I was recently interviewed by a Hungarian podcaster, mostly about my participation in the early days of game development in Hungary, but also about my more recent work, including my scientific contributions.

I just listened to the interview and thankfully, I didn’t say anything colossally stupid.

A very nice article about our work on the Solar Gravitational Lens was published a few days ago on Universe Today, on account of our recent preprint, which shows quantitative results assessing the impact of image reconstruction on signal and noise.

Because the SGL is such an imperfect lens, the noise penalty is substantial. However, as it turns out, it is much reduced when the projected image area is large, such as when an exoplanet in a nearby star system is targeted.

While this is good news, the Sun’s gravitational field has other imperfections. We are currently working on modeling these and assessing their impact on noise. Next comes the problem of imaging a moving target: an exoplanet that spins, which is illuminated from varying directions, and which may have varying surface features (clouds, vegetation, etc.) Accounting for all these effects is essential if we wish to translate basic theory into sound scientific and engineering requirements.

So, the fun continues. For now, it was nice to see this piece in Universe Today.

The ghosts of Halloween have not completely forsaken us.

Here is the driveway of one of our neighbors tonight:

I doubt there will be many trick-or-treaters, but it was nonetheless good to see this. I especially appreciated the lit candle that turned a jack-o-lantern into, well, an actual jack-o-lantern. But it is really the other pumpkin that looked truly frightening. Thank you, neighbor!

I don’t usually write about such matters, but a letter like this one is always a nice one to get even when there is no raging pandemic:

Let this serve as a public service reminder: If you are, like me, in your fifties, especially if you are a male, with a sedentary lifestyle (spending your days in your office chair), perhaps overweight: You are at risk. Early detection may mean the difference between surviving to a ripe old age in good health vs. dying before you get to enjoy life as a pensioner.

I rarely remember my dreams. It was therefore striking when this morning I woke up from a vivid dream. In my dream, I visited my long dead grandmother’s old apartment, except that she was very much alive, sitting in front of a desk facing the window of her room. I stood at her doorway, not wanting to get any closer, COVID-19 and all. I said to her that we should keep our distance, and at first she nodded but then, bah, she approached me anyway with the intent to hug and kiss me. Not having any better ideas, I quickly held up the sheet of paper or book or whatever it was that I had in my hands, so that instead of kissing each other on the cheek, we ended up kissing through that paper object. I truly was worried that if we are careless, we risk her frail health.

In actuality, my grandmother, who was born in 1901, passed away 26 years ago. I was wondering what prompted this dream. Then I realized: last night, I saw an image on Twitter, a 1908 Canadian painting titled Mrs. Davies at the Sewing Machine, by Albert Henry Robinson.

Not quite the same as my grandmother’s room, but it has the same vibe, same atmosphere.

What an unusual dream.

Yes, I loved my grandmother very much. But I don’t think I ever saw her using a sewing machine.

So I try to start a piece of software that accesses a classic serial port.

The software locks up. The process becomes unkillable. Because, you know… because. Microsoft has not yet discovered kill -9 I guess.

(Yes, I know that unkillable zombie processes exist under Linux/UNIX, too. But in the past 25 years, I remember exactly one (1) occasion when a Linux process was truly unkillable, hung in a privileged kernel call, and actually required a reboot with no workaround. On Linux, this is considered a bug, not a feature. In contrast, on Windows this is a regular occurrence. Then again, on Linux I have fine-grained control and I can update pretty much everything other than the kernel binary, without ever having to reboot.)

Ok-kay… this means Windows has to be restarted. Fine. At least let me check if there are any Windows updates. Oops… error, because an “update service is shutting down” or whatever.

Oh well, let’s restart. The browser (Edge) will remember my previously opened tabs, right?

After restart, another program tells me that it has an update. Clicking on the update button opens the browser with the download link. Fine. Just checking, in the browser history all my previously opened tabs (lots of them) are still there. Good.

Meanwhile, Windows Update does come to life and tells me that I need to restart my system. Couldn’t you freaking tell me this BEFORE I restarted?

