Centroids of Arcs

This morning I computed the centroid of a circular arc and was pleasantly surprised by some of the results. I think the exercise would fit well into a calculus textbook. This little interactive app I built shows how the centroid of a circular arc evolves as the arc length is changed: https://www.geogebra.org/graphing/s6mybsje

In more serious work, I'm still reading about nonlinear optimization in hopes of getting a grip on a larger problem I'm wrestling with.

In Spanish verb practice, I focused mostly on present tense verb conjugation today. I went through about 25 verbs today--hoping to develop a bit of an instinct about speaking the correct conjugation quickly.

My river walk was very windy today:

Perhaps the windiest day I've experienced here in Sevilla.

Mexican food, one of our staples back in Walla Walla, is hard to come by here. Laura has developed a pretty good method of making refried beans from pinto beans:

We had bean burritos for dinner and they were muy excelente.

To celebrate Friday, we hit the helado place for dessert. I went with my old standby, "brownie".

We're big fans of the Whitman women's tennis team. In honor of their home opener today vs. Seattle U. we sent them a selfie of us on the Triana bridge wearing our team sweatshirts:

The end of January

Another month in the books. We arrived in Spain 7 months ago. In some ways, it seems longer, in other ways, shorter.

This morning I took the derivative of an integral with respect to a parameter in its domain of integration. the result was unexpectedly intuitive and, therefore, the exercise was enjoyable. Not quite sure how to use it in what I'm trying to do overall, but sometimes you just do stuff.

I did more Spanish. I think I need to conjugate haber, hacer, ser, estar, tener, querer every day for a while.

Even though rain was threatening, I ran a load of laundry and hung it on the roof. Then I went out for a run. It sprinkled on me while I was running, which worried me. It was also quite windy. When I got back home, I went straight to the roof. All the clothes were there and relatively dry. I took them all in and hung them on the indoor rack for the rest of the day. They're dry now, so that was a success. Here's the grey view of Sevilla from the bridge at the far end of my run:

I've started a data science project that attempts to characterize students at Whitman that complete STEM degrees using their first-year academic information. As with all data science projects, there is going to be a lot of data wrangling before I can actually implement the clustering algorithm. Data science is a lot like house painting. You spend most of your time prepping the house to be painted rather than actually painting.

I continued to read Factfulness. Today Rosling distinguished between the frightening and the dangerous and pointed out how ill-equipped humans are to separate the two. Spiders are frightening, but not dangerous. Cars are dangerous, but not frightening. Fright is a response that evolved over millions of years in the species. It used to correlate well with danger, but not so much anymore.

Projector

Continuing to get to know my centroid problem. Worked a couple of interesting and confirming examples this morning.

I tried to use the pen on my Dell tablet today, but the batteries were dead. This pen takes 1 AAAA battery and 2 319 batteries. Neither of them seem to be available in the stores around here, so I ordered them on Amazon.es. The pen on my surface still works, so I'll just stick with that for now. It does suggest that the pen issues I had with my Dell earlier may have simply been low batteries. We'll see.

I did a little extra Spanish today since it's a class day. We had 3 students today (including me), so much more like a normal class. I like this teacher, she's not afraid to correct you. The teacher I had last semester was much more lenient. I think I learn better when somebody is correcting me in real time.

I went to the grocery story today for the first time since getting back to Spain. Laura had prepared a lot of meals over the weekend before I got here, so we were pretty well stocked for a bit. Now it's back to the more normal pattern of shopping every day.

It was rainy this afternoon. Here's an uncharacteristically gloomy picture of the river:

After dinner, I decided to have one of my Christmas beers--a Blue Moon. A nice change of pace from the usual Cruzcampo:

There's an interesting advertising campaign down at the river. Projectors are shining across the river to paint these movie posters on the Triana bank:

The images are remarkably clear for a projection across maybe 200 meters. My shadow was razor sharp:

I read another chapter of Factfulness. The lesson of the evening is to not assume that data can be projected forward linearly. If that were the case, your cute children that grew so quickly in their first years would be 20 feet tall when they graduated from high school. He goes on to note that the world population growth has already leveled off and that the actual population will level off by about 2100 at about 11 billion. After that, it's likely to begin to drop.

Coercive continuous functions

Did you know that a coercive, continuous function on a closed set has a global minimum? Neither did I until today. It's a good theorem. Just what I needed.

I made a list and mostly stuck to it today. Productive day.

Here's my Spanish verb spreadsheet. Definitely good practice. It's slow going right now, but my hope is to develop a bit of an instinct for conjugation:

I continued reading Factfulness today. The lesson for today is that people tend to be biased towards pessimism when it comes to human progress. Though the data supporting an improving world over the past two centuries is overwhelming, we nevertheless think that the world is getting worse. Rosling attributes this to a natural tendency to pay attention to negative things and to ignore positive things because negative things are threats to our existence and positive things aren't. From an evolutionary perspective, we are selected to pay attention to negative things because that improves our chances of survival. As such, we consume media that is predominantly bad news, choose politicians that campaign on fear, and talk to each other mostly about negative things. We're not built to see the positive things--especially on timescales of centuries, but the data is undeniable.

I walked another 5 miles today. I'm putting off running for another couple of days. I need to ease back into it. It's amazing how many electric scooters there are in Sevilla:

Piety

I slept until 9:30am this morning--very late for me. Still jet lagging I guess. In an effort to get back into the groove, I made a schedule of activities today and mostly stuck to it. Largely because of that, I was pretty productive today.

I read a couple of interesting articles about centroids (centers of gravity). The notion dates back to Euclid and Archimedes, but no one really knows where it originated. It's such a basic idea that it probably didn't originate with a single mathematician, but rather just emerged. The centroid is the balance point of a shape. For example, if you've ever balanced a plate on one finger, you found the centroid of the plate. The problem of finding such balance points is a recurring theme in geometry. I've been interested in developing a generalization of the centroid. This new project has me reading as many papers about them as I can.

My next task was to review my Spanish. I started my next Spanish language class today. Having been thinking and communicating in English for the past two weeks, my Spanish is rusty. I made some good progress there. I found a spreadsheet containing over 600 Spanish verbs and their conjugations in 20 different tenses. Laura helped me to cut out a lot of the tenses that I don't need right now and to focus on just 5 of them. Now I can pick a random line in the spreadsheet and practice conjugating.

I've been trying to read books that might be valuable to the data science class I'm developing. I finished Homo Deus by Yuval Noah Harari. A deeply philosophical, but clarifying look at human history. The burning unanswered question of the text ends up being: What is the purpose of our conscious awareness? Without a clear answer, the inevitable course of human development seems to be usurpation by unconscious artificial intelligence. I've now moved on to Factfulness by Hans Rosling (thanks Rachel). The premise of this book is that we seem to have an unwarranted negative view of the state of our world. We think that most of the world is poorer, more violent, and less educated than it actually is.

My new Spanish class was good. My new teacher, Piedad (means 'piety' in English), is very nice. Sadly, I was the only one of the 4 students enrolled in the class to show up today. I think this is largely the result of an email from the school administration saying that the class wasn't going to meet on Mondays moving forward. I checked in with the school this morning and was told that the class was returning to its original Mon/Wed schedule. I suspect that the other students in the class were not told of this return to normal. That said, it was nice to have 90 mins one-on-one with the teacher.

I didn't do my river walk until after class today. It was cool as the sun dipped, but the sky was lovely:

This sad sight is the end of the milk duds I brought back from the US. Jo-Anne bought a couple boxes for me before I left. They're not available here in Spain and Laura and I really like them every once in a while: