One of the things you see all over San Miguel de Allende are stellated dodecahedra.

A dodecahedron is a 12-sided solid. The twelve faces of a regular dodecahedron are all regular pentagons (equal length sides, equal angles).

If you put a pentagonal pyramid on each of those faces, that is, use each pentagon as a base for a five-sided figure, you get a small (or “the first”) stellated dodecahedron.

According to Wolfram Alpha this figure first appeared in 1430 in a mosaic by Paolo Uccello. It’s on the floor of St. Mark’s in Venice:

In San Miguel you see it in street art, like the above metal sculpture that was on a corner near where I was staying. It’s also featured in tourist trinkets and souvenirs. Here’s a shop with such items (you can see me in the mirror):

Note the cobblestone street reflected below me!

This picture is from just outside the church at Atotonilco. My contact on the ground in SMdA tells me the 12 points on the star represent the 12 months of the year, and the star is a symbol of peace and unity.

The stellated dodecahedron is featured in “sacred geometry.” This New Age stuff goes back to the Greeks as the dodecahedron was one of Plato’s fundamental figures (the so-called Platonic solids).

Whatever your religious bent, you’ll probably find compatriots in San Miguel. México is a Catholic country (I saw people routinely cross themselves when they walked in front of a church) but it’s also a 21st-century place. There are all kinds! San Miguel attracts a lot of outsiders and oddballs and the modern spiritualist would probably find the vibe to their liking.

I like how this particular design seems to cross the cultural barriers. It’s certainly got its Catholic bona fides, being featured in the Basilica Cattedrale Patriarcale di San Marco, after all. (That’s “St. Mark’s” in Italian.)

And yet the hippies, the tourists, the ex-pats, and the residents have all adopted it as a symbol of the city. It’s hard to argue with peace and unity.

I was almost named for the Patron Saint of Travelers. But the Irish have a well-known habit of turning long names into nicknames and diminutives (Chris, Chrissy, Christy, etc.) and my Mom didn’t like that. So my Dad came up with Mark (from St. Mark the Evangelist, he of the gospels) and they stuck “Christopher” in the middle.

The picture is from the church at Atotonilco, a village a dozen kilometers west of San Miguel de Allende. Officially it is the Santuario de Jesús Nazareno de Atotonilco and it is still a functioning church as well as a tourist destination. The interior artwork, which includes frescoes, murals, oil paintings, statuary, woodwork, gilding, and you-name-it, is from the 17th and 18th centuries and is a high point of Mexican Baroque. It’s impossible to capture the grandeur and garishness of the scene by photography. You really have to see it for yourself!

I’m a Catholic school kid and a former altar boy so religious art is old hat for me. But the stuff at Atotonilco is so over-the-top that I was overwhelmed. The sincerity of the work is palpable—you really feel the faith that sustained the artists and artisans who crafted this sprawling masterpiece.

I particularly liked the peculiar Latin twist on the Catholic iconography. The famous scene on Calvary with Jesus crucified between the two thieves (Luke 23:32) is altered. Traditionally, one thief is a mere burglar, the other a cruel robber. The Mexicans felt that a violent criminal should not share the site with the Savior and his cross is moved to another area of the altar and so there are only two crosses on display. And the Roman soldier who pierces Jesus’ side with his lance (John 19:34) is instead a caballero in full conquistador garb.

St. Christopher medallions have been worn by the faithful for centuries. Invoking San Cristóbal’s grace and protection at the start of a journey or upon arrival at your destination was supposed to ward off things like the plague as well protect you against highwaymen and other dangers.

Tom Waits summoned up the saint in his tune “Hang On St. Christopher” from Frank’s Wild Years (1987):

Hang on St. Christopher, now don’t let me go
Get to me Reno, got to bring it in low
Put my baby on the flat car, got to burn down the caboose
Get ’em all jacked up on whiskey, then we’ll turn the mad dog loose
Hang on St. Christopher on the passenger side
Open it up, tonight the devil can ride
Oh yeah, oh yeah

México is a mountainous place. I spent a week in the city of San Miguel de Allende, which is in the state of Guanajuato, and its 6700′ elevation (2042 m) had me out of breath the entire time.

The view above is from just a few miles east of the city center, on the walk back from the botanical garden (El Charco del Ingenio). And yes, it’s cobblestones the entire way.

This region of the country is known as the Bajio which strangely enough means “lowlands.” As you can see there are high mountains surrounding the broad plains the people inhabit. Thus, lowlands. The Bajio was the economic and cultural center of colonial México and gave birth to the country’s independence movement. Places like San Miguel de Allende and Santiago de Querétaro (the nearest airport) are sort of equivalent to our own revolutionary Boston and Philadelphia. Much of the modern Mexican economy is centered in the region as well as the traditional industries of agriculture and mining. México produces about one-fourth of the world’s silver.

