I am a software developer and author of computer books. I also work on some problems in theoretical physics. For more information, please visit my personal Web site at http://www.vttoth.com/.

We just released another beautiful new version of Maxima, 5.45.0. This time around, it also includes changes (for the first time in years) to the tensor packages, based on a very comprehensive set of proposed patches by a devoted Maxima user.

We have a new manuscript on arXiv. Its title might raise some eyebrows: Algebraic wave-optical description of a quadrupole gravitational lens.

Say what? Algebra? Wave optics? Yes. It means that in this particular case, namely a gravitational lens that is described as a gravitational monopole with a quadrupole correction, we were able to find a closed form description that does not rely on numerical integration, especially no numerical integration of a rapidly oscillating function.

Key to this solution is a quartic equation. Quartic equations were first solved algebraically back in the 16th century by Italian mathematicians. The formal solution is usually considered to be of little practical value, as it entails cumbersome algebra, and polynomial equations can be routinely and efficiently solved using numerical methods.

But in this case… The amazing thing is that the algebraic solution reveals so much about the physics itself!

Take this figure from our paper, for instance:

On the left is light projected by the gravitational lens, its so-called point-spread function (PSF) which tells us how light from a point source is distributed on an imaginary projection screen by the lens. On the right? Why, that’s the discriminant of the quartic equation

$$x^4-2\eta\sin\mu \, x^3+\big(\eta^2-1\big)x^2+\eta\sin\mu \, x+{\textstyle\frac{1}{4}}\sin^2\mu=0,$$

in a plane characterized by polar coordinates $$(\eta,\tfrac{1}{2}\mu)$$, that is, $$\eta$$ as a radial coordinate and $$\tfrac{1}{2}\mu$$ as an azimuthal angle. When the discriminant is positive, the equation is expected to have four real (or four complex) roots; everywhere else, it’s a mix of real and imaginary roots. This direct connection between the algebra and the lensing phenomenon is unexpected and beautiful.

The full set of real roots of this equation can be shown in the form of an animation:

Of course one must read the paper in order for this animation to make sense, but I think it’s beautiful.

How good is this quartic solution? It is uncannily accurate. Here is a comparison of the PSF computed using the quartic solution and also using numerical integration, as well as some enlarged details from the so-called caustic boundary:

It’s only in the immediate vicinity of the caustic boundary that the quartic solution becomes less than accurate.

We can also use the quartic solution to simulate images seen through a telescope (i.e., the Einstein ring, or what survives of it, that would appear around a gravitational lens when we looked at the lens through a telescope with a point source of light situated behind the lens.) We can see again that it’s only in the vicinity of the caustic boundary that the quartic solution produces artifacts instead of accurately reproducing it when spots of light widen into arcs:

This paper was so much joy to write! Also, for the first time in my life, this paper gave us a legitimate, non-pretentious reason to cite something from the 16th century: Cardano’s 1545 treatise in which the quartic solution (as well as the cubic) are introduced, together with discussion on the meaning of taking the square root of negative numbers.

No, it’s not one of my cats posting a blog entry.

Rather, it’s a whimsical title someone gave to the following composition:

I started my day listening to this. I am still smiling. I think it sounds a little bit like Klingon opera, or perhaps like a piano piece written by a Klingon composer. But it’s not bad, not bad at all.

I was watching a documentary on Netflix and a photo caught my attention. A beautiful, old photograph (shown in color in the documentary, but I suspect it was colorized, so I am including a black-and-white version instead that I found online) showing a young mother and her child, along with a stuffed toy animal:

This photo depicts the sister of Setsuko Thurlow (née Nakamura), a Japanese-Canadian peace activist, herself a survivor of the Hiroshima atomic bomb.

Unfortunately, her sister Ayako was not that lucky. She and her young son Eiji were badly burnt and soon perished.

I get it why the atomic bomb was deemed necessary. With everything I know today, I still would not, could not have made a decision different from that made by Harry Truman back in July, 1945 even if it meant that I could not ever sleep soundly afterwards throughout the remainder of my life. Not with some 10,000 people, most of them civilians, dying in the Pacific theater every day of the war.

Even so… War is horrifying.

Strangely, it’s the toy animal that humanized this picture for me more than anything else.

Last fall, I received an intriguing request: I was asked to respond to an article on the topic of dark matter in an online publication that, I admit, I never heard of previously: Inference: International Review of Science.

