Spinor Info

Danzon n°2 (again)

Apr 132021

I didn’t realize it was more than 11 years ago.

It is rare that a piece of music has such an impact on you that you remember clearly the first time you heard it. Yet I do remember it very well: I first heard Danzon n°2 by Arturo Márquez on Highway 401, on my way to the Perimeter Institute in Waterloo, listening to the CBC on the radio.

What I didn’t realize that it was this long ago. More than 11 years already!

I heard this amazing piece of music again tonight, on Sirius XM. Different performance, but just as spirited as the one I am familiar with.

Gastronome no. 1

History No Responses »

Apr 132021

I am reading about the closure of an iconic grocery store in central Moscow.

What an amazing place. What amazing history: a store, opened in 1901, which survived the Communist revolution (though it was nationalized and renamed Gastronome no. 1), survived the collapse of the USSR, and even strived in the past 20 years before it began losing customers as a result of the changing demographic of the Russian capital. Depending in large part on tourists and already struggling to remain profitable, Yeliseyevsky’s was particularly ill-suited to survive a global pandemic that all but shut down the tourist industry.

And now apparently Yeliseyevsky’s is no more. It closed for good on April 11 after 120 years in business.

What a sad ending for such an iconic place.

Truth is singular

Film, Politics No Responses »

Apr 122021

My all time favorite movie is Cloud Atlas. I know, others have not reacted to this movie quite as powerfully as I have, but for whatever reason, the movie “got me”. (The fact that I first saw it during my first ever visit to the Middle East, in an Abu Dhabi hotel room, just a few days after flying over the war-torn Iraq-Iran border region while enjoying British Airways’ business class hospitality, may have had something to do with it.)

The movie has many memorable quotes. Banal, you might say, but even banalities sometimes reflect profoundly on our reality.

On particular quote echoes in my mind today as I witness, day after day, even in my relatively close circle of friends, the “relativization” of facts in our post-truth era. A key character in the movie is interviewed by an archivist just before her scheduled execution. To put her at ease, the archivist reassures her: “Remember, this isn’t an interrogation or trial. Your version of the truth is all that matters.” The protagonist, looking deeply in the eyes of the archivist, responds: “Truth is singular. Its versions are mis-truths.”

Yes, it should be that self-evident. Truth is singular. A and ¬A cannot simultaneously be true: A ∧ ¬A = 0 always. It is elementary formal logic.

But in our increasingly Göbbelsian 21st century, formal logic no longer matters. Instead, we have “alternative facts”. Instead, everyone feels entitled to question, even deny, facts that conflict with their Weltanschauung.

Yes, I said Göbbelsian. No, I am not trying to serve as an example of Godwin’s law by needless comparisons to Nazis. Rather, it is a recognition that the legacy of Göbbels, the evil genius of modern communication, continues to reverberate nearly a century later, as various actors push their versions of the truth. Göbbels taught us how to “sell” alternative facts: blatant lies are easy to falsify, lies by omission are much harder to catch.

A pluralistic society thrives on differences of opinion. Good people whose priorities differ may come to different conclusions based on the same set of facts. But when there is disagreement over the facts themselves, society breaks down. And that’s what we face today. The facts have now become matters of opinion.

I could name a number of issues from climate change to gender roles where the facts should be indisputable but they aren’t. But my concern transcends any specific topic. I simply worry that if we all retreat into our alternative facts bubbles, consensus or compromise become impossible. Where that leads, I don’t know but it is deeply worrying.

Messaging

Communication, Culture, Politics No Responses »

Apr 102021

Black lives matter. No argument there.

But, unfortunately, so does messaging. Dr. Göbbels knew this. The communists also knew this, hence their emphasis on “agitation and propaganda”. But, truth to tell, unlike the Third Reich, the left always sucked at it. That’s why, in Kádár’s Hungary, for instance, instead of being content with a regime that delivered a solid system of universal health care and a consistently high quality public system of education that included free tertiary education, we joked about living in the “happiest of the barracks”, took the regime’s successes for granted without acknowledging them, and grumbled daily about its numerous shortcomings.

The political left seems to be intent on continuing this tradition. Their messaging sucks.

A few days ago, I grumbled about the Mayor of London who proclaimed that there are too many white men in science and engineering.

Not too few women. Not underrepresented minorities. Not the need to increase the appeal and accessibility of science and engineering professions to women and minorities. Nope. Too many white men. The resulting backlash was both predictable and completely unnecessary.

