A few days ago, I posted an old Far Side cartoon about an accident at a virology lab. It was intended as humor, appropriate in light of the announcement that the US government seeks additional information concerning the possible role of the Wuhan virology lab in the pandemic. This investigation was triggered by the revelation that back in November 2019, researchers from that lab became sick with symptoms similar to those of CODID-19, compounded by secrecy by the Chinese government.

I think this investigation is warranted. I do not prejudge its outcome.

I do feel it is important to mention, however, that there is a difference between engineering a virus vs. releasing a virus. The fact that COVID-19 is not an engineered virus was well-established early on. Conclusions can of course change in the light of new information but I don’t think there is much room for change here. It has all the hallmarks of a virus that jumped from animals to humans (which such viruses, I am told, often do) and none of the hallmarks of a bioengineered virus. So I think in light of that it is quite unlikely that the virus was the result of, e.g., a botched bioweapons experiment or worse yet, an intentional pandemic.

Could it have been accidentally released? That’s another story altogether. The mandate of the Wuhan lab, I understand, is to research illnesses such as SARS or COVID-19. This lab produced many research papers over the years warning the world that a much more serious pandemic than the SARS epidemic is possible, even likely. Those papers were prophetic, but largely unheeded. It would be ironic if the same lab was found responsible in the end for causing the very pandemic that it tried to help prevent, and if the Chinese government played a role in suppressing information that, early on, could have saved many lives, they should be held responsible.

But for now, we don’t know if any of this is true. The Far Side cartoon was not intended to imply anything. It is just… funny, and uncannily prophetic. Just like the Wuhan lab’s research papers from years past.

Thanks to a share on Facebook, I now know exactly what happened in Wuhan in November, 2019.

This.

Sweet dreams…

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.

No, it’s not one of my cats posting a blog entry.

Rather, it’s a whimsical title someone gave to the following composition:

I started my day listening to this. I am still smiling. I think it sounds a little bit like Klingon opera, or perhaps like a piano piece written by a Klingon composer. But it’s not bad, not bad at all.

I was watching a documentary on Netflix and a photo caught my attention. A beautiful, old photograph (shown in color in the documentary, but I suspect it was colorized, so I am including a black-and-white version instead that I found online) showing a young mother and her child, along with a stuffed toy animal:

This photo depicts the sister of Setsuko Thurlow (née Nakamura), a Japanese-Canadian peace activist, herself a survivor of the Hiroshima atomic bomb.

Unfortunately, her sister Ayako was not that lucky. She and her young son Eiji were badly burnt and soon perished.

I get it why the atomic bomb was deemed necessary. With everything I know today, I still would not, could not have made a decision different from that made by Harry Truman back in July, 1945 even if it meant that I could not ever sleep soundly afterwards throughout the remainder of my life. Not with some 10,000 people, most of them civilians, dying in the Pacific theater every day of the war.

Even so… War is horrifying.

Strangely, it’s the toy animal that humanized this picture for me more than anything else.

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.