But when I looked, I saw that the article in question was written by a scientist with impressive and impeccable credentials (Jean-Pierre Luminet, Director of Research at the CNRS Astrophysics Laboratory in Marseille and the Paris Observatory), and other contributors of the magazine included well-known personalities like Lawrence Krauss or Noam Chomsky.

More importantly, the article in question presented an opportunity to write a response that was not critical but constructive: inform the reader that the concept of modified gravity goes far beyond the so-called MOND paradigm, that it is a rich and vibrant field of theoretical research, and that until and unless dark matter is actually discovered, it remains a worthy pursuit. My goal was not self-promotion: I did not even mention my ongoing collaboration with John Moffat on his modified theory of gravity, MOG/STVG. Rather, it was simply to help dispel the prevailing myth that failures of MOND automatically translate into failures of all efforts to create a viable modified theory of gravitation.

I sent my reply and promptly forgot all about it until last month, when I received another e-mail from this publication: a thank you note letting me know that my reply would be published in the upcoming issue.

And indeed it was, as I was just informed earlier today: My Letter to the Editor, On Modified Gravity.

I am glad in particular that it was so well received by the author of the original article on dark matter.

I began writing this last night, when my stepfather Tibor was still alive, albeit just barely.

He passed away this morning after a brief illness, spending his last few nights in a hospital. What began as shortness of breath turned out to be a massive case of pneumonia that now weakened his whole body. At 93 this is not exactly surprising: we don’t live forever and this is how we die.

I decided that I shall not grieve. Instead, I celebrate. I celebrate a life of 93 years, the good life of a good man, who treated me always as though I was his own son.

I celebrate a life that was lived mostly in good health, near perfect health as a matter of fact, except for a few scary moments in the past decade. But he recovered from it all, and up until last week, really, though he had mobility issues, he still looked radiantly healthy, 20 years younger than his true age.

So there will be no 50th wedding anniversary with my Mom in 2024. No 100th birthday party in 2028. So what? The life that he lived is still a very, very good life.

Here are a few pictures.

My Mom and Tibor met in 1974 in the resort that my stepfather managed. This picture is, I believe, from April 1974. The woman standing was the programs manager (“kultúros”) of the resort.

Here’s another, undated picture of Tibor from roughly the same time period:

Tibor and my Mom built a beautiful house in Visegrád. This is Tibor in the living room, around 1990 or so, under a small Christmas tree.

As communism came to an end, it upset the economy in many ways. In his late 50s, Tibor found a new way to earn an income: he bought a pickup truck and offered moving and delivery services.

This was Tibor just last year, when I last saw him in person, a visit to Hungary that now feels miraculous to have happened at all, in the calm before the storm, before the pandemic changed the world:

And now he is gone.

Just yesterday I came across my all time favorite movie quote on Facebook, a quote from Blade Runner:

All those moments will be lost in time, like tears in rain. Time to die.

The CBC just published a very informative article on the history of vaccine manufacturing in Canada, explaining why this G7 country, one of the top industrialized nations on Earth, is entirely dependent on imports when it comes to COVID-19 vaccinations.

It really is disgraceful. Canada’s Connaught Labs, founded in 1914, was at the forefront of global vaccine production for many decades.

But then came the decline. Vaccine production is not always a profitable enterprise. Connaught Labs was eventually nationalized by Pierre Trudeau’s government but then, as far as I am concerned inexplicably, the emphasis for this now Crown corporation was to turn a profit!

Why???

Eventually, it was reprivatized by Mr. Mulroney, who promised that the action will bring “net benefits” to Canadians.

Yeah, right.

The federal government is now investing serious monies to expand capabilities for future pandemics. I can only hope that this lesson is not going to be forgotten anytime soon.

So the other day, I made a foolish decision: I objected to a self-described progressive activist’s recurring, disparaging use of the expression, “white people”, on Twitter.

In response, I learned the following, thanks to helpful strangers:

1. I am suffering from white fragility;
2. As I am a man, I am suffering from male fragility;
3. I am wallowing in prejudices;
4. Even if I am not from the US, there are issues in Canada, too, so…
5. I am a racist;
6. I am afraid of being called a racist;
7. I benefit from systemic racism and need to be educated about it;
8. And finally, this gem: I should shut up and listen.

OK, just to be clear, I am no more concerned about being called a racist than I am about being called a bicycle, on account of being neither. However, this reaction speaks volumes. In this new, progressive world, virtue signaling is key if you want progressives to like you. Saying disparaging things about white people gets you credit. Extra credit if you yourself happen to be white and practice a little self-loathing in public.

