Jan 162019

I run across this often. Well-meaning folks who read introductory-level texts or saw a few educational videos about physical cosmology, suddenly discovering something seemingly profound.

And then, instead of asking themselves why, if it is so easy to stumble upon these results, they haven’t been published already by others, they go ahead and make outlandish claims. (Claims that sometimes land in my Inbox, unsolicited.)

Let me explain what I am talking about.

As it is well known, the rate of expansion of the cosmos is governed by the famous Hubble parameter: \(H\sim 70~{\rm km}/{\rm s}/{\rm Mpc}\). That is to say, two galaxies that are 1 megaparsec (Mpc, about 3 million light years) apart will be flying away from each other at a rate of 70 kilometers a second.

It is possible to convert megaparsecs (a unit of length) into kilometers (another unit of length), so that the lengths cancel out in the definition of \(H\), and we are left with \(H\sim 2.2\times 10^{-18}~{\rm s}^{-1}\), which is one divided by about 14 billion years. In other words, the Hubble parameter is just the inverse of the age of the universe. (It would be exactly the inverse of the age of the universe if the rate of cosmic expansion was constant. It isn’t, but the fact that the expansion was slowing down for the first 9 billion years or so and has been accelerating since kind of averages things out.)

And this, then, leads to the following naive arithmetic. First, given the age of the universe and the speed of light, we can find out the “radius” of the observable universe:


or about 14 billion light years. Inverting this equation, we also get \(H=c/a\).

But the expansion of the cosmos is governed by another equation, the first so-called Friedmann equation, which says that

$$H^2=\dfrac{8\pi G\rho}{3}.$$

Here, \rho is the density of the universe. The mass within the visible universe, then, is calculated as usual, just using the volume of a sphere of radius \(a\):

$$M=\dfrac{4\pi a^3}{3}\rho.$$

Putting this expression and the expression for \(H\) back into the Friedmann equation, we get the following:


But this is just the Schwarzschild radius associated with the mass of the visible universe! Surely, we just discovered something profound here! Perhaps the universe is a black hole!

Well… not exactly. The fact that we got the Schwarzschild radius is no coincidence. The Friedmann equations are, after all, just Einstein’s field equations in disguise, i.e., the exact same equations that yield the formula for the Schwarzschild radius.

Still, the two solutions are qualitatively different. The universe cannot be the interior of a black hole’s event horizon. A black hole is characterized by an unavoidable future singularity, whereas our expanding universe is characterized by a past singularity. At best, the universe may be a time-reversed black hole, i.e., a “white hole”, but even that is dubious. The Schwarzschild solution, after all, is a vacuum solution of Einstein’s field equations, wereas the Friedmann equations describe a matter-filled universe. Nor is there a physical event horizon: the “visible universe” is an observer-dependent concept, and two observers in relative motion or even two observers some distance apart, will not see the same visible universe.

Nonetheless, these ideas, memes perhaps, show up regularly, in manuscripts submitted to journals of dubious quality, appearing in self-published books, or on the alternative manuscript archive viXra. And there are further variations on the theme. For instance, the so-called Planck power, divided by the Hubble parameter, yields \(2Mc^2\), i.e., twice the mass-energy in the observable universe. This coincidence is especially puzzling to those who work it out numerically, and thus remain oblivious to the fact that the Planck power is one of those Planck units that does not actually contain the Planck constant in its definition, only \(c\) and \(G\). People have also been fooling around with various factors of \(2\), \(\tfrac{1}{2}\) or \(\ln 2\), often based on dodgy information content arguments, coming up with numerical ratios that supposedly replicate the matter, dark matter, and dark energy content.

 Posted by at 10:13 pm
Jan 162019

In the political campaign leading up to the 2018 parliamentary elections in Hungary, an unlikely villain emerged on the election posters of the governing party: the Hungarian-American billionaire George Soros. “Let’s not allow Soros to have the last laugh,” screamed the posters, featuring an unflattering black-and-white photograph of the aging philanthropist.

While there was little doubt that this was all part of a cynically engineered election campaign, now we know exactly how it came to be, thanks to a piece of investigative journalism published in Das Magazin, a weekly supplement to several Swiss newspapers. A review of their article was also featured on 24.hu, a leading Hungarian news portal.

The anti-Soros campaign was the brainchild of George Birnbaum and his mentor, the late Arthur Finkelstein, experts on the technique of negative campaigning. They started working for Viktor Orban in 2008, contributing to his success in the 2010 election campaign. They had an easy task: the then ruling Socialist Party was wildly unpopular and thus easy to target. But after Orban’s second election victory in 2014, the Socialist Party was no longer a useful scapegoat. A new enemy was needed.

