Well, that would be Victor Gabriel Toth, not me, but nonetheless, it is still creepy to see an obituary in the Ottawa Citizen containing, albeit with a minor spelling variation, my name.

I never met this Victor Toth, even though at one point, I was told, I might have been working just two floors above him at the Nortel building on Merivale Road, a building in which several floors were rented by Canada Post.

Well, Victor Toth, you had a long life and, I hope sincerely, a happy one. I hope your family is not so much grieving as celebrating your long life.

Then again, I also sincerely hope that I won’t be following in your footsteps anytime soon, as I have plenty more to do in this world before it’s my time to depart.

Yesterday, we said goodbye to our old car, a very nice Honda Accord that served us faithfully for four years.

The lease expired, so we opted to lease a new one. Another Honda Accord. (Incidentally, 2018 marks the 30th year that I’ve been purchasing Hondas, from this very same dealership.)

The old car was nice. The new car… Well, it’s amazing what even four years can mean these days when it comes to vehicle automation.

The level of automation in this vehicle is amazing. It can start itself, it can steer itself. It has full situational awareness, with radar all around. Apparently, it even monitors the driver for alertness (I’ll have to read up on exactly how it accomplishes that.) During the short drive home, it once applied the brakes when its adaptive cruise control was on and someone moved into the lane ahead of us. It was braking a little harder than I’d have preferred, though. And at one point, as the lane markings were a little ambiguous, it gently resisted my attempt to depart from what it thought was the correct lane.

In principle, it appears, this car has all the components for it to be fully autonomous, except that perhaps its array of sensors is not sufficient for it to be fully safe. But really, the only thing missing is the software. And even the way it is, it is beginning to feel more like a partner in driving than a dumb machine; a partner that also has a well-developed instinct for self-preservation.

Welcome to the future, I guess.

What can I say?

Shit. Hitting. Fan.

A couple of statements from the past 24 hours:

If there is a strike by the Americans, then…the missiles will be downed and even the sources from which the missiles were fired.” – Russian Ambassador to Lebanon Alexander Zasypkin, on Hezbollah’s al-Manar TV.

Russia vows to shoot down any and all missiles fired at Syria. Get ready Russia, because they will be coming, nice and new and “smart!” You shouldn’t be partners with a Gas Killing Animal who kills his people and enjoys it!” – United States president Donald J. Trump, on Twitter.

Suddenly, I have this almost irresistible urge to grab a shovel and start digging a fallout shelter.

While I still can.

A headline on Euronews caught my attention earlier today: Syria: A bigger role for the EU?

Good, thought I. The Russians might not like it though, thought I. But that’s okay, as a matter of fact, it might help bring rogue EU countries like Hungary in line, thought I. It might help presenting a united front against an increasingly ill-behaved Russia.

And then I caught myself, as I realized that I just rediscovered a truth that is as old as civilization itself: how conflict, the threat of war, or war itself can unite a people.

You know what? Much as I like the great European experiment, much as I cherish the fact that my once worthless Hungarian passport grants me European citizenship, if the price of keeping it together is more involvement in conflicts like Syria, it might not be worth it.

The recent discovery of a galaxy, NGC1052-DF2, with no or almost no dark matter made headlines worldwide.

 Nature 555, 629–632 (29 March 2018)

Somewhat paradoxically, it has been proclaimed by some as evidence that the dark matter paradigm prevails over theories of modified gravity. And, as usual, many of the arguments were framed in the context of dark matter vs. MOND, as if MOND was a suitable representative of all modified gravity theories. One example is a recent Quora question, Can we say now that all MOND theories is proven false, and there is really dark matter after all? I offered the following in response:

First of all, allow me to challenge the way the question is phrased: “all MOND theories”… Please don’t.