I used to have zero patience for my conservative-leaning white friends and acquaintances who were complaining about “anti-white racism” as they marched off to vote, or otherwise express support, for that stable genius, the Orange Person. But in light of this little Twitter exchange, I am somewhat less incredulous and more sympathetic.

No, I am still not rooting for Trumpists and their fellow travelers in other countries. But I do have a point to make, not that I expect the most vocally self-righteous progressives to listen: If you manage to turn someone like me (I am not exactly a stereotypical raging white supremacist) into a skeptic, do not be surprised if you lose by a landslide in future election cycles. Tone it down please. There is no need to turn into enemies people who dare to criticize excessive rhetoric, who see nuances where you only see black-and-white, who present inconvenient facts even when those being inconvenienced by them are not from the conservative camp. Listen to their criticism, don’t automatically reject their thoughtful objections in self-righteous indignation, in the name of ideological purity.

As for the Twitter exchange, I ended up doing something I do extremely rarely, unfollowing, even blocking some people when the conversation began to veer towards personal insults. (Because, you know, if you run out of thoughtful arguments, name-calling always works. Right.)

This morning, a drone took flight. It successfully took off from the ground, hovered for a few seconds, and then landed safely.

What, you ask? How is this supposed to be a big deal? There are millions of drones out there, kids playing with them and whatnot.

Oh, but this drone is special, and not only because it carries a small piece of fabric from the Wright brothers’ very first airplane.

It is special because it flew on Mars.

Yesterday it was hardware, today it was software.

An e-mail that I sent to a bell.ca address was rejected.

Perhaps I am mistaken but I believe that these Bell/Sympatico mailboxes are managed, handled by Yahoo!. And Yahoo! occasionally made my life difficult by either rejecting mail from my server or dropping it in the recipient’s spam folder. I tried to contact them once, but it was hopeless. Never mind that my domain, vttoth.com, is actually a few months older (July 1, 1994 as opposed to January 18, 1995) than Yahoo!’s and has been continuously owned by a single owner. Never mind that my domain was never used to send spam. Never mind that I get plenty of spam from Yahoo! accounts.

Of course you can’t fight city hall. One thing I can do, instead, is to implement one of the protocols Yahoo wants, the DKIM protocol, to authenticate outgoing e-mail, improving its chances of getting accepted.

But setting it up was a bloody nuisance. So many little traps! In the end, I succeeded, but not before resorting to some rather colorful language.

This little tutorial proved immensely helpful, so helpful in fact that I am going to save its contents, just in case:

https://www.web-workers.ch/index.php/2019/10/21/how-to-configure-dkim-spf-dmarc-on-sendmail-for-multiple-domains-on-centos-7/

Very well. It is time to return to more glamorous activities. It’s not like I don’t have things to do.

Working from my home office and running my own equipment (including server equipment) here means that I have some rather mundane tasks to perform. As a one-man band, I am my own IT support, and that includes software, as well as hardware.

The less glamorous part of software support is installing updates and patches, resolving driver conflicts, keeping external equipment such as routers and network switches up to date.

The less glamorous part of hardware support? Mostly it involves dust. Ginormous dust bunnies, that is.

Ever heard of the expression, “rat’s nest”? It is sometimes used to describe the tangle of cables and wires that hide behind a computer. Now imagine a computer to which several USB hubs, ten external hard drives and additional equipment are connected, most of which have their own power supply. Yes, it’s ugly. Especially if those little power bricks are plugged into a haphazardly assembled multitude of cheap power strips.

And dust collects everywhere. Thick, ugly dust, made of human dandruff, cat dandruff, hair (human and cat), fluff from clothing, crumbs from many past meals. Normally, you would just vacuum up this stuff, but you don’t want to disturb the rat’s nest. Plugs can come lose. You might lose data. And even if you don’t, simply finding the plug that came lose can be a royal pain in the proverbial.

Long story short, I’ve had enough. The other day, I ordered the longest power strip I could find on Amazon, with 24 outlets, complete with mounting brackets. And yesterday, I managed to affix it to the underside of my main desk.

Which means that yesterday and today, working my way through the list one piece of equipment at a time, I managed to move all power plugs to this new power strip. As it hangs from the underside of my desk, it’s most importantly not on the floor. So the floor can be (gasp!) cleaned.