Meanwhile, self-righteous warriors of the progressive left declare people like J. K. Rowling a public enemy. Shouldn’t someone with her storytelling prowess be enlisted as a friend and ally? No… deviate in the slightest from the unwritten standards of leftist orthodoxy, and you are labeled a backward, hateful somethingophobe. Like the California university professor who dared to mention a common Chinese expression in his lecture on communication: “na ge” (那个), a common pause word. Oh, how the righteous pounced! This insensitive white professor must be secretly a racist white supremacist! How dare he utter a word that sounds like, well… dare I write it down? Or do I, too, have to fear repercussions from the thought police if I dare spell out the infamous N-word in its entirety? The incident drew criticism from Chinese students and comparisons to Mao’s cultural revolution, and they were not wrong.

Then there are these calls to “defund the police”. The first time I heard this expression I was perplexed. Sure, I know there exist crazy anarchists who want no uniformed authority whatsoever on our streets, but I was also certain that this was not the meaning that the expression was intended to convey. And I was right. The original intent is to divert funds away: let the police do policing when they must, but use the funds wisely, to prevent those cultural and socioeconomic circumstances that lead to situations that need policing in the first place. Makes sense, right?

But that’s not the message that a call to “defund the police” conveys. Many who are rightfully angered by police excess want to, well, literally defund the police. And now their voices are amplified beyond reason, seemingly representing mainstream progressive attitudes. Needless to say, that’s all their opponents need to spread fear and concern among their followers: Look, they tell you, these leftist idiots, these commie anarchists want to leave your streets unprotected from thieves and murderers! They want to turn your country into a failed state like Venezuela!

So yes, black lives matter. And I know what you mean. You mean “Black lives matter, too.” You mean “Not only white lives matter.” You are not suggesting that lives other than black lives matter less.

But when you just say, “black lives matter”, you hand a propaganda victory to your opponents on a silver platter. Even stereotypical rednecks, those undereducated and unintelligent “deplorables”, can retort easily with “but I thought all lives matter!” and gain the moral upper hand.

I happen to support many (most? all?) key progressive ideas. I do think black lives (also) matter. I do believe it is a good idea to attack socioeconomic problems at their roots as opposed to just policing the consequences. I understand that words can hurt, dehumanize, and contribute to systemic racism. I do agree that we must do better to involve women and minorities in science and engineering professions.

But, dear progressives, when I look at your messaging… continuing a century-old tradition, you remain your own worst enemies.

A curious cat

Cats, Personal No Responses »

Apr 062021

World, please say hello to Freddy.

Freddy has been with us for more than two years now. He is a very funny cat. Strong-willed, to be sure; he might even bite you if he disapproves of your behavior. (No, he has not bitten off any fingers or earlobes yet.) And he likes… green peas. Or kernels of corn. And like one of our past kitties, Pipacs, Freddy also stole a freshly cooked potato from the kitchen not too long ago.

Last but not least, I should mention that his favorite toys are small pompoms. We have many of those, on account of my wife’s knitting. So I have a box of pompoms right here, next to my desk. Freddy often shows up here and, after carefully sniffing the pompoms, selects one, takes it from the box, puts it down on the floor and sits down proudly next to it, quietly meowing a few times. That is my cue to pick up the pompom and throw it down the stairs, with Freddy sprinting after it. Often, he then spends a good half hour playing with that pompom.

He also occasionally plays with his somewhat larger buddy, Rufus. I suppose Rufus looks just like a big gray-and-white pompom…

Success with cups

Food, Personal 2 Responses »

Apr 052021

My success story of the day involves two cups.

A few days ago, I heard my wife grumbling loudly in the kitchen. I went downstairs to see what was wrong. She showed me a pair of cups, a teacup, inside which there was one of our brand new espresso cups.

And when I say inside, I mean wedged inside. Firmly and utterly stuck, quite impossible to remove.

We tried to separate them using force, but they wouldn’t budge. We obviously didn’t want to break either cup. Not that they are terribly expensive but the teacup, well, we’re quite fond of these teacups and as for the espresso cup, it was brand new, I only just purchased the set off Amazon a few days earlier.

Force failed to do the trick so we tried to be clever. Use some oil to make it slick? Nope. Dishwasher detergent? That didn’t work either. I tried holding the outer cup, upside down, under hot water in the hope that thermal expansion might loosen the smaller cup inside; nope.

Nonetheless we thought that a temperature difference might help, so we filled the cups with water and put them in the freezer. Once the water was frozen solid, we took them out and placed them in a pot of boiling water. Again, the hope was that the high heat would cause the larger cup to expand, while the ice keeps the smaller cup cold, allowing it to fall out. Nope.

