Jan 112022

My name is not the rarest, but also not terribly common. I never met another Viktor Toth in person, but over the years, I came across a few and I’ve at least been in close contact with one.

The first Viktor Toth I read about as a teenager was featured with his girlfriend in some silly magazine for young Pioneers in then-communist Hungary.

Around the same time, I also read about a Viktor Toth in a small town in Hungary, who butchered his unfortunate wife with an axe. Yikes!

When I came to Ottawa, Canada, I was surprised to learn that there was already a Victor Toth in the local phone book. I never met him, but I did end up working with a gentleman who knew him.

It was still relatively early in the Internet era when I first searched for my own name, in the context of the small Hungarian town of Visegrad where I once lived. Much to my surprise, I found a Viktor Toth but it wasn’t me. It was a Hungarian astronomer who organized a conference that happened to take place in that small town. (Much later, he and I got in touch and even collaborated a little, contributing an article to a Hungarian popular science magazine about the future of radio astronomy in the country.)

There is a Viktor Toth who is an internationally renowned jazz saxophonist; unfortunately the type of improvisation-based modern jazz he plays is not my favorite subgenre, but he seems very well regarded.

And finally, there’s the Viktor Toth who recently put his pet rat into a virtual reality harness and had him play Doom. For the record, the only rat I own is this one, and he definitely doesn’t play Doom:

 Posted by at 12:25 am
Dec 312021

Y’all heard the joke: twenty-twenty-two,
It will be just like twenty-twenty, too.
But I really hope it will not be so.
We really just can’t give it another go.

 Posted by at 9:06 pm
Dec 242021

Although we are not religious, we celebrate Christmas.

And I still cannot think of a better way to celebrate Christmas than with the words of the astronauts of Apollo 8, and the sense of awe they felt when they became the first human beings ever in the history of our species to be completely cut off from Mother Earth, when their spaceship disappeared behind the Moon.

Earthrise from Apollo 8

Re-emerging, they read passages from the Book of Genesis to their audience, with Frank Borman concluding with the words:

[G]ood night, good luck, a Merry Christmas – and God bless all of you, all of you on the good Earth.

To me, this is the most beautiful Christmas message ever.

 Posted by at 2:38 am
Dec 242021

For the record: The Viktor Toth who has recently become quite popular on YouTube by placing his pet rat into a virtual reality harness and letting him play Doom is not me.

Even if I were inclined to do such an experiment with a live animal (I am not) it would be one of my cats, and the retro game of choice would be Duke Nukem.

You see, I was never really a fan of Doom.

 Posted by at 1:44 am
Nov 202021

I kept staring at my calendar.

November 20. November 20. Why is this date memorable?

Then it suddenly popped into my mind. My father was born exactly 115 years ago, on November 20, 1906, in what was then Austria-Hungary, in the fine city of Temesvár, today known by its Romanian name as Timișoara.

He passed away in the fall of 1985, not long before I left Hungary.

 Posted by at 4:55 pm
Nov 142021

I am sure everybody had people like my friend Ken in their lives: People who, often by pure chance, played a major role in shaping our lives at critical turning points. When I came to Canada in 1987, I met several people who opened doors for me, offered me opportunities when I needed them most, or simply rewarded me with their friendship.

Ken Bowman was one such person. A mid-level manager at Canada Post in 1989, he was running the little project that I joined. I needed the income badly as my previous contract work ended months prior and I was rapidly running out of money. But the project itself was also interesting, challenging even. Oh, and the machines were fabulous: IBM PS/2-70 workstations with very large (by the standards of the time) hard drives, high resolution color monitors, laser printers… Lovely work.

I worked there for about nine months, but the friendships proved lasting. Some time later, Ken joined the company that was set up by a couple of my teammates on this project. He led the business side of one of my favorite development projects, which involved not only a product catalog but also an engineering and load sizing component, with plenty of interesting physics.