MOND (MOdified Newtonian Dynamics) is not a theory. It is an ad hoc, phenomenological replacement of the Newtonian acceleration law with a simplistic formula that violates even basic conservation laws. The formula fits spiral galaxy rotation curves reasonably well, consistent with the empirical Tully—Fisher law that relates galaxy masses and rotational velocities, but it fails for just about everything else, including low density globular clusters, dwarf galaxies, clusters of galaxies, not to mention cosmological observations.

MOND was given a reprieve in the form of Jacob Beckenstein’s TeVeS (Tensor—Vector—Scalar gravity), which is an impressive theoretical exercise to create a proper classical field theory that reproduces the MOND acceleration law in the weak field, low velocity limit. However, TeVeS suffers from the same issues MOND does when confronted with data beyond galaxy rotation curves. Moreover, the recent gravitational wave event, GW170817, accompanied by the gamma ray burst GRB170817 from the same astrophysical event, thus demonstrating that the propagation speed of gravitational and electromagnetic waves is essentially identical, puts all bimetric theories (of which TeVeS is an example) in jeopardy.

But that’s okay. News reports suggesting the death of modified gravity are somewhat premature. While MOND has often been used as a straw man by opponents of modified gravity, there are plenty of alternatives, many of them much better equipped than MOND to deal with diverse astrophysical phenomena. For instance, f(R) gravity, entropic gravity, Horava—Lifshitz gravity, galileon theory, DGP (Dvali—Gabadadze—Porrati) gravity… The list goes on and on. And yes, it also includes John Moffat’s STVG (Scalar—Tensor—Vector Gravity — not to be confused with TeVeS, the two are very different animals) theory, better known as MOG, a theory to which I also contributed.

As to NGC1052-DF2, for MOG that’s actually an easy one. When you plug in the values for the MOG approximate solution that we first published about a decade ago, you get an effective dynamical mass that is less than twice the visible (baryonic) mass of this galaxy, which is entirely consistent with its observed velocity dispersion.

In fact, I’d go so far as to boldly suggest that NGC1052-DF2 is a bigger challenge for the dark matter paradigm than it is for some theories of modified gravity (MOG included). Why? Because there is no known mechanism that would separate dark matter from stellar mass.

Compare this to the infamous Bullet Cluster: a pair of galaxy clusters that have undergone a collision. According to the explanation offered within the context of the dark matter paradigm (NB: Moffat and Brownstein showed, over a decade ago, that the Bullet Cluster can also be explained without dark matter, using MOG), their dark matter halos just flew through each other without interaction (other than gravity), as did the stars (stars are so tiny compared to the distance between them, the likelihood of stellar collisions is extremely remote, so stars also behave like a pressureless medium, like dark matter.) Interstellar/intergalactic clouds of gas, however, did collide, heating up to millions of degrees (producing bright X-rays) and losing much of their momentum. So you end up with a cloud of gas (but few stars and little dark matter) in the middle, and dark matter plus stars (but little gas) on the sides. This separation process works because stars and dark matter behave like a pressureless medium, whereas gas does not.

But in the case of NGC1052-DF2, some mechanism must have separated stars from dark matter, so we end up with a galaxy (one that actually looks nice, with no signs of recent disruption). I do not believe that there is currently a generally accepted, viable candidate mechanism that could accomplish this.

I just came across this delightful drawing on Twitter. It’s from a Franck D. Nijimbere (@nijfranck). I don’t know if it is his original creation or if he found it elsewhere, but it describes a situation in life with which I am more thoroughly familiar than I care to admit.

Nijimbere’s caption: “When the deadline comes too close…”

Yes. I’ve been there way too many times <sigh>.

I just read that Elon Musk nixed Tesla’s and SpaceX’s Facebook pages.

Much as I admire Musk, I will not follow his example. I am not planning to delete my Facebook account.

Facebook is not the problem. It is a symptom.

The actual problem is much broader. The Internet that brought us together is also responsible for creating fragmented communities, echo chambers if you wish. When our primary source of news is like-minded people, memes and links we exchange with each other, often uncritically, without checking their veracity, there is a problem. It makes no difference if the content delivery vehicle is Facebook, Twitter, plain old e-mail or anything else.