Oh well, might as well… restart #2.

After restart, let’s open the browser. History… and all my previously opened tabs are gone. The only thing the bloody browser remembers is the single tab that contained the download link for that application.

@!##%@#!@. And @#$$!@#@!. And all their relatives, too. Live or deceased. And any related deities. Oh well, let’s restore the bleeping tabs manually; fortunately, I also had most of them opened in Chrome, so I could reopen them, one by one, in Edge. (Maybe there’s a more efficient way of doing this, but I wasn’t going to research that.) Meanwhile, I also restarted Visual Studio 2019. It told me that it had an update. Having learned from previous experience, I shut down a specific service that was known to interfere with the update. It proved insufficient. When Visual Studio was done updating, it told me that “only one thing” remains: a teeny weeny inconsequential thing, ANOTHER BLOODY RESTART. Because, ladies and gentlemen, in the fine year of 2020, the great software company Microsoft has not yet found a way to UPDATE A BLEEPING APPLICATION without restarting the WHOLE BLEEPING WORLD. Or at the very least do me a bleeping failure and warn IN ADVANCE that the update may require a restart. My favorite coffee mug survived, but only just barely. I almost smashed it against the wall. So here we go… restart #3. It was nearly two hours ago that I innocently tried to turn on that program that required access to the serial port. Since then, I probably aged a few years, increased my chances of a stroke and other illnesses related to high pressure, barked at my beautiful wife and my cats, almost smashed my favorite mug, lost several browser tabs but also my history in some xterm windows, and other than that, accomplished ABSOLUTELY NOTHING. Thanks for nothing, Microsoft. And I actually like Microsoft. Imagine what I’d be saying if I hated them. My favorite Twitter accounts: @PossumEveryHour, @RaccoonEveryHr, @RatsEveryHour,@ekichoTAMA, @evilbmcats, @giantcat9. I also love the Facebook Bird Misidentification Page. I think I should limit my social media consumption to these groups. For mental health, you know. I have a travel radio. It is a SONY ICF-SW1. It is an amazing little radio, probably the nicest radio ever made by anyone. It looks more like jewelry than a radio. It is an immensely capable universal receiver, with continuous tuning in the AM band between 150 and 29995 kHz, and in the FM band between 76 and 108 MHz. About the only shortcoming that was mentioned by its critics is that it is a shame that such a radio does not offer the ability to selectively pick modulation schemes (e.g., narrowband FM, SSB). I bought this radio maybe a quarter century ago, back in the 1990s. (So I guess it qualifies as an antique, despite the fact that there really are no comparable receivers out there that I know about.) I thought about buying one for quite some time but at first, I refrained as the radio was quite pricey. But one day, while waiting for my flight back home at Budapest Airport, I could not resist anymore: I saw the radio at the duty free shop and bought it. Come to think of it, it must have been 1993 or earlier, because as I recall, the radio was already in my possession when I visited Beijing in the fall of ’93. As such, it began to show signs of age, its sound quality deteriorating because of aging electrolytic capacitors. A few months ago, I purchased a capacitor kit off eBay, in the hope that I might be able to repair the radio. In fact, I began the repair job back in the summer, starting with taking the radio apart; not an easy task by itself, as it requires not just the removal of countless screws, not just carefully separating snap-together parts of the radio’s case without causing damage, but also desoldering several wires. Back in the summer, I successfully replaced two capacitors but then I put the radio aside. It was hard work, and very easy to make irreversible mistakes working on submillimeter scale parts with a soldering iron. As I attempted to replace a third capacitor last night, I managed to rip up a small patch of the printed circuit board. I was able to repair the damage with a piece of wire, but this was the point when I said, enough is enough; “do no harm” should be my mantra, and I certainly do not wish to destroy this beautiful little device. So I decided to forego the rest, in the hope that the two largest capacitors that I replaced (the third was a backup capacitor for the microprocessor, to keep it powered while replacing batteries) would be sufficient. I did, however, replace the display backlight: the original backlight was a low-luminosity green LED, which I replaced with a modern, high-luminosity white LED that I received as part of the kit. Putting everything back together was a challenge, too, and not just because the light didn’t work at first (bad soldering on my part). Ultimately I managed, though I ended up with four surplus screws with no place to go. (I think I know where they’re from, but they are redundant, and there’s no way I am going to take this radio apart again just to put those screws back in.) And much to my surprise, the radio works, and its sound quality indeed improved noticeably. As I was studying the circuit diagram of the radio, I kept wondering what possessed SONY to produce a little marvel like this. This radio is insanely complex, with its multiple circuit boards in an absolutely tiny package. The number of distinct parts (each carefully labeled