Today’s editorial cartoon in the Toronto Star perfectly captures how many Canadians, myself included, feel about the Canada-US border:

What can I say. Things are not looking good in Trumpia. In fact, things are looking so bad that after months of denial, even the narcissist-in-chief decided to wear a bleeping mask today while visiting a hospital.

I have been trying to remember why the American attitudes towards COVID-19 felt vaguely but strangely familiar. It just hit me. It was the 1970s oil crisis, and the general attitude by leaders in the former Soviet Bloc. This was a crisis of the decadent capitalist West, they told us. The pandemic of fuel shortages, mile long lines at gas stations, high energy prices would not reach us, they told us. Well… they were wrong. Just like those Americans who refuse to wear masks, who refuse to take precautions, who refuse to accept the need to shut down nonessential businesses, because, you know, it’s just like a bad case of the flu…

This may not be an all-time record-breaking day according to Environment Canada (supposedly, the peak temperature today at Ottawa Airport was 34.8 C at 2 PM) but it sure is hot.

You could be forgiven if you thought that this measurement is of the body temperature of a COVID-19 patient with mild symptoms, not the outdoor temperature on our balcony, measured in the shade:

As I said… really hot. Praise be to air conditioning.

I am with Margaret Atwood, Noam Chomsky, David Frum, Francis Fukuyama, Michael Ignatieff, Garry Kasparov, J.K. Rowling, Salman Rushdie and Fareed Zakaria (just a few of the names that I readily recognize) on this one.

“Cancel culture” is wrong. Seeking to find offense where no offense was intended is stupid. It fosters conflict, not understanding. It divides, it doesn’t unite us.

In short, “cancel culture” is not what intelligent people do. It is what mobs do.

And a mob, even when it acts in the name of the highest of ideals, is still a mob.

Ultimately, cancel culture does exactly that: It cancels culture.

The very culture that is our best defense against division. Against prejudice. Against populism.

I grew up in a country with closed borders. I despise closed borders. I find the right to travel, unimpeded, almost as fundamental as the right to breathe.

Yet… For the time being, I support fully the closure of the US-Canada border. As a matter of fact, I wish it was kept even more tightly closed.

What Americans are doing to themselves is unfathomable. That they have an narcissist idiot, an incompetent imbecile running the White House is one thing. But all the other idiots, from state governors to individual citizens, who ignore the threat, cheer as their nation abandons the World Health Organization, even condemn their immunocompromised children to death?

When you live next to a lunatic asylum, you do want to keep your front door under lock and key.

A few hours ago, my phone rang and my friend David told me the sad news: His father, Peter Ada-Winter passed away*.

I’ve known Peter since the late 1970s. He was an educator who played a pioneering role in the introduction of computer programming and computer science into the Hungarian school curriculum.

Peter was a true scholar. His home, a cramped apartment in Budapest’s historic Castle District, was full of books. The walls were lined with tall bookshelves. His large desk was also covered with teetering piles of textbooks, newspapers, and computer printouts.

Peter was the son of Ernő Winter, engineer, physicist and inventor, a towering figure in the early development of vacuum tube technology in the 1920s.

Born in 1923, Peter survived the Holocaust that wiped much of his extended family off the face of the Earth.

He was in his mid-40s when, in 1968, he was asked to organize a regular computer programming course for high school students in the same high school where I studied a decade later.

I met Peter when I became friends with his son David in high school. I always looked up to him. I learned quite a few things from him. Not just technical matters, basic human values as well.

Peter’s interest in information technology never diminished. In the mid-1980s, together with his son David they published a book on the 8-bit ZX Spectrum microcomputer. In the 1990s and early 2000s, despite his advancing age, Peter became well acquainted with the Internet; surfing the Web for news became part of his daily life.

Even after he passed 90, Peter remained in good health and mentally active. Only in the last few years did his health begin to gradually decline. Nonetheless, David remained hopeful that they would be able to celebrate Peter’s 100th birthday in 2023 with a ginormous birthday cake. These hopes were squashed by the news David received today.