After this experiment failed for the third time earlier this afternoon, I sat down with the cups in hand and once again, tried brute force. The outer cup was still quite hot to the touch, the inner cup still quite cold and this may have helped; suddenly, I felt them budge, and after one more pull, they were separated, completely undamaged.

I was… absolutely delighted. Later I remarked to my wife that we humans are creatures of simple pleasures. Never mind the animations I completed just today using gravitational lenses of arbitrary shape. Never mind the work I am doing on another project on payment processor integration, or yet another project involving Microsoft Teams. (Yes, I multitask. Virtual desktops can be quite handy.) All of that is fun, sure, but it’s having been able to separate these poor cups without breaking or damaging them that really made my day.

Censored by Facebook

Canada, Internet, Local Ottawa No Responses »

Apr 042021

You know, I am beginning to sympathize with all those Trumpists, Fake News afficionados, anti-vaxxers, flat Earthers and the like.

The other day, I commented on a post concerning the 34 Ottawa area pharmacies that are designated as AstraZeneca vaccination sites by Doug Ford’s government.

I disagreed that this was a political decision, despite the fact that I didn’t vote for Mr. Ford, and that, in fact, I voted for the MPP in question who raised this issue in the first place. I suggested that we should leave such hyperpartisan politicking to our American friends. Last but not least, I was able to find some mapping data from StatCan and from a Twitter post (which I can no longer find — thanks for nothing, Facebook!) that, when overlaid, showed that the vaccination sites roughly correspond to the population density map of the Ottawa region.

Facebook, unfortunately, concluded that my post goes against their community guidelines as spam, despite the fact that (I swear!) I was not trying to sell any Russian brides, fake PPE, dubious cryptocurrency investment schemes, or steal anyone’s social insurance number.

None of it ever stopped Facebook from delivering Trumpist garbage, genuine Fake News, anti-vaxxer nonsense, even flat Earth propaganda to my account.

So dear Facebook… You played an instrumental part in turning America into a lunatic asylum, you played an instrumental part in helping the January 6 insurrection happen, you continue to play an instrumental part in radicalizing America and the world, you continue to let Putin’s trolls and China’s agents provocateurs own you, not to mention losing the personal data of more than 500 million of us… but you censor my post as spam because of your broken algorithms? Forgive the strong language but please, just fuck off.

I wonder if this blog post survives on Facebook or gets censored as well…

Kalach

Food, Hungary, Personal No Responses »

Apr 032021

My beautiful wife is getting really good at this.

She just made this kalach (kalács), Hungarian style braided sweetbread/eggbread, on account of Easter.

It is absolutely yummy for breakfast. Might work for lunch and dinner, too, if you ask me.

Yes, it has raisins in it. I love kalach with raisins.

Broken Budapest

History, Hungary No Responses »

Mar 272021

Courtesy of Radio Free Europe, here are some images (yes, do click on the link for the full experience) of the city of my birth, Budapest, in ways you may never have seen before, superimposing images from 1945 and the present.

It is incredible, what this beautiful city went through during that war. (Reminder to those who blame Stalin for the destruction: It was Hungary that declared war on the Soviet Union using a bombing that might have been staged, and which in any case was minor, as a pretext.)

The city is beautiful again. I visited just over a year ago, literally days before the world shut down on account of the COVID-19 pandemic. Whatever my thoughts about Hungarian politics and attitudes, it was a very pleasant trip with many pleasant encounters.

And looking at these horrific images of past devastation, I was reminded that even though I have not lived there since 1986, it remains the city where I was born and grew up: most places I recognized at a glance, in both the “before” and the “after” photos. Only Ottawa comes close as a place that I know this intimately.

Battle of the birds

Canada, Nature No Responses »

Mar 272021

Bald eagles have a fearsome reputation as predators of the sky. They also symbolize the great United States of America.

Canada geese? Not so fearsome. They are best known for pooping a lot. (If you ever walked through an Ottawa park after it was visited by a flock of geese, you know what I am talking about.)

Yet just like the country that they are named after, these geese are not so timid after all. Here is a recent series of images (and if you search online, you see that this by no means is an exception) captured by a PEI photographer of a Canada goose, fighting off a bald eagle:

Reader’s Digest version: The eagle remained hungry that day.

Eldest Mouse

Cats, Internet No Responses »

Mar 262021

Courtesy of The New Yorker, we now know the history of Lawyer Cat, otherwise known (as we now know) as Eldest Mouse.

