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/.

Aug 072019

Yesterday, we posted our latest paper on arXiv. Again, it is a paper about the solar gravitational lens.

This time around, our focus was on imaging an extended object, which of course can be trivially modeled as a multitude of point sources.

However, it is a multitude of point sources at a finite distance from the Sun.

This adds a twist. Previously, we modeled light from sources located at infinity: Incident light was in the form of plane waves.

But when the point source is at a finite distance, light from it comes in the form of spherical waves.

Now it is true that at a very large distance from the source, considering only a narrow beam of light, we can approximate those spherical waves as plane waves (paraxial approximation). But it still leaves us with the altered geometry.

But this is where a second observation becomes significant: As we can intuit, and as it is made evident through the use of the eikonal approximation, most of the time we can restrict our focus onto a single ray of light. A ray that, when deflected by the Sun, defines a plane. And the investigation can proceed in this plane.

The image above depicts two such planes, corresponding to the red and the green ray of light.

These rays do meet, however, at the axis of symmetry of the problem, which we call the optical axis. However, in the vicinity of this axis the symmetry of the problem is recovered, and the result no longer depends on the azimuthal angle that defines the plane in question.

To make a long story short, this allows us to reuse our previous results, by introducing the additional angle β, which determines, among other things, the additional distance (compared to parallel rays of light coming from infinity) that these light rays travel before meeting at the optical axis.

This is what our latest paper describes, in full detail.

 Posted by at 9:10 pm
Jul 242019

Rutger Hauer was a Dutch actor. He is best known perhaps for his role in the science-fiction cult classic Blade Runner, in particular for his improvised tears in rain soliloquy, spoken by the character Roy Batty just before his death:

I’ve seen things you people wouldn’t believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhäuser Gate. All those moments will be lost in time, like tears in rain. Time to die.

I just learned that Hauer himself died a few days ago, after a brief illness, at age 75.

 Posted by at 6:55 pm
Jul 192019

The world is celebrating the 50th anniversary of one of the most momentous events in human history: the first time a human being set foot on another celestial body.

It is also a triumph of American ingenuity. Just as Jules Verne predicted a century earlier, it was America’s can-do spirit that made the Moon landing, Armstrong’s “one small step” possible.

And today, just like 50 years ago, their success was celebrated around the world, by people of all nationality, religion, gender or ethnicity.

But that’s not good enough for some New York Times columnists.

Instead of celebrating the Moon landing, Mary Robinette Kowal complains about the gender bias that still exists in the space program. Because, as we learn from her article, this evil male chauvinistic space program was “designed by men, for men”. Because, you know, men sweat in different areas of their body and all. Even in the office, temperatures are set for men, which leaves women carrying sweaters.

Sophie Pinkham goes further. Instead of celebrating America’s success on July 20, 1969, Pinkham goes on to praise the Soviet space program in a tone that might have been rejected even by the editors of Pravda in 1969 as too over-the-top. Because unlike America, the Soviets put the first woman in space! Their commitment to equality did not stop there: They also sent the first Asian man and the first black man into orbit. Because, we are told, “under socialism, a person of even the humblest origins could make it all the way up.”

Just to be clear, I am not blind to gender bias. We may have come a long way since the 1960s, but full gender equality has not yet been achieved anywhere: not in the US, not in Canada, not even in places like Iceland. And racism in America remains a palpable, everyday reality. Back in 1969, things were a lot worse.

But to pick the 50th anniversary of an event that, even back in the turbulent 1960s, had the power to unify humanity, to launch such petty rants? That is simply disgraceful. Or, as the New York Post described it, obscene.

The New York Post also makes mention of one of the female pioneers of the US space program, Margaret Hamilton, whose work was instrumental in making the Apollo landings possible. Yet somehow, neither Pinkham nor Kowal found it in their hearts to mention her name.

I have to wonder: Are columnists like Pinkham or Kowal secretly rooting for Donald Trump? Because they certainly seem to be doing their darnedest best to alienate as many voters as possible, from what appears to be an increasingly bitter, intolerant, ideological agenda on the American political left.

 Posted by at 6:49 pm
Jul 162019

Fifty years ago today, fifty years ago this very hour in fact, at 9:32 AM EDT on July 16, 2019, Apollo 11 was launched.

Moonbound Apollo 11 clears the launch tower. NASA photo

And thus began a journey that, arguably, remains the greatest adventure in human history to date.

