Apparently, a growing number of people are framing the question concerning Russia’s war in Ukraine in terms of peace vs. justice. Peace would mean some kind of a settlement to end the fighting now, even if it means granting, e.g., territorial concessions to Russia to avoid humiliating Putin. In contrast, continuing to fight for Ukraine’s liberation is about justice.

In my view, it is dangerously wrong to present Russia’s war of aggression in these terms. Peace without justice is simply not possible. Believing otherwise amounts to repeating the tragic errors of 1938: When Britain’s Prime Minister, Neville Chamberlain, triumphantly returned from the Munich conference carrying a document with Hitler’s signature, declaring that he brought “peace for our time”.

We all know how “our time” lasted. The grand total of 11 months.

That’s what peace without justice looks like. A despot like Putin is only encouraged by what he sees as weakness, signs of the cowardly decadence of the West. And just as he has now done repeatedly (!) in the past, he will happily ignore any agreement he signs today once he sees an opportunity, once he thinks that conditions are in his favor.

No. We must categorically reject such compromise. Much as we desire peace, we must not confuse lasting, robust peace with an armistice that only allows the despot to regroup, learn from his lessons, and start his aggression anew at the first viable opportunity. And his success might encourage other nations to resort to armed aggression, knowing that the West is too weak, too divided to stand up against them.

It is an unfortunate fact of human history that sometimes the shortest, surest route to “peace for our time” is through the battlefield. I wish the war stopped right now, with no more suffering, no more destruction, no more killing. But if the price we will likely pay is a greater, deadlier war tomorrow, I’d rather we do what it takes to avoid it.

And yes, I recognize that it’s easy for me to say these things from the comfort of an armchair in a peaceful city many thousands of miles away from Ukraine. But you know what? It’s also easy to speculate about these things in Washington or Brussels. How about we ask the Ukrainians? Do they want peace now, even with concessions? Or do they prefer to liberate their homeland and ensure that the Russians will be in no mood to attack again anytime soon?

Because this, after all, is the other lesson of 1938. Nobody asked the Czechs. The decision was made by the great powers without consulting those who would actually be paying the price in blood.

It’s been a while since I last presented to the world our cat, Master Rufus.

News on CNN: Apparently hundreds of thousands of Ukrainians are now in “filtration camps” in Russia. That is to say, concentration camps.

Make no mistake about it, this is just the beginning of evil. As the West continues to flirt with various forms of authoritarianism or illiberalism, Russia has gone full-blown Nazi, with a war of conquest, severe oppression at home, an idolized leader and a national ideology of predestined greatness held back only by some evil international conspiracy.

Our only hope… ONLY hope is that they remain as incompetent and as corrupt as they are, with an ill-prepared military using substandard training and equipment as monies have been syphoned away to finance the oligarchs’ superyachts, and with a Ukrainian nation more capable of defending itself against this horrific aggression than anyone thought possible.

But so long as we have elder statesmen like Kissinger advocating a Munich-style appeasement, the world remains in danger. Bullies cannot be appeased; it just encourages them to come back and ask for more. Kissinger, of all people, should be intimately aware of this lesson of history.

And even if escalation is avoided, the fallout of the conflict, especially the looming global food crisis, can be devastating.

All it takes is a couple of generations to forget the lessons of history and start anew. So we keep making the same mistakes over and over again.

From time to time, I promise myself not to respond again to e-mails from strangers, asking me to comment on their research, view their paper, offer thoughts.

Yet from time to time, when the person seems respectable, the research genuine, I do respond. Most of the time, in vain.

Like the other day. Long story short, someone basically proved, as part of a lengthier derivation, that general relativity is always unimodular. This is of course manifestly untrue, but I was wondering where their seemingly reasonable derivation went awry.

Eventually I spotted it. Without getting bogged down in the details, what they did was essentially equivalent to proving that second derivatives do not exist:

$$\frac{d^2f}{dx^2} = \frac{d}{dx}\frac{df}{dx} = \frac{df}{dx}\frac{d}{df}\frac{df}{dx} = \frac{df}{dx}\frac{d}{dx}\frac{df}{df} = \frac{df}{dx}\frac{d1}{dx} = 0.$$

Of course second derivatives do exist, so you might wonder what’s happening here. The sleight of hand happens after the third equal sign: swapping differentiation with respect to two independent variables is permitted, but $$x$$ and $$f$$ are not independent and therefore, this step is illegal.

I pointed this out, and received a mildly abusive comment in response questioning the quality of my mathematics education. Oh well. Maybe I will learn some wisdom and refrain from responding to strangers in the future.

