Conan's father states:
The secret of steel has always carried with it a mystery. You must learn its riddle, Conan. You must learn its discipline. For no one - no one in this world can you trust. Not men, not women, not beasts. This you can trust.
The exact riddle and answer are never explicitly stated. The implied answer, from the movie and Nietzsche quote that opens the film, is that the will forged through overcoming hardship is stronger than steel. The demonstration of forging a sword through fire and hammering in the opening credits makes this plain. The movie depicts Conan surviving in his early life when others do not. Conan loses his life and love before finally defeating Thulsa Doom in the climactic battle. The final victory comes when Conan overcomes Doom's hypnosis in a battle of will.
(The fact that the solution is never stated aloud fits the theme. My interpretation is that Crom will judge the person's actions rather than accept a verbal answer.)
The opposite of the Enigma of Steel is the Deceit of Silicon. Where an enigma is a truth hidden in a mystery, a deceit is a lie hidden in apparent truth. When heated, steel becomes stronger. When silicon is heated, it becomes brittle glass. Wielding a sword requires skill and strength. Using a silicon-based processor requires a few swipes or key presses. Steel makes no promises other than to be heavy and make you work. Silicon tempts you with algorithms to make you famous and deliver the world to your doorstep, if you submit to its will.
As an teacher, I repeatedly fall for the Deceit of Silicon. As education moves further away from in-person classes, it is easy to think of my classes as a chance to show the world my genius as an math communicator. In reality, I plan my lessons on how they affect my YouTube analytics instead of how students learn best. Getting a new subscriber or two only adds to my false conviction that I am one the right path. My many students would disagree.
(I realize that some of this is due to ADHD symptoms that I will have to address at the end of the semester.)
Students need to be aware of this phenomenon too. There are cell phone apps and YouTube videos that will help them get through a math class. This may get them through today's homework assignment, but that is putting off the reckoning until the next day. Many current college students finished high school math during COVID. It was easy to believe they were learning by getting passing grades. However, the day they have to show mastery is now.
If this sounds like you, then do not worry. Make peace with the fact you have some gaps in your math preparation and make plans to fill them. College professors will not be as forgiving as your high school teachers, so there is no avoiding it. Just know that, like Conan, the extra effort will not kill you. It will make you stronger as a student.
I have two pet peeves in this world: people wasting my time and me wasting other peoples time. I recently realized that I've been wasting my students' time and my time by creating videos that could be Blackboard announcements. I've decided to stop making as many videos and focus on other ways of connecting with students.
During my online teaching professional development, I was taught to use introduction videos to help students start to form a connection with their instructor. Of course, I can't stop with just one video. I have to make a video for each week of the course. Since I'm terrible on camera, these videos take longer to make than is reasonable. Also, no one watches the videos after the second week of the semester.
To try to maintain some personal connection, I plan to record the weekly posts as an audio file and upload it next to the script. That way students can choose either option. This also covers my bases for accessibility. Because audio files are easier to edit and looking good on camera isn't an issue, the whole process goes faster.
Student view of a finished welcome message.
Also, it is possible to use the recording process to create videos as well. It works pretty well to solve a problem and scan each step in the process. I can create PowerPoints with the scans and other text and then save the whole thing as a series of images. A video editing program can assemble the images with the narration. It is possible to do this entire process in PowerPoint, but I like to edit the audio first. This post from the Audacity wiki shows exactly how I edit my audio.
Long term, I'd like to assemble all of the audio recordings into a single file for students to download. This is an idea I picked up from Michael Wesch. It may not work as well with math as it does with anthropology, but that's a problem for later.
Since my perfectionist tendencies have to be appeased somehow, I decided to build a recording area in my messy garage. With $45 worth of PVC pipe and Harbor Freight moving blankets, I managed to pull something together. There is a frame built out the PVC pipe and some fittings. The blankets are clamped to the frame. It's not professional quality, but a little effort goes a long way.
I can fit myself, a microphone, and a recorder in there.
In October of 2021, Matt Parker - number 3 on my list of YouTube man crushes - and Hannah Fry released a video on YouTube demonstrating how to measure the radius of the Earth using a tall building and protractor.
Their attempt was moderately successful despite facing several obstacles.
On a recent family vacation, I realized I had the perfect opportunity to make a more accurate measurement.
Keep reading to see how our estimates compare.
Hannah and Matt
The process outlined in the video requires an observer to climb to a high point and measure the angle of declination down to the horizon. Using your elevation, the angle of declination, and some surprisingly elementary trigonometry, you can calculate the radius of the Earth. This method was devised by 10th Century mathematician al-Biruni. Using his method, al-Biruni was able to calculate the radius with surprising accuracy.
Hannah and Matt had several difficulties to overcome in their experiment. The main problem was getting their measuring equipment through building security. Additionally, Matt insisted on measuring the height of The Shard through trigonometry.