I was six years old in 1969, hooked on the novels of Jules Verne. With Apollo 11, Verne’s bold imagination became the reality of the day.

 Posted by at 9:25 am
Jul 152019

In 1929, probably just weeks before the great stock market crash, people were entertained by the sight of thousands of burning radio sets.

Some suggested that the apparent zeal with which these poor radios were burned had to do with the fact that they were obsolete regenerative receivers, notorious sources of radio frequency interference.

But no, the pictures make it clear that many of these old radios were simple tuned radio frequency (TRF) sets, not regenerative units. Besides, it was not until the early 1930s that superheterodyne receivers began to dominate the market.

No, this was just good old capitalism. People were encouraged to trade in old, “obsolete” radios and purchase new ones. And the wanton destruction of the old sets became a public spectacle.

One can only wonder about the amount of toxic smoke that was produced by this stunt. Not that anyone cared back in 1929.

 Posted by at 10:40 am
Jul 152019

Galileo is the world’s third global satellite navigation system, built by the European Union, operating in parallel with the American GPS system and Russia’s GLONASS. It has been partially operational since 2016, with a full constellation if satellites expected to enter service this year.

But as of early Monday, July 15, Galileo has been down for nearly four days, completely inoperative in fact:

As of the time of this writing, no explanation is being offered, other than one article mentioning an unspecified issue with Galileo’s ground-based infrastructure.

It really is difficult to comprehend how such a failure can occur.

It is even more difficult to comprehend the silence, the lack of updates, explanations, or any information about the expected recovery.

 Posted by at 12:59 am
Jul 032019

There is always a first time for everything.

I have spent more than 56 years on this planet so far, but today was the first time that I managed to lock myself in a bathroom.

I was heading to see my dentist, in a bit of a hurry when I went to the bathroom one last time and slammed the bathroom door. (I was angry because I missed the bus that would have taken me to my destination comfortably.) When I was trying to exit the bathroom, the doorknob did not function. It rotated freely, and the door remained stuck.

My wife was fortunately at home. Unfortunately, the doorknob on the other side of the door didn’t do a thing either.

I was trying to force the door open using makeshift implements. My wife was trying to do the same from the other side.

After a few minutes, I realized that I would not be able to make it to the dentist on time, so I phoned their office. They were very nice and understanding. What they thought about me is another matter.

After another fifteen minutes I was ready to give up. I resigned myself to having to spend half the afternoon in a tiny bathroom (a tiny powder room, really) as I called our condominium manager for help.

But just then, while I was talking to our condo manager, my wife succeeded. With the help of an axe and a kitchen knife, she was able to force the door open. I was free! And the door was not damaged too badly either.

Grabbing my screwdriver, I disassembled the door lock. I found that an essential part, the spindle, became detached from the knob to which it is normally attached, and ended up completely inside the other knob. Thus it could no longer perform its essential function of actuating the latch. The problem was trivial to fix.

Thank goodness I was not alone at home. Thank goodness my wife didn’t give up so easily and managed to free me. And thank goodness I am not claustrophobic.

 Posted by at 5:07 pm
Jul 012019

I have been thinking about this supposedly historic meeting between Trump and Kim at the DMZ.

One TV talking head criticized Trump’s last-minute invitation. “These meetings should be preceded by months of preparations by experts,” he said, or something to this effect. I remember, I was actually waking down the stairs towards my kitchen as I exclaimed, “Those experts had 65 years at their disposal.”

In short, I am not going to blame Trump for trying something different. Trying, of course, is not the same as succeeding.

Can Trump succeed? Can this meeting be the beginning of something meaningful, like Captain Picard’s meeting with the Tamarian captain, who was speaking in the allegorical Tamarian language in that famous Star Trek: The Next Generation episode?

Or, far more likely, is it just a misguided attempt by a narcissistic world leader who grossly overvalues his own skills at personal diplomacy, reminding me of the last Kaiser of Imperial Germany, Wilhelm II?

I am not optimistic, but for what it’s worth, I am rooting for Trump. If he succeeds, the world becomes a slightly better, slightly safer place.