This morning, Google greeted me with a link in its newsstream to a Hackaday article on the Solar Gravitational Lens. The link caught my attention right away, as I recognized some of my own simulated, SGL-projected images of an exo-Earth and its reconstruction.

Reading the article I realized that it appeared in response to a brand new video by SciShow, a science-oriented YouTube channel.

Yay! I like nicely done videos presenting our work and this one is fairly good. There are a few minor inaccuracies, but nothing big enough to be even worth mentioning. And it’s very well presented.

I suppose I should offer my thanks to SciShow for choosing to feature our research with such a well-produced effort.

Saturday afternoon was stormy. The lights flickered a bit during the storm, my UPSs came online several times. But then the storm left, and everything was back to normal.

At least here in Lowertown.

I didn’t check the news, so it was not until later Sunday that I learned, from a social media post from a friend who has been without power since, just how bad things really got.

And how bad they still are.

Hydro Ottawa’s map is still mostly red. Now “only” about 130,000 customers are affected, which is certainly less than the peak of well over 170,000, but to put that into perspective, Hydro Ottawa has a total of less than 350,000 customers; that means that at one point, more than half the city was without power.

As a Hydro official said on CTV News tonight, their distribution system is crushed.

And then there are all the downed trees, destroyed traffic lights, not to mention severely damaged homes and businesses. Not quite a like a war zone (of which we had seen plenty on our TV screens, courtesy of Mr. Putin’s “special military operation” in Ukraine) but close.

And of course the damage doesn’t stop at Hydro Ottawa’s borders: Hundreds of thousands more are without power in Eastern Ontario and also Quebec.

Dear Russia,

In the wake of Finland’s imminent decision to join NATO, you threaten again. You present yourself as the victim of aggression by Nazis.

So let’s take stock. Who did what in Europe since 1945?

In 1953, you used your military force to crush an uprising against hardline communist tyranny in East Germany.

In 1956, you did the same thing in Budapest, inflicting severe damage on my city of birth, still recovering from the devastations of WW2.

In 1968, you crushed the Prague Spring with tanks.

Kudos to you: You refrained from the direct use of military force in Poland in 1980, though you supported the regime that imposed martial law.

After the Soviet collapse, as the newly independent Russian Federation you supported separatists in the Transnistria region of Moldova.

You waged not one but two wars in Chechnya in the 1990s, with tens of thousands killed and cities like Grozny leveled.

In 2008, you launched a war against Georgia, seizing territory and creating two phony mini-republics.

In 2014, you launched another war, against Ukraine, seizing the Crimea and parts of the Donetsk and Luhansk regions, creating a permanent war zone, even shooting down a civilian airliner that flew over the area on a scheduled route.

And now you attempted a full-scale war, hoping to decapitate Ukraine, Blitzkrieg-style, and resorting to horrific, genocidal tactics of purposefully targeting civilians when your ineptitude and Ukrainian resistance thwarted your plans.

But you are the good guys. I get it. Meanwhile, what did evil, imperialist, Nazi NATO do? How many times were you attacked by NATO nations? What territories were seized by NATO?

Oh, I get it. NATO bombed Belgrade. Never mind that the goal was not to seize territory or even change a regime, simply to stop the (now well-documented) ongoing genocide in Kosovo. Because, I get it, that’s what Nazis do: they stop genocide. And you, the good guys?

This video speaks for itself.

Still wondering why Finland is keen on joining NATO?

They don’t want to end up like this hapless car dealership owner and his security guard.

Killed by Putler’s Russist thugs.

It’s now Monday, May 9, 2022. And it is an anniversary of sorts.

No I am not talking about Putin and his planned “victory” parade, as he is busy desecrating the legacy of the Soviet Union’s heroic fight in the Great Patriotic War against a genocidal enemy.

I am referring to something much more personal. This sentence:

I watched The Matrix, for the first time. I’ve seen Dark City, and I loved it. I have heard all sorts of bad things about The Matrix, so I had low expectations. I was pleasantly surprised. Maybe not as well done as Dark City, it was nevertheless a surprisingly intelligent movie for a blockbuster.

Not very profound or insightful, is it.

But it happens to be my first ever blog entry, written when I still refused to call a blog a “blog”, calling it instead my “Day Book”, in the tradition of the late Jerry Pournelle.

So there. Will I be around twenty years from now? Perhaps more pertinently, will the world as we know it still be around?

What can I say? I am looking forward to marking the 40th anniversary of my blog on May 9, 2042, with another blog entry, hopefully celebrating a decent, prosperous, safe, mostly peaceful world.

There are things I am learning about the Roman Empire that I never knew. What a magnificent society it really was.