Ken’s partner at this company had a long, difficult-to-spell last name. One day, they received personally addressed but otherwise identical pieces of junk mail. The partner’s name was spelled flawlessly. Ken’s? Not so much. The envelope just read “Kenowman”. Needless to say, this earned him the obvious instant nickname: from this point on, he was often called Obi wan Kenowman, or just Obi wan for short. He loved it.

Even after he retired, we stayed in touch. Whether it was the politics of the day, a reaction to one of my silly blog posts, or just a picture of his beautiful cat Cimarron, I received missives from him occasionally, mostly in the form of lengthy text messages. And before the pandemic changed the world, we also met from time to time. Seeing him in person, I was actually worried about his health: he lost a great deal of weight, more than what I’d consider healthy.

Ken with one of his grandsons, two elegant gentlemen in happier times.
Photo courtesy Hollis Bowman.

Sadly, it appears that my concerns were not unfounded. One morning a few days ago I received an e-mail from Ken’s daughter Hollis that her Dad was now in palliative care. And before I could even respond, a second e-mail arrived: her Dad passed away.

And just like that, another friend is gone. If I am counting it right, Ken is the fifth person who played an oversize role in shaping the first couple of years of my life here in Canada. Inevitably it makes me wonder, who’s next? (Let that be a plea to my remaining friends: please stay healthy and take good care of yourselves!)

For now, though, Ken, I’ll miss hearing your voice on the phone from time to time. I’ll miss getting text messages from you about the state of the world. I’ll miss pictures from you about your beautiful cat.

I’ll miss you. Thank you for having been a part of my life.

 Posted by at 11:52 pm
Nov 122021

In 1973, my Mom and I visited my aunt here in Ottawa. It was a remarkable journey for 10-year old me. The differences between Hungary, then firmly behind the former Iron Curtain, and Canada were… astonishing. (Let’s just say that this experience firmly inoculated me against any communist claims about building a better society.) The trip was equally impactful on my Mom, though of course she experienced it quite differently as an adult.

At the time, my Mom spoke very little English. So when my aunt and her husband decided to take her to a movie theatre to see the latest James Bond movie, the first one with Roger Moore in the title role, they assured her that they will provide a running translation.

Then the film began and they quickly found out that translation was not necessary after all. At least insofar as these opening shots were concerned.

To this day, we cannot stop laughing when we think back of this moment.

 Posted by at 8:46 pm
Nov 122021

Today, I saw a funny post on Quora about how to pet a rabbit. Apparently, rabbits should not be picked up (fragile skeletal structure, bones that break easily) and also hate it when their tail is touched. I was about to make a cheeky comment on pulling either a rabbit or a cat by the tail. But first I wanted to fact check something quickly on Google, and that’s when I came across this article about tail pull injuries that cats sometimes suffer.


I admit I pulled our cats by the tail every once in a while. It’s funny, but also effective when you need to pull a cat back when he’s about to run out of the house or do something he’s not supposed to do.

Except… Except that, as I now learn, cats’ tails get injured relatively easily, and the injury can be devastating, affecting the bundle of nerves that exit the spinal column, which control much of their lower body. The least devastating consequence is losing mobility of the tail, but the injury can also lead to paralysis of the hind legs and incontinence. In short, ruining a cat’s life.

I did not know this. I am glad I never inadvertently caused injury to one of our cats. But I will never pull a cat by the tail again.

 Posted by at 7:31 pm
Oct 202021

Earlier today, I noticed something really strange. A lamp was radiating darkness. Or so it appeared.

Of course there was a mundane explanation. Now that the Sun is lower in the sky and the linden tree in front of our kitchen lost many of its leaves already, intense sunlight was reflecting off the hardwood floor in our dining area.

Still, it was an uncanny sight.

 Posted by at 11:27 pm
Sep 282021

I live in a condominium townhouse. We’ve been living here for 25 years. We like the place.

Our unit, in particular, is the middle unit in a three-unit block. The construction is reasonably sound: proper foundations, cinderblock firewalls between the units, woodframe construction within, pretty run-of-the-mill by early 1980s North American standards. We have no major complaints.

