I just watched a news conference held by the University of Waterloo, on account of Donna Strickland being awarded the Nobel prize in physics.

This is terrific news for Canada, for the U. of Waterloo, and last but most certainly not least, for women in physics.

Heartfelt congratulations!

Years ago, I accepted the role of release manager for the Maxima computer algebra system. It proved to be more laborious than I assumed (mostly for two things: assembling changelogs, and dealing with build glitches) but it still has its upside. Right now, it is my pleasure to announce that Maxima 5.42 has been released on the unsuspecting public. Enjoy!

Michael Atiyah, 89, is one of the greatest living mathematicians. Which is why the world pays attention when he claims to have solved what is perhaps the greatest outstanding problem in mathematics, the Riemann hypothesis.

Here is a simple sum: $$1+\frac{1}{2^2}+\frac{1}{3^2}+…$$. It is actually convergent: The result is $$\pi^2/6$$.

Other, similar sums also converge, so long as the exponent is greater than 1. In fact, we can define a function:

\begin{align*}\zeta(x)=\sum\limits_{i=1}^\infty\frac{1}{i^x}.\end{align*}

Where things get really interesting is when we extend the definition of this $$\zeta(x)$$ to the entire complex plane. As it turns out, its analytic continuation is defined almost everywhere. And, it has a few zeros, i.e., values of $$x$$ for which $$\zeta(x)=0$$.

The so-called trivial zeros of $$\zeta(x)$$ are the negative even integers: $$x=-2,-4,-6,…$$. But the function also has infinitely many nontrivial zeros, where $$x$$ is complex. And here is the thing: The real part of all known nontrivial zeros happens to be $$\frac{1}{2}$$, the first one being at $$x=\frac{1}{2}+14.1347251417347i$$. This, then, is the Riemann hypothesis: Namely that if $$x$$ is a non-trivial zero of $$\zeta(x)$$, then $$\Re(x)=\frac{1}{2}$$. This hypothesis baffled mathematicians for the past 130 years, and now Atiyah claims to have solved it, accidentally (!), in a mere five pages. Unfortunately, verifying his proof is above my pay grade, as it references other concepts that I would have to learn first. But it is understandable why the mathematical community is skeptical (to say the least).

A slide from Atiyah’s talk on September 24, 2018.

What is not above my pay grade is analyzing Atiyah’s other claim: a purported mathematical definition of the fine structure constant $$\alpha$$. The modern definition of $$\alpha$$ relates this number to the electron charge $$e$$: $$\alpha=e^2/4\pi\epsilon_0\hbar c$$, where $$\epsilon_0$$ is the electric permeability of the vacuum, $$\hbar$$ is the reduced Planck constant and $$c$$ is the speed of light. Back in the days of Arthur Eddington, it seemed that $$\alpha\sim 1/136$$, which led Eddington himself onto a futile quest of numerology, trying to concoct a reason why $$136$$ is a special number. Today, we know the value of $$\alpha$$ a little better: $$\alpha^{-1}\simeq 137.0359992$$.

Atiyah produced a long and somewhat rambling paper that fundamentally boils down to two equations. First, he defines a new mathematical constant, denoted by the Cyrillic letter $$\unicode{x427}$$ (Che), which is related to the fine structure constant by the equation

\begin{align*}\alpha^{-1}=\frac{\pi\unicode{x427}}{\gamma},\tag{1.1*}\end{align*}

where $$\gamma=0.577…$$ is the Euler–Mascheroni constant. Second, he offers a definition for $$\unicode{x427}$$:

\begin{align*}\unicode{x427}=\frac{1}{2}\sum\limits_{j=1}^\infty 2^{-j}\left(1-\int_{1/j}^j\log_2 x~dx\right).\tag{7.1*}\end{align*}

(The equation numbers are Atiyah’s; I used a star to signify that I slightly simplified them.)