I am not going to give up the opportunity offered by Facebook to stay in touch with old friends, with classmates I have not seen in years if not decades, with other people I would not even know were it not for the Internet. This is priceless.

But when I want to get informed about the world, I do not turn to Facebook. I do not forward memes. I might give a perfunctory “Like” to something that appears in my feed, but I do not believe it without checking first. And most importantly, I use other sources to keep myself informed.

Yet I fear the problem is even greater than this, and once again, ditching Facebook may be precisely the wrong answer. I recall what it was like when I was growing up in Hungary in the 1960s, 1970s. We had one national television channel. (OK, make that one-and-a-half, because there was a Channel 2, but with only a very short broadcast day in the evenings, initially, only a few days a week. And on Mondays, both channels were off the air.) This means that we all watched the same things. No matter which part of the country, which walk of life you came from, you knew the same television personalities I knew, you heard the same jokes, you watched the same drama.

It was probably never quite like this in North America, where there were always a multitude of channels since the dawn of television. Still, back in the old days, “multitude” meant maybe a half dozen choices if you were in a major metro area. So the shared cultural experience was still there. Not anymore. And never mind television, with hundreds of cable and satellite channels and numerous online alternatives. On top of that comes social media, with its propensity to create microcommunities.

Again, the problem is not that you stay in touch with your circle of friends. That’s great! The problem is that your circle of friends becomes your primary source of news and views about the world. You reinforce each other’s beliefs, making it harder and harder to contemplate alternative viewpoints.

So keep Facebook. Do stay in touch with old friends or distant family members. But for heaven’s sake, don’t use Facebook to inform yourself. Ditch the memes. Stop sharing anything other than cute cat pictures. And be the most suspicious when you see something that you are inclined to believe. It’s not the lies and deceptions you hate that are the most dangerous; it is the lies and deceptions that you are most likely to believe that will fool you. This is something state-sponsored Russian trolls know all too well.

Our kitty Pipacs is still doing okay.

Today, he managed to show the oddest of faces when my wife attempted to take a picture:

Don’t worry, he was just yawning.

What we haven’t seen is any poop from him in the past 36 hours or so, and he seemed to be a bit under the weather at times. I hope it doesn’t mean that his bowel is obstructed again. We know he’s living on borrowed time, but we hope that there is still a little bit more time out there for him to borrow.

Every once in a while, my hopes, or perhaps delusions, that we live in a less dark world, are crushed.

This was the case moments ago, when I watched this undercover report by Channel 4 about Cambridge Analytica.

The company’s excuses, shown at the end of the report, are especially pathetic. “No, Mr. Policeman,” says the petty thief, “I wasn’t trying to steal that item when you caught me red-handed, I was just testing the security of the merchant.”

Yeah, right.

Breaking news on CNN: Another school shooting in America.

My only problem with CNN’s reporting is… why do they call this “Breaking News”?

That label should be reserved for news that is, well, unexpected and breaking. School shootings happen with such regularity, they should be part of CNN’s regularly scheduled programming.

Anybody interested in hiring a competent TV repairman?

No, just kidding. Nobody makes a living from TV repair anymore. (On the other hand, if you are interested in hiring a competent IT contract professional… but I digress.)

Still, I have this compulsion, trying to repair broken things even when they have little or no practical utility. So it came to be that I felt compelled to repair this old SANYO AVM-2664U analog 26″ CRT TV, with a circuit board that was buzzing louder than a hive of angry wasps, as shown in this thermal infrared video which I made while I was hunting for possible hotspots on the circuit board:

Eventually, I managed to track down the problem: One lousy little capacitor.

As I told my wife, it would be fun, doing this for a living. Unfortunately, nobody is likely to pay hundreds, maybe even thousands of dollars to repair an old television set that not even thrift stores want anymore (too heavy, too obsolete). Yet another perfectly useless skill in the year 2018.