For instance, the Romans were not only master builders of sewers and roads, but also invented traffic management. Julius Caesar restricted the use of private vehicles to the last two hours of daylight. Business deliveries had to be made at night.

The Embattled Driver in Ancient Rome

What blew me away, however, was their use of… plumbing? I mean, aqueducts are one thing, but to have bona fide valves, water faucets in businesses and homes? Now that blew me away.

And speaking of sewers, the Romans might have been master sewer builders but it appears some form of a sewer system may have existed almost ten thousand (!!!) years earlier in a settlement in Anatolia. That’s just… wow.

A beautiful study was published the other day, and it received a lot of press coverage, so I get a lot of questions.

This study shows how, in principle, we could reconstruct the image of an exoplanet using the Solar Gravitational Lens (SGL) using just a single snapshot of the Einstein ring around the Sun.

The problem is, we cannot. As they say, the devil is in the details.

Here is a general statement about any conventional optical system that does not involve more exotic, nonlinear optics: whatever the system does, ultimately it maps light from picture elements, pixels, in the source plane, into pixels in the image plane.

Let me explain what this means in principle, through an extreme example. Suppose someone tells you that there is a distant planet in another galaxy, and you are allowed to ignore any contaminating sources of light. You are allowed to forget about the particle nature of light. You are allowed to forget the physical limitations of your cell phone’s camera, such as its CMOS sensor dynamic range or readout noise. You hold up your cell phone and take a snapshot. It doesn’t even matter if the camera is not well focused or if there is motion blur, so long as you have precise knowledge of how it is focused and how it moves. The map is still a linear map. So if your cellphone camera has 40 megapixels, a simple mathematical operation, inverting the so-called convolution matrix, lets you reconstruct the source in all its exquisite detail. All you need to know is a precise mathematical description, the so-called “point spread function” (PSF) of the camera (including any defocusing and motion blur). Beyond that, it just amounts to inverting a matrix, or equivalently, solving a linear system of equations. In other words, standard fare for anyone studying numerical computational methods, and easily solvable even at extreme high resolutions using appropriate computational resources. (A high-end GPU in your desktop computer is ideal for such calculations.)

Why can’t we do this in practice? Why do we worry about things like the diffraction limit of our camera or telescope?

The answer, ultimately, is noise. The random, unpredictable, or unmodelable element.

Noise comes from many sources. It can include so-called quantization noise because our camera sensor digitizes the light intensity using a finite number of bits. It can include systematic noises due to many reasons, such as differently calibrated sensor pixels or even approximations used in the mathematical description of the PSF. It can include unavoidable, random, “stochastic” noise that arises because light arrives as discrete packets of energy in the form of photons, not as a continuous wave.

When we invert the convolution matrix in the presence of all these noise sources, the noise gets amplified far more than the signal. In the end, the reconstructed, “deconvolved” image becomes useless unless we had an exceptionally high signal-to-noise ratio, or SNR, to begin with.

The authors of this beautiful study knew this. They even state it in their paper. They mention values such as 4,000, even 200,000 for the SNR.

And then there is reality. The Einstein ring does not appear in black, empty space. It appears on top of the bright solar corona. And even if we subtract the corona, we cannot eliminate the stochastic shot noise due to photons from the corona by any means other than collecting data for a longer time.

Let me show a plot from a paper that is work-in-progress, with the actual SNR that we can expect on pixels in a cross-sectional view of the Einstein ring that appears around the Sun:

Just look at the vertical axis. See those values there? That’s our realistic SNR, when the Einstein ring is imaged through the solar corona, using a 1-meter telescope with a 10 meter focal distance, using an image sensor pixel size of a square micron. These choices are consistent with just a tad under 5000 pixels falling within the usable area of the Einstein ring, which can be used to reconstruct, in principle, a roughly 64 by 64 pixel image of the source. As this plot shows, a typical value for the SNR would be 0.01 using 1 second of light collecting time (integration time).

What does that mean? Well, for starters it means that to collect enough light to get an SNR of 4,000, assuming everything else is absolutely, flawlessly perfect, there is no motion blur, indeed no motion at all, no sources of contamination other than the solar corona, no quantization noise, no limitations on the sensor, achieving an SNR of 4,000 would require roughly 160 billion seconds of integration time. That is roughly 5,000 years.

And that is why we are not seriously contemplating image reconstruction from a single snapshot of the Einstein ring.

I am beginning to wonder if the American political system is truly broken beyond repair.

I wonder what this means for Canada. No change? Will we become a safe haven for refugees from Gilead, as in The Handmaid’s Tale? Or will we be this new America’s Ukraine?

I am afraid that we will find out.