Month: April 2023

Movie Review: Chevalier

As the movie ‘Chevalier’ begins we are attending a musical performance in late 18th century France. A small orchestra, by today’s standards, is on stage while front and center a young man is playing a solo violin while also conducting. As the concerto ends the young man introduces himself as Wolfgang Amadeus Mozart and asks if anyone in the audience has a request, something that never happens at a concert today.

The composer Mozart actually lived with the Chevalier de Saint-Georges for a summer while he visited Paris. I expect the two musicians played together quite often. (Credit: Classic FM)

A voice from the back asks if he could accompany Mozart. When the famous composer agrees a young black man, dressed as a French Nobleman steps on stage. Mozart is rather surprised, “Is this a jest’, “Who put you up to this?” he asks. Willing to go along with what he thinks is a joke Mozart being to play a cadenza, the black man quickly follows suit and the two violinists are soon deep in a musical duel. After a few minutes Mozart realizes that his opponent is a little bit better than he is, Mozart was really a pianist after all, so he turns to one of the orchestra members and asks, “Who the f%*k is that?”

A contemporary portrait of Joseph Bologne, the Chevalier de Saint-Georges, the subject of the new movie ‘Chevalier’. (Credit: LA Opera)

So we are introduced to Joseph Bologne, the Chevalier de Saint-Georges, wonderfully played by actor Kelvin Harrison jr. Once regarded as the most accomplished man in all of Europe in the movie we learn that Joseph is the son of a wealthy plantation owner in the French colony Guadeloupe named Georges Bologne and one of his black slave girls named Nanon, played by actress Ronke Adekoluejo. At the age of seven Georges returns to France to enroll his half-black bastard son in a musical academy, the boy is exceptionally good with the violin. Before leaving Georges gives his son one last piece of advice, “Be exceptional, they can’t stop you if you’re exceptional!” Joseph never sees his father again.

Poster for the film ‘Chevalier’. (Credit: IMDB)

Joseph does become exceptional. In addition to his musical ability Joseph becomes the most celebrated swordsman in France, the film shows his famous bout against fencing master Alexandre Picard. This ability with the sword earns him the title Chevalier de Saint-Georges from Queen Marie Antoinette, actress Lucy Boynton. Joseph’s main ambition is to become the Director of the Paris Opera and his chief romantic desire is the Marquise Marie-Josephine de Montalembert, a married woman, played by actress Samara Weaving.

The french Queen Marie Antoinette, plays a bigger role in the movie ‘Chevalier’ than she did in the real history of Joseph Bologne. Once again Hollywood feels it has to introduce historic figures everyone knows whether they belong in the story or not. (Credit: Commonsensemedia)

Both goals come to naught because of course Joseph is a black man and, as his mother puts it, “Just a tourist in their world.” In response to his rejection by French nobility Joseph joins with the revolutionary elements in Paris and helps to bring down the ancient regime.

Joseph’s affair with a married white Marquise is the central theme of ‘Chevalier’ even though historically it was only a insulting rumour. (Credit: Rotten Tomatoes)

The story of the Chevalier de Saint-Georges is an important one, one that needs to be told. His music is only now being rediscovered; I recently bought two CDs of his concertos and symphonies. Joseph was also a statesman and soldier, he served his country, he was a French citizen, both as a Chevalier and after the revolution he helped form the first all-black regiment in the French army. Nevertheless he was black and we all know how even today systematic racism conspires to keep blacks, however exceptional, in their places. The ‘Chevalier’ is an attempt to reestablish the reputation of a man who really was exceptional.

The 2016 film ‘Hidden Figures’ covered many of the same themes as ‘Chevalier’. Stories of talented people who are deliberately ignored because they don’t fit our picture of what a talented person should look like are stories that need to be told. (Credit: 20th Century Studios)

The music in ‘Chevalier’, as performed by the London Contemporary Orchestra is excellent, as are the costumes. Also the movie was filmed in the city of Prague, the same location as the movie ‘Amadeus’. All of which make ‘Chevalier’ enjoyable as well as important.