Stephen Hawking died earlier today.

Hawking was diagnosed with ALS in the year I was born, in 1963.

Defying his doctor’s predictions, he refused to die after a few years. Instead, he carried on for another astonishing 55 years, living a full life.

Public perception notwithstanding, he might not have been the greatest living physicist, but he was certainly a great physicist. The fact that he was able to accomplish so much despite his debilitating illness made him an extraordinary human being, a true inspiration.

Here is a short segment, courtesy of CTV Kitchener, filmed earlier today at the Perimeter Institute. My friend and colleague John Moffat, who met Hawking many times, is among those being interviewed:

Very well, having grown up in a police state of sorts myself, I know I should not take these things lightly. There are plenty of political prisoners in China, and now that Xi declared himself president for life, I expect things to get worse, not better.

Still… I could not help myself, I was laughing out loud as I read the story of an elderly Chinese woman who took revenge of a fortune teller because contrary to his predictions, she did live to see 2018 after all.

According to the South China Morning Post, Mrs. Wang ran into the fortune teller in a park and in her anger, she started vandalizing his stall. But then, “[a] police officer intervened and asked the fortune-teller to apologise to Wang for causing mental suffering.”

Thank you, Mr. anonymous Chinese police officer, for doing exactly what a sensible person should have done. Good to know that common sense is still alive and well in some parts of the world.

There is a very interesting concept in the works at NASA, to which I had a chance to contribute a bit: the Solar Gravitational Telescope.

The idea, explained in this brand new NASA video, is to use the bending of light by the Sun to form an image of distant objects.

The resolving power of such a telescope would be phenomenal. In principle, it is possible to use it to form a megapixel-resolution image of an exoplanet as far as 100 light years from the Earth.

The technical difficulties are, however, challenging. For starters, a probe would need to be placed at least 550 astronomical units (about four times the distance to Voyager 1) from the Sun, precisely located to be on the opposite side of the Sun relative to the exoplanet. The probe would then have to mimic the combined motion of our Sun (dragged about by the gravitational pull of planets in the solar system) and the exoplanet (orbiting its own sun). Light from the Sun will need to be carefully blocked to ensure that we capture light from the exoplanet with as little noise as possible. And each time the probe takes a picture of the ring of light (the Einstein ring) around the Sun, it will be the combined light of many adjacent pixels on the exoplanet. The probe will have traverse a region that is roughly a kilometer across, taking pictures one pixel at a time, which will need to be deconvoluted. The fact that the exoplanet itself is not constant in appearance (it will go through phases of illumination, it may have changing cloud cover, perhaps even changes in vegetation) further complicates matters. Still… it can be done, and it can be accomplished using technology we already have.

By its very nature, it would be a very long duration mission. If such a probe was launched today, it would take 25-30 years for it to reach the place where light rays passing on both sides of the Sun first meet and thus the focal line begins. It will probably take another few years to collect enough data for successful deconvolution and image reconstruction. Where will I be 30-35 years from now? An old man (or a dead man). And of course no probe will be launched today; even under optimal circumstances, I’d say we’re at least a decade away from launch. In other words, I have no chance of seeing that high-resolution exoplanet image unless I live to see (at least) my 100th birthday.

Still, it is fun to dream, and fun to participate in such things. Though now I better pay attention to other things as well, including things that, well, help my bank account, because this sure as heck doesn’t.

Saturday evening, the President of the United States, Donald J. Trump talked to some Republicans behind closed doors. But a recording has been leaked.

Here is what Mr. Trump said, among other things, in response to Xi Jinping turning China back to strongman rule by removing term limits from China’s constitution: “He’s now president for life. President for life. No, he’s great,” Trump said. “And look, he was able to do that. I think it’s great. Maybe we’ll have to give that a shot some day.

Having read, and then heard, these words, I was filled with a combination of dread, disgust, despair and revulsion.

Fuck you, Trump. Fuck you, Republican cheerleaders who sacrifice everything sacred for party loyalty and for power.