San Miguel de Allende is named for a priest (Franciscan friar Juan de San Miguel) and a patriot (captain-turned-general Ignacio Allende y Unzaga). It’s a UNESCO World Heritage site and a popular tourist destination for Mexicans as well as international visitors.

I was there just after the Day of the Dead festivities which drew 100,000 people. It was still a busy time in the city but the big rush was over. I hear from my contact on the ground that the last of the tourists have left and the Plaza Centro is quiet. When I was in town at least three mariachi bands roamed the place nightly competing for listeners! This really is the off-season.

A large number of ex-pats from the States and other places inhabit San Miguel. It’s been famed as an art colony since before World War II and its allure is still strong. Nonetheless it is also a real Mexican city with schoolkids, senior citizens, taxicabs, commuter buses, shops, and businesses and all the things that make an entire community.

It’s a very interesting place to visit and I’ll have more on that in my next post.

It’s for real:

This should be a bigger story. Alas, it’s the times: Make America Grossly Apathetic.

We can look on the bright side: a warmer Iceland is a more welcoming Iceland. More tourists, more migrants, more economic opportunity. Everyone wins!

Apparently Antarctica is the only place left on the planet that is mosquito-free.

In other news, family matters have induced me to travel to México. I leave today and will be back in a week. I’m looking forward to the adventure.

For about 2200 bucks you can get yourself some platinum. The US Mint has coins with a face value of 100 bucks containing one troy ounce of 0.9995 platinum. Like gold and silver, element no. 78 is a “precious” metal and is used for both bullion (non-coin applications like ingots and bars) and specie (coinage). Of course only an idiot would actually use platinum, gold, or silver as legal tender. We have paper for that! Here’s a platinum coin:

Platinum is rare, similar to gold in crustal abundance. Like gold, it doesn’t corrode. One of its uses is in catalytic converters so all of us are connected with this “noble” metal in some way.

Platinum has a variety of specialized industrial uses but only a tiny amount of the stuff (about 200 metric tons annually) is actually mined and sold on the world market. That’s a little over six million troy ounces. By comparison world gold production is nearly 100 million troy ounces per year.

Platinum is obtained as a by-product from copper and nickel mining.

The first thing I learned in Computer Science 1 at UC Berkeley in the fall of 1977 was GIGO. That stands for “Garbage In, Garbage Out.”

If you write bad code, you will get bad output.

You don’t want the GO or “Garbage Out” part to happen. So, you make sure the GI or “Garbage In” part doesn’t happen!

Today’s AI (mostly Large Language Models) are trained on data. Data is just a fancy word for “all the junk in the world.” Since computers don’t “know” anything, that is, they have no morals, ethics, or values, they can’t “decide” what is good information or what is bad information.

AI engineers started with the assumption of controlled environments and trustworthy inputs. But those things exist only in labs. In the real world there is plenty of garbage. And when AIs can slurp from the entire internet, they can embed corrupt material. They can incorporate suspicious code and ingest poisoned documents. Even if the programming works the way it is supposed to, the outputs can be foolish and stupid because you can’t trust the inputs.

This is the part the AI industry doesn’t want to talk about. You see, the industry has prioritized efficiency over integrity. Doing things right takes time and thus costs money.

From Bruce Schneier, one of my go-to sources on all things tech (along with Molly White):

Integrity isn’t a feature you add; it’s an architecture you choose. So far, we have built AI systems where “fast” and “smart” preclude “secure.” We optimized for capability over verification, for accessing web-scale data over ensuring trust. AI agents will be even more powerful—and increasingly autonomous. And without integrity, they will also be dangerous.

What kind of architectures do you think the Titans of AI will choose for their systems? Which ones have they already chosen?

The so-called “alkali metals” form column one—the first period—of the periodic table. Some of these are familiar, like lithium (#3), sodium (#11), and potassium (#19). We know these things from compounds like lithium carbonate, the medical “lithium” that is used to treat mood disorders. Of course we need sodium chloride (table salt) in our daily diet for its essential role in our physiology. And we eat bananas (or drink OJ) to get potassium salts, another life-sustaining nutrient.