Being Principal Skinner

Art, History, Society No Responses »

Mar 262021

So I learned today that J. K. Rowling writes hate-filled drivel on Twitter (her last post is from December 4 but never mind), and that forgiving Einstein for being a man of his times when he wrote about the white and Chinese races in the 1920s is the same as forgiving the Nazis.

Makes me sympathize more than ever with Principal Skinner.

This intolerant cultural orthodoxy that is promoted by virtue signaling champions of progressive tolerance not only fails to protect those who actually need it most (last time I checked, capitalizing Black has not reduced violence against black people, introducing a multitude of made-up pronouns has not eliminated transphobia, and preaching against white supremacist mathematics education—yes, this really is a thing!—has not brought potable drinking water or meaningful jobs to indigenous communities here in Canada), it also creates a backlash by feeding the trolls who promote actual racism and hate.

Here is a recent example: a tweet by the Mayor of London and the reaction. The tweet said, in part, “There’s no good reason why 65% of people working in science and engineering should be white men.” In one of the responses, we read “Fixing it? That deems it to be broken, in an 85% white country I would have expected the white % to be higher.”

The commenter obviously doesn’t know how to use a calculator, otherwise he would have pondered how 42.5% (assuming half of that white 85% are males) of the population can have 65% of the science and engineering jobs, whereas the remaining 57.5% gets only 35%. Which means that if you’re a white man, you have a 2.5 times better chance to get a job in science and engineering. But aside from the obvious innumeracy, there is this greater problem: by his careless choice of words, the Mayor of London may have made things worse.

And unlike Principal Skinner’s dilemma, this should have been easy to fix. Just say, “There’s no good reason why only 35% of the people working in science and engineering should be women or come from a non-white background” and right there, he’d have avoided feeding the trolls who promote the idea, ever so popular among frustrated, unsuccessful white men, that they are the victims here of identity politics. More careful words would have helped keeping the focus on the second part of the message, which describes genuine action to address the problem in a constructive, dare I say progressive way: “So far we’ve helped 10,000 young Londoners learn these subjects so they can follow their dreams.”

So how about if we stop vilifying J. K. Rowling* and others who do not flawlessly conform to the ideals of some narrow-minded progressive orthodoxy, stop condemning historical figures who lived decades or centuries ago for having failed to live up to the standards of the present, end “cancel culture” and instead start supporting policies that actually help those in need, even if it means sacrifices such as (gasp!) higher taxes?

Naw, why bother. It’s so much easier to just condemn people as racist misowhatever somethingophobes. Makes you feel good!

*Since I wrote this blog entry, I also learned that Rowling is an anti-Semite. How do we know? Why, those gold-loving goblin bankers in Harry Potter, with their obviously Jewish appearance, hooked noses and all.

I kid you not.

Canal blocked

Commerce, Economy, Transportation No Responses »

Mar 242021

For more than a day now, I’ve been watching the news about a giant container ship that is blocking the Suez Canal. Supposedly it now “partially refloated”, whatever that means.

In the process, I learned about vesselfinder.com, a Web site that tracks ships on the high seas, much like sites like flightradar24.com track airplanes. Here it is, a real-time snapshot of this stuck vessel:

I have no idea though why the ship is given the name “EVER GIVEN” here. Its actual name, written on the side of the ship in giant block letters, appears to be “EVERGREEN”. (Or not. I’ve since learned that EVERGREEN is the name of the company, not the ship.) And yes, it does block the canal in spectacular fashion.

Given the importance of this shipping route, I wonder why this is not bigger news than it appears to be. Is it perhaps because the general expectation is that the problem will be resolved shortly, causing no more than minor delays in some shipments? I hope.

Consumerism and communism

Culture, History, Hungary, Personal No Responses »

Mar 192021

I remembered something today. A set of playing cards.

I never had a card deck like this but some of my grade school classmates did. This was the (very) early 1970s in communist Hungary. It was through these cards that I first learned of the existence of luxury sports cars, supercars like Ferrari, racecars like Lotus.

It was cards like these:

These were not some imports from the decadent West. Not subtle imperialist propaganda. These cards were produced by the state-owned Playing Card Factory (yes, that was the name of the company!) and they were much coveted by many 7-year olds. Like me.

But now that I think back, it makes me wonder: Exactly what were they thinking? I mean, this was a bleeping communist dictatorship (of the goulash variety, but still). What on Earth did they think they were doing, these self-appointed masters of agitprop, poisoning our young, impressionable minds with such blatant Western consumerist propaganda?