in the service manual with replacement order numbers) is astonishing. Was it a labor of love? Were they showing off? Probably both. In the last few days, I was: 1. scolded in one Facebook group, when I commented on a post and made a mention of other personalities (who are not directly connected to the topic of the group), intended to serve as examples showing that the issue being discussed was a much broader one; 2. had a repost of mine of a funny image to a humor group unceremoniously deleted, for supposedly reposting “ad nauseam” something that I have not yet seen in that group since I became a member a few months ago. Yes, I know, discussion group moderation is a thankless task. Been there, done that. But, as I often reminded all-powerful witches and wizards in our favorite MUD (Multi-User Dungeon) games, there is no point overdoing the policing. It sucks away the fun for everyone. By all means, step in and police blatant violations… but also be wise and know when it is more appropriate not to notice things, even when they technically qualify as infractions. The goal, simply put, is to make things fun for everyone, not to enforce rules at all costs. In short, rules exist for our convenience, not the other way around. If only people were this conscientious when it comes to pandemic-related rules for social distancing and wearing masks… Rules that are there, you know, because they actually save lives? Oh well. Done ranting for the day. Tonight, Slava Turyshev sent me a link to an article that was actually published three months ago on medium.com but until now, escaped our attention. It is a very nice summary of the work that we have been doing on the Solar Gravitational Lens to date. It really captures the essence of our work and the challenges that we have been looking at. And there is so much more to do! Countless more things to tackle: image reconstruction of a moving target, imperfections of the solar gravitational field, precision of navigation… not to mention the simple, basic challenge of attempting a deep space mission to a distance four times greater than anything to date, lasting several decades. Yes, it can be done. No it’s not easy. But it’s a worthy challenge. “I don’t always lie on the floor,” Master Rufus told me today… …”but when I do, I do so with dignity.” A few weeks ago, Christian Ready published a beautiful video on his YouTube channel, Launch Pad Astronomy. In this episode, he described in detail how the Solar Gravitational Lens (SGL) works, and also our efforts so far. I like this video very much. Especially the part that begins at 10:28, where Christian describes how the SGL can be used for image acquisition. The entire video is well worth seeing, but this segment in particular does a better job than we were ever able to do with words alone, explaining how the Sun projects an image of a distant planet to a square kilometer sized area, and how this image is scanned, one imaginary pixel at a time, by measuring the brightness of the Einstein-ring around the Sun as seen from each pixel location. We now understand this process well, but many more challenges remain. These include, in no particular order, deviations of the Sun from spherical symmetry, minor variations in the brightness of the solar corona, the relative motion of the observing probe, Sun, exosolar system and target planet therein, changing illumination of the target, rotation of the target, changing surface features (weather, perhaps vegetation) of the target, and the devil knows what else. Even so, lately I have become reasonably confident, based on my own simulation work and our signal-to-noise estimates, as well as a deconvolution approach under development that takes some of the aforementioned issues into consideration, that a high-resolution image of a distant planet is, in fact, obtainable using the SGL. A lot more work remains. The fun only just began. But I am immensely proud to be able to contribute to of this effort. I met Gabor David back in 1982 when I became a member of the team we informally named F451 (inspired by Ray Bradbury of course.) Gabor was a close friend of Ferenc Szatmari. Together, they played an instrumental role in establishing a business relationship between the Hungarian firm Novotrade and its British partner, Andromeda, developing game programs for the Commodore 64. In the months and years that followed, we spent a lot of time working together. I was proud to enjoy Gabor’s friendship. He was very knowledgeable, and also very committed to our success. We had some stressful times, to be sure, but also a lot of fun, frantic days (and many nights!) spent working together. I remember Gabor’s deep, loud voice, with a slight speech impediment, a mild case of rhotacism. His face, too, I can recall with almost movie like quality. He loved coffee more than I thought possible. He once dropped by at my place, not long after I managed to destroy my coffee maker, a stovetop espresso that I accidentally left on the stove for a good half hour. Gabor entered with the words, “Kids, do you have any coffee?” I tried to explain to him that the devil’s brew in that carafe was a bitter, undrinkable (and likely unhealthy) blend of burnt coffee and burnt rubber, but to no avail: he gulped it down like it was nectar. After I left Hungary in 1986, we remained in sporadic contact. In fact, Gabor helped me with a small loan during my initial few weeks on Austria; for this, I was very grateful. When I first visited Hungary as a newly minted Canadian