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.

I have been working from home pretty much exclusively for much of my life, certainly for the past 25+ years.

To many, it is a new experience. I think I can offer a few useful words of advice. A few lessons I learned.

• Always get up in the morning. Working from home does not mean that you can sleep until noon. Keep a regular schedule.
• Always dress. Do not sit down to work in pajamas or a nightgown. It’s okay to wear clothes such as those half-torn pair of jeans that you’d no longer wear outside. But do dress. Also be mindful of personal hygiene. Working from home is no excuse for stinky breath or smelly feet.
• Create a dedicated workspace. Let your family know that when you are sitting there, you are, in fact, at work. Tell them to respect that and allow you to focus on the work that you do, without unnecessary distractions.
• Indeed, do not let yourself get distracted. Sure, it’s okay to take a break and watch that press conference on COVID-19, or perhaps even watch half an episode of your favorite Netflix show. Kind of like taking a break at the water cooler, chatting with colleagues. But then get back to work!
• Do not consume alcohol while working. You wouldn’t be sipping whiskey, Mad Men style, in the office either, would you?
• Do eat regular meals. Have a lunch break.
• Don’t be a workaholic: When you are done for the day, you are done for the day. Working at home does not mean an obligation to work through the night or through the weekend.

OK, enough patronizing advice. My apologies. Not sure what I was thinking. It’s time for me to get back to work.

I returned from a brief trip to Hungary yesterday.

My return flight was a bit eerie. Here is a picture of a part of the business class section of this Austrian Airlines 767:

It was not quite this empty (I tried to avoid photographing any passengers, for obvious privacy reasons) as there were a few passengers there, but only a few. Most reservations were canceled.

Is this dramatic response to the coronavirus justified? Parts of China, all of Italy under quarantine? Schools, public gatherings canceled around the world? A cruise ship industry in crisis, a global airline industry poised to lose hundreds of billions of dollars? Planes flying empty just to maintain the respective airlines’ claims on lucrative routes, or planes not flying at all, like the A380 fleet of Lufthansa?

Meanwhile, as Trump himself is fond to point out, the number of conformed coronavirus infections (most of which result in a mild illness, nothing more) worldwide is dwarfed by the number of influenza deaths this flu season.

Of course the flu is (more or less) predictable. The coronavirus is not. And its fatality ratio is much higher.

Even so, I have to admit that I wonder if the cure is causing more harm than the disease.

Then again… if we are just one minor mutation away from a Spanish Flu like pandemic, perhaps the drastic steps are justified. After all, at least some folks are criticizing the WHO for not going far enough, for failing to declare a global pandemic.

No matter what, flying back home in the time of coronavirus was an eerie experience. It was a bit like something straight out of the first episode of a science-fiction television series.

And yes, I was using my limited supply of hand sanitizer quite liberally. After all, you can never be certain…

And then, my Mom almost spat out her tea.

That happened when I told her about the pitiful attempt of mid-level management to deal with the persistent smell of sewage at the Parliament station of Ottawa’s defect-plagued new LRT system: the installation of bathroom air fresheners at dozens of locations around the station.

You see, I was visiting my Mom in Budapest. The city has an old underground line that was constructed back in 1896, but it also has a modern subway network, the first of which (line 2 in the current numbering scheme) was opened to the public in 1970, when I was seven years old.

That line used Soviet technology, Soviet trains, a Soviet signaling system. And it… just worked, from day one, each and every day, each and every hour of the day.

I spent one afternoon riding public transportation in Budapest. I traveled on this old line 2, which is presently using 90s era equipment and trains. I traveled on line 3, which uses recently rebuilt trains of the original Soviet variety. And I traveled on line 4, which is a modern, 21st century line with completely automated, driverless trains.

All three lines just… work. They work reliably. The rare instances when the system is interrupted are usually caused by events beyond the operators’ control, such as someone jumping in front of a train. And that 19th century relic, line 1, rebuilt and renovated in 1973, works reliably, too.

Meanwhile in Ottawa, and least the air fresheners have since been removed. But the stink remains, if you are fortunate (or unfortunate?) enough to be able to visit Parliament station when the service operates, at least at a reduced capacity.

Our most comprehensive paper yet on the Solar Gravitational Lens is now online.

This was a difficult paper to write, but I think that, in the end, it was well worth the effort.

We are still investigating the spherical Sun (the gravitational field of the real Sun deviates ever so slightly from spherical symmetry, and that can, or rather it will, have measurable effects) and we are still considering a stationary target (as opposed to a planet with changing illumination and surface features) but in this paper, we now cover the entire image formation process, including models of what a telescope sees in the SGL’s focal region, how such observations can be stitched together to form an image, and how that image compares against the inevitable noise due to the low photon count and the bright solar corona.

We have had at least one cat in the house for nearly 24 years. More than one, for nearly 20 years.

Never before did I have a problem with cats and wires. And believe you me, I have plenty of wires in this house, especially in my study.

A few days ago, our cat Freddy overnight decided to attack my wired earbuds that I use with my desktop computer for Skype. He completely chewed through the (thin, rubbery, and I guess tasty) wire in several places, and eventually left the scene with his “trophy”, the separated earbuds.