Atiyah claims that this sum is difficult to calculate and then goes into a long-winded and not very well explained derivation. But the sum is not difficult to calculate. In fact, I can calculate it with ease as the definite integral under the summation sign is trivial:

\begin{align*}\int_{1/j}^j\log_2 x~dx=\frac{(j^2+1)\log j-j^2+1}{j\log 2}.\end{align*}

After this, the sum rapidly converges, as this little bit of Maxima code demonstrates (NB: for $$j=1$$ the integral is trivial as the integration limits collapse):

(%i1) assume(j>1);
(%o1)                               [j > 1]
(%i2) S:1/2*2^(-j)*(1-integrate(log(x)/log(2),x,1/j,j));
log(j) + 1
---------- + j log(j) - j
(- j) - 1          j
(%o2)             2          (1 - -------------------------)
log(2)
(%i3) float(sum(S,j,1,50));
(%o3)                         0.02944508691740671
(%i4) float(sum(S,j,1,100));
(%o4)                         0.02944508691730876
(%i5) float(sum(S,j,1,150));
(%o5)                         0.02944508691730876
(%i6) float(sum(S,j,1,100)*%pi/%gamma);
(%o6)                         0.1602598029967022


Unfortunately, this does not look like $$\alpha^{-1}=137.0359992$$ at all. Not even remotely.

So we are all left to guess, sadly, what Atiyah was thinking when he offered this proposal.

We must also remember that $$\alpha$$ is a so-called “running” constant, as its value depends on the energy of the interaction, though presumably, the constant in question here is $$\alpha$$ in the infrared limit, i.e., at zero energy.

It is not every day that you see devastation on this scale in our fine city:

That happens to be the Merivale electrical substation. What can I say… looks “previously owned, slightly used”. No wonder substantial chunks of the city are still without power, two days after the tornado hit.

There is a white rabbit who set up residence near my wife’s allotment garden.

This is obviously not a wild animal. He may be okay for now, but for how long? How long before either a predator finishes it off, or bad weather sets in?

In short, I think it needs a home. I have no idea what to do with a rabbit and we have two cats already. But perhaps a good soul sees this post…

Outraged over ever increasing phone bills, today I decided to cancel our second landline.

We used to use this line a fair deal. It was, back in the days of dial-up modems, my phone line for incoming dial-up calls (e.g., when I was traveling) and also a means to maintain a backup, low-speed Internet connection. It was occasionally used by my wife, as it was the line to which a dual-mode Skype-and-landline phone was connected.

And, of course, it was used for that miracle of 20th century technology: facsimile transmissions.

Of course, this is 2018 now, and I have not used a dial-up data connection in at least a decade. No travel computer of mine had a modem, in fact, since the early 2000s. My old travel kit, containing various country-specific phone plugs, even a screwdriver and alligator clips, lies on a shelf, forgotten. And Skype? Microsoft betrayed many Skype users, myself included, when they irreversibly changed the Skype protocol, rendering old Skype-compatible hardware useless. Yes, I feel a bit bitter about it… I liked that Skype phone, I even fixed it once when its original microphone died and had to be replaced. Now it’s just another worthless piece of junk electronics. And once the Skype phone was no longer useful for, well, Skype, my wife also stopped using it as a landline phone, opting instead to use her mobile phone for local calls.

As for faxes… How quaint. Faxes. When was the last time you sent a fax? Or received one? I cannot remember.

To make a long story short, this second line has remained pretty much unused for the past year or two. Yet Bell kept ratcheting up the price. My most recent monthly phone bill for the two landlines reached \$125, and that’s where I decided to draw the line. I called up Bell in the hope that they might have a decent offer for a long-time customer but no, nothing. In fact, it almost felt as if they wanted me to get rid of that second line. (Makes you wonder what the hell is going on there.) So… the second line has been terminated.

Well, supposedly anyway. It was at least six hours ago that Bell told me that the line would be deactivated within 15-120 minutes… but it still gives a dial tone, and I can still ring it. Go figure. I suspect the line will be dead tomorrow anyway.

OK, so we’ve had Trump for nearly two years now, and we know that the White House has become a combination of kindergarten and insane asylum. My conservative friends still support Trump because he “delivers”, and are willing to completely overlook the fact that this president is not only a bumbling dilettante, an offensive excuse of a human being (waste of skin, to borrow a phrase from Lexx, a science-fiction series from a few years ago) but quite possibly a traitor to his nation, too, working for Putin’s Russia.

But if I hoped that Trump’s opposition is any better, they bitterly disappoint each and every day.

Take, for instance, the made-up controversy of a Kavanaugh aide presumably flashing “white power” hand signs while sitting behind Kavanaugh during his Supreme Court hearing, visible to cameras. Never mind that the hand sign was, in fact, a perfectly ordinary OK sign. Never mind that it was a well-documented Internet hoax from last year that suggested that this OK sign is, in fact, a secret hand gesture used by white supremacists. None of that stops many of my liberal friends from tweeting and retweeting the meme, complete with obscenities and death threats. Fact checking is for wimps, I guess.