And now I even have room to access my workstation’s side panels, if need be. One of these days, I might even be able to vacuum its back, removing years’ worth of dust from its fan grids. But for now, I contend myself with the knowledge that I freed up four (!) cheap power strips, a three-outlet extension cable, and a three-outlet plug, all of which were fully in use. What a liberating feeling.

Having spent a fair amount of time today on all fours under my desk, however, did prompt me to mutter, “I am too old for this,” several times this afternoon… especially as I still feel a bit under the weather, an unpleasant aftereffect, no doubt, of the COVID-19 vaccine I received yesterday.

Our vaccination appointment is booked. Yippie!

Yes, it is the AstraZeneca vaccine. No, I am not concerned about blood clots. The risks are very small, and are far outweighed by the benefits of becoming vaccinated. (Our family doctor enthusiastically agrees.)

Stereotypes hurt people.

Television, sitcoms in particular, often rely on stereotypes. But it’s not always a Bad Thing. When the stereotype itself is the object of ridicule, kind of holding up a mirror for the audience to look into, stereotypes can actually help turn ours into a better society. The Big Bang Theory is a good example: its Jewish (Howard Wolowitz) and Indian (Raj Koothrappali) protagonists mock not Jews and Indians but our prejudices.

But other stereotypes are more troubling. One notable example, discussed recently, is the character Apu Nahasapeemapetilon in The Simpsons: a stereotypical Indian-American running a convenience store, speaking with a funny accent.

Yes, I recognize that the line between mocking people being stereotyped vs. mocking people who stereotype others is a thin one. But I think it is drawn somewhere between The Big Bang Theory and The Simpsons. The Big Bang Theory‘s humor is defensible because it does not dehumanize the protagonists. The Simpsons, sadly, doesn’t fare that well. No wonder Hank Azaria no longer wants to be the voice of Apu.

However, when it comes to the point of a Caucasian voice actor voicing a non-Caucasian character, I think we are going one step, no, make that one giant leap, too far.

You see, I thought actors, you know, act. That is, pretend to be something they are not.

But now you are telling me that a naturally blond actress cannot play a brunette? Or a Jewish actor cannot play a German officer?

Or is this concern specifically reserved for, I don’t know, “race”? Or what’s the new catchphrase, people who are “racialized”? (Whatever the devil that means.) Because somehow, the color of your hair doesn’t matter but the color of your skin makes you… different?

And does it go both ways? Are Indian actors forbidden to play Europeans? Are black actors forbidden to play white roles? In any case, who decides what kind of acting is acceptable, and what crosses the line? Heaven forbid, into the territory of “cultural appropriation”?

In my all time favorite movie, Cloud Atlas, several actors play as many as a half dozen different roles, in different eras and cultures. These include a Korean actress playing, in one storyline, the role of the wife of a 19th century San Francisco lawyer. Another Korean actress, in a male (!) role, plays as a bellboy in 1970s San Francisco. Hugo Weaving plays the role of a sadistic female nurse in early 21st century Scotland, but also the role of an authoritarian Korean politician in 22nd century New Seoul. And so on.

You can guess which of these roles were criticized by some. “Yellowface” we were told, as if Cloud Atlas had anything to do with Hollywood’s racist past from many decades ago. Nothing could be further from the truth.

Rather, what that movie told me with its choice of actors and roles is that skin color, this so-called “race”, matters as little as the color of your hair or your eyes. It means nothing. We are all members of the one and only human race. And just as a blond actress can play the role of a brunette or a male actor can play in a female role, a black actor can play as a white person while a person of European descent can credibly play a Korean. Because these superficial differences in appearance mean nothing.

The suggestion that a white actor cannot lend his voice to an Indian character in a cartoon is preposterously backward. It seems designed to maintain racial discrimination. It, to use that fashionable phrase again, promotes and preserves racialization, instead of helping us progress towards a post-racial society in which all human beings are judged by the strength of their character, and the color of their skin matters no more than the color of their hair.

I didn’t realize it was more than 11 years ago.

It is rare that a piece of music has such an impact on you that you remember clearly the first time you heard it. Yet I do remember it very well: I first heard Danzon n°2 by Arturo Márquez on Highway 401, on my way to the Perimeter Institute in Waterloo, listening to the CBC on the radio.

I heard this amazing piece of music again tonight, on Sirius XM. Different performance, but just as spirited as the one I am familiar with.

I am reading about the closure of an iconic grocery store in central Moscow.