Needless to say, I was not amused.

And then two days ago, while I was sitting on the porcelain throne in the little programmers’ room, I suddenly heard a loud noise from my study. A few seconds later, I heard my wife cry out in anguish: “Your mouse!”

Yup. The poor mouse, completely separated from its plug, was by then hanging from Freddy’s mouth as he was proudly exiting the scene.

Was I ever pissed. Before I even got downstairs, my wife locked Freddy in the downstairs powder room. I went there with the remnants of the mouse and impressed upon him just how angry I was. No, don’t worry, I did not harm Freddy. I would rather poke my eyes out first. I love the little guy dearly, but even if I didn’t, I do not harm living creatures. Darnit, I feel bad swatting fruit flies. I would most certainly not hurt a cat. But yell at him? Oh yes. Throwing the remnants of the mouse wire at him? Yes. Smashing the mouse in front of him showing just how upset I was? Absolutely.

When I left him in the sink with the remnants of the mouse, I think he knew. When I let him out of the powder room some time later, he was not afraid of me (much to my relief) but he remained very subdued. And when I was finally talking to him again the next day, he seemed relieved.

Will he stop chewing wires? I hope so. I am now liberally applying cat repellent to the wires on and under my desk and also around my servers. We are also giving Freddy snacks rich in fiber; cats supposedly don’t need fiber, but sometimes they do. And we will visit the vet soon for a checkup, just to be on the safe side.

Silly cat. What kind of a cat steals a mous… Oh wait.

A year ago today, I was looking forward to 2019 with skepticism. I expressed concern about a number of things. Not everything unfolded according to my expectations, and that’s good news. What can I say, I hope 2020 will continue the trend of defying pessimistic predictions.

• The political crisis in the United States continues to simmer with Trump’s impeachment, but it remains less dramatic than I feared;
• NATO and the EU remain intact for now, though unresolved issues remain;
• An orderly Brexit is now possible with Johnson’s election victory; I still think the Brits are shooting themselves in the foot with this idiocy, but an orderly Brexit may be the best possible outcome at this point;
• Sliding towards authoritarianism in places like Hungary and Poland remains a grave concern, but there is also pushback;
• Russia continues to muck up things in untoward ways, but there was no significant (e.g., military) escalation;
• China is ramping up its campaign against the Uyghurs with an ever widening system of concentration camps but there was no significant escalation with respect to their neighbors;
• Japan, sadly, resumed whaling, but so far I believe the impact is minimal;
• Brazil continues to wreak havoc in the rain forest, but there is pushback here as well;
• Lastly, Canada did have elections, but populism was crushed (for now at least) with the defeat of Maxime Bernier’s People’s Party.

And now here we are, entering the roaring twenties! A decade that will bring things like Prohibition and organized crime in the United States, institutionalized antisemitism in Hungary, the rise of fascism in Italy, the Great Depression… no, wait, that was a century ago. Here’s to hoping that humanity got a little wiser in the past 100 years.

Speaking of that century, my wife’s Mom and mine can now both tell us that they lived in every decade of a century, having been born in the 30’s and now living in the 20’s.

Very well, I’ve been had. I lost all my bitcoin savings.

Don’t worry, it was not much. Approximately 0.0113 bitcoins. Just over a hundred US dollars at current exchange rates. And it’s not like I didn’t know from the onset that something fishy was going on. Of course I was not planning to hand over my hundred bucks to a scam artist, but I figured the learning experience was worth the risk. I had no idea how things would play out, except for one thing: I knew I was not going to get richer, but my risk was limited to my meager bitcoin holdings.

Here is how it began. I became acquainted with an Neale H. Spark* on Quora. At first, we exchanged some private messages, in part about some of the answers I wrote. But soon, he started talking about the business he is in, cryptocurrency. He seemed legit: I looked him up. A cryptocurrency expert, member of a listed cryptocurrency company’s advisory board. He asked if I wanted to invest some bitcoins into cloud mining, because supposedly, I can make “8% a day”.

OK, red flags are up. Nobody, and I mean nobody, is paying you 8% daily interest. That this was a scam, of that I had no doubt, but I just couldn’t resist: I had to understand how the scheme worked.

It so happened that I actually had some bitcoins, those 0.0113 BTC, in a bitcoin wallet. So what the heck… let’s play along.

As soon as I agreed to become his victim (not that he called me that, mind you), this Mr. Spark kindly set up a “mining enabled” bitcoin account for me at blockchain.com. He provided me with all necessary details and soon enough, I was able to manage the account. I then transferred my bitcoin holdings from my other wallet to this one.

And within 24 hours, I received about 0.0008 bitcoins. And again, 24, 48, 72 hours later. I was told by Mr. Spark that this money is not completely free money: that there will be a “mining fee”, which sounded odd because how can they charge any fee to my bitcoin account? But you know what, let’s see what happens. Indeed, after about a week of regular, daily payments, four days ago I actually got charged about 0.0008 bitcoins. But the payments continued: after two more payments, my bitcoin holdings were getting close to double my initial investment.