citizen, after the collapse of communism there, Gabor was one of the few close friends that I sought out. I was hugely impressed. Gabor was now heading a company called Banknet, an international joint venture bringing business grade satellite-based Internet service to the country. When our friend Ferenc was diagnosed with lung cancer, Gabor was distraught. He tried to help Feri with financing an unconventional treatment not covered by insurance. I pitched in, too. It was not enough to save Feri’s life: he passed away shortly thereafter, a loss I still feel more than two decades later. My last conversation with Gabor was distressing. I don’t really remember the details, but I did learn that he suffered a stroke, and that he was worried that he would be placed under some form of guardianship. Soon thereafter, I lost touch; his phone number, as I recall, was disconnected and Gabor vanished. Every so often, I looked for him on the Internet, on social media, but to no avail. His name is not uncommon, and moreover, as his last name also doubles as a first name for many, searches bring up far too many false positives. But last night, it occurred to me to search for his name and his original profession: “Dávid Gábor” “matematikus” (mathematician). Jackpot, if it can be called that. One of the first hits that came up was a page from Hungary’s John von Neumann Computer Society, their information technology history forum, to be specific: a short biography of Gabor, together with his picture. And from this page I learned that Gabor passed away almost six years ago, on November 10, 2014, at the age of 72. Well… at least I now know. It has been a privilege knowing you, Gabor, and being able to count you among my friends. I learned a lot from you, and I cherish all those times that we spent working together. A few hours ago, my phone rang and my friend David told me the sad news: His father, Peter Ada-Winter passed away*. I’ve known Peter since the late 1970s. He was an educator who played a pioneering role in the introduction of computer programming and computer science into the Hungarian school curriculum. Peter was a true scholar. His home, a cramped apartment in Budapest’s historic Castle District, was full of books. The walls were lined with tall bookshelves. His large desk was also covered with teetering piles of textbooks, newspapers, and computer printouts. Peter was the son of Ernő Winter, engineer, physicist and inventor, a towering figure in the early development of vacuum tube technology in the 1920s. Born in 1923, Peter survived the Holocaust that wiped much of his extended family off the face of the Earth. He was in his mid-40s when, in 1968, he was asked to organize a regular computer programming course for high school students in the same high school where I studied a decade later. I met Peter when I became friends with his son David in high school. I always looked up to him. I learned quite a few things from him. Not just technical matters, basic human values as well. Peter’s interest in information technology never diminished. In the mid-1980s, together with his son David they published a book on the 8-bit ZX Spectrum microcomputer. In the 1990s and early 2000s, despite his advancing age, Peter became well acquainted with the Internet; surfing the Web for news became part of his daily life. Even after he passed 90, Peter remained in good health and mentally active. Only in the last few years did his health begin to gradually decline. Nonetheless, David remained hopeful that they would be able to celebrate Peter’s 100th birthday in 2023 with a ginormous birthday cake. These hopes were squashed by the news David received today. Though I share David’s sense of grief, I reminded him that instead of grieving, we should remember the long, productive life of a very good man. Someone that I feel privileged to have known. *No, not a COVID-19 statistic. Simply old age. Long overdue, but I just finished preparing the latest Maxima release, version 5.44. I am always nervous when I do this. It is one thing to mess with my own projects, it is another thing to mess with a project that is the work of many people and contains code all the way back from the 1960s. I am one of the maintainers of the Maxima computer algebra system. Maxima’s origins date back to the 1960s, when I was still in kindergarten. I feel very privileged that I can participate in the continuing development of one of the oldest continuously maintained software system in wide use. It has been a while since I last dug deep into the core of the Maxima system. My LISP skills are admittedly a bit rusty. But a recent change to a core Maxima capability, its ability to create Taylor-series expansions of expressions, broke an important feature of Maxima’s tensor algebra packages, so it needed fixing. The fix doesn’t amount to much, just a few lines of code: It did take more than a few minutes though to find the right (I hope) way to implement this fix. Even so, I had fun. This is the kind of programming that I really, really enjoy doing. Sadly, it’s not the kind of programming for which people usually pay you Big Bucks… Oh well. The fun alone was worth it. One of the most fortunate moments in my life occurred in the fall of 2005, when I first bumped into John Moffat, a physicist from The Perimeter Institute in Waterloo, Ontario, Canada, when we both attended the first Pioneer Anomaly conference hosted by the International Space Science Institute in Bern, Switzerland. This chance encounter turned