One obvious target presented itself: International capital, represented by the IMF and the EU, who dictated the conditions accompanying foreign loans that helped Hungary recover from the financial crisis. But an abstract target is not good enough. As Finkelstein once remarked, Americans fought not National Socialism but Hitler in WW2; not Al-Qaeda but Osama bin Laden in the War on Terror.

The narrative was given. One of the leading ideologues of Orban’s party, Maria Schmidt, director of the “House of Terror”, a museum dedicated to the victims of hardline communist terror in the early 1950s, readily provided it: a Hungary that was always the innocent victim, surrounded by enemies, yet protecting its identity and defending Christianity from adversaries ranging from the Ottoman Empire centuries ago to the investment bankers of the present day. All that was needed was a person who embodies this threat.

According to Das Magazin, Finkelstein and Birnbaum used a telephone survey to determine if Soros was known sufficiently well among would-be voters to serve as the target of a negative campaign. He proved to be the perfect enemy. He qualifies as a liberal, and he represents something hated by conservatives: a successful investor who wants to weaken capitalism. On the other hand, as he is not a politician and doesn’t even live in Hungary, he has no means to fight back.

The 2015 migration crisis was the icing on the cake. An essay Soros once wrote predicting a large number of refugees was relabeled the “Soros-plan”, demonstrating that Soros wanted to flood Hungary, and Europe in general, with Muslim “migrants”. By extension, any NGOs supported by Soros became targeted, as well as the Soros-founded Central European University, which was ultimately driven out of the country altogether, moving its main campus to Vienna.

The Soros-project was so successful, it was exported to other “markets”: anti-Soros voices were heard from Columbia to Kenya, from Israel to Australia. Even Donald Trump once asserted that the “caravan” heading towards America’s borders is funded by Soros.

The antisemitic overtone of the campaign is unmistakeable. Ironically, Finkelstein and Birnbaum are both Jewish. Birnbaum denied that the campaign had anything to do with antisemitism. He even claimed, rather improbably, that he did now know that Soros himself was Jewish. But Das Magazin reminds us that Finkelstein has not refrained in the past from supporting a candidate with known antisemitic views and that despite being gay, he also supported anti-gay politicians in the US.

 Posted by at 9:57 pm
Jan 162019

Theresa May lost the Brexit vote in Britain’s parliament. This means that still nothing has been decided when it comes to Brexit. Will it be a hard crash? Will Britain withdraw its Article 50 letter? Is there still room for compromise?

I know, I know, it’s not my country and I probably know a lot less about British politics than I should in order to voice a coherent opinion but still… what is about to happen will affect all of us, even outside of Britain, and may have a crucial impact on global stability as the world of 2019 is becoming ever more chaotic.

Many blame Theresa May for this uncertainty. Some call her incompetent. I do not believe that to be true. On the contrary, Theresa May tried to pull off the impossible and she almost succeeded. She was able to negotiate a Brexit plan that the EU accepted, and yet which minimized the negative impact on the British economy.

In other words, she managed to respect the will of the majority while at the same time protecting them from the worst consequences of their stupidity. In the process, she achieved a better deal than I expected under any reasonable set of circumstances.

As to who the true incompetents are… Perhaps incompetent is the wrong word when it comes to characterizing those callously opportunistic British politicians who plunged their country into this crisis in the first place, or the sometimes misguided, sometimes outright xenophobic voters who fell for the siren call to “Make Britain Great Again”.

Theresa May tried the impossible and she almost managed to make it happen. Despite originally supporting the “remain” option, May diligently worked on obtaining a decent separation deal. Still, it was not good enough. May’s political tragedy is that she sought compromise where no compromise was possible. Those who voted against Brexit were unlikely to cheer for any Brexit deal, no matter how sweetened. Those who voted for separation see any compromise as a betrayal of the will of the people; in fact, many are openly in favor of a “hard” Brexit, oblivious or indifferent with regards to the likely consequences.

When Jeremy Corbyn accused her of placing her party’s interests ahead of her nation’s, cameras showed May as she vehemently shook her head. And I think I understand why.

 Posted by at 9:40 pm
Jan 112019

I first read about this in George Takei’s Twitter feed. Then I checked it on Snopes, and it is true.

There really was a 1958 episode of a television Western (an episode titled The End of the World, of the series Trackdown), in which a character named Trump, a con artist, proposes to build an impenetrable wall to protect a town’s inhabitants.

Snopes confirms: the episode is real. In fact, the full episode is available on YouTube.

 Posted by at 1:21 am
Jan 092019

This editorial cartoon from the New York Daily News is not new; it seems to be from 2016, drawn by Bill Bramhall. I only just saw it though, in the feed of a Facebook friend.

Yet I think it is even more appropriate today, now that we have seen two years of the Trump presidency.