Although best known today as a musician, Joseph Bologne first achieved fame as a swordsman. (Credit: IMDB)

Unfortunately, as all too often happens in Hollywood, ‘Chevalier’ tends to prefer tired clichés over historical accuracy. In fact Joseph was originally enrolled in a fencing academy not a musical one. The romance with the Marquise Marie-Josephine is only a salacious rumour and had nothing to do with Joseph’s losing his bid for the Paris Opera. Also the friendship between Joseph and the French Queen is greatly overblown.

Cliches in Hollywood have become so numerous that people have even taken to publishing lists of them. (Credit: MovieCliches.com)

Perhaps more importantly is the relationship between Joseph and his father. Georges Bologne did not just abandon his son at school but actually asked his brother Joseph to look in on the boy from time to time. Then, just two years later Georges returned to France with Joseph’s mother Nanon. The three lived together in Paris for nine years before Georges returned to Guadeloupe to attend to his possessions there. Georges did apparently care for both his son and his mistress, although at that time the relationship must have been extremely complicated. In a better world Joseph and his parents may have been just a normal happy family.

For most of our nation’s history interracial marriage was a crime in many states. It wasn’t until 1967 that the Supreme Court finally struck down all laws banning interracial marriage. (Credit: Freedom to Marry)

I’d like to add another criticism, after the movie’s first scene Mozart disappears from the film and several people I know who saw the movie came away thinking that Mozart hated Joseph. Nothing could be farther from the truth, Mozart greatly admired the Chevalier and if fact Joseph conducted the world premiers of about a half a dozen Mozart symphonies, and the French premiers of many more. Mozart and Joseph had another thing in common as well, they were both Masons.

Like Mozart, Ben Franklin, George Washington and over a dozen other US Presidents, the Chevalier de Saint-Georges was a member of the Masons. (Credit: Grand Lodge of Ohio)

The glossing over of such facts is a great shame because the story of ‘Chevalier’ is too important a lesson for us today to allow it to be obscured by Hollywood clichés. So I still highly recommend that you go see ‘Chevalier’ so that you can be introduced to someone who is really worth knowing. The world needs more people like Joseph Bologne regardless of their colour, sex, nationality or whatever characteristic we use in order to hate each other.

Mathematicians have discovered a single geometric shape that tiles but when doing so does not generate a repeating pattern. I wonder what kind of art M. C. Escher could have created with such a figure.

We’re all familiar with the way that certain geometric figures, the square being the simplest, can be fitted together so there are no gaps or overlaps, the pieces all fit together perfectly. This geometric property is known as tiling because throughout history we humans have tiled floors and walls both for construction and to produce works of art.

A Simple but still interesting Tile. Hundreds of such patterns can be easily generated by squares, rectangles, triangles etc. (Credit: Freepik)

As I said there are some geometric figures that can be tiled like squares, rectangles, triangles, and hexagons. At the same time there are geometric shapes that will not produce a perfectly fitted tile, like stars, five or six sided, and octagons. There are also tiled patters that can be formed using two different geometric figures like a diamond and a parallelogram (see figure below). In mathematical terms such figures or combinations of figures are said to ‘admit’ tiling.

A couple of examples of geometric shapes that do not admit tiling. (Credit: Math and Multimedia)
A tiling pattern formed from two geometric figures can quickly become quite complex. (Credit: Pinterest)

You may have noticed that all of the figures I mentioned above are straight lined shapes rather than curved figures like a circle or a teardrop. While it is true that it is easier to find straight lined shapes that tile there are many known curved shapes that tile as well.

Here’s a simple but still very interesting tile pattern made from a single curved figure. (Credit: VectorStock)

Mathematicians have explored the properties of tiled patterns ever since the days of the ancient Greeks, if not even earlier. One of the most important features of the tiling of geometric figures is that they almost always repeat themselves over and over again in identical patterns. For some of the more elaborate geometric shapes, and especially for combinations of two or more figures the repeating section may be quite large, nevertheless the greater majority of tiled figures repeat themselves over and over again.

