Stephen Hawking passed away over a month ago, but I just came across this beautiful tribute from cartoonist Sean Delonas. It was completely unexpected (I was flipping through the pages of a magazine) and, I admit, it had quite an impact on me. Not the words, inspirational though they may be… the image. The empty wheelchair, the frail human silhouette walking away in the distance.

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.

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:

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.

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.

I was surprised by the number of people who found my little exercise about kinetic energy interesting.

However, I was disappointed by the fact that only one person (an astrophysicist by trade) got it right.

It really isn’t a very difficult problem! You just have to remember that in addition to energy, momentum is also conserved.

In other words, when a train accelerates, it is pushing against something… the Earth, that is. So ever so slightly, the Earth accelerates backwards. The change in velocity may be tiny, but the change in energy is not necessarily so. It all depends on your reference frame.

So let’s do the math, starting with a train of mass $$m$$ that accelerates from $$v_1$$ to $$v_2$$. (Yes, I am doing the math formally; we can plug in the actual numbers in the end.)

Momentum is of course velocity times mass. Momentum conversation means that the Earth’s speed will change as

$\Delta v = -\frac{m}{M}(v_2-v_1),$

where $$M$$ is the Earth’s mass. If the initial speed of the earth is $$v_0$$, the change in its kinetic energy will be given by

$\frac{1}{2}M\left[(v_0+\Delta v)^2-v_0^2\right]=\frac{1}{2}M(2v_0\Delta v+\Delta v^2).$

If $$v_0=0$$, this becomes

$\frac{1}{2}M\Delta v^2=\frac{m^2}{M}(v_2-v_1)^2,$

which is very tiny if $$m\ll M$$. However, if $$|v_0|>0$$ and comparable in magnitude to $$v_2-v_1$$ (or at least, $$|v_0|\gg|\Delta v|$$), we get

$\frac{1}{2}M(2v_0\Delta v+\Delta v^2)=-mv_0(v_2-v_1)+\frac{m^2}{2M}(v_2-v_1)^2\simeq -mv_0(v_2-v_1).$

Note that the actual mass of the Earth doesn’t even matter; we just used the fact that it’s much larger than the mass of the train.

So let’s plug in the numbers from the exercise: $$m=10000~{\rm kg}$$, $$v_0=-10~{\rm m}/{\rm s}$$ (negative, because relative to the moving train, the Earth is moving backwards), $$v_2-v_1=10~{\rm m}/{\rm s}$$, thus $$-mv_0(v_2-v_1)=1000~{\rm kJ}$$.

So the missing energy is found as the change in the Earth’s kinetic energy in the reference frame of the second moving train.

Note that in the reference frame of someone standing on the Earth, the change in the Earth’s kinetic energy is imperceptibly tiny; all the $$1500~{\rm kJ}$$ go into accelerating the train. But in the reference frame of the observer moving on the second train on the parallel tracks, only $$500~{\rm kJ}$$ goes into the kinetic energy of the first train, whereas $$1000~{\rm kJ}$$ is added to the Earth’s kinetic energy. But in both cases, the total change in kinetic energy, $$1500~{\rm kJ}$$, is the same and consistent with the readings of the electricity power meter.

Then again… maybe the symbolic calculation is too abstract. We could have done it with numbers all along. When a $$10000~{\rm kg}$$ train’s speed goes from $$10~{\rm m}/{\rm s}$$ to $$20~{\rm m}/{\rm s}$$, it means that the $$6\times 10^{24}~{\rm kg}$$ Earth’s speed (in the opposite direction) will change by $$10000\times 10/(6\times 10^{24})=1.67\times 10^{-20}~{\rm m}/{\rm s}$$.

In the reference frame in which the Earth is at rest, the change in kinetic energy is $$\tfrac{1}{2}\times (6\times 10^{24})\times (1.67\times 10^{-20})^2=8.33\times 10^{-16}~{\rm J}$$.

However, in the reference frame in which the Earth is already moving at $$10~{\rm m}/{\rm s}$$, the change in kinetic energy is $$\tfrac{1}{2}\times (6\times 10^{24})\times (10+1.67\times 10^{-20})^2-\tfrac{1}{2}\times (6\times 10^{24})\times 10^2$$$${}=\tfrac{1}{2}\times (6\times 10^{24})\times[2\times 10\times 1.67\times 10^{-20}+(1.67\times 10^{-20})^2]$$$${}\simeq 1000~{\rm kJ}$$.

