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

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

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

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

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

Take this figure from our paper, for instance:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Here are a few pictures.

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

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

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

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

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

And now he is gone.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Our vaccination appointment is booked. Yippie!

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

World, please say hello to Freddy.

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

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

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

My success story of the day involves two cups.

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

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

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

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

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

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

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

My beautiful wife is getting really good at this.

It is absolutely yummy for breakfast. Might work for lunch and dinner, too, if you ask me.

Yes, it has raisins in it. I love kalach with raisins.

I remembered something today. A set of playing cards.

I never had a card deck like this but some of my grade school classmates did. This was the (very) early 1970s in communist Hungary. It was through these cards that I first learned of the existence of luxury sports cars, supercars like Ferrari, racecars like Lotus.

It was cards like these:

These were not some imports from the decadent West. Not subtle imperialist propaganda. These cards were produced by the state-owned Playing Card Factory (yes, that was the name of the company!) and they were much coveted by many 7-year olds. Like me.

But now that I think back, it makes me wonder: Exactly what were they thinking? I mean, this was a bleeping communist dictatorship (of the goulash variety, but still). What on Earth did they think they were doing, these self-appointed masters of agitprop, poisoning our young, impressionable minds with such blatant Western consumerist propaganda?

Ah, the sweet irony.

Somebody just reminded me: Back in 1982-83 a friend of mine and I had an idea and I even spent some time building a simple simulator of it in PASCAL. (This was back in the days when a 699-line piece of PASCAL code was a huuuuge program!)

So it went like this: Operative memory (RAM) and processor are separate entities in a conventional computer. This means that before a computer can do anything, it needs to fetch data from RAM, then after it’s done with that data, it needs to put it back into RAM. The processor can only hold a small amount of data in its internal registers.

This remains true even today; sure, modern processors have a lot of on-chip cache but conceptually, it is still separate RAM, it’s just very fast memory that is also physically closer to the processor core, requiring less time to fetch or store data.

But what if we abandon this concept and do away with the processor altogether? What if instead we make the bytes themselves “smart”?

That is to say what if, instead of dumb storage elements that can only be used to store data, we have active storage elements that are minimalist processors themselves, capable of performing simple operations but, much more importantly, capable of sending data to any other storage element in the system?

The massive number of required interconnection between storage elements may appear like a show-stopper but here, we can borrow a century-old concept from telephony: the switch. Instead of sending data directly, how about having a crossbar-like interconnect? Its capacity will be finite, of course, but that would work fine so long as most storage elements are not trying to send data at the same time. And possibly (though it can induce a performance penalty) we could have a hierarchical system: again, that’s the way large telephone networks function, with local switches serving smaller geographic areas but interconnected into a regional, national, or nowadays global telephone network.

Well, that was almost 40 years ago. It was a fun idea to explore in software even though we never knew how it might be implemented in hardware. One lesson I learned is that programming such a manifestly parallel computer is very difficult. Instead of thinking about a sequence of operations, you have to think about a sequence of states for the system as a whole. Perhaps this, more than any technical issue, is the real show-stopper; sure, programming can be automated using appropriate tools, compilers and whatnot, but that just might negate any efficiency such a parallel architecture may offer.

Then again, similar ideas have resurfaced in the decades since, sometimes on the network level as massively parallel networks of computers are used in place of conventional supercomputers.

Gotta love the Y2K bug in the header, by the way. Except that it isn’t. Rather, it’s an implementation difference: I believe the PDP-11 PASCAL that we were using represented a date in the format dd-mm-yyyy, as opposed to dd-MMM-yyyy that is used by this modern Pascal-to-C translator. As I only allocated 10 characters to hold the date in my original code, the final digit is omitted. As for the letters "H J" that appear on top, that was just the VT-100 escape sequence to clear the screen, but with the high bit set on ESC for some reason. I am sure it made sense on the terminals that we were using back in 1982, but xterm just prints the characters.

The next in our series of papers describing the extended gravitational lens (extended, that is, in that we are no longer treating the lensing object as a gravitational monopole) is now out, on arXiv.

Here’s one of my favorite images from the paper, which superimposes the boundary of the quadrupole caustic (an astroid curve) onto a 3D plot showing the amplitude of the gravitational lens’s point-spread function.

I was having lots of fun working on this paper. It was, needless to say, a lot of work.

Every once in a while, strange coincidences occur that make me wonder if we live in a simulation after all.

Take today. Just moments ago, I ran across a tweet by Trump’s former director of communications (for 10 days), Anthony Scaramucci:

I found the reference to Max Headroom amusing; it’s been a while since I last saw any mention of this once iconic television series (which I happened to like very much.)

But then, no more than two minutes later, I ran across a Quora question that I was asked to answer, only to find an existing answer (good one, incidentally) that begins with a quote:

What exactly are the odds that I run across two completely unrelated Max Headroom references within minutes of each other?

Of course the fact that Max Headroom was an AI personality living its own virtual existence is just icing on the proverbial cake…

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.