Despite it’s complexity the repeating pattern of this tile is easily apparent. (Credit: repper.app)

Those few combinations that do not repeat themselves have been given the special name of Penrose tiles after a small class of which was discovered back in the 1970s. Since then mathematicians have searched in vain for an elusive ‘Einstein’ tile, a single geometric figure that would tile perfectly but without creating a repeating pattern. (By the way the name Einstein does not refer to physicist Albert Einstein but rather to the meaning of the German word einstein, ‘one stone’.

The recently discovered ‘einstein’ tile. Despite being a single geometric figure that admits tiling it nevertheless generates no repeating pattern. (Credit:Science News)

Now a group of mathematicians from a quartet of Universities, Yorkshire, Cambridge, Waterloo and Arkansas, have found that elusive one stone, a thirteen sided irregular figure that they have christened ‘the hat’. As can be seen in the figure ‘the hat’ obviously does not develop a simple repeating pattern. In order to officially declare their result to be an einstein however the researchers had to prove that there would never be a repeating pattern by using what is known as a geometric incommensurability argument.

Many artists have made self-portraits but this one by M. C. Escher is just the best in my opinion. (Credit: National Gallery of Art)

The mathematicians who discovered ‘the hat’ expect that the most likely use of their figure will be in the arts and I’m certain it won’t take long before some artist takes up the challenge. Which brought to my mind what artistic creations the celebrated graphic artist Maurits Cornelis Escher, better known as M. C. Escher, might have done with ‘the hat’. Escher became famous both for turning tiled geometric figures into living animals, but also by then using those ‘living tiles’ in a larger work of art that contained less abstract elements as well.

Escher would often start by designing a tiling pattern that consisted of living creatures, in this case little reptiles. (Credit: Instructables)
Then use that pattern as a part of a larger, non-tiled work that are just breath taking in their imagination. (Credit: Wikipedia)

M.C. Escher lived from 1898 to 1972 in the Netherlands producing woodcuts, lithographs and mezzotints rather than paintings or sculptures like most of his contemporaries. Most of Escher’s works were greatly inspired by mathematical ideas, including artistic explorations of infinity, reflection and even hyperbolic geometry. During much of his life Escher was mostly ignored by the arts community, even today many artists regard him more as an uninspired workman rather than a true artist. In scientific circles however, Escher’s ideas and inventiveness slowly gained him a large following, one that continues to grow to this day.

Escher often used the ability of 2 dimensional drawings to show physical phenomenon that are impossible in the real world. Follow the water in this image! (Credit: NHPR)
Escher worked during the period of time when Relativity and Quantum Mechanics were revolutionizing out views of reality. No wonder that his works are loved by Physicists and Mathematicians. (Credit: Swann Auction Galleries)

Escher produced literally dozens of ‘living tiles’ using birds, fishes and even human beings as the tiled shape. Arguably the most famous of his tiled efforts is ‘Reptiles’, see figure above, which contains a page with a tiled pattern of lizards but at one end live lizards are coming out of the page, walking around a bit before sinking back into the flat reptile pattern.

Swans turning into fish is one of Escher’s simpler examples of tiling of one animal into another. (Credit: Museum of Fine Arts Houston)

Throughout his work Escher was fascinated by repeated patterns of one, two or even three geometric figures, many of which he would turn into living creatures. I’m certain that Escher would have been thrilled by the challenge of working with ‘the hat’, a figure that tiles but never repeats.

Space News for April 2023: Analyzing the results from NASA’s DART mission and how the discovery of a new asteroid may mean that we have to use those results sooner than we thought!

You may recall back last September when NASA’s DART spacecraft slammed into an asteroid as a first test of a planetary defense system, see my post of 8 October 2022. The DART mission, which stands for Double Asteroid Redirection Test, was designed to see if it was possible to alter the trajectory of an asteroid that was on a collision course with Earth as a way of preventing that impact.