Except that… for the past several years, every so often the house wobbled a bit. Almost imperceptibly, but still. At first, I thought it was a minor earthquake (not uncommon in this region because it is still subject to isostatic rebound from the last ice age; in fact we did live through a couple of notable earthquakes since we moved in here.) But no, it was no earthquake.

I thought perhaps it was related to the downtown light rail tunnel construction? But no, the LRT tunnels are quite some ways from here and in any case, that part of the construction has been finished long ago.

But then what the bleep is it? Could I be just imagining things?

Our phones have very sensitive acceleration sensors. Not for the first time, I managed to capture one of these events. A little earlier this afternoon, I heard the woodframe audibly creak as the house began to move again. I grabbed my phone and turned on a piece of software that samples the acceleration sensor at a reasonably high rate, about 200 times a second. Here is the result of the first few seconds of sampling:

The sinusoidal signal is unmistakably there, confirmed by a quick Fourier-analysis to be a signal just above 3 Hz in frequency:

Like Sheldon Cooper in The Big Bang Theory, I can claim that no, I am not crazy, and in this case not because my mother had me tested but because my phone’s acceleration sensor confirms my perception: Something indeed wobbles the house a little, enough to register on my phone’s acceleration sensor, measuring a peak-to-peak amplitude of roughly 0.05 m/s² (the vertical axis in the first graph is in g-units.) That wobble is certainly not enough to cause damage, but it is, I admit, a bit unnerving.

So what is going on here? A neighbor engaging in some, ahem, vigorous activity? Our current neighbors are somewhat noisier than prior residents, occasionally training their respective herds of pygmy elephants to run up and down the stairs (or whatever it is that they are doing). But no, the events are just too brief in duration and too regular. Underground work, perhaps a secret hideout for the staff of the nearby Chinese embassy? Speaking of which, I admit I even thought that this ~3 Hz signal might be related to the reported cases of illness by embassy staff at several embassies around the world, but I just don’t see the connection: even if those cases are real and have an underlying common cause (as opposed to just mere random coincidences) it’s hard to see how a 3 Hz vibration can have anything to do with them.

OK, so I have a pretty good idea of what this thing isn’t, but then, what the bleepety-bleep is it?

 Posted by at 3:50 pm
Aug 142021

I am not happy admitting it, but it’s true: There have been a few occasions in my life when I reacted just like this XKCD cartoon character when I first encountered specific areas of research.

 Posted by at 11:48 am
Aug 122021

Fergus was a cat. A beautiful, beautiful gray cat, who belonged to my cousin and her husband.

This is Fergus, just a few days ago.

This photo shows just what a beautiful creature Fergus was. Yet perhaps it also reveals that he was not well. Though he still enjoyed the late morning sun in the backyard, he was already very unwell, sickened by leukemia.

Fergus departed this world Tuesday evening, euthanized by the same mobile vet who euthanized our long-haired cat Fluffy six years ago.

Even though I did not know Fergus well, I am deeply saddened by his passing. I am rather fond of cats. Every time I look a cat in the eye, I sense a miracle as I contemplate how those little eyeballs see this magnificent universe in which we live. And whenever a cat leaves us and walks away into the great unknown, the world that they leave behind feels like a much duller place in their absence.

 Posted by at 12:38 am
Jul 302021

On my eighth birthday, I received a gift from a nice couple, friends of my Mom.

It was a Hungarian-language book bearing the title, “Wonders of the World,” in Hungarian, translated from the German original that was written by German-Jewish authors Artur Fürst and Alexander Moszkowski.

It was an old book, published in the 1930s. A dark green hardcover, with the etched image of a skyscraper for illustration on the cover. Its dust jacket, if it ever had one, was long gone.

But never mind that, it’s the content on these yellowed pages that matters.

