Every so often, I am presented with questions about physics that go beyond physics: philosophical questions of an existential nature, such as the reasons why the universe has certain properties, or the meaning of existence in light of the far future.

I usually evade such questions by pointing out that they represent the domain of priests or philosophers, not physicists. I do not mean this disparagingly; rather, it is a recognition of the fact that physics is about how the universe works, not why, nor what it all means for us humans.

Yesterday, I came across a wonderful 1915 painting by Russian avant-garde painter Lyubov Popova, entitled Portrait of a Philosopher:

What can I say? This painting sums up how I feel perfectly.

Oh, moments after posting about not having worthwhile subjects to post about, I suddenly remembered something that I have been meaning to post about for some time. That is to say, Moore’s law in computing, the idea that the capabilities of computer technology roughly double every 18-24 months or so.

It has been true for a long while. Gordon Moore made this observation back in 1965, when I was just two years old.

I observed a form of Moore’s law as I was swapping computer hardware over the years. My first major planned upgrade took place in 1992, when I built a really high end desktop computer (it even had a CD-ROM drive!) for many thousands of dollars. Months later, my older desktop machine found a new life as my first ever Linux server, soon to be connected to the Internet using on-demand dial-up.

The new desktop machine I built in ’92 lasted until 1998, when it was time to replace it. For the first time, I now had a computer that could play back DVDs without the help of external hardware. It also had the ability to capture and display video from cable. Ever since, I’ve been watching TV mostly on my computer screen. I watched the disaster unfolding on September 11, 2001 and the tragic end of the space shuttle Columbia on February 1, 2003 on that computer.

Next came 2004, when I executed a planned upgrade of workstation and server, along with some backup hardware. Then, like clockwork, 2010 and finally, 2016, when I built these fine machines, with really decent but low power (hence low thermal stress) Xeon CPUs, three of them.

And now here we are, in late 2022. More than six years have passed. And these computers do not feel the least bit obsolete. Their processors are fast. Their 32 GB of RAM is more than adequate. Sure, the 1 TB SSDs are SATA, but so what? It’s not like they ever felt slow. Video? The main limitation is not age, simply finding fanless video cards of decent capabilities that a) make no noise, b) don’t become a maintenance nightmare with dust-clogged fans.

I don’t feel like upgrading at all. Would feel like a waste of money. The only concern I have is that my server runs a still supported, but soon-to-be-obsoleted version of CentOS Linux. My workstation runs Windows 10 but support won’t be an issue there for quite a while.

And then there are the aging SSDs. Perfectly healthy as far as I can tell but should I risk relying on them after more than 6 years? Even high-end SSDs are becoming dirt cheap nowadays, so perhaps it’s time to make a small investment and upgrade?

Moore’s Law was originally about transistor counts, and transistor counts continue to rise. But transistor counts mean nothing unless you’re interested in counting transistors. Things that have meaning include execution speed, memory capacity, bandwidth, etc. And on all these fronts, the hardware that I built back in 2016 does not feel obsolete or limiting. In fact, when I look at what I would presently buy to build new machines, quite surprisingly the specs would only differ marginally from my six year old hardware. Prices aren’t that different either. So then, what’s the point, so long as the old hardware remains reliable?

There are only about six days left of the month of October and I have not yet written anything in this blog of mine this month. I wonder why.

Ran out of topics? Not really, but…

… When it comes to politics, what can I say that hasn’t been said before? That the murderous mess in Ukraine remains as horrifying as ever, carrying with it the threat of escalation each and every day? That it may already be the opening battle of WW3?

Or should I lament how the new American radical right — masquerading as conservatives, but in reality anti-democratic, illiberal authoritarianists who are busy dismantling the core institutions of the American republic — is on the verge of gaining control of both houses of Congress?

Do I feel like commenting on what has been a foregone conclusion for months, Xi “Winnie-the-pooh” Jinping anointing himself dictator for life in the Middle Kingdom, ruining the chances of continuing liberalization in that great country, also gravely harming their flourishing economy?

Or should I comment on the fact that prevalent climate denialism notwithstanding, for the first time in the 35 years that I’ve lived in Ottawa, Canada, our air conditioner came online in the last week of October because the house was getting too hot in this near summerlike heat wave?

Naw. I should stick to physics. Trouble is, apart from the fact that I still feel quite unproductive, having battled a cold/flu/COVID (frankly, I don’t care what it was, I just want to recover fully) my physics time is still consumed with wrapping up a few lose ends of our Solar Gravitational Lens study, now that the NIAC Phase III effort has formally come to a close.

Still, there are a few physics topics that I am eager to revisit. And it’s a nice form of escapism from the “real” world, which is becoming more surreal each and every day.

I looked up a book, States of Matter by David Goodstein, yesterday on Amazon, thinking about purchasing it. Except that Amazon told me that I last purchased this book on February 12, 2020.

I did?

I quickly checked my library database. Many-many years ago, I did a complete inventory of all our books, and since then, I’ve been keeping that database meticulously updated. New books that come to our house land on my desk and stay there until I enter them into the database. This is the only way to keep that database synchronized with reality.