But the actual metals are rare. Outside of chemistry class most folks will never see these things as pure metals. They are typically stored under oil as they oxidize rapidly in the presence of air. I used to toss a chunk of sodium into a bucket of water (outdoors, of course!) for the lovely explosion it made. Lithium, sodium, and potassium are less dense than water and will float. But they will react violently with the water, releasing hydrogen gas which the heat of the reaction will then ignite. Very cool! And the pH of the water surges up, making it alkaline, hence the name “alkali” metals.

Rubidium, #37, has all the same properties as the above except it is denser than water. And it has no known biological function. But it is capable of replacing potassium in organisms and thus can be used as a biomarker.

Rubidium has few industrial uses but has many technical applications in research laboratories. It is used as a laser target, for example, and in atomic clocks. It is named for the ruby color the compounds emit when ignited, and some of the salts are used in fireworks.

I recently finished reading Charles Darwin’s The Origin of Species.

The full title is actually On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life.

It is an extraordinary work. Mostly because it is one of the few scientific pieces of great importance that is immediately accessible to the general reader. One is hard-pressed to read Newton’s epochal Principia, even though it has a helpful diagram on almost every page, because it is mostly a math book. You need scratch paper and a pencil by your side! The same can be said for Copernicus or Kepler. Albert Einstein’s papers from 1905 that established his reputation are short, but dense and obscure. And again the math is a barrier.

Perhaps something like Rachel Carson’s Silent Spring compares, although that is a very brief book and was clearly written for mainstream reception. Darwin was writing to his fellow naturalists. Her book, it could be argued, had a similar impact. Carson’s views have ultimately prevailed among the citizenry, few would argue with her claims today. Darwin, not so much. Anti-evolutionary sentiment is very strong in American education and politics despite its widespread acceptance throughout the world.

The discovery of genetics and the means of inheritance only strengthened Darwin’s (and Alfred Russel Wallace’s) evolutionary schemes. No scientist today questions the idea of the mutability of species. Darwin’s book actually addresses a simple question: does life change over time? Most authorities of Darwin’s time (the book was published in 1859) believed that all living species were specifically created. A species, by definition, was immutable.

The Origin demolishes that point of view. What makes it a great book is that Darwin does it with a scalpel and a smile. The book is not a polemic. It’s a careful, humble, and meticulous exposition of something that became obvious to Darwin over the course of his journeys and studies. He brings the reader along with a clear awareness of the arguments against his ideas and shows how the old ways of thinking just don’t work as well.

That’s the key. Darwin shows, chapter after chapter, how natural selection and variation account for what we actually see in the natural world. It becomes clear that the objections to an evolutionary outlook are grounded in philosophy and religion, not in observation of real things.

The Origin shows a powerful but patient intellect at work. Darwin does not like to leap to conclusions despite his passion for his theory. He takes great pains to support his claims and show how evolution, as a paradigm for the study of life, is more illuminating, more interesting, and more encompassing than the existing modes of thought.

He makes his case. By the end of the book you can see how the new theory supplants the old because it has better explaining power. Reading Darwin helps you understand the scientific method. He starts with the facts: his observations and the results of his experiments; and the mountains of evidence from the work of others. Then, and only then, does he postulate the unifying concepts.

Be suspicious of arguments that start with the principles first. The principles should emerge from the evidence. If you state the theory at the beginning, it will be easy to find examples that support your point of view. If you look first, and then examine what you find, you might have a chance to figure out the big ideas. The first method is biased. The second gives the truth an opening.

Earth is known as a watery planet. Problem is, despite all the water, most of it is salty. There’s really not all that much fresh water available.

You can live perhaps for a few days without water. That’s a simple fact of biology that cannot be transcended no matter how smart, rich, or technologically-enabled you are! Our Silicon Valley Tech Bro Overlords can die of thirst just as easily as the rest of us.

It would behoove the human race to take better care of its freshwater resources.

Hafnium (Hf) is found with zirconium and that’s how most of it is obtained. The two elements are very similar although zirconium is about half as dense as hafnium.

The ores of titanium (rutile and ilmenite) are the source for zirconium and thus for hafnium. Zirconium is used as cladding for fuel rods in nuclear reactors. It has to be pure and any hafnium has to be separated out. The hafnium thus obtained is used for nuclear reactor control rods as it is a good neutron absorber.

A control rod speeds up or slows down a nuclear chain reaction due to its ability to regulate the flow of neutrons. Those neutrons are supplied by the fuel rods (uranium, usually). A nuclear reactor is a collection of fuel rods and control rods. Their movement in and out of the reactor core regulates the rate of fission. The heat energy from nuclear fission (atom-splitting) is sent to a boiler that makes steam. The steam runs a turbine which ultimately drives an electrical generator.

Hafnium is used in alloys and its oxides are used in integrated circuits.