It was from this book that I first learned about statistical fallacies, for instance. What is the probability that when you leave your home, the first 200 people you encounter are all males? Astronomically small, you might conclude. 2−200 ~ 6.223 × 10−61 to be a bit more precise, assuming half the population is male. A probability this small is firmly in the category of never happens. Until one morning, you step outside and the first thing you see is an all-male battalion of soldiers marching down the street…

I was reminded of this book today as I was reading about recent pronouncements of “breakthrough” infections among the vaccinated, and the reminder by experts that in a population that has a high vaccination rate, such cases are to be expected. It does not mean that the vaccine is worthless. It simply means that as the virus runs out of unvaccinated victims, to the extent it can still cause damage, increasingly it will be among the vaccinated folks. Which should make sense, except, as we well know, roughly 90% of statistical fallacies are committed by right-handed people…

Anyhow, much to my surprise, this book I love so much, from which I learned so much as a pre-teen, remains well-known in the country where it was originally published under the title Das Buch der 1000 Wunder. So well-known, in fact, that current German-language editions are readily available on Amazon, nearly a century after its initial publication. So I guess I am not the only person who finds the insights and information presented in this unassuming volume immensely valuable, especially for a child.

So let this serve as my notice of gratitude across time and space to “uncle Sandor and aunt Eva,” as they inscribed their names in the book along with their birthday wishes, for what I can now truly call a gift of a lifetime.

 Posted by at 11:32 pm
Jul 152021

I wrote an answer today on Quora that, I realized, belongs in my blog.

The question was about once significant medieval towns in Europe that have since faded into obscurity.

And I had the perfect answer, on account of having lived there back in the 1970s: The town of Visegrád in northern Hungary (known these days on account of the Visegrad Four, the informal alliance of the Czech Republic, Hungary, Poland and Slovakia which began with a summit in this town held in 1991).

Once the capital of the Kingdom of Hungary, and also home of the Summer Palace of King Matthias Corvinus during the heyday of said kingdom, today the town (really, a village; it gained the legal status of town only because of its historical significance, not on account of its population, which numbers less than 2,000) is just a minor settlement at the Danube Bend, where where the river Danube makes a 90-degree turn towards Budapest.

I used to live in a building just at the base of the stocky Salamon tower near the center of this image. Image from Wikipedia.

Visegrád is a fascinating town, full of history. Unfortunately, because of said history, most of it is in the form of barely recognizable ruins. Ruins of a citadel at the top of Castle Hill, its last functioning remains blown up by the victorious Austrians after the failed struggle for Hungarian independence in the early 18th century. Ruins of the sprawling Summer Palace complex, used by locals as a source of building material for centuries until very little of the original buildings remained. Ruins of the tower of Salamon, part of the lower castle, rebuilt decades ago using modern materials and housing a museum, but badly in need of repairs. And more ruins, ruins going back to Roman times, everywhere.

The name of the town itself is of Slavic origin (literally means high castle I believe) but many of the town’s present-day inhabitants are of German descent. I recall names of classmates like Gerstmayer or Fröhlich, and it was not uncommon to hear family members talking to each other in German on the streets of the town when I lived there as a child.

I have fond memories of the place; I attended school there from grades 6 to 8 before moving back to Budapest. I still visit Visegrád from time to time when I am in Hungary, albeit only as a tourist, as I no longer really know anybody there. It is, to be sure, a very popular tourist destination: the Danube Bend is spectacular, and the hills surrounding the area are crisscrossed by well-marked, well-maintained tourist trails. And, well, ruins or no ruins, the history of the place is absolutely fascinating.

But looking at the tiny village, its single church, small school, its sole tiny movie theatre, the few narrow streets with mostly single-story buildings, you’d never guess the rich history of the town.

Church of St. John the Baptist, in the center of Visegrád. Lovely clock. Google Street View image.

 Posted by at 11:53 pm
Jun 262021

My beautiful wife and I both received our second jabs today.

Our first dose was AstraZeneca, but it is now recommended to choose an mRNA vaccine for the second dose. My remaining concern is whether this mixed shot is good enough to enter other countries, the United States in particular, where the AZ vaccine never received emergency FDA approval. We shall see… worst case, I guess, is that we will need a third dose.

 Posted by at 1:37 pm
May 182021

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.

 Posted by at 5:35 pm
May 132021

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.

 Posted by at 4:38 pm