Forgive my vulgar outburst but this crossed a line. This REALLY crossed a line. I grew up in a communist state, not on a freaking golf course courtesy of rich daddy, like this megalomaniac asshole who has no idea what he is idiotically blabbering about, cheering on a commie dictator because apparently he, too, would love to be president for life.

I think that with this statement, Trump abdicated the informal position of “leader of the free world”. A true leader of the free world would never cheer on a commie dictator, not even as a tasteless joke. He may be America’s President, but with these words, he has declared himself an enemy of the world that I call free.

To my American friends who believe Trump is doing a good job protecting the US economy: I think it is telling that US stock markets are hurting more today than their Canadian counterparts, despite the fact that Canada is the primary target of Trump’s proposed steel and aluminum tariffs:

What can I say. Be careful what you wish for. And we have not even discussed how Canada (or Europe) might retaliate. But in the end, we will all be losers, no matter what the narcissistic idiot in the White House thinks about the wonderful job that he is doing.

I am playing with JavaScript and HTML5. Three-dimensional transformations.

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CNN
Cable News Network

It's more fun than I thought. And gives a whole new meaning to the word, "spin", as I am listening to CNN.

No, it isn’t Friday yet.

But it seems that someone at CTV Morning Live wishes it was. Why else would they have told us that yesterday, February 28, was a Thursday? (Either that or they are time travelers from 2019.)

Then again, maybe I should focus on what they are actually saying, not on a trivial mistake they made: that even as parts of Europe that rarely see snow are blanketed by the white stuff, places in Canada and Siberia see unprecedented mild weather. A fluke or further evidence of climate change disrupting the polar vortex?

Enough of politics and cats. Time to blog about math and physics again.

Back in my high school days, when I was becoming familiar with calculus and differential equations (yes, I was a math geek) something troubled me. Why were certain expressions called “linear” when they obviously weren’t?

I mean, an expression like $$Ax+B$$ is obviously linear. But who in his right mind would call something like $$x^3y + 3e^xy+5$$ “linear”? Yet when it comes to differential equations, they’d tell you that $$x^3y+3e^xy+5-y^{\prime\prime}=0$$ is “obviously” a second-order, linear ordinary differential equation (ODE). What gives? And why is, say, $$xy^3+3e^xy-y^{\prime\prime}=0$$ not considered linear?

The answer is quite simple, actually, but for some reason when I was 14 or so, it took a very long time for me to understand.

Here is the recipe. Take an equation like $$x^3y+3e^xy+5-y^{\prime\prime}=0$$. Throw away the inhomogeneous bit, leaving the $$x^3y+3e^xy-y^{\prime\prime}=0$$ part. Apart from the fact that it is solved (obviously) by $$y=0$$, there is another thing that you can discern immediately. If $$y_1$$ and $$y_2$$ are both solutions, then so is their linear combination $$\alpha y_1+\beta y_2$$ (with $$\alpha$$ and $$\beta$$ constants), which you can see by simple substitution, as it yields $$\alpha(x^3y_1+3e^xy_1-y_1^{\prime\prime}) + \beta(x^3y_2+3e^xy_2-y_2^{\prime\prime})$$ for the left-hand side, with both terms obviously zero if $$y_1$$ and $$y_2$$ are indeed solutions.

So never mind that it contains higher derivatives. Never mind that it contains powers, even transcendental functions of the independent variable $$x$$. What matters is that the expression is linear in the dependent variable. As such, the linear combination of any two solutions of the homogeneous equation is also a solution.

Better yet, when it comes to the solutions of inhomogeneous equations, adding a solution of the homogeneous equation to any one of them yields another solution of the inhomogeneous equation.

Notably in physics, the Schrödinger equation of quantum mechanics is an example of a homogeneous and linear differential equation. This becomes a fundamental aspect of quantum physics: given two solutions (representing two distinct physical states) their linear combination is also a solution, representing another possible physical state.