And now I am reading about the bitter fate of a paper exploring the mathematics behind a controversial hypothesis dating back to Darwin’s times, called the “Greater Male Variability Hypothesis” (GMVH). The GMVH basically asserts that there are more idiots and more geniuses among men than women. It was Darwin who first noted that such greater variability is prevalent across many species in the animal kingdom. But politically correct guardians of science publishing would have none of that. Poor Darwin… the right hates him because he dares to challenge the idea that the world was created 6,000 years ago, but now the left hates him, too, because he dares to offer us politically incorrect science. The paper by Theodore P. Hill was first accepted and then rejected by journals, including a journal that already published the paper online, only to replace it with another a few days later. Never even mind the attack on academic freedom that this represents, but how about blatant sexism? You know, those impressionable young female scientists, fragile little flowers that they are, who cannot handle scientific truth and must be protected at all costs, unlike their ever so manly male colleagues…

One of the guests on Fareed Zakaria’s show today on CNN was Jonathan Haidt, one of the authors of the book, The Coddling of the American Mind. The authors explore the consequences of what they dub “safetyism”: Keeping children away from danger, real or perceived, at all costs, thus denying them a chance to become independent human beings. The result, according to the book, is that rates of anxiety, depression, even suicide are rising at an alarming rate, even as both students and professors on college campuses walk on eggshells, less they offend someone with a careless word, or heaven forbid, a hand gesture…

All in all, I am ready to conclude that the world is going bonkers, and those who seek salvation from Trump’s political opposition on the left (or seek salvation left-wing political opposition to right-wing populism and nativism elsewhere in the world) are deluding themselves.

Regardless of what I think of Trump’s dilettantism, adventurism or downright treasonous behavior, two wrongs do not make a right.

Anonymous senior officials secretly sabotaging the duly elected president? That is a cure that may be much worse than the disease. It amounts to no less than a bloodless coup.

Yes, I purposefully included a picture of Trump’s inauguration as a reminder that, for all his shenanigans, he is the duly elected president. There are constitutional means to remove a president through impeachment or through the 25th Amendment. The constitution, as far as I know, does not entitle anonymous, unelected officials, no matter how well-intentioned, to sabotage a president. That creates a precedent that is far worse than Trump’s incompetence or even (if my suspicions are proven true) treasonous behavior.

This tragic piece of news from this weekend escaped my attention. Brazil’s National Museum and its collection of some 20 million artifacts, going up in flames in a devastating fire.

And it’s not just artifacts. One thing mentioned was irreplaceable written and audio records, which likely have not yet been digitized, of indigenous languages no longer spoken.

The scale of devastation becomes clear from aerial photos, which show that almost nothing remained between the building’s exterior walls.

It is almost incomprehensible that such a disaster could take place in a national museum. The loss… it’s beyond belief.

If you are still running the desktop version of Skype on a Windows 10 computer, be careful before you click “Install now” when the Skype Update dialog appears on your screen.

You see, “the latest version of Skype” that is ready to install is the crappy, worthless, dysfunctional “Metro” version of Skype, which now Microsoft is keen on pushing out to unsuspecting customers, who may naively think that this update, like so many updates before it, is merely another security and functionality fix.

Why am I so hostile to Metro Skype (aka. Skype 8)? I tried using it in the last few weeks. I really did. Here are just a few of my issues with it:

1. It is not possible to change incoming call notifications, which currently interrupt whatever the hell you might have been doing, stealing focus.
2. It is not possible to tell Skype 8 to use your desktop speaker for incoming call rings, when you are using an earpiece for the actual call.
3. The “Metro” UI is buggy. By way of a rather blatant example, when I call a landline contact in Hungary (+36 country code, 1 for Budapest), once the call connects, it shows up in the UI as a call to +1 361 … Needless to say, any attempt to redial fails.
4. Other “by design” annoyances in the UI, for instance, when there is an incoming message or call that I do not answer, I get a notification in the Chat tab, but the contact is not brought to the top of the list; I have to scroll down manually, hoping that I do not accidentally skip over the contact that appears in boldface.
5. Though I do not use it, many do: apparently Skype 8 is not integrated with callto: links on Web pages.

In short, the new UI offers a much poorer user experience, it has serious functional deficiencies, and it is buggy.

What I would like to know is what on Earth is going on in the heads of those at Microsoft who are pushing this “upgrade”. And who is going to give me back the hours that I wasted on this boneheaded nonsense.

At least for now, it is still possible to reinstall Desktop Skype by following the direct download link. Just be sure not to “upgrade” by accident afterwards.