Enough blogging about personal stuff like our cats. Here is a neat little physics puzzle instead.

Solving this question requires nothing more than elementary high school physics (assuming you were taught physics in high school; if not, shame on the educational system where you grew up). No tricks, no gimmicks, no relativity theory, no quantum mechanics, just a straightforward application of what you were taught about Newtonian physics.

We have two parallel rail tracks. There is no friction, no air resistance, no dissipative forces.

On the first track, let’s call it A, there is a train. It weighs 10,000 kilograms. It is accelerated by an electric motor from 0 to 10 meters per second. Its kinetic energy, when it is moving at $$v=10~{\rm m/s}$$, is of course $$K=\tfrac{1}{2}mv^2=500~{\rm kJ}$$.

Next, we accelerate it from 10 to 20 meters per second. At $$v=20~{\rm m/s}$$, its kinetic energy is $$K=2000~{\rm kJ}$$, so an additional $$1500~{\rm kJ}$$ was required to achieve this change in speed.

All this is dutifully recorded by a power meter that measures the train’s electricity consumption. So far, so good.

But now let’s look at the B track, where there is a train moving at the constant speed of $$10~{\rm m/s}$$. When the A train is moving at the same speed, the two trains are motionless relative to each other; from B‘s perspective, the kinetic energy of A is zero. And when A accelerates to $$20~{\rm m/s}$$ relative to the ground, its speed relative to B will be $$10~{\rm m/s}$$; so from B‘s perspective, the change in kinetic energy is $$500~{\rm kJ}$$.

But the power meter is not lying. It shows that the A train used $$1500~{\rm kJ}$$ of electrical energy.

Question: Where did the missing $$1000~{\rm kJ}$$ go?

First one with the correct answer gets a virtual cookie.

It’s the same, each and every Christmas. As Christmas Eve approaches, I remember that famous moment from 49 years ago. The astronauts of Apollo 8 just orbited the Moon. It was Christmastime. These three men were a thousand times farther from the Earth than any human being in history. It was an awe-inspiring moment. Once radio contact with the distant Earth was re-established, the three astronauts took turns reading the first ten verses of Genesis. Frank Borman then closed the broadcast with words that, in my mind, remain the most appropriate words for this evening: “good night, good luck, a Merry Christmas – and God bless all of you, all of you on the good Earth.

The Internet (or at least, certain corners of the Internet where conspiracy theories thrive) is abuzz with speculation that the extrasolar asteroid ‘Oumuamua, best known, apart from its hyperbolic trajectory, for its oddly elongated shape, may be of artificial, extraterrestrial origin.

Some mention the similarity between ‘Oumuamua and Arthur C. Clarke’s extraterrestrial generational ship Rama, forgetting that Rama was a ship 50 kilometers in length, an obviously engineered cylinder, not a rock.

But then… I suddenly remembered that there was another artificial object of extrasolar origin in the science-fiction literature. It is Iilah, from A. E. van Vogt’s 1948 short story Dormant. Iilah is not discovered in orbit; rather, it lays dormant on the ocean floor for millions of years until it is awakened by the feeble radioactivity of isotopes that appear in the ocean as a result of the use and testing of nuclear weapons.

Iilah climbs out of the sea and is thus discovered. It becomes an object of study by a paranoid military, which ultimately decides to destroy it using a nuclear weapon.

Unfortunately, the energy of the explosion achieves the exact opposite: instead of destroying Iilah, it fully awakens it, making it finally remember its original purpose. Iilah then sets itself up for a tremendous explosion that knocks the Earth out of orbit, ultimately causing it to fall into the Sun, turning the Sun into a nova. Why? Because Iilah was programmed to do this. Because “robot atom bombs do not make up their own minds.”

Artist’s impression of ‘Oumuamua

So here is the thing… the Iilah of van Vogt’s story had almost the exact same dimensions (it was about 400 feet in length) and appearance (a rock, like rough granite, with streaks of pink) as ‘Oumuamua.

Go figure.

Sci-Hub is a Russian Web site that contains pirated copies of millions of research papers.

Given that many of these papers are hidden behind hefty paywalls, it is no surprise that Sci-Hub has proven popular among researchers, especially independent researchers or researchers in third world countries, whose institutions cannot afford huge journal subscription fees.