The Dart spacecraft was intentionally send to crash into the small asteroid Dimorphos, which orbits around the larger asteroid Didymos. By carefully measuring the orbital period of Dimorphos astronomers can calculate the change in the asteroid’s velocity that the collision caused. (Credit: DART – NASA)

The target for the DART spacecraft was the asteroid Dimorphos, a 160m wide space rock that orbits around a larger, 750m asteroid named Didymos. By slamming into Dimorphos at 6km per second it was hoped that the 600kg DART spacecraft would change the time it takes the smaller asteroid to orbit around the bigger one. In astronomy it’s just easier to measure the time it takes something to happen rather than positions or distances.

Long before we could measure the distance to the Moon astronomers knew how long it took the Moon to orbit the Earth simply by keeping track of the Moon’s Phases. In astronomy it’s just easier to measure time than distance. (Credit: MoonConnection.com)

Dimorphos’ orbital period around Didymos before the collision with DART had been measured at approximately 11 hours and 55 minutes. After the collision astronomers back here on Earth took their time to accurately measure the new period. Once the new orbital period had been determined the laws of orbital dynamics could be used to calculate how much the asteroid’s velocity had been changed.

Once astronomers have measured the orbital period P, they can then use orbital mechanics, this is Kepler’s third law, to calculate other quantities like the average distance r between the two bodies. (Credit: burro.astr.cwru.edu)

It wouldn’t have to be by much either for the test to be successful because if you can change an asteroid’s trajectory by only one meter per second a year before it hits the Earth then that asteroid would miss our planet by more than 25,000 km. That’s why NASA’s plan for protecting Earth is to locate any potentially dangerous asteroids and if any are headed our way to gently alter their trajectory years before they get here. That’s considered to be a safer and less costly way to protect the Earth than Hollywood’s usual technique of blowing them up with nuclear weapons.

In the movie ‘Meteor’ the US and USSR send a bunch of H-bombs to blow up an asteroid that’s headed for Earth. NASA hopes to develop a bit more gentle technique. (Credit: Amazon.com)

So the DART spacecraft slammed into Dimorphos and the collision was so brilliant that several telescopes back here on Earth were able to photograph it. Not only was the impact itself impressive but the force of the collision ejected a large amount of material from the surface of Dimorphos generating a tail behind the asteroid similar in appearance to a comet’s. Since then astronomers have been observing Dimorphos in order to learn just how successful the DART mission was.

Image of the actual DART collision. The big asteroid Didymos is lower left while Dimorphos is upper right and obviously erupting in some fashion. (Credit: New York Times)

Now the results are in and it is clear that DART did better than anyone had expected. In a series of five papers in the journal Nature astronomers and aerospace engineers presented a detailed account how the DART collision changed the Didymos-Dimorphos system. NASA had hoped that the collision would reduce Dimorphos’ orbital period by seven minutes, from 11 hours 55 minutes down to 11 hours 48 minutes but instead the orbital period dropped by 33 minutes, more than four times what was predicted. The scientists are convinced that it was the large amount of ejected material knocked off the asteroid that generated the larger than anticipated result. Based on ground observations it is estimated that as much as 0.5% of Dimorphos’ entire mass may have been exploded into space, and remember for every action there is an equal an opposite reaction.

The trail of ejected material from Dimorphos. The amount of material ejected by the DART collision is estimated to be as much as half a percent of Dimorphos’ total mass. (Credit: El Pais in English)

So the DART mission clearly showed that the idea of protecting Earth from an asteroid impact by nudging it slightly years before the asteroid reaches us is a good one. More than that however DART gave scientists and engineers a good baseline for determining exactly how to go about giving an asteroid that nudge.