 Posted by at 7:02 pm
Jun 182019

So on the one hand… here I am, praising Canada for being true to its values, only to learn yesterday that Quebec’s provincial legislature approved a ban on “religious symbols”. Not once in my life did I worry when I was being served by a person wearing a kippa, a cross, a turban or a headscarf that nature that they might discriminate against me. Should I have been? Perhaps naively, I always felt privileged to live in a society in which persons wearing kippas, crosses, turbans or headscarves were welcome, even into positions of authority. But now I am worried that a person whose religion demands wearing a kippa, a cross, a turban or a headscarf will not be allowed to serve me anymore. And that’s even before I look at the more hypocritical aspects of the bill.

But then, I learn that south of the border, social justice warriors scored another “victory”: at Bowling Green State University, Ohio, they managed to get the name of silent era film star Lillian Gish stripped from the university’s Gish Film Theater because a student union protested on account of her role in the rather racist 1915 silent classic Birth of a Nation.

I fundamentally disagree with the idea of judging the past by the standards of the present. I dare hope that our societies are becoming better over time, and thus our standards are higher, but it is grossly unfair to the memory of those from generations ago when they are judged by standards that did not even exist at the time. But putting all that aside… isn’t it obvious that such acts of cultural intolerance (committed, ironically, in the name of tolerance) are just oil on the fire? That those who are behind the rise of xenophobia, nationalism, racism and intolerance will see such acts as proof that their grievances of valid, that it is truly they (and by “they”, I mean mostly middle-aged or older white men) who are being prosecuted here?

Are these truly the only choices out there? Xenophobic nationalism and Islamophobia vs. social justice militants? Where have all the sane people gone? Please come back wherever you are and help put an end to this madness.

 Posted by at 5:44 pm
Jun 132019

The news this morning is that former PM Jean Chrétien suggested that Canada should stop the extradition proceedings against Huawei CFO Meng Wanzhou, as a means to win back the freedom of the two Canadian hostages in China, Michael Kovrig and Michael Spavor. (Yes, I called them hostages.)

The case against Huawei runs a lot deeper, however, than the financial fraud Ms. Meng is alleged by US authorities to have committed.

There is also the question of espionage, including the possibility that Huawei’s 5G equipment cannot be trusted because of firmware or hardware level backdoors.

I repeatedly encountered the suggestion that this issue can be trivially remedied by using end-to-end encryption. Unfortunately, end-to-end encryption, even if properly implemented (ignoring for the moment our own Western governments’ recurrent pleas to have built-in backdoors in any such encryption algorithms), solves only part of the problem.

It still allows Huawei to steal metadata, such as where calls are routed or the amount and nature of data traffic between specific endpoints. Worse yet, no encryption prevents Huawei from potentially sabotaging the network when called upon to do so by the Chinese government.

For this reason, I reluctantly came to the conclusion that the US ban against Huawei is justified and appropriate. It must, of course, be accompanied by a suitable increase in spending on researching 5G communications technologies, because otherwise, we risk shooting ourselves in the foot by banning the use of equipment that is technologically superior to the available alternatives. This is a new situation for the West: The last time the West faced a great power adversary that matched Western scientific and technological capabilities was in the 1930s, with Nazi Germany.

As for Ms. Meng, I think the suggestion to suspend the extradition process is wholly inappropriate. It would signal to the world that Canada is willing to suspend the rule of law for the sake of hostages. However strongly I feel about Messrs. Kovrig and Spavor, however strongly I desire to see them released, this is not a price Canada should be willing to pay.

 Posted by at 5:56 pm
Jun 052019

And before I forget: Last week, wearing my release manager hat I successfully created a new version of Maxima, the open-source computer algebra system. As a result, Maxima is again named one of SourceForge’s projects of the week, for the week of June 10.

The release turned out to be more of an uphill battle than I anticipated, but in the end, I think everything went glitch-free.

Others have since created installers for different platforms, including Windows.

And I keep promising myself that when I grow up, I will one day understand exactly what git does and how it works, instead of just blindly following arcane scripts…

 Posted by at 1:50 pm
May 312019

Here is a thought that has been bothering me for some time.

We live in a universe that is subject to accelerating expansion. Galaxies that are not bound gravitationally to our Local Group will ultimately vanish from sight, accelerating away until the combination of distance and increasing redshift will make their light undetectable by any imaginable instrument.

Similarly, accelerating expansion means that there will be a time in the very distant future when the cosmic microwave background radiation itself will become completely undetectable by any conceivable technological means.