It of course is a reference to one of the scariest scenes from the 1979 movie Alien. I don’t know if the caption (those words were uttered by Ash, the film’s robot antagonist who is willing to sacrifice the spacecraft’s human crew in order to return the alien to his corporate masters ) was part of the original version of the cartoon, but it is this caption that makes the cartoon especially poignant these days.

 Posted by at 10:43 pm
Jan 092019

So I figured I’d try Office 2019. It came out a few months ago, and I have the MSDN license and everything, so why not give it a test drive. I downloaded the DVD installation image, and ran setup.

Immediately, I was presented with a cryptic error message:

What the devil does this mean? I am installing from a Microsoft-provided DVD image. Surely, it has all the required files?

The “Go online…” link was of no use. Just some generic stuff about installation failures.

A quick online search, however, revealed the culprit: Office 2019 won’t install unless Office 2016 is removed first.

Not something I am inclined to do at this time, not without thoroughly testing Office 2019 first to make sure that it behaves the way I like it (I am especially worried about Outlook and my encrypted imap connection, which can be a bitch to set up.)

In any case… in the software industry, 30 years ago already we had installers that gracefully recognized an existing installation of the same package, and offered either an upgrade or a side-by-side install. Or, worst case, they offered a meaningful error message, informing the hapless user that the prior version must be uninstalled first. Because, you know, chances are anyone installing Office 2019 might already have a copy of Office 2016 installed on their system?

I guess none of that is needed in 2019. After all, what kind of a dumb user am I if I don’t immediately understand Error code 30182-1 (2)?

 Posted by at 9:25 pm
Jan 062019

I almost forgot: a couple of months ago, I was interviewed over the telephone by a journalist who wanted to know my thoughts about one of my favorite moments in manned space exploration: The Apollo 8 “Genesis” moment, the reading of the opening verses of the Old Testament, on Christmas Day, 1968, by the astronauts of Apollo 8 as their spacecraft emerged from behind the Moon.

Today, something reminded me of this interview and I did a quick search. Lo and behold, there it is: My words, printed in The Boston Globe on December 23, 2018:

“It was a beautiful moment, and Genesis is part of our Western cultural heritage,” said Viktor Toth, an atheist and a senior research fellow at Carleton University in Ottawa, Canada, who played the lead role in the investigation of the Pioneer Anomaly, the mysterious acceleration of the Pioneer 10 and 11 spacecrafts in deep space. “This was an awe-inspiring thing: Human beings for the first time cut off from the Earth, and then they reemerged and saw the Earth again. The message was entirely appropriate.”

Though shortened, this pretty accurately reflects what I actually said during that roughly 10-minute conversation with the journalist.

 Posted by at 10:12 pm
Jan 042019

Even as China was celebrating the first successful landing of a spacecraft on the far side of the Moon, NASA’s New Horizons continued to radio back data from its New Year’s Day encounter with Ultima Thule: a strange, “contact binary” asteroid in the Kuiper belt, far beyond Pluto.

Ultima Thule will remain, for the foreseeable future, the most distant celestial object visited by spacecraft. While there is the odd chance that New Horizons may find another target within range (as determined by the on-board fuel available, which limits trajectory corrections, and the aging of its nuclear power source that provides electricity on board), chances are it won’t happen, and it won’t be until another deep space probe is launched, quite possibly decades from now, before we get a chance to see a world as distant as Ultima Thule.

Another piece of news from the New Horizons project is that so far, the probe found no moon orbiting Ultima Thule. No Moon At All.

 Posted by at 8:46 pm
Jan 032019

OK, the far side of the Moon is not really dark, but it is kind of hard to see. But now, from the department of unqualified good news: China successfully landed its spacecraft, Chang’e 4 (named after the Chinese Moon goddess), on the dark side of the Moon, and it has already sent us back some pictures.

This is big. Really big. To make it happen, China first had to launch a lunar orbiter, Queqiao (“Magpie bridge”), in order to maintain communication with the lander. And being on the far side of the Moon, the lander is completely shielded from radio signals from the Earth, which means an unprecedented opportunity to study radio signals of extrasolar origin.

Chang’e 4 also carried a rover, Yutu-2, which has since been deployed.

By any reasonable measure, this is a huge success for China’s space program, and for humanity overall. Hopefully, both lander and rover will remain operational and able to fulfill their scientific objectives.

 Posted by at 9:40 pm
Jan 012019

So here is what I expect from 2019.