Ah, the sweet irony.

Massively parallel computing

Computers, Cybernetics, Personal, Programming No Responses »

Mar 162021

Somebody just reminded me: Back in 1982-83 a friend of mine and I had an idea and I even spent some time building a simple simulator of it in PASCAL. (This was back in the days when a 699-line piece of PASCAL code was a huuuuge program!)

So it went like this: Operative memory (RAM) and processor are separate entities in a conventional computer. This means that before a computer can do anything, it needs to fetch data from RAM, then after it’s done with that data, it needs to put it back into RAM. The processor can only hold a small amount of data in its internal registers.

This remains true even today; sure, modern processors have a lot of on-chip cache but conceptually, it is still separate RAM, it’s just very fast memory that is also physically closer to the processor core, requiring less time to fetch or store data.

But what if we abandon this concept and do away with the processor altogether? What if instead we make the bytes themselves “smart”?

That is to say what if, instead of dumb storage elements that can only be used to store data, we have active storage elements that are minimalist processors themselves, capable of performing simple operations but, much more importantly, capable of sending data to any other storage element in the system?

The massive number of required interconnection between storage elements may appear like a show-stopper but here, we can borrow a century-old concept from telephony: the switch. Instead of sending data directly, how about having a crossbar-like interconnect? Its capacity will be finite, of course, but that would work fine so long as most storage elements are not trying to send data at the same time. And possibly (though it can induce a performance penalty) we could have a hierarchical system: again, that’s the way large telephone networks function, with local switches serving smaller geographic areas but interconnected into a regional, national, or nowadays global telephone network.

Well, that was almost 40 years ago. It was a fun idea to explore in software even though we never knew how it might be implemented in hardware. One lesson I learned is that programming such a manifestly parallel computer is very difficult. Instead of thinking about a sequence of operations, you have to think about a sequence of states for the system as a whole. Perhaps this, more than any technical issue, is the real show-stopper; sure, programming can be automated using appropriate tools, compilers and whatnot, but that just might negate any efficiency such a parallel architecture may offer.

Then again, similar ideas have resurfaced in the decades since, sometimes on the network level as massively parallel networks of computers are used in place of conventional supercomputers.

Gotta love the Y2K bug in the header, by the way. Except that it isn’t. Rather, it’s an implementation difference: I believe the PDP-11 PASCAL that we were using represented a date in the format dd-mm-yyyy, as opposed to dd-MMM-yyyy that is used by this modern Pascal-to-C translator. As I only allocated 10 characters to hold the date in my original code, the final digit is omitted. As for the letters "H J" that appear on top, that was just the VT-100 escape sequence to clear the screen, but with the high bit set on ESC for some reason. I am sure it made sense on the terminals that we were using back in 1982, but xterm just prints the characters.

Middle class life

Economy, History, Politics, Television No Responses »

Mar 152021

The cartoon series The Simpsons is into its 32nd season this year. It has been picked up for at least another two seasons by Fox.

The Simpsons depicts a “typical” American family of five: Homer the breadwinner, with only a high-school diploma, holding a dead-end but secure job as a safety inspector at the Springfield Nuclear Plant, Marge the housewife, mother of three children and the three kids, two of them school-age, one still a toddler. The Simpsons live in a detached house in a suburb and own two cars. They are not rich, but they do have disposable income: Homer spends his evenings gulping down beer as Moe’s Tavern, Marge never seems to have a problem paying for groceries.

In other words, The Simpsons live the American dream: a comfortable North American middle class lifestyle from a single income.

A dream that, as lamented in a recent opinion article in The Atlantic, is no longer attainable.

This, I think, really explains it all. The polarization of American politics. The emergence of extremism. The appeal of slogans like “Make America Great Again”. The “we have nothing to lose” attitude that led many to vote for Trump, despite their misgivings.

And it is by no means a US-only phenomenon. Income inequality may not be as bad in Canada as it is in the US, but the middle class is not doing spectacularly well here either. Europe, too, is not heading in the right direction.

Lest we forget the lessons of history, this is precisely what provides fertile ground for totalitarian ideologies like fascism and communism. When liberal democracy fails to deliver on society’s most basic promise, the ability to provide a life as good as, but preferably better than your own for your children, people turn to other ideas. That was just as true a century ago as it is today.