In this very distant future, the Local Group of galaxies will have merged already into a giant elliptical galaxy. Much of this future galaxy will be dark, as most stars would have run out of fuel already.

But there will still be light. Stars would still occasionally form. Some dwarf stars will continue to shine for trillions of years, using their available fuel at a very slow rate.

Which means that civilizations might still emerge, even in this unimaginably distant future.

And when they do, what will they see?

They will see themselves as living in an “island universe” in an otherwise empty, static cosmos. In short, precisely the kind of cosmos envisioned by many astronomers in the early 1920s, when it was still popular to think of the Milky Way as just such an island universe, not yet recognizing that many of the “spiral nebulae” seen through telescopes are in fact distant galaxies just as large, if not larger, than the Milky Way.

But these future civilizations will see no such nebulae. There will be no galaxies beyond their “island universe”. No microwave background either. In fact, no sign whatsoever that their universe is evolving, changing with time.

So what would a scientifically advanced future civilization conclude? Surely they would still discover general relativity. But would they believe its predictions of an expanding cosmos, despite the complete lack of evidence? Or would they see that prediction as a failure of the theory, which must be remedied?

In short, how would they ever come into possession of the knowledge that their universe was once young, dense, and full of galaxies, not to mention background radiation?

My guess is that they won’t. They will have no observational evidence, and their theories will reflect what they actually do see (a static, unchanging island universe floating in infinite, empty space).

Which raises the rather unnerving, unpleasant question: To what extent exist already features in our universe that are similarly unknowable, as they can no longer be detected by any conceivable instrumentation? Is it, in fact, possible to fully understand the physics of the universe, or are we already doomed to never being able to develop a full picture?

I find this question surprisingly unnerving and depressing.

 Posted by at 1:37 am
May 152019

Technology changes. Things that were once revolutionary and new eventually become obsolete.

Sometimes with surprising rapidity.

Which is how I ended up, years ago, buying things that were ultimately not only never used, but were never even taken out of shrink wrap.

Take this 3-pack of high quality SONY 90-minute audio cassettes. When I bought them, I had little doubt that they would be used, and soon, and that future purchases would follow. Never happened.

Or how about this answering machine tape? Back then, I needed them. After all, you never want to be without a spare tape for your answering machine. Except… Well, never mind.

Perhaps a little more surprising is this box of blank DVDs. I have several more boxes of different types, but they have been opened and at least a few disks were put to use. But this box? Completely unused, in the original shrink wrap. Not too long ago, burning a CD or a DVD was something I did almost daily. But when I built new computers a couple of years ago, I no longer even bothered putting DVD drives in them. I have an external USB drive that works fine for software (mostly operating system) installations. And I can still use it, e.g., to rip a CD. But burning one? What for? My USB dongle on my key chain has many times the capacity of a DVD.

I still have never-used floppy disks, too, but not in unopened, shrink-wrapped packages.

Looking around, I am trying to guess what technology will be next, going the way of the dodo. Hard drives, perhaps? Sure they’re being replaced by SSDs but they still offer a price advantage and better reliability as long-term storage. Desktop computers? Unlikely, for content creators or developers like myself. Or maybe things are settling down a bit? I don’t know.

For what it’s worth, I also have a record player and a VCR next to my desk. The VCR was a super-expensive, top-of-the-line VCR that can handle all TV standards, which is why I bought it. I used it to digitize many tapes, including PAL/SECAM tapes from Europe. I have not used that VCR in many years; not even sure it still works. Its display does show the time, but it is very faint. The record player, however, is relatively new. Vinyl has made a comeback of sorts, so record players are being made again. I didn’t buy into the new (retro?) vinyl craze, but we did have a few older records that we liked very much, and which were not readily available on CD, so the player was needed to digitize them as well.

 Posted by at 12:50 pm
May 132019

I have learned to love the voice of Doris Day.

Her version of No Moon At All is one of my all-time favorites.

Early this morning, I found out that she passed away. May she rest in peace.

 Posted by at 12:53 pm
May 082019

The Globe and Mail managed to publish today one of the saddest editorial cartoons I ever saw:

There really is nothing that I can add. The cartoon speaks for itself.

 Posted by at 11:42 am
May 082019

Today was a most unpleasant day for a whole host of reasons, so by the time I finished my dinner, I needed a distraction.

And then I recalled: Just the other day, I read that China’s most successful sci-fi blockbuster to date, The Wandering Earth, is now on Netflix.