Imagine a health care system that is created and managed without the help of doctors. Imagine getting radiation treatment without the help of medical physicists.

Imagine an education system that is created and managed without educators.

Imagine a system of highways and railways created and managed without transportation engineers.

Imagine an electrical infrastructure that is created and managed without electrical engineers. Nuclear power plants without physicists. An economy that is managed without professional economists. A communications infrastructure created and managed without radio engineers, software and network engineers.

This is Doug Ford’s vision for the province of Ontario, presented by none other than Doug Ford himself through his Twitter feed, as he proudly proclaims that his government, his party, won’t listen to academics: the very people that we pay so that they learn and offer their professional knowledge for the benefit of the public.

Guess this is what happens when ideology and blatant populism trump facts. (Pun unintended, but disturbingly appropriate.)

I have Google ads enabled on this site. Not really worth the effort; my blog site generates mere cents of revenue on a good day.

More recently, I noticed that Google started placing ads between paragraphs inside articles. I would like this if it improved the site’s profitability. But it didn’t.

And those ads are very disruptive, even when (or perhaps especially when) the ad is closely related to the content. Recently, I found myself apologizing more than once when I showed a blog post to someone, because of the silly, disruptive ads in the middle.

What can I say? I turned these ads off. I like Google ads as a source of revenue, but this was taking it one step too far.

Yesterday, I received a nice surprise via e-mail: A link to a new article in Astronomy magazine (also republished by Discover magazine) about our efforts to solve the Pioneer Anomaly.

I spent several years working with Slava Turyshev and others on this. It was a lot of very hard, difficult work.

As part of my (both published and unpublished) contributions, I learned how to do precision modeling of satellite orbits in the solar system. I built a precision navigation application that was sufficiently accurate to reconstruct the Pioneer trajectories and observe the anomaly. I built a semi-analytical and later, a numerical (ray-tracing) model to estimate the directional thermal emissions of the two spacecraft.

But before all that, I built software to extract telemetry from the old raw data files, recorded as received by the Deep Space Network. These were the files that lay forgotten on magnetic tape for many years, eventually to be transferred to a now obsolete optical disc format and then, thanks to the efforts of Larry Kellogg, to modern media. My own efforts, to make sense of these telemetry files, is what got me involved with the Pioneer Anomaly project in the first place.

These were fun days. And I’d be lying if I said that I have no tinge of regret that in the end, we found no anomalous acceleration. After all, confirmation that the trajectories of these two Pioneers are affected by an unmodeled force, likely indicating the need for new physics… that would have been tremendous. Instead, we found something mundane, relegated (at best) to the footnotes of science history.

Which is why I felt a sense of gratitude reading this article. It told me that our efforts have not been completely forgotten.

I often advise my clients that although automation is great, it must be accompanied by well-tested fallback procedures and training, to ensure that they can continue operations even when systems fail. This is especially important in the case of life-critical applications or, for that matter, in applications related to major centers transportation and infrastructure centers.

Today, there was a perfect example that took place at Gatwick Airport in London. Due to a problem with an underground cable, their flight information system failed. That meant no more functioning displays showing departure times and gate numbers. Yet the airport was able to continue operations with no cancellations or delays, and with very few passengers missing connecting flights.

How? Why, they used whiteboards.

Yes. Whiteboards, maintained by officials carrying walkie-talkies.

Now here is the thing. Although the scenes were described as “chaotic” by some, reality was the exact opposite. To quote a spokesperson: “The airport’s manual contingency plan – which included displaying information manually in the terminals and having extra staff on hand to help direct passengers – worked well and tens of thousands of passengers departed on time and no flights were cancelled.”

This is exactly what “business continuity” means. I hope that the person at Gatwick who insisted that such plans must be in place and ensured that not just whiteboards, walkie-talkies and markers but also adequately trained personnel were available when needed, will get not just a commendation but a nice raise.

Over the years, I ended up with several Microsoft accounts, and it is a mess. Here is how it happened.

I had a Microsoft account since time immemorial, associated with my personal e-mail. I had my MSDN subscription under this account.

I also had a Hotmail account since time immemorial.

I had a Skype account since time immemorial, too, associated with my personal e-mail. I used my standard, preferred username as my Skype name.

The Hotmail account became an Outlook account once Microsoft acquired Hotmail and created outlook.com. Thus, this became a separate Microsoft account. My standard, preferred username became a Microsoft Live ID.