Meanwhile, Mr. Spark called me several times on the phone. It was always a bad connection, suggesting to me that he was using a VoIP phone, but for what it’s worth, his calls came from a California number consistent with his place of residence. He was advising me that I should invest a lot more; that investors who put in a full bitcoin or more (that would be \$10,000 US) are doing much better. I told him that I’d think about it. He asked when I might make my decision. I said he’d be the first to know. He did not sound happy.

Indeed, the phone calls stopped and for the past two days, I received no e-mail notification of payments in my bitcoin wallet either. So earlier today, I went to check the wallet, and whoops: all my bitcoins are gone. The wallet has been zeroed out two days ago.

I sent this Mr. Spark a Quora message but I am not expecting a reply. On the other hand, I think I can reconstruct what actually happened, so my bitcoins were, after all, well spent: I did learn some intriguing details.

For starters, I am pretty certain that the Quora account doesn’t actually belong to the real Neale H. Spark. I tried to find information online about Mr. Spark but I was unable to locate a valid e-mail address or social media account. The person is undoubtedly real, mentioned in a 201█ press release by G█████ T███████████ as a newly minted member of their advisory board. But Mr. Spark seems like a rather private person with little visible online presence.

The Quora account was only created about a month ago. It has very low activity.

The aggressive sales tactics seemed odd from a noted expert, and represented another indication of fraud. But how exactly was the fraud committed?

Here is how. It all started when “Mr. Spark” kindly set up that “mining-enabled” Bitcoin wallet for me on blockchain.com. I knew something was not kosher (what exactly is a “mining enabled” account, pray tell?) but in my ignorance of the technical details of cryptocurrency wallets, I could not quite put my finger on it. When I received the account info, everything checked out and I was able to secure the account, restricting transactions with two-factor authentication and even by IP address.

However, unbeknownst to me, “Mr. Spark” must have copied down the blockchain.com wallet backup phrase: twelve words. The company warns me: Anyone with access to my backup phrase can access my funds. What I didn’t know is that the backup phrase can be used anywhere. They need not access the wallet through blockchain.com; with the appropriate cryptocurrency software, they can recreate the wallet and empty it.

Which means that my entire blockchain.com wallet was compromised from the onset. Never mind the steps that I took, setting up two-factor authentication and all… It was never really my wallet to begin with.

The big warning sign was when the crook first processed a “mining fee”. I did not understand the details, but I knew that something was wrong. No third party can take money from your bitcoin wallet, “mining enabled” or otherwise. Yet at the same time, I continued to receive small payments, so I was still waiting for the other shoe to drop.

I guess eventually “Mr. Spark” decided that I am unlikely to invest more into his scheme, but more likely, I was not his only or biggest victim. You don’t set up an elaborate scam like this, with a fake social media account, fake phone number and all to just steal a hundred bucks from someone. (That would be a less effective, and certainly more risky, way of making money than working at minimum wage.)

There is the usual, “if it’s too good to be true” lesson here: Nobody is going to pay you 8% interest a day. OK, I knew that. I also knew that cloud mining is a very risky proposition, the returns are not spectacular and fraud is rampant. I didn’t have to spend a hundred bucks to learn this.

But there is also a valuable technical lesson. I had zero experience with cryptocurrency wallets in the past, and thus I did not realize that anyone setting up the wallet basically has a permanent, irrevocable key to that wallet. And when a sum, however small, goes missing from your bitcoin wallet, it is a guaranteed indicator that the wallet is compromised.

There is also another other thing that I did not realize until today. Namely that the Spark account on Quora is almost certainly a fake, an impersonation. In fact, it was not until I actually asked myself, “how can this chap commit such fraud under his own name?” that I came up instantly with the obvious answer: he didn’t. Rather, a scamster used the name and credentials of a respectable but social media shy expert to set up shop and rip off his victims. That I did not think of this possibility earlier is a consequence of my prejudice. I had very low expectations to begin with, when it comes to people in the speculative cryptocurrency business. So neither the cheap VoIP line nor the pushy behavior raised additional red flags: I was wondering what scam the real Neale Spark was dragging me into, I did not expect to be dealing with an impostor.

*Name altered to protect the privacy and reputation of the person who was impersonated.

My favorite cartoons are Kliban’s cats, but the Dilbert comic strips represent a close second.

Today’s Dilbert offers a perfect demonstration why.

I could actually be the consultant that Dilbert’s pointy-haired boss is looking for. Over the years, I learned one very important thing about this business: As a consultant, my job is to offer my best advice to my customer, but then whatever decision they make, it’s theirs to make, not mine. My job is to continue supporting them to the best of my abilities.

In my career, I have seen customers make bad decisions that destroyed their projects. I offered my advice. When it was ignored, I did not take it personally. Neither that nor judging the customer are part of my job description. That is not to say that I do not feel regret, or that I did not often second-guess myself: Could I have offered better advice? Could I have been more convincing? Why was my advice not accepted?

But judging? Nope. That would be rather unprofessional.

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.

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.

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…