What an amazing place. What amazing history: a store, opened in 1901, which survived the Communist revolution (though it was nationalized and renamed Gastronome no. 1), survived the collapse of the USSR, and even strived in the past 20 years before it began losing customers as a result of the changing demographic of the Russian capital. Depending in large part on tourists and already struggling to remain profitable, Yeliseyevsky’s was particularly ill-suited to survive a global pandemic that all but shut down the tourist industry.

And now apparently Yeliseyevsky’s is no more. It closed for good on April 11 after 120 years in business.

What a sad ending for such an iconic place.

My all time favorite movie is Cloud Atlas. I know, others have not reacted to this movie quite as powerfully as I have, but for whatever reason, the movie “got me”. (The fact that I first saw it during my first ever visit to the Middle East, in an Abu Dhabi hotel room, just a few days after flying over the war-torn Iraq-Iran border region while enjoying British Airways’ business class hospitality, may have had something to do with it.)

The movie has many memorable quotes. Banal, you might say, but even banalities sometimes reflect profoundly on our reality.

On particular quote echoes in my mind today as I witness, day after day, even in my relatively close circle of friends, the “relativization” of facts in our post-truth era. A key character in the movie is interviewed by an archivist just before her scheduled execution. To put her at ease, the archivist reassures her: “Remember, this isn’t an interrogation or trial. Your version of the truth is all that matters.” The protagonist, looking deeply in the eyes of the archivist, responds: “Truth is singular. Its versions are mis-truths.”

Yes, it should be that self-evident. Truth is singular. A and ¬A cannot simultaneously be true: A ∧ ¬A = 0 always. It is elementary formal logic.

But in our increasingly Göbbelsian 21st century, formal logic no longer matters. Instead, we have “alternative facts”. Instead, everyone feels entitled to question, even deny, facts that conflict with their Weltanschauung.

Yes, I said Göbbelsian. No, I am not trying to serve as an example of Godwin’s law by needless comparisons to Nazis. Rather, it is a recognition that the legacy of Göbbels, the evil genius of modern communication, continues to reverberate nearly a century later, as various actors push their versions of the truth. Göbbels taught us how to “sell” alternative facts: blatant lies are easy to falsify, lies by omission are much harder to catch.

A pluralistic society thrives on differences of opinion. Good people whose priorities differ may come to different conclusions based on the same set of facts. But when there is disagreement over the facts themselves, society breaks down. And that’s what we face today. The facts have now become matters of opinion.

I could name a number of issues from climate change to gender roles where the facts should be indisputable but they aren’t. But my concern transcends any specific topic. I simply worry that if we all retreat into our alternative facts bubbles, consensus or compromise become impossible. Where that leads, I don’t know but it is deeply worrying.

Black lives matter. No argument there.

But, unfortunately, so does messaging. Dr. Göbbels knew this. The communists also knew this, hence their emphasis on “agitation and propaganda”. But, truth to tell, unlike the Third Reich, the left always sucked at it. That’s why, in Kádár’s Hungary, for instance, instead of being content with a regime that delivered a solid system of universal health care and a consistently high quality public system of education that included free tertiary education, we joked about living in the “happiest of the barracks”, took the regime’s successes for granted without acknowledging them, and grumbled daily about its numerous shortcomings.

The political left seems to be intent on continuing this tradition. Their messaging sucks.

A few days ago, I grumbled about the Mayor of London who proclaimed that there are too many white men in science and engineering.

Not too few women. Not underrepresented minorities. Not the need to increase the appeal and accessibility of science and engineering professions to women and minorities. Nope. Too many white men. The resulting backlash was both predictable and completely unnecessary.

Meanwhile, self-righteous warriors of the progressive left declare people like J. K. Rowling a public enemy. Shouldn’t someone with her storytelling prowess be enlisted as a friend and ally? No… deviate in the slightest from the unwritten standards of leftist orthodoxy, and you are labeled a backward, hateful somethingophobe. Like the California university professor who dared to mention a common Chinese expression in his lecture on communication: “na ge” (那个), a common pause word. Oh, how the righteous pounced! This insensitive white professor must be secretly a racist white supremacist! How dare he utter a word that sounds like, well… dare I write it down? Or do I, too, have to fear repercussions from the thought police if I dare spell out the infamous N-word in its entirety? The incident drew criticism from Chinese students and comparisons to Mao’s cultural revolution, and they were not wrong.