Possible future mission to visit an Asteroid, or perhaps push one out of our way? (Credit: Forbes)

And we may have to make use of that knowledge before long because NASA has recently announced that the space agency has discovered a small asteroid that might, emphasis on might, collide with Earth on Saint Valentine’s day in the year 2046, 23 years from now. The new asteroid has been given the name 2023 DW and is about 47m in size so it’s considerably smaller that Dimorphos. Still if an asteroid that size were to strike a heavily populated area it could cause a lot of damage. Right now the Jet Propulsion Labouratory (JPL) estimates that 2023 DW has about a 1 in 560 chance of striking our planet while the European Space Agency puts the odds at 1 in 625. You can be certain that astronomers are keeping a close eye on 2023 DW and so over the next year or so those estimates are likely to change.  If asteroid 2023 DW continues to be a threat who knows, it may very well become the first target of a real attempt to use the lessons from DART to protect our planet from an asteroid impact.

New Studies indicate that Sea Level Rise due to Climate Change over the next 100 years could be far worse than previously expected. Meanwhile the big Oil companies continue to make record profits.

Over the last several years various aspects of Climate Change have been getting a bit more attention in the news than previously. Both the continuing drought in the Western North America, East Africa and Europe as well as the abnormally severe storms, hurricanes, tornadoes along with massive floods throughout the world have been making so many headlines that global warming can no longer be completely ignored.

So far this year has been unprecedented in the number and destruction of Tornadoes here in the US. How anyone can continue to doubt the reality of Climate Change is beyond my understanding. (Credit: American Museum of Natural History)

Now all of that news coverage is a good thing but all of those stories about changing weather patterns have obscured another piece of the climate change problem, sea level rise. Sea level rise may not get the headlines, basically because we haven’t begun to see the worst effects of it yet, but millimeter by millimeter it just keeps it just keeps on building, a measured 20cm rise worldwide over the last 100 years. Already some of its effects have been noticed in low laying parts of the world like the Mississippi delta or islands like the Seychelles. At the same time the entire US gulf and Atlantic coasts have been subjected to an ever growing number of ‘King Tides’, periodic flooding of land areas even when there has been no rain for days. In the city of Miami seawater has been known to come bursting out of sewers while the Sun is shining brightly.

While Hurricanes, Tornadoes and Droughts get the most press coverage, King Tides caused by the slow but constant rise in sea level are becoming a regular nuisance in many coastal cities. (Credit: Science / How Stuff Works)

Now two news studies, each looking at the long term consequences of sea level rise from opposite directions have concluded that the problem will become much worse, much quicker than expected. The first study, published in the journal Nature Communications by an international team of scientists details the results of a series of model based computer simulations.

The ice in Greenland is melting faster than ever and now there is evidence that the ice is melting from the bottom up indicating that the whole ice cap could become unstable! (Credit: CNN)

Those results predict that not only will the melting of the ice caps on both Greenland and Antarctica continue, but that the melting will accelerate, causing a much greater rise in sea level by the end of the century. In fact the models show that, if global temperature rise should exceed 1.8ºC above pre-industrial levels the melting of the ice caps would reach irreversible, catastrophic amounts with a sea level rise by the year 2100 estimated at one meter above today’s level.

It was all smiles as the nations of the world agree to keep global temperature rise below 1.5 degrees back in 2015. It seems however that nobody realized that meant that had to do something other than just smile! (Credit: State of the Planet – Columbia University)

Now remember, ever since the Paris climate accords of 2015 both scientists and politicians have been pushing for a limit of 1.5ºC rise in global temperature, and pretty much failing to do anything substantial to actually stop the world from going past that goal. Indeed, the latest estimates have the global temperature rise going above 1.5ºC sometime in the next five years. And once we’re past 1.5ºC can 1.8ºC be far behind. So the amount of water being dumped into the oceans by melting ice caps is going to increase rapidly, threatening the low laying areas of every nation on Earth.

Worst case scenario for sea level rise here in the US. Even without this extreme case many of our largest cities will become unlivable due to constant floodings and storm damage. (Credit: Forbes)

The second paper concerns those low laying areas and concludes that we have been greatly underestimating the amount of global land area that will be lost due to sea level rise. The study, published in the American Geophysical Union’s journal Earth’s Future, utilizes data from NASA’s ICESat-2 LiDAR satellite, which was launched back in 2018, to determine the elevation above sea level of land areas throughout the globe.