into a 15-year collaboration and friendship. It was, to me, immensely beneficial: I learned a lot from John who, in his long professional career, has met nearly every one of the giants of 20th century physics, even as he made his own considerable contributions to diverse areas ranging from particle physics to gravitation. In the past decade, John also wrote a few books for a general audience. His latest, The Shadow of the Black Hole, is about to be published; it can already be preordered on Amazon. In their reviews, Greg Landsberg (CERN), Michael Landry (LIGO Hanford) and Neil Cornish (eXtreme Gravity Institute) praise the book. As I was one of John’s early proofreaders, I figured I’ll add my own. John began working on this manuscript shortly after the announcement by the LIGO project of the first unambiguous direct detection of gravitational waves from a distant cosmic event. This was a momentous discovery, opening a new chapter in the history of astronomy, while at the same time confirming a fundamental prediction of Einstein’s general relativity. Meanwhile, the physics world was waiting with bated breath for another result: the Event Horizon Telescope collaboration’s attempt to image, using a worldwide network of radio telescopes, either the supermassive black hole near the center of our own Milky Way, or the much larger supermassive black hole near the center of the nearby galaxy M87. Bookended by these two historic discoveries, John’s narrative invites the reader on a journey to understand the nature of black holes, these most enigmatic objects in our universe. The adventure begins in 1784, when the Reverend John Michell, a Cambridge professor, speculated about stars so massive and compact that even light would not be able to escape from its surface. The story progresses to the 20th century, the prediction of black holes by general relativity, and the strange, often counterintuitive results that arise when our knowledge of thermodynamics and quantum physics is applied to these objects. After a brief detour into the realm of science-fiction, John’s account returns to the hard reality of observational science, as he explains how gravitational waves can be detected and how they fit into both the standard theory of gravitation and its proposed extensions or modifications. Finally, John moves on to discuss how the Event Horizon Telescope works and how it was able to create, for the very first time, an actual image of the black hole’s shadow, cast against the “light” (radio waves) from its accretion disk. John’s writing is entertaining, informative, and a delight to follow as he accompanies the reader on this fantastic journey. True, I am not an unbiased critic. But don’t just take my word for it; read those reviews I mentioned at the beginning of this post, by preeminent physicists. In any case, I wholeheartedly recommend The Shadow of the Black Hole, along with John’s earlier books, to anyone with an interest in physics, especially the physics of black holes. My lovely wife, Ildiko, woke up from a dream and asked: If you have a flower with 7 petals and two colors, how many ways can you color the petals of that flower? Intriguing, isn’t it. Such a flower shape obviously has rotational symmetry. Just because the flower is rotated by several times a seventh of a revolution, the resulting pattern should not be counted as distinct. So it is not simply calculating what number theorists call the $$n$$-tuple. It is something more subtle. We can, of course, start counting the possibilities the brute force way. It’s not that difficult for a smaller number of petals, but it does get a little confusing at 6. At 7 petals, it is still something that can be done, but the use of paper-and-pencil is strongly recommended. So what about the more general case? What if I have $$n$$ petals and $$k$$ colors? Neither of us could easily deduce an answer, so I went to search the available online literature. For a while, other than finding some interesting posts about cyclic, or circular permutations, I was mostly unsuccessful. In fact, I began to wonder if this one was perhaps one of those embarrassing little problems in combinatorial mathematics that has no known solution and about which the literature remains strangely quiet. But then I had another idea: By this time, we both calculated the sequence, 2, 3, 4, 6, 8, 14, 20, which is the number of ways flowers with 1, 2, …, 7 petals can be colored using only two colors. Surely, this sequence is known to Google? Indeed it is. It turns out to be a well-known sequence in the online encyclopedia of integer sequences, A000031. Now I was getting somewhere! What was especially helpful is that the encyclopedia mentioned necklaces. So that’s what this problem set is called! Finding the Mathworld page on necklaces was now easy, along with the corresponding Wikipedia page. I also found an attempt, valiant though only half-successful if anyone is interested in my opinion, to explain the intuition behind this known result:$$N_k(n)=\frac{1}{n}\sum_{d|n}\phi(d)k^{n/d},$$where the summation is over all the divisors of $$n$$, and $$\phi(d)$$ is Euler’s totient function, the number of integers between $$1$$ and $$d$$ that are relative prime to $$d$$. Evil stuff if you asked me. Much as I always liked mathematics, number theory was not my favorite. In the case of odd primes, such as the number 7 that occurred in Ildiko’s dream, and only two colors, there is, however, a simplified form:$$N_2(n)=\frac{2^{n-1}-1}{n}+2^{(n-1)/2}+1.