Then there are these calls to “defund the police”. The first time I heard this expression I was perplexed. Sure, I know there exist crazy anarchists who want no uniformed authority whatsoever on our streets, but I was also certain that this was not the meaning that the expression was intended to convey. And I was right. The original intent is to divert funds away: let the police do policing when they must, but use the funds wisely, to prevent those cultural and socioeconomic circumstances that lead to situations that need policing in the first place. Makes sense, right?

But that’s not the message that a call to “defund the police” conveys. Many who are rightfully angered by police excess want to, well, literally defund the police. And now their voices are amplified beyond reason, seemingly representing mainstream progressive attitudes. Needless to say, that’s all their opponents need to spread fear and concern among their followers: Look, they tell you, these leftist idiots, these commie anarchists want to leave your streets unprotected from thieves and murderers! They want to turn your country into a failed state like Venezuela!

So yes, black lives matter. And I know what you mean. You mean “Black lives matter, too.” You mean “Not only white lives matter.” You are not suggesting that lives other than black lives matter less.

But when you just say, “black lives matter”, you hand a propaganda victory to your opponents on a silver platter. Even stereotypical rednecks, those undereducated and unintelligent “deplorables”, can retort easily with “but I thought all lives matter!” and gain the moral upper hand.

I happen to support many (most? all?) key progressive ideas. I do think black lives (also) matter. I do believe it is a good idea to attack socioeconomic problems at their roots as opposed to just policing the consequences. I understand that words can hurt, dehumanize, and contribute to systemic racism. I do agree that we must do better to involve women and minorities in science and engineering professions.

But, dear progressives, when I look at your messaging… continuing a century-old tradition, you remain your own worst enemies.

World, please say hello to Freddy.

Freddy has been with us for more than two years now. He is a very funny cat. Strong-willed, to be sure; he might even bite you if he disapproves of your behavior. (No, he has not bitten off any fingers or earlobes yet.) And he likes… green peas. Or kernels of corn. And like one of our past kitties, Pipacs, Freddy also stole a freshly cooked potato from the kitchen not too long ago.

Last but not least, I should mention that his favorite toys are small pompoms. We have many of those, on account of my wife’s knitting. So I have a box of pompoms right here, next to my desk. Freddy often shows up here and, after carefully sniffing the pompoms, selects one, takes it from the box, puts it down on the floor and sits down proudly next to it, quietly meowing a few times. That is my cue to pick up the pompom and throw it down the stairs, with Freddy sprinting after it. Often, he then spends a good half hour playing with that pompom.

He also occasionally plays with his somewhat larger buddy, Rufus. I suppose Rufus looks just like a big gray-and-white pompom…

My success story of the day involves two cups.

A few days ago, I heard my wife grumbling loudly in the kitchen. I went downstairs to see what was wrong. She showed me a pair of cups, a teacup, inside which there was one of our brand new espresso cups.

And when I say inside, I mean wedged inside. Firmly and utterly stuck, quite impossible to remove.

We tried to separate them using force, but they wouldn’t budge. We obviously didn’t want to break either cup. Not that they are terribly expensive but the teacup, well, we’re quite fond of these teacups and as for the espresso cup, it was brand new, I only just purchased the set off Amazon a few days earlier.

Force failed to do the trick so we tried to be clever. Use some oil to make it slick? Nope. Dishwasher detergent? That didn’t work either. I tried holding the outer cup, upside down, under hot water in the hope that thermal expansion might loosen the smaller cup inside; nope.

Nonetheless we thought that a temperature difference might help, so we filled the cups with water and put them in the freezer. Once the water was frozen solid, we took them out and placed them in a pot of boiling water. Again, the hope was that the high heat would cause the larger cup to expand, while the ice keeps the smaller cup cold, allowing it to fall out. Nope.

After this experiment failed for the third time earlier this afternoon, I sat down with the cups in hand and once again, tried brute force. The outer cup was still quite hot to the touch, the inner cup still quite cold and this may have helped; suddenly, I felt them budge, and after one more pull, they were separated, completely undamaged.

I was… absolutely delighted. Later I remarked to my wife that we humans are creatures of simple pleasures. Never mind the animations I completed just today using gravitational lenses of arbitrary shape. Never mind the work I am doing on another project on payment processor integration, or yet another project involving Microsoft Teams. (Yes, I multitask. Virtual desktops can be quite handy.) All of that is fun, sure, but it’s having been able to separate these poor cups without breaking or damaging them that really made my day.