  • The most severe political crisis in the United States since the Civil War, as investigations close in on Trump and his immediate family, and as House Democrats fail to rein in the firebrands among them;
  • A Trump administration that takes further steps to undermine the traditional system of Western alliances, including NATO and the EU;
  • A severe crisis in Britain as a no-deal Brexit unfolds; or when the government or Parliament come to their senses and “defying the will of the people” make a last-minute about-face;
  • An unfolding political crisis in the EU as member states like Hungary slide further towards authoritarianism, with some of the other European nations all too eager to follow, and the rest feeling helpless in light of their inability to deal with the domestic rise of nationalism and xenophobia;
  • A more assertive Russia that, sensing the weakness of nations it perceives as its main rivals, feels free to take aggressive steps, including the possibility of a more overt war with Ukraine;
  • China, facing an economic slowdown and rising criticism of Xi Jinping’s authoritarianism, turning towards more domestic repression and a more aggressive stance confronting its neighbors and in the South China Sea;
  • Japan, having announced its decision to leave the International Whaling Commission, resuming the culling of whales, because, as we all know, those magnificent creatures take up all the space in the oceans that is needed instead to store discarded bits of plastic;
  • Brazil, with its newly elected right-wing president at the helm, wreaking havoc in the rain forest, which he promised to privatize;
  • And last but not least, a bitter election campaign here in Canada, which will show to the world that this country, too, has its demons, in the form of nationalism, racism and xenophobia, and all all it takes is an unscrupulous populist or two to bring it all to the surface.

There are probably a few more things that I could add to this list, but these are at least some of the reasons why thinking about 2019 fills me with a sense of foreboding.

On a happier note, here is what I ask from Santa, come Christmas 2019: I want to be proven wrong on all of the above points. I desperately want to be wrong, foolishly wrong on all of the above points. Feel free to ridicule me on December 31 if none of my dire predictions come true. Nothing would make me happier.

 Posted by at 11:04 pm
Jan 012019

Today, I answered a question on Quora about the nature of \(c\), the speed of light, as it appears in the one equation everyone knows, \(E=mc^2.\)

I explained that it is best viewed as a conversion factor between our units of length and time. These units are accidents of history. There is nothing fundamental in Nature about one ten millionth the distance from the poles to the equator of the Earth (the original definition of the meter) or about one 86,400th the length of the Earth’s mean solar day. These units are what they are, in part, because we learned to measure length and time long before we learned that they are aspects of the same thing, spacetime.

And nothing stops us from using units such as light-seconds and seconds to measure space and time; in such units, the value of the speed of light would be just 1, and consequently, it could be dropped from equations altogether. This is precisely what theoretical physicists often do.

But then… I commented that something very similar takes place in aviation, where different units are used to measure horizontal distance (nautical miles, nmi) and altitude (feet, ft). So if you were to calculate the kinetic energy of an airplane (measuring its speed in nmi/s) and its potential energy (measuring the altitude, as well as the gravitational acceleration, in ft) you would need the ft/nmi conversion factor of 6076.12, squared, to convert between the two resulting units of energy.

As I was writing this answer, though, I stumbled upon a blog entry that discussed the crazy, mixed up units of measure still in use worldwide in aviation. Furlongs per fortnight may pretty much be the only unit that is not used, as just about every other unit of measure pops up, confusing poor pilots everywhere: Meters, feet, kilometers, nautical miles, statute miles, kilograms, pounds, millibars, hectopascals, inches of mercury… you name it, it’s there.

Part of the reason, of course, is the fact that America, alone among industrialized nations, managed to stick to its archaic system of measurements. Which is another historical accident, really. A lot had to do with the timing: metric transition was supposed to take place in the 1970s, governed by a presidential executive order signed by Gerald Ford. But the American economy was in a downturn, many Americans felt the nation under siege, the customary units worked well, and there was a conservative-populist pushback against the metric system… so by 1982, Ronald Reagan disbanded the Metric Board and the transition to metric was officially over. (Or not. The metric system continues to gain ground, whether it is used to measure bullets or Aspirin, soft drinks or street drugs.)

Yet another example similar to the metric system is the historical accident that created the employer-funded healthcare system in the United States that American continue to cling to, even as most (all?) other advanced industrial nations transitioned to something more modern, some variant of a single-payer universal healthcare system. It happened in the 1920s, when a Texas hospital managed to strike a deal with public school teachers in Dallas: For 50 cents a month, the hospital picked up the tab of their hospital visits. This arrangement became very popular during the Great Depression when hospitals lost patients who could not afford their hospital care anymore. The idea came to be known as Blue Cross. And that’s how the modern American healthcare system was born.

As I was reading this chain of Web articles, taking me on a tour from Einstein’s \(E=mc^2\) to employer-funded healthcare in America, I was reminded of a 40-year old British TV series, Connections, created by science historian James Burke. Burke found similar, often uncanny connections between seemingly unrelated topics in history, particularly the history of science and technology.

 Posted by at 2:25 pm