So here is what I wanted to do at one point: I wanted to use my personal e-mail as my Office 365 and SharePoint online login. But for reasons I no longer remember, there were obstacles along the way. To resolve this problem, I first moved my MSDN subscription to my Outlook account. I then changed my old Microsoft account to be identified not by my personal e-mail but by my Gmail address. This freed up my personal e-mail address to be used as an Office 365/SharePoint online user account.

But then, one day when I was trying to use Windows 10 Quick Assist to offer assistance to someone, the software told me that I need not only to log on to Microsoft, but associate my account with my Skype account. OK, I’ll bite the bullet, I said… and associated my original Microsoft account (now under my Gmail address) with Skype.

And now I am having a problem. Skype tells me that my account has two aliases: The Gmail address and my standard username. But if anyone sends a contact request to my standard username, I get nothing. Today, I figured out why: these requests go to my other Microsoft account! (The one I never used with Skype.) Presumably it’s because my standard username also happens to be my Microsoft Live ID.

Curiously, if I actually log on to Skype using my standard username, I get connected to my Gmail-associated Microsoft account (which is what I want.)

Needless to say, there is no option to merge two Microsoft accounts. There is no option to unmerge a Microsoft account and a Skype account either. I cannot even add my old personal e-mail address as an alias to either of my Microsoft account; presumable because it is now set up as my Office 365/SharePoint online user account, I receive an error message indicating that a “work or school” e-mail cannot be an alias.

As far as I am concerned, this is an unholy mess. Just writing down what happened made my head spin a little. And I really wish I didn’t have to waste a good two hours of my life earlier this morning simply to get to the bottom of it all. (It all began when I made an unsuccessful Skype-to-landline call to Hungary and tried to call again using Skype on my mobile; the software, having updated itself, asked me to log in, and inadvertently, I logged in with the wrong ID. Bad idea, which I eventually remedied by shutting down Skype, deleting all Skype data on the phone, and then restarting Skype and starting all over again.)

As a reminder to myself, here is an excellent page that explains the difference between Microsoft and Office 365 accounts.

There is a joke I heard a long time ago about Khrushchev and Hungary’s communist leader Kádár going bear hunting. It seems perfectly appropriate to retell using Putin and Trump instead, especially in light of their meeting and, ahem, spectacular press conference in Helsinki today.

Putin and Trump go hunting. They shoot a bear. On their way back to the hunting lodge, they stop at a McDonalds for Trump to grab a burger. Putin stays outside. When Trump gets back to their pickup truck, the bear is gone.

“What bear?” responds Putin.

Trump looks perplexed. “You see, we just went hunting, right?”

“Right,” says Putin.

“And we went up this hill, right?”

“Right,” says Putin.

“And then we spotted a bear, didn’t we?”

“That we did,” says Putin.

“Which we then shot.”

“And then we put him on the truck.”

“We did indeed,” confirms Putin.

“And then we stopped here at this McDonalds. I went in, and you stayed outside with the bear, right?”

“That is indeed so,” says Putin.

“So then, where the devil is the bear?” asks Trump.

“What bear?” responds Putin.

MJ the cat has been a regular visitor in our neighborhood in the past 13 years. Spotting him on a bright March day was always regarded by us as the first sign of spring after a long, dark, cold winter.

Alas, MJ is about to depart this world. He was taken by someone to the Humane Society’s shelter a few days ago. He has since been reunited with his owner, but we learned the bad news: he is very ill, and he will be euthanized tonight.

Goodbye, MJ. The neighborhood will not be the same without you. I can only hope that spring will still come next year.

An interesting article appeared on the Web site of BBC News today.

It describes a US president who is anti-immigration, who has a proclivity for conspiracy theories, and who appoints his own daughter to a prominent role in the White House.

But no, it is not Donald J. Trump. It is Millard Fillmore, who became the 13th president of the United States after the death of Zachary Taylor, under whom Fillmore served as Vice-President.

One of the least known among US presidents perhaps, Fillmore nonetheless played a role in the destruction of the Whig Party and the subsequent rise of the Republican Party and their 1860 nominee for President, Abraham Lincoln. It was also under Fillmore’s presidency that the controversial Compromise of 1850 was accomplished. Whether it postponed the Civil War or was a contributing cause remains a subject of debate to this day.

Fillmore’s political career collapsed after his one term. The Whig Party, already in tatters, did not nominate him in 1852. His life was afflicted by tragedies, as he lost his wife and his only daughter in rapid succession shortly after leaving office.

