Category: Uncategorized

It’s time for another virtual trip through our Amazing Earth. Unlike previous entries, I’d like to show you a place I’ve actually been. Let’s go south – as far south as I have ever been. Welcome to Puerto Montt, Chile.

The map below shows where to find it (click for a larger view), on the Pacific coast about 60% of the way down the length of Chile:

Although the map shows that there is a lot of Chile still remaining to the south, Puerto Montt is the only even-slightly-large city until you get all the way down to Punta Arenas. Thus, it acts as the gateway to the beautiful wilderness of Patagonia to the south. It also acts as a gateway into Chile. In the late 1800s, while millions of European immigrants were coming to the United States, they were also coming to Chile. Puerto Montt acted as Chile’s version of Ellis Island, the entry point for the largest number of immigrants. It’s even named after an immigrant: Manuel Montt, President of Chile from 1851 to 1861, was born in Catalonia.

The city has about 200,000 people – similar to Providence, Rhode Island – and it lies about as far to the south of the equator as Providence does to the north. This zoomed-in map shows the area around Puerto Montt more clearly (click for a larger view).

The city lies at the end of a large bay, offering a sheltered harbor on the South Pacific. The island to the southwest is Chiloé, home of one of Chile’s most famous national parks, as well as the ancestral home of the potato.

I had the good fortune of visiting during a recent trip to the Chilean capital of Santiago, itself a lovely city that I could write about extensively. I had an extra day after my work event ended, so I looked at a number of possible destinations for a quick one-day trip. Puerto Montt had the best combination of affordable plane tickets and “that looks like a cool place,” so I went there. By the time I rented a car and sat in surprisingly elaborate traffic to get from the airport to the city, I had only three hours to visit, but it was well worth it.

Sadly, I don’t have any pictures, because my camera was out of charge and I left the charger in a different hemisphere. But once again, Google Earth comes to the rescue and shows me a view of the city similar to my own view (click for a larger version):

This photo also marks the approximate location of my Terra Ultima Australis – the farthest south I have ever been.

Puerto Montt is a lovely city, and I highly recommend it as an unexpected tourist destination. But it has another side, because it was the home of an important and tragic episode of Chilean history. More about that on Monday.

Welcome to a new occasional feature of my blog, named after a segment of my favorite moose-related classic TV series:

[youtube https://www.youtube.com/watch?v=syBRZGU95aA&w=560&h=315]

The poetic performance I embedded above is funny enough on its own, and might be the topic of a future post. But the point today is just this: I like moose, and I like poetry.

Sometimes I find a poem that deeply speaks to me in some sense, and the purpose of this new Bullwinkle’s Corner series is to share them with you. You’ll find that quite a few of them are in foreign languages, because I love the sound of other languages. And today, with tools like Google Translate, it’s easier than ever to know what the words mean.

The first in the series is a particularly powerful one, from Portuguese poet Alberto Caiero – who didn’t actually exist, because he was one of several pen names used by famous Portuguese poet Fernando Pessoa (1888-1935). (Thus Caiero might be eligible for one of my Except They Weren’t posts, an author simply using a pen name is not that exciting.)

Here is the poem: the original words in Portuguese are on the left, my English translation is on the right.

I love this poem. I find it strangely comforting, because it reminds me that the world will go on without me when I’m gone, and that the world will be OK. All I can do is to do the best I can while I’m here.

I had a whole post written and ready to go. It was beautiful – personal, deeply emotional, and hopefully even a bit insightful. But, oh, then I saw this tweet.

In case you’ve been living under a tea tree plant — or just don’t follow American Rules Football — here’s the backstory. Colin Kaepernick is a former player who ignited a huge controversy during the 2016 preseason by kneeling during traditional pregame performance of The Star-Spangled Banner as a protest against racism and police brutality in the United States. Some saw it as a brave stand against injustice, some saw it as disrespectful to the sacrifice of U.S. troops.

Of course, the protest has spread far beyond Kaepernick, with more than 200 players joining in at various times. So it’s not just about one person, and it hasn’t been for a while. But Kaepernick has always been the public face of the protests, and the flashpoint of controversy. If you want to see rageful opinions flying from all directions, especially from conservatives, go to an NFL fan forum and just post “Colin Kaepernick” and nothing else.

After the 2016 season, Kaepernick elected to forgo his contract and become a free agent, eligible to be hired by other teams – and no other teams hired him. In November 2017, he filed a grievance against the NFL, claiming that owners colluded to keep him out of the league. On August 28, 2018, an arbitrator ruled that the case could go to trial.

Today’s announcement means that Kaepernick will be the new face of Nike’s ad campaign. He won’t be the only athlete featured, but he’ll be the most prominent. I think the campaign’s tagline is particularly poignant:

Believe in something. Even if it means sacrificing everything.