Journal publishers do provide a service (at least those few journals that still take these tasks seriously) as they go through a reasonably well-managed peer review process and also perform quality copy editing. But… the bulk of the value comes not from these services, but from the research paper authors and the unpaid peer reviewers. In short, these publishers take our services for free (worse yet, often there are publication charges!) and then charge us again for the privilege to read what we wrote. No wonder that even in the generally law-abiding scientific community there is very little sympathy for journal publishers.

Nonetheless, publishers are fighting back, and the American Chemical Society just won a case that might make it a lot harder to access Sci-Hub from the US in the future. For what it’s worth, it hasn’t happened yet, or maybe we are immune in Canada:

$dig +short sci-hub.io 104.31.86.37 104.31.87.37$ traceroute sci-hub.io
[...]
9 206.223.119.180 (206.223.119.180) 46.916 ms 44.267 ms 66.828 ms
10 104.31.87.37 (104.31.87.37) 31.017 ms 29.719 ms 29.301 ms

I don’t know, but to me it looks as just another case of using the legal system to defend a badly broken, outdated, untenable business model.

Today, a “multi-messenger” observation of a gravitational wave event was announced.

This is a big freaking deal. This is a Really Big Freaking Deal. For the very first time, ever, we observed an event, the merger of two neutron stars, simultaneously using both gravitational waves and electromagnetic waves, the latter including light, radio waves, UV, X-rays, gamma rays.

From http://iopscience.iop.org/article/10.3847/2041-8213/aa91c9

The significance of this observation must not be underestimated. For the first time, we have direct validation of a LIGO gravitational wave observation. It demonstrates that our interpretation of LIGO data is actually correct, as is our understanding of neutron star mergers; one of the most important astrophysical processes, as it is one of the sources of isotopes heavier than iron in the universe.

Think about it… every time you hold, say, a piece of gold in your hands, you are holding something that was forged in an astrophysical event like this one billions of years ago.

Move over, Donald Trump. To heck with you, hurricane victims in Puerto Rico. See if I care about Catalonia voting for independence. Here is some real news™ from Canada instead, about a branch of the Royal Bank of Canada, which has been closed since August because a family of raccoons decided to make the ceiling of the place their new home.

Toronto bank branch closed after raccoon family moves in, damages the place.

The damage is extensive. The branch will reportedly stay closed until sometime in October.

You have to admit though that these animals are cute. Even when they are doing their best and try to look ferocious and angry.

Interesting forecast, courtesy of the Weather Network earlier this afternoon:

Yes, that is a snow symbol in the upper left corner. And yes, my American friends, the 29 degrees is Centigrade.

Warm snow, I guess.

(The “Accumulating snow” headline for Goose Bay is probably valid. But the upper left corner was supposed to describe current conditions here in Ottawa.)

So here it is: another gravitational wave event detection by the LIGO observatories. But this time, there is a twist: a third detector, the less sensitive European VIRGO observatory, also saw this event.

This is amazing. Among other things, having three observatories see the same event is sufficient to triangulate the sky position of the event with much greater precision than before. With additional detectors coming online in the future, the era of gravitational wave astronomy has truly arrived.

Today is September 25. In one of the coldest capital cities in the world. Yet this is the temperature according to the weather monitor gadget on my desktop (but also according to the thermometer on our balcony):

Yes, 3233 C. Or 9091 F for my American friends. The record for this day? A little under 30 C.

No, it does not feel like autumn at all.

On an unrelated note, yes, I do like to use desktop gadgets on Windows 10.

Predatory journals have been plaguing the academic publishing world for many years, and the problem is getting worse. As a recent Nature article revealed, even experienced researchers get scammed by them sometimes. Inexperienced, researchers, especially from non-English speaking countries, are easy prey.

The rise of predatory publishing. From Wikipedia.

Take, for instance, this researcher who recently sent me his paper after it has been published in a predatory pay-to-publish open access journal. He saw the fact that his paper was accepted a validation of his ideas. In reality, his paper was badly flawed, its main conclusions based on naive mistakes that would have been pointed out by a competent referee (or even editor!) during a normal peer review process. But predatory journals are not interested in rejecting papers; they are into maximizing their revenue.