The duo's results are:
Height of observation deck: 263m (Actual: 244 m)
Angle of Declination: 1.5 degrees
Radius of Earth: 875 km (Actual: 6371'ish km)
Visiting the Perfect Location
Visiting the perfect location for this experiment was a lucky coincidence for me. There was a mountain with high elevation located close to the sea on our vacation itinerary: Haleakala. The lack of building security is a plus.
Photo Credit: Emily Sears
Standing on the top of a volcano was the one experience I wanted out of the trip. We took a tour bus up for sunrise. The pickup time was 2:30 am, which sucked. The rest of the trip was amazing.
There was a healthy crowd at the Visitor Center. Fortunately, everyone was respectful. That is not always a guarantee, but the Aloha Sprit was with us tourists. The light of sunrise played nicely with the cloud layer below. I was able to poke around the crowd to get a few shots. The thinner air at the top made moving around more difficult. I hiked up to the higher observation area, and had to stop every few minutes to catch my breath.
Silhouette of the Crowd. Photo Credit: Chris Sears
The view from the top. Photo Credit: Chris Sears
The clouds enhanced the natural beauty, but they worked against my secondary objective for this trip. Finding the horizon turned out to be a problem. The clouds started to break enough to see the ocean. If we had stayed for an extra half hour or so, the view of the horizon would have been clearer. With the tour bus loading, I made the best measurement I could.
A measurement of 0.95 degrees seemed good enough for me. I remembered that Hannah and Matt should have measured around 0.5 degrees from The Shard. A larger angle is expected from a higher height. I was happy with the result. My family was happy I stopped talking about math for the rest of the morning.
The view of the horizon. Photo Credit: Chris Sears
0.95 degrees was the best I was going to get. Photo Credit: Connor Sears
After returning to the mainland, it was time to crunch the numbers. Here are the results:
Height of observation: 2960 m (Rounded to three significant digits and adjusted for standing below the Visitor Center)
Angle of declination: 0.95 degrees
Radius of Earth: 21500 km (Actual: 6371'ish km)
Well, that is disappointing. Matt and Hannah were off by 86.3% of the actual value. I was off by 238%. Looks like I'll be eating the humble pi tonight.
It is possible to work backward to find the proper angle measurement for a height of 2.96 km. I should have measured 1.75 degrees. This is one time where aiming for the clouds was the wrong thing to do.
The video below shows how I made the computations.
The past month has served as a sieve for my interests and priorities. Now that I'm off contact for the academic year, the pressure to perform is gone. The main realization born of this freedom is how much energy I spend on existential crises. I worry so much about leaving a legacy that I forget to get stuff done. I'll spare you the manifest of the contents of my navel and move on to the actionable bits.
The most recent change is deleting my regular site. The purpose was to serve as a virtual filing cabinet of all my materials. Blogger is capable of serving this purpose with less upkeep. Best to move it all to one place. The pages of this site will expand over the summer. Also, the URL now directs to the blog.
I deleted my TikTok account. If social media were food, TikTok is cake. Baking a cake can be an act of high skill and artistry. However, the nutritional value is always low. YouTube is saturated with instructional videos, so TikTok looked like a fertile place to stake a claim. After some reflection, I realized it is very difficult to post meaningful instructional videos on TikTok. The format is designed to keep a person's attention on the site, not to watch a few videos and start their homework.
Admitting that I'm late to the YouTube game and cannot possibly catch up to other creators is actually liberating. I'll never be Sal Khan or James Sousa. (I never wanted to be the former.) I can make the videos I need for teaching and be happy about it. Keeping one eye on the YouTube algorithm leaves only eye to create content.
My potential calculator channel on YouTube is getting repurposed. The plan was to have a separate channel for short calculator tutorials. YouTube Shorts gets higher views than regular videos. Conventional wisdom says that mixing shorts with regular videos will confuse the algorithm. Since I don't care about appeasing the YouTube algorithm with my math channel, I'm going to give up on the idea of a separate calculator channel. Instead, I'll create a coding channel instead. I have a natural niche in how I use computer programming. Building a channel out of that should be both fun and an opportunity for self-expression.
I had a busy day updating my worksheets for Foundations of College Algebra. After scrambling all year to get above water, I finally arranged to get the help I needed. The rest of the department and I are sharing our materials. I have been polishing my worksheets to share. As I finish them, I'll post them on my main site.
Now that the semester is winding down, I can turn my focus to lower priority tasks. That includes updating my site. My goal is to put an entire Calculus textbook on TikTok and collecting the videos in the website. To get caught up, I made the following changes:
Set the URL to point to the Google site and not this blog.
Add subpages to the Video Calculus Textbook for Introduction to Calculus, Fundamental Theorem of Calculus, and Integral by Substitution.
Remove the subpages from the site navigation.
Embed four TikTok's into the pages above.
I'm still on the fence about using YouTube or TikTok for math videos. My mind says YouTube and my heart says TikTok. More on that later.