Though I share David’s sense of grief, I reminded him that instead of grieving, we should remember the long, productive life of a very good man. Someone that I feel privileged to have known.

*No, not a COVID-19 statistic. Simply old age.

Here are the number of new confirmed COVID-19 cases per day, here in the province of Ontario:

In the great United States:

And in the entire world:

The plots tell the story. I don’t think that there is anything that I can add.

Dame Vera Lynn is no longer with us.

She was 103 years old.

In response to the COVID-19 pandemic, the Parliament of Hungary granted Viktor Orban’s government extraordinary powers to rule by decree. Opponents likened this to the infamous “enabling act” that marked the end of the Weimar Republic in 1933.

In response, Mr. Orban and his supporters argued that the government has no intention of abusing these powers, and that Mr. Orban should be judged by how he relinquishes these extraordinary powers once the crisis is over.

So here it is: Parliament just voted to end the state of emergency and requested the government to take the necessary steps to return to normalcy. So far so good. The corresponding act of Parliament is short and sweet, and to the point. The legal part of the text is only four terse clauses. In my translation:

1. The Legislature requests the government to end, in accordance with section 54, paragraph 3 of the Constitution, the state of emergency that was declared in government decree 40/2020 (March 11) (henceforth: the state of emergency).

2. The act of Parliament concerning measures against the coronavirus, Bill 12 (2020), is no longer in force.

3. (1) The present act – with the exceptions defined in paragraph (2) – shall be considered in force the day after it is proclaimed.

(2) Clauses 2 and 4 shall be considered in force when the state of emergency ends.

(3) The calendar day when clauses 2 and 4 shall be considered in force will be decided by the Prime Minister as soon as the date is known, by immediately proclaiming the date in the Hungarian Gazette.

4. Clause 2 of this bill, in accordance with section 29, paragraph 3; section 2, paragraph 1; section 24, paragraph 9, section 31, paragraphy 3; section 35, paragrapha 1; and section 54, paragraph 4, is considered fundamental.

All looks kosher, right?

But just in case you are still paying attention… there was also a second bill on the table. It has an unassuming title: “About the rules of transition concerning the end of the state of emergency and health preparedness”. Seems eminently reasonable, since under the state of emergency, the government has taken many steps, all of which must be reconciled with the system of laws and regulations.

And there is a lot. This supplementary bill is not four pages. It is 247 (two hundred forty seven) pages in PDF form. Yikes!

And on page 135, we read clause 97:

97. Changes to Bill 128 of 2011 concerning emergency preparedness and modifications of related laws

§339 Section 5 of Bill 128 of 2011 concerning emergency preparedness and modifications of related laws will be amended by the following subclause 24/A:

“24/A Emergency acts of government in case of a state of emergency concerning a human epidemic causing mass rates of infection”

§51/A. (1) The Government, in order to prevent, or mitigate the consequences of, a human epidemic that causes mass rates of infection, threatening lives and property, in order to protect the health and life of citizens of Hungary in a declared state of emergency – in addition to the emergency measures and rules described in subclauses 21-24 – in order to guarantee the lives, health, personal security, security of property, and legal protection of citizens and the stability of the national economy, may, by decree, suspend certain laws, deviate from existing laws and make other extraordinary decisions.

(2) The Government may practice the authority prescribed in paragraph (1) – to the necessary extent, in proportion with the desired outcome – in order to prevent, deal with, and eliminate an epidemic, and furthermore, to prevent or avoid such an outbreak.

There you have it. There are many other clauses concerning other laws, and most seem quite reasonable and appropriate considering the circumstances. But this one?

I highlighted the problem text in red. The law gives the government extraordinary powers. But, though the words seem reassuring on the surface, it offers no checks and balances concerning any justification of invoking these powers and the extent to which they are practiced. In the right hands, these are powers that can be used wisely in case of another pandemic or a resurgence of COVID-19, and I am sure Mr. Orban’s supporters believe that this is precisely how the government will use these powers (if at all). But opponents of Mr. Orban are concerned, not without grounds, about the lack of checks and balances and the very real possibility that these powers can go unchecked in the wrong hands.

In short, this is precisely what many feared: That though the state of emergency is lifted, a backdoor remains, a means for Mr. Orban’s government to have its cake and eat it, too, relinquish its extraordinary powers yet keeping them at the same time.

In the end, it of course all depends on how the law is put into practice. But for now, my conclusion is that the concerns of Mr. Orban’s opposition are not unfounded.

I just happened upon this 30-year old John Cleese sketch, where else? On John Cleese’s own Twitter feed, of course.

What can I say? Just perfect. As appropriate today as it was three decades ago, perhaps even more so.

In 1889, a story by Jules Verne (believed to have been written actually by his son, Michel Verne) was published in the American magazine Forum under the title, “In the Year 2889“.

In it, among other things, Verne envisions video conferencing.

Verne’s story was illustrated by George Roux, who is best known for his numerous illustrations for Verne’s science-fiction novels. I suspect that this particular picture was made in 1889 or 1890 (when Verne’s story, which appeared originally in English, was republished in France.)

I find this image mind-boggling. That 130 years ago, back in the 19th century, someone was able to envision… well, something that, for all intents and purposes, looks pretty much like what many of us are doing today.

Long overdue, but I just finished preparing the latest Maxima release, version 5.44.

I am always nervous when I do this. It is one thing to mess with my own projects, it is another thing to mess with a project that is the work of many people and contains code all the way back from the 1960s.

In case anyone doubted that modern birds are descendants of dinosaurs, here is a reminder: the shoebill.

These amazing creatures are apparently quite docile with humans, but eat baby crocodiles for lunch, which they kill by decapitating them.

They really look like survivors of the K-T asteroid impact. They are… I think they are beautiful.

Amidst all the tension that has been unleashed in the United States, there is this small ray of hope.

A black flight attendant on a Southwest flight initiated a conversation with a white passenger, who was reading the book White Fragility: Why It’s So Hard for White People to Talk About Racism, by Robin DiAngelo.

The white passenger’s remark, “It’s our fault. We have to start these conversations,” caught her by surprise. A short conversation followed. Then the big revelation: The unassuming gentleman happened to be Doug Parker, CEO of American Airlines.

I can already hear some of my friends objecting: “It’s not our fault!” Do not misconstrue Parker’s words (perhaps they weren’t even quoted verbatim.) He of course didn’t mean, I am sure, that every white person must bear personal responsibility for every vile act of racism that happens in America or elsewhere.

Rather, what I read into those words is an acknowledgement of a simple reality: In an unequal relationship, the dominant party has the power to make change for the better. In America, this means whites.

The fact that the CEO of a company as large as American Airlines recognizes this is, well, a ray of hope. As is the fact that he traveled, unassumingly, as an ordinary economy passenger on a competitor’s flight. As rising inequality between the super-wealthy and the stagnating middle class plagues Western societies, the US in particular, as disadvantaged minorities fall even further behind, it is nice to know that at least some folks in positions of power recognize that their wealth and status also come with a huge responsibility. Especially if the nice thoughts are also followed by deeds.

I don’t always like commercial publishers. Some of their textbooks are prohibitively expensive, yet often lacking in quality. (One persistent exception is Dover Publications, who published some of the best textbooks I own, as low-cost paperbacks.)

Last night, however, I was very pleasantly surprised by Springer, who made several hundred textbooks across a range of disciplines available for free, on account of COVID-19.

I did not get greedy. I didn’t download titles indiscriminately. But I did find several titles that are of interest to me, and I gladly took advantage of this opportunity.

Thank you, Springer.

Still playing with some COVID-19 maps, so here is another one: This one ranks countries by the number of COVID-19 cases per 1,000 square kilometers.

What’s the point, you might ask? Well, when there are lots of people confined to a small area, even a few cases can mean trouble; in contrast, when you have many cases but spread over half a continent, you may never come across a single infected person in your travels.

Again, the color legend remains a little whacky; it is logarithmic, but I don’t know how to convince this R package to display it nicely.

The numbers are pretty high. It goes without saying that densely populated microstates like Monaco win the contest, but then there is Qatar (3494), Belgium (1866), the Netherlands (1324), the UK (1051)… numbers that are way too high. For comparison, the USA is at 180, Hungary at 41, Russia at 20 (no surprise there), China at 9 (!), and so is Canada.

Maps that show the spread and mortality rate of COVID-19 are worrisome, to say the least.

So here is something slightly more encouraging: the day-to-day growth rate of COVID-19 infections, in the world, the United States, Canada, and the province of Ontario where I live.

What this plot shows is that the growth rate has been consistently and steadily decreasing (note that the vertical axis is logarithmic). Furthermore, the overall behavior of the worldwide, US, and Canadian plots is remarkable similar.

Of course this plot is also a reflection of the fact that the cumulative number of cases increases, so even if the number of new cases remains steady, the growth rate will indeed decrease. Nonetheless, it demonstrates that at least for now, the pandemic’s exponential spread has been arrested.  This can, of course, change for the worse quite dramatically if we lose our collective patience and start relaxing too soon.

I suppose the most important thing to know about COVID-19 is not so much the total number of cases or deaths, but the number of cases or deaths per million people. A number like 1,000 deaths is huge in a country of one million, a drop in the bucket in a country like India or China.

In that vein, I produced two maps using my rather rusty R programming skills. I am sure I could have done a better job labeling the legend, but there is only so much time I wanted to spend on this. The color bar legend is logarithmic between its two end values.

First, the cumulative number of cases per million people (May 22 data):

Next, deaths per million:

Not a pretty picture. It appears that the countries that are the most disproportionately affected (or the most likely to offer accurate reports?) are in Europe (including Russia), North and South America and the Middle East.

But now, here is perhaps the scariest map of all:

Yes, in many countries more than 10% of the confirmed cases result in death. The global average is 6.4 per 100 confirmed cases. The fact that COVID-19 is deadly in countries with underdeveloped health care systems is perhaps understandable, but the fact that the reddest parts of the map are places with the most sophisticated health care systems in the world is food for thought.

I am one of the maintainers of the Maxima computer algebra system. Maxima’s origins date back to the 1960s, when I was still in kindergarten. I feel very privileged that I can participate in the continuing development of one of the oldest continuously maintained software system in wide use.

It has been a while since I last dug deep into the core of the Maxima system. My LISP skills are admittedly a bit rusty. But a recent change to a core Maxima capability, its ability to create Taylor-series expansions of expressions, broke an important feature of Maxima’s tensor algebra packages, so it needed fixing.

The fix doesn’t amount to much, just a few lines of code:

It did take more than a few minutes though to find the right (I hope) way to implement this fix.

Even so, I had fun. This is the kind of programming that I really, really enjoy doing. Sadly, it’s not the kind of programming for which people usually pay you Big Bucks… Oh well. The fun alone was worth it.

One of the most fortunate moments in my life occurred in the fall of 2005, when I first bumped into John Moffat, a physicist from The Perimeter Institute in Waterloo, Ontario, Canada, when we both attended the first Pioneer Anomaly conference hosted by the International Space Science Institute in Bern, Switzerland.

This chance encounter turned into a 15-year collaboration and friendship. It was, to me, immensely beneficial: I learned a lot from John who, in his long professional career, has met nearly every one of the giants of 20th century physics, even as he made his own considerable contributions to diverse areas ranging from particle physics to gravitation.

In the past decade, John also wrote a few books for a general audience. His latest, The Shadow of the Black Hole, is about to be published; it can already be preordered on Amazon. In their reviews, Greg Landsberg (CERN), Michael Landry (LIGO Hanford) and Neil Cornish (eXtreme Gravity Institute) praise the book. As I was one of John’s early proofreaders, I figured I’ll add my own.

John began working on this manuscript shortly after the announcement by the LIGO project of the first unambiguous direct detection of gravitational waves from a distant cosmic event. This was a momentous discovery, opening a new chapter in the history of astronomy, while at the same time confirming a fundamental prediction of Einstein’s general relativity. Meanwhile, the physics world was waiting with bated breath for another result: the Event Horizon Telescope collaboration’s attempt to image, using a worldwide network of radio telescopes, either the supermassive black hole near the center of our own Milky Way, or the much larger supermassive black hole near the center of the nearby galaxy M87.

Bookended by these two historic discoveries, John’s narrative invites the reader on a journey to understand the nature of black holes, these most enigmatic objects in our universe. The adventure begins in 1784, when the Reverend John Michell, a Cambridge professor, speculated about stars so massive and compact that even light would not be able to escape from its surface. The story progresses to the 20th century, the prediction of black holes by general relativity, and the strange, often counterintuitive results that arise when our knowledge of thermodynamics and quantum physics is applied to these objects. After a brief detour into the realm of science-fiction, John’s account returns to the hard reality of observational science, as he explains how gravitational waves can be detected and how they fit into both the standard theory of gravitation and its proposed extensions or modifications. Finally, John moves on to discuss how the Event Horizon Telescope works and how it was able to create, for the very first time, an actual image of the black hole’s shadow, cast against the “light” (radio waves) from its accretion disk.

John’s writing is entertaining, informative, and a delight to follow as he accompanies the reader on this fantastic journey. True, I am not an unbiased critic. But don’t just take my word for it; read those reviews I mentioned at the beginning of this post, by preeminent physicists. In any case, I wholeheartedly recommend The Shadow of the Black Hole, along with John’s earlier books, to anyone with an interest in physics, especially the physics of black holes.

Heaven knows why I sometimes get confused by the simplest things.

In this case, the conversion between two commonly used cosmological coordinate systems: Comoving coordinates vs. coordinates that are, well, not comoving, in which cosmic expansion is ascribed to time dilation effects instead.

In the standard coordinates that are used to describe the homogeneous, isotropic universe of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the metric is given by

$$ds^2=dt^2-a^2dR^2,$$

where $$a=a(t)$$ is a function of the time coordinate, and $$R$$ represents the triplet of spatial coordinates: e.g., $$dR^2=dx^2+dy^2+dz^2.$$

I want to transform this using $$R’=aR,$$ i.e., transform away the time-dependent coefficient in front of the spatial term in the metric. The confusion comes because for some reason, I always manage to convince myself that I also have to make the simultaneous replacement $$t’=a^{-1}dt.$$

I do not. This is nonsense. I just need to introduce $$dR’$$. The rest then presents itself automatically:

\begin{align*} R’&=aR,\\ dR&=d(a^{-1}R’)=-a^{-2}\dot{a}R’dt+a^{-1}dR’,\\ ds^2&=dt^2-a^2[-a^{-2}\dot{a}R’dt+a^{-1}dR’]^2\\ &=(1-a^{-2}\dot{a}^2{R’}^2)dt^2+2a^{-1}\dot{a}R’dtdR’-d{R’}^2\\ &=(1-H^2{R’}^2)dt^2+2HR’dtdR’-d{R’}^2, \end{align*}

where $$H=\dot{a}/a$$ as usual.

OK, now that I recorded this here in my blog for posterity, perhaps the next time I need it, I’ll remember where to find it. For instance, the next time I manage to stumble upon one of my old Quora answers that, for five and a half years, advertised my stupidity to the world by presenting an incorrect answer on this topic.

This, incidentally, would serve as a suitable coordinate system representing the reference frame of an observer at the origin. It also demonstrates that such an observer sees an apparent horizon, the cosmological horizon, given by $$1-H^2{R’}^2=0,$$, i.e., $$R’=H^{-1},$$ the distance characterized by the inverse of the Hubble parameter.