There used to be a wonderful list of predatory, maintained by Jeffrey Beall. Unfortunately, Beall decided to take down his Web site, thus depriving us of an essential resource.

In my response to the aforementioned researcher, I listed a few criteria by which a predatory publisher can be identified. I know, I know, such lists exist, but these are characteristics that I personally consider important:

1. Open access: Obviously not all open access journals are predatory, and there are a few predatory journals that are not open access. But the vast majority are, since they (for obvious reasons) cannot build a real subscriber base, so their main or sole source of revenue is author fees.
2. Publication fee that is often too low to cover the real costs of publishing: The publication fees charged by legitimate journals to publish papers, e.g., with open access easily run up to a thousand dollars or more. It indeed costs that much to guide a paper through the peer review process and then prepare it for publication through a proper copy editing and proofreading process.
3. No real history to the journal: Predatory journals tend to be new, with few (if any) notable papers.
4. Low quality papers with uncorrected English (typos, grammatical mistakes, incomprehensible sentences) from unknown authors: All it takes is one peek at papers with very bad quality English to know that the journal has no real editorial staff or policies and they publish anything so long as the fees are paid.
5. Many papers that do not appear on arxiv.org, as having been rejected there for quality reasons: If the journal specializes in an area that is covered by arXiv, e.g., theoretical physics or astrophysics, yet the papers published by it do not appear on arXiv, that is an almost certain indicator that it is a journal preferred by cranks and crackpots, whose submissions are rightfully rejected by arXiv moderators.
6. An unusually large number (often hundreds) of young journals from the same publisher: Predatory publishers tend to launch a very large number of journals, e.g., dozens if not hundreds of “British journal of this” or “American journal of that” or similar names designed to suggest legitimacy. (Lately, some predatory publishers even went so far as to hijack the name of obscure but distinguished journals, e.g., from Eastern Europe.)
7. No association with any known, reputable research organization, publication house or university: Reputable, top quality journals are usually associated with a research institution. For instance, Physical Review is published by the American Physical Society; Science is published by the American Association for the Advancement of Science. A variant on this theme is when the journal is, in fact, associated with an institution but the institution itself is phony.

This list of criteria is, of course, not complete. But I am quite certain that any journal that scores high on all seven of these is, in fact, a predatory journal.

NASA’s Cassini spacecraft is no more.

Launched 20 years ago, Cassini arrived at Saturn in 2004 and has been studying the ringed giant ever since. Cassini also carried the Huygens probe, which executed a successful descent into the dense atmosphere of Saturn’s moon Titan, and even transmitted data from its surface.

Its fuel nearly exhausted, Cassini was steered into a trajectory that led to its intentional demise: a fiery plunge into Saturn’s atmosphere earlier this morning. As planned, the spacecraft was able to transmit observations until the very end, when its thrusters were no longer able to maintain its attitude during the descent.

Program manager Earl Maize and operations team manager Julie Webster embrace after signal loss.

I feel sad that Cassini is gone, but I should also feel elated because it has been an incredibly successful mission. I just hope I live long enough to see another probe visiting Saturn, perhaps a probe or set of probes that are designed to land on Titan, maybe even sail its hydrocarbon seas, in search of possible life on that icy world.

Here is a belated picture of yesterday’s solar eclipse, taken by my friend David in New York City:

His equipment is (semi-)professional but the solar filter that he used wasn’t. Still, it is a heck of a lot better than anything I was able to see (or project with a makeshift pinhole camera). I suggested to him to obtain a quality solar filter by 2024. Who knows, we may meet in Watertown to watch totality.

I just came across an interesting slide.

It was part of a presentation by Bill Foster, a member of an endangered species in the United States Congress: a scientist turned politician. He gave a talk at the April meeting of the American Physical Society. This slide from his talk speaks for itself:

I don’t have data for Canada, other than a list of a grand total of 6 engineers serving in our federal House of Commons. That low number suggests that Canada’s Parliament would not be positioned too far from the U.S. Congress in this chart.

Is this a bad thing? I hesitate, because I note that totalitarian regimes tend to have many scientists among their leaders. Is it because scientists are more likely to prefer authoritarianism? Or more likely to serve autocrats? I don’t know. I do know that as a free citizen, I much prefer to be governed by a dysfunctional Congress or Parliament than by a totalitarian Politburo, regardless of the number of scientists in these bodies.