So it was time for movie night. I watched it. And it was… fun.

It is not a flawless movie by any means. And the so-called “science” is as warped, as bogus as the science behind any Hollywood blockbuster.

But it was fast-paced, visually stunning, engaging, and occasionally even had sparks of genuine humor, just in the right quantities.

In short, it is on par with any A-rated sci-fi blockbuster from Hollywood.

One suggestion: Watch it with subtitles in the original Mandarin. This is not meant to be a criticism of the voice actors of the English-language dubbed version. It just… didn’t feel authentic. And you might miss out on subtleties, such as (ok, this is one of the less subtle subtleties, I admit) when one character: a blonde, mixed-race Chinese-Australian man from Beijing who speaks Mandarin as a native throughout the film, suddenly shouts “Fuck this shit! No fucking way!” in unaccented English when he makes an uncharacteristically self-sacrificing move, risking his own life.

 Posted by at 12:51 am
May 052019

There is this wonderful Tom Waits song (Waits may be the only artist I know who presents cacophonic noise as “music” and yet the result is something I don’t hate), Earth Died Screaming. The title is borrowed from The Earth Dies Screaming, a 1964 British film, scenes from which are used in the Tom Waits music video.

The British movie is about an alien invasion. But a friend of mine used this phrase a lot lately as he is posting about environmental disasters, such as the ever growing islands of plastic in the ocean, the rapid, wholesale disappearance of species, or the still callous attitude of greedy humans who continue to engage in wanton destruction.

And then there are the bugs.

It wasn’t that long ago that I read somewhere online the observation that nowadays, when you go on a highway drive on a summer evening, your windshield no longer gets covered with bugs. Sure, some of it might be explained by the more streamlined shape of automobiles, allowing laminar airflow and letting the bugs escape… but it isn’t a very convincing explanation and I, too, noticed that the bugs are no longer a major problem.

And then, I read about vanishing insect populations in National Geographic.

Here are a couple of sentences worth quoting:

“In October 2017 a group of European researchers found that insect abundance (as measured by biomass) had declined by more than 75 percent within 63 protected areas in Germany—over the course of just 27 years.” Or that “within a relatively pristine rainforest in Puerto Rico, the biomass of insects and other arthropods like spiders had fallen between 10- and 60-fold since the 1970s.”

If this doesn’t scare the bejesus out of you, maybe it should.

 Posted by at 11:26 pm
May 052019

I just finished reading Miranda Carter’s superb book, George, Nicholas and Wilhelm, about the three royal cousins who, often unwittingly, helped pave the road to WWI.

Though the book was written many years before Trump ascended to the White House, the parallels between Wilhelm and Trump are frighteningly inescapable.

What this means for the future, I don’t know. Like Trump, Wilhelm was at least as much a symptom as he was a cause: A symptom of a society with deep divisions and unresolved problems. Like the war that began in 1914, a future conflict may end up destroying the fruits of an unprecedented era of prolonged prosperity and progress, leading to chaos and disaster instead. And given the advances in technology and the proliferation of weaponry, including nuclear weapons, a future conflict will be much, much worse than anything the world has seen, including the horrors WWII.

Carter seems to have the same sense of apprehension, if her article published in The New Yorker last year is any indication. And she warns, rightfully in my opinion, that just as it was the case with Wilhelm, the real consequences may only come long after Trump is gone in the White House.

Oh well. To cheer myself up, I began reading Mary Beard’s SPQR instead, a modern history of ancient Rome. Oh wait… the Rome that transitioned from a popular republic to an autocratic empire? Yes, the very same.

 Posted by at 11:20 pm
May 022019

I meant to post this yesterday, but I didn’t have the time. Besides, it is not something you post without permission from the other party involved. The other party being my beloved wife Ildiko, that is.

You see, yesterday marked the 40th anniversary of us meeting, on a cloudy, rainy May 1 in the town of Győr, Hungary, where we were both attending a national high school chemistry competition.

And it so happened that a short while (maybe just a few weeks?) later, our high school class had a day trip to the fine town of Pécs, Ildiko’s hometown, so she and I had a chance to meet again. And one of my friends had a Polaroid camera:

Darn, I was so much thinner than today.

Ildiko, on the other hand, looks just as beautiful now as she did on that late spring day in 1979.

 Posted by at 5:56 pm