But of course, Kaepernick’s opponents would counter that “sacrificing everything” can mean more than a career as a football player.

So how should we react to today’s announcement?

First, let me be clear: I have supported the player’s right to protest, and I believe the issues they are protesting against are real and troubling to this country which I love. My thought today is:

In my mind, it all depends on exactly what Darren Rovell means by “Nike has been paying Colin Kaepernick all along.” Do they mean since it became clear he would not be signed by another team? Since the protests came to national attention? Or… do they mean since before the first time he kneeled?

This is either an incredibly brave stand by Nike… or it’s the most cynical PR stunt in the history of PR. And right now we don’t have enough information to know which it is.

I’ll update this post as we learn more.

Last Wednesday, I continued my series on People Who Are Not What They Seem with Malba Tahan, the Islamic intellectual and writer who was actually the fictional alter ego of a Brazilian math teacher, created to help his students learn word problems.

That post ended on a mathematical cliffhanger (bwahahahaha!). Our heroes, Tahan and his friend Beremiz Samir, happened upon an argument among three brothers about how to divide up their father’s inheritance. Their father left them a herd of 35 camels, with the following instructions (as reported by the eldest brother):

According to the express wishes of my father half of them belong to me, one-third to my brother Hamed, and one-ninth to Harim, the youngest.

Samir’s solution was clever, but it required some risk – he added into the herd the camel that Tahan was riding, making a new herd of 36. He then divided the new herd according to the father’s instructions: one-half (18) to the eldest, one-third (12) to the middle, and one-ninth (4) to the youngest. All three brothers were satisfied with this arrangement, which left two camels remaining. One, of course, was Tahan’s that had been added at the beginning. Samir requested the other as his payment for arranging this solution – and since all three brothers were satisfied, they agreed. Samir grabbed the strongest, most beautiful member of the herd, and the pair rode off together into the sunset.

It’s a happy ending. Everyone is satisfied, especially our heroes. And you have to admire Samir’s Raven-level trickeration in getting something for nothing. But how did he solve the problem?

When faced with a word problem, often the best first step is to write down what you know and what you want to find out. Before Tahan and Samir arrive, here is the situation the brothers face:

• What we know
  • Total camels: 35
  • Fraction to each brother: eldest: $latex \frac{1}{2}&s=3$, middle: $latex \frac{1}{3}&s=3$, youngest: $latex \frac{1}{9}&s=3$
• What we want to find out
  • How many camels should each brother get?

In theory, this should be an easy problem: for the eldest brother, divide 35 by 2, and repeat for the others. Thus, the eldest brother should get 17 $latex \frac{1}{2}$ camels — not too pleasant for the camel! And besides, half a camel is not that useful anyway. Clearly a better solution is needed.

Tahan and Samir arrive, Samir offers Tahan’s camel for the herd, and the problem changes. Now we have:

• What we know
  • Total camels: 36
  • Fraction to each brother: eldest: $latex \frac{1}{2}&s=3$, middle: $latex \frac{1}{3}&s=3$, youngest: $latex \frac{1}{9}&s=3$
• What we want to find out
  • How many camels should each brother get?

Now we’re getting somewhere.

36 divided by 2 is 18, 36 divided by 3 is 12, and 36 divided by 9 is 4. Thus, the three brothers get eighteen, twelve, and four camels, all of which give them full camels instead of useless fractional camels.*

Adding up all three brothers’ camelshare gives 18 + 12 + 4 = 34 camels, with two remaining from the herd. One was Tahan’s, one is now Samir’s. Everything is A-OK.

But where did that extra camel come from?

Re-read the father’s instructions again, carefully:

According to the express wishes of my father half of them belong to me, one-third to my brother Hamed, and one-ninth to Harim, the youngest.

At this stage, there are two ways to approach the problem. The slightly easier way is to convert the fractional shares. You can always multiply the top (numerator) of a fraction by any number, and the bottom (denominator) by the same number, and the fraction will be the same. One-half ($latex \frac{1}{2}$) is the same as two-fourths ($latex \frac{2}{4}$). So, let’s multiply each fractional camelshare by the number of camels, which is now 36. Thus, the father’s instructions now read:

According to the express wishes of my father $latex \frac{18}{36}$ of them belong to me, $latex \frac{12}{36}$ to my brother Hamed, and $latex \frac{4}{36}$ to Harim, the youngest.

Or, if you prefer, you can convert the fractions to percentages (rounded to the nearest tenth of a percent):

According to the express wishes of my father 50% of them belong to me, 33.3% to my brother Hamed, and 11.1% to Harim, the youngest.

Either way, it quickly becomes clear: the father’s will was incomplete! The percentages don’t add up to 100%, so no matter how many camels were in the herd, some would be left over after the division.

Cool, huh?

*Useless Fractional Camels is the name of my They Might Be Giants cover band.