Substituting $$n=7$$, we indeed get 20.

Finally, a closely related sequence, A000029, characterizes necklaces that can be turned over, that is to say, the case where we do not count mirror images separately.

Oh, this was fun. It’s not like I didn’t have anything useful to do with my time, but it was nonetheless a delightful distraction. And a good thing to chat about while we were eating a wonderful lunch that Ildiko prepared today.

Two weeks, or to be precise, fifteen and a half days ago, I was walking the streets of downtown Vienna, enjoying a bright late winter day, eating a bit of authentic Viennese street food and a fabulous slice of cake in a Vienna coffee house. The next day, I boarded a flight at a busy Vienna Airport. To be sure, some signs were already present that not everything was normal. The plane had fewer passengers than usual, especially in business class. There was news of Lufthansa grounding all their A380 superjumbos, and when I asked our pilot about this, he just shook his head, not knowing what the future would bring. But all this felt distant; the world around us, by and large, still felt normal, busy as usual, with people lining up at checkpoints, roadways busy with traffic, airplanes landing and departing at regular intervals.

Today, fifteen days later, we visited our favorite deli store in a nearly completely deserted Byward Market in downtown Ottawa. I literally could have parked in the middle of the street. The store was open (we phoned ahead to make sure) but deserted as well. All the good food there… will it ever sell? Will they at least get a chance to donate some of it, e.g., to the Food Bank or to a nearby shelter? Will they be able to stay open? Will they be able to stay in business?

I don’t know what hit me more, this store or the Web site of Vienna Airport. You know, the same airport where I stood in line, two weeks ago, to go through customs and security.

Not much of a chance of a lineup today.

How will our world recover from this?

My wife and I went on a shopping spree.

No, we didn’t win the lottery. But apart from our desire to support our local economy in times of crisis, we were also rather worried that our favorite deli store in the Byward Market may be forced to close for an indefinite period of time.

So we stocked up on things. That said, I hope they are able to stay open. I hope they are able to stay in business. Other deli stores have shut their doors. I hope Continental remains open and that the owner and employees stay healthy.

In the meantime, I thank them for serving us.