Well they finally did it, NASA put a LASER in space. Don’t worry this one is intended to measure land elevations not blast cities to rubble. (Credit: ICESat-2 -NASA)

Previous measurements of land elevations were carried out by airplanes using radar, but those measurements were inaccurate, primarily because radar cannot penetrate beneath vegetation to the true ground surface. The ICESat-2 satellite uses the much more precise Light Detection and Ranging (LiDAR) that is better able to determine the true elevation of land areas.

Elevation maps showing the hight above sea level of land areas are a common tool in geography but if sea level continues to rise we are going to need to redo all of them! (Credit: SERC)

What the researchers found was the elevation of much of the world’s low laying land areas was being overestimated. Not by much, only a meter or two for the most part, but when coupled with a one meter rise in sea level it means that just about twice as much of the world is going to sink beneath the ocean by the year 2100 than was previously thought.

Salt Marshes are among the richest and most important ecological environments in the world. A 1 meter rise in sea level would result in most of the world’s salt marshes simply disappearing. (Credit: The Pew Charitable Trusts)

That means that millions more people will see their homes swept away by floods. Whole nations like Bangladesh may simply cease to exist while seacoasts around the world will be inundated. Rich cities like Miami and Boston may be able to afford to build dikes to preserve them, but what about poorer cities like Mumbai and Bangkok? What about the numerous small coastal towns in New Jersey, North Carolina, Florida and Texas?

One of the most densely populated counties in the world Bangladesh is also probably the most threatened by sea level rise. (Credit: UCAR Center for Science Education)

So it may not be long before you start hearing more and more stories on the news about widespread flooding across the globe. It’ll happen slowly, millimeter by millimeter as the sea rises, but it’s going to happen.

By building a large interconnected system of dykes the people of the Netherlands succeeded in building a country that is mostly below sea level. However that task took centuries to complete and Holland isn’t that big a country. Imagine the cost of doing that for the whole world! (Credit: Quora)

Now, if you find the latest estimates on sea level rise and the flooding of the world’s coastlines associated with it to be a bit depressing then here’s some news that I’m certain will cheer you up. The major oil companies have recently all announced that they made record profits during last year 2022. So even as the planet burns up you can still have a safe investment for your 401K that will be paying dividends in the post-apocalyptic hellscape to come.

Is this what the future holds for New York and other coastal cities? (Credit: Rolling Stone)

For the record, Exxon-Mobile posted a profit in 2022 of $55.7 Billion, that’s profit, not sales, while Shell announced $39.9 Billion in profit. The other oil giants saw similar levels of profit, Chevron $35.5 Billion, BP $27.7 while France’s Total Energies announced $36.6 Billion. All of these numbers were records for each company and came while the world was recovering from the Covid-19 pandemic and tittering on the brink of a recession.

Even as people all over the world complained about the sharp rise in the price of gas the oil companies were quite happy. (Credit: Bloomberg.com)

Of course the oil giants insist that they did nothing wrong, it was the pandemic’s fault really. You see during all of the Covid lockdowns the demand for oil and natural gas dropped so they all had to cut way back on production. Then last year, as life throughout the world began to return to normal the demand for oil and natural gas shot up. Add to that Russia’s invasion of Ukraine, Russia is the world’s third largest oil producer and second largest producer of natural gas, and the price for a barrel of oil went through the roof. There was nothing the oil companies could do; the law of supply and demand literally forced them to make ungodly amounts of money.

How much is Russian oil paying for Russia’s war in Ukraine? How many wars so far this millennia have been fueled by oil? (Credit: Fair Observer)

All of which is just more evidence of how hard it is going to be to get the human race to stop polluting the world with fossil fuels. There are simply too many people making too much money from oil and natural gas, I won’t even mention coal, for them to be simply outlawed. The question therefore becomes how much of the world’s land mass has to be flooded, how severe do storms have to become, how many people have to suffer in droughts or wildfires before we finally do something? And will it be too late by then?