Uncanny similarities notwithstanding, there are also significant differences between Fillmore and Trump. Though described by Queen Victoria as the handsomest man she had ever seen, Fillmore was no rich playboy; he was born in poverty, and he was worried about making a living after leaving the White House, as he was not independently wealthy. And he was certainly a more humble man than Trump: He refused to accept an honorary doctorate from Oxford, stating that he had no “literary or scientific attainment” that would justify the diploma. Besides, his lack of a classical education meant that he spoke no Latin, yet “no man should accept a degree he cannot read”. Somehow, I doubt that such considerations would prevent the 45th president from accepting such an honor.

In 1856, Fillmore again ran for the presidency as the candidate of the newly formed American Party, but only carried the state of Maryland. He died in 1874.

Bashing Trump is a favorite pastime of mine and that of many of my friends. To be sure, there are plenty of reasons to despise the man: His obvious racism, misogyny, narcissism, nepotism, corruption, his authoritarian tendencies, just to name a few.

But putting the focus on these characteristics leads us to miss a very important point. As a Republican president, Trump delivers. He does precisely what his base (who did elect him, after all) were hoping for. Putting conservative justices on the Supreme Court, who might reverse Roe v. Wade and other landmark “liberal” decisions? Check. Sabotaging Obamacare? Check. Making a stand against immigration? Check. A protectionist economic policy? Check. Standing up even against the Republican establishment in Washington? Check.

Trump’s base, by the way, also happen to distrust liberal democracy, and may not be adverse to a more authoritarian, strongman-style rule, so long as it is their strongman. As such, they are far less alarmed by the ease with which Trump gets along with other strongmen and the difficulty he has with the leaders of liberal democracies that are America’s traditional allies. This may even be seen as part of his “alpha male” personality, a sign of his strength.

So even if we take the hatemongering, Islamophobia, racism and other unsavory factors out of the equation, Trump is to many a dream come true: He is delivering precisely what they hoped to see from a Republican president.

And it is because of this that they are willing to turn a blind eye to Trump’s personal shortcomings. It may appear hypocritical, but ultimately, it’s just good old political pragmatism.

For this reason, I think it is deeply misguided to focus on the failings of Trump. This visceral reaction to Trump’s personality does not resonate with his base. If anything, it strengthens their perception that their political opposition is a bunch of disloyal losers: unpatriotic liberals who would rather see the man they despise fail, even if it harms America. (That conservatives behaved exactly like this in their opposition to Obama may not cross their minds. In fact, the very fact that they themselves behaved in this manner may be a reason why they so easily believe that their liberal opposition is no different.)

Is left-wing populism the answer? Supporters of Bernie Sanders undoubtedly think so. But I have my doubts. Why would left-wing populism be any better than its right-wing counterpart? In both cases, we end up with leaders who are dilettantes and demagogues. The problem these days (and this issue is not confined within the borders of America; look at Europe, or look right here, at the Canadian province of Ontario) is the collapse of the center. The end of fact-based governance by an increasingly despised technocratic “elite”.

The irony of it is that this liberal world order, for all its failings, kept the world together with no major conflict for the past 70-odd years, a golden age of possibly unprecedented growth and prosperity. (And not just in the first world; just look at global statistics of life expectancy, literacy rates, and other measures that show just how much life improved throughout much of the planet since 1945.) Yet not only is it rejected, it is rejected most vehemently by those who benefited from it the most.

There was another, similar golden era of near unprecedented growth and prosperity: The second half of the 19th century, all the way up to 1914. Yet even as more and more thinkers were convinced that the era of wars between major powers is a thing of the past, the world was heading towards the disaster called the Great War, which plunged the world into chaos, destroyed the prevailing world order, created the circumstances for the rise of the twin evils of communism and fascism, and eventually led to a second world war and the industrial-scale mass murder of the Holocaust.

I don’t know where the world is heading today, but I admit I think about 1914 a lot.

A while back, I wrote about the uncanny resemblance between the interstellar asteroid ‘Oumuamua and the fictitious doomsday weapon Iilah in A. E. van Vogt’s 1948 short story Dormant.

And now I am reading that Iilah’s, I mean, ‘Oumuamua’s trajectory changed due to non-gravitational forces. The suspect is comet-like outgassing, but observations revealed no gas clouds, so it is a bit of a mystery.

Even if this is purely a natural phenomenon (and I firmly believe that it is, just in case it needs to be said) it is nonetheless mind-blowingly fascinating.