Another paper

Astronomy, Personal, Physics, Space No Responses »

Mar 142021

The next in our series of papers describing the extended gravitational lens (extended, that is, in that we are no longer treating the lensing object as a gravitational monopole) is now out, on arXiv.

Here’s one of my favorite images from the paper, which superimposes the boundary of the quadrupole caustic (an astroid curve) onto a 3D plot showing the amplitude of the gravitational lens’s point-spread function.

I was having lots of fun working on this paper. It was, needless to say, a lot of work.

Science and religion

Religion, Science No Responses »

Mar 142021

I am reading about Heino Falcke.

Dr. Falcke is a scientist. He is the leader of the Event Horizon Telescope project, the first successful attempt to image the event horizon (actually, the shadow of the photon sphere cast on the accretion disk background) of a black hole.

One of the Event Horizon Telescope participating facilities, at Pico Veleta

Dr. Falcke also happens to be religious. A lay pastor, no less, in the Protestant Church in the Netherlands.

He represents yet another example of how faith and the sciences need not be in conflict.

I happen to be nonreligious. I even mock religion (not the religious! Never!) occasionally when I talk about “imaginary friends”, “sky daddy” or the “Flying Spaghetti Monster”. My mockery is not intended to hurt: rather, this truly is how I feel about these supernatural concepts, as surreal, outlandish flights of fancy, fairy tales, nothing more.

Yet I think I understand how faith can also give strength to people. Offer motivation. Fill their lives with meaning.

It has been invariably my experience that the company of a person of faith who is open-minded and capable of critical thinking is much preferable to that of a dogmatic atheist.

In any case, while I may not have much respect for the supernatural aspects of religion, I certainly take no issue with the basic tenets of Christianity, such as loving thy neighbor or not committing murder. If the core message of religion is to try to be a decent human being, well, I don’t need to believe in imaginary friends to accept and fully embrace these principles.

This always reminds me how the best description of Christianity I ever came across came from a devoted atheist, the late Douglas Adams (of Hitchhiker’s Guide to the Galaxy fame): “And then, one Thursday, nearly two thousand years after one man had been nailed to a tree for saying how great it would be to be nice to people for a change […]”

Gravitoelectromagnetism

Physics No Responses »

Mar 142021

Because I’ve been asked a lot about this lately, I thought I’d also share my own take on this calculation in my blog.

Gravitoelectromagnetism (or gravitomagnetism, even gravimagnetism) is the name given to a formalism that shows how weak gravitational fields can be viewed as analogous to electromagnetic fields and how, in particular, the motion of a test particle is governed by equations that are similar to the equations of the electromagnetic Lorentz-force, with gravitational equivalents of the electric and magnetic vector potentials.

Bottom line: no, gravitoelectromagnetism does not explain the anomalous rotation curves of spiral galaxies. The effect is several orders of magnitude too small. Nor is the concept saved by the realization that spacetime is not asymptotically flat, so the boundary conditions must change. That effect, too, is much too small, at least five orders of magnitude too small in fact to be noticeable.

To sketch the key details, the radial acceleration on a test particle due to gravitoelectromagnetism in circular orbit around a spinning body is given roughly by

$$a=-\frac{4G}{c^2}\frac{Jv}{r^3},$$

where $r$ is the orbital speed of the test particle. When we plug in the numbers for the solar system and the Milky Way, $r\sim 8~{\rm kpc}$ and $J\sim 10^{67}~{\rm J}\cdot{\rm s}$, we get

$$a\sim 4\times 10^{-16}~{\rm m}{\rm s}^2.$$

This is roughly 400,000 times smaller than the centrifugal acceleration of the solar system in its orbit around the Milky Way, which is $\sim 1.6\times 10^{-10}~{\rm m}/{\rm s}^2.$

Taking into account that our universe is not flat, i.e., deviations from the flat spacetime metric approach unity at the comoving distance of $\sim 15~{\rm Gpc},$ only introduces a similarly small contribution on the scale of a galaxy, of ${\cal O}(10^{-6})$ at $\sim 15~{\rm kpc}.$

A more detailed version of this calculation is available on my Web site.

Canadian art

Art, Canada No Responses »

Mar 062021

I just came across this painting on Twitter.

I find it poignantly beautiful. According to the description by the artist, Antony John, the cow in the painting is old, on her last pregnancy, as she stares outside at a late winter Southwestern Ontario landscape. The equipment in the room may appear scary but it is nothing sinister. It is used to help with difficult pregnancies; the artist also intended it as a metaphor representing the inexorable pull of time.

I fell in love with this painting the moment I saw it.

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