The Goodstein book is not in the database.

I do not remember ordering it. I do not remember receiving it. Yet it clearly happened: The credit card transaction is there, duly entered into my books. The e-mails from Amazon, duly archived in the appropriate folder.

Now it is true that it happened just two and a half weeks before my last overseas trip. Could it be that I simply forgot about this order in the days leading up to my travel, and then never realized that the order failed to arrive? Perhaps. But then, why do I remember clearly other books that I ordered around the same timeframe? Besides, though my trip was upcoming it was not that close; this order and the supposed delivery happened two weeks before my departure.

I would be less suspicious, mind you, were it not for the fact that another weird thing happened yesterday. I have a tiny promotional toy sitting on my monitor. Yesterday, I found its identical twin brother in a box in which I was looking for something else altogether. This is definitely beginning to feel like that moment in The Matrix when Neo sees a black cat cross the hall… and then, a moment later, the same black cat cross the same hall in the same direction once again.

Still doesn’t help me with the Goodstein book. Should I keep looking for it? Under the rug, perhaps? Cat dragged it off to the litter box? Or should I just write it off and buy another copy?

One of the many novels by prolific 1930s Hungarian author Jenő Rejtő featured a horrific penal colony somewhere in colonial French Africa. Near the end of the novel, one of the minor protagonists, the military commander of the colony, already in retirement in Rome, recalls the past. As he enjoys the beautiful view from his window, he thinks that “and right now, Bahr el Sudan also exists for sure, and Tiguer, the corporal with the red moustache, is just now hanging a wet blanket, which smells like horses, over the window. This is a strange and unsettling notion.

Sometimes I feel the same way, not so much with respect to distant places in the present, but distant places in the past.

Take this image, a montage of two photographs taken from a wonderful Hungarian photographic archive that someone just shared on Facebook, showing an intersection in downtown Budapest, not far from where I grew up.

The picture predates us living there but not by much; it was taken in 1961, we moved there in 1967, but everything looked pretty much the same. I know this intersection like the back of my hand: the stores, the buildings, everything.

And when I view this image, it comes to life in my mind. It feels tangibly real. I can even smell the smells: the smell of freshly ground coffee (I even remember the noise made by the electric grinder) in that deli store on the corner, the smell of paint and household solvents permeating the hardware store next door. The sound made by those trolley buses as they rolled down the cobblestoned street (only the intersection was asphalt-paved at the time) as it even rattled our fourth-floor living room windows.

It all feels so real… it is a deeply unsettling thought that I am separated from what is depicted in this image not just by distance but also by time. The view that I am looking at is older than I am, as it was taken 62 years ago.

Oops. It’s past midnight already, so technically it was yesterday but to me it is still today, September 12.

The sixtieth anniversary of John F. Kennedy’s famous “we choose to go to the Moon” speech. How many more years before another human sets foot on the Moon?

Oh, and it was thirty years ago that Ildiko and I became married.

Yup, that’s us; 1979 vs. 2019.

Inspired by the story of that carbonized loaf that survived the eruption of Mount Vesuvius in 79 AD, my beautiful wife surprised us this morning with a loaf of bread, made according to a recreation of the Roman recipe:

It’s yummy. Looks great and tastes great, too. Those pesky Romans knew what they were doing.

I have a sign next to our front door, on the inside, warning those who are stepping out:

Occasionally I wonder if I might be overreacting to the state of things in this world. Not today.

I admit, my first reaction was that it must be a satire site. As far as I can tell, it is not.

Now someone please tell me how the world is not one nice, big, comfy insane asylum.

OK, I just made a meme.

Yes, they keep calling.

On an unrelated note, may the unforgettable Nichelle Nichols rest in peace.

Doesn’t this cloud, photographed in the skies above Ottawa by my beautiful wife moments ago, look just like the USS Enterprise?

Maybe it is, doing its time-traveling thing, with a malfunctioning cloaking device.

When the Rogers outage hit us, especially seeing that equipment remained physically connected but became unreachable for the outside world, I was immediately drawn to the conclusion that this was a cascading configuration error, invalid routes advertised through BGP, not some physical equipment problem or a cyberattack.

I guess I was not wrong (though I should stress that making such a general assessment after the fact from the comfort of my own chair is easy; finding the specific causes and resolving the problem, now that’s the hard part and I’m sure there are more than a few Rogers network engineers whose hair got a bit grayer in the past 48 hours). Cloudflare offered their own analysis, in which they pointed out that indeed, the outage was preceded by a sudden, unexpected burst of BGP advertisements. Here are two plots from Cloudflare’s blog post, montaged together so that the timestamps match:

Whatever the specific action was that resulted in this, it is truly spectacular how it killed all of Rogers’s network traffic at around 4:45 AM Friday morning.

Today, things were slowly coming back to normal. But just to add to the fun, earlier this afternoon first my workstation and later, two other pieces of hardware lost all connectivity here on my home office network. What the… Well, it turned out that the router responsible for providing DHCP services needed a kick in the proverbial hind part, in the form of a reboot. Still… Grumble.

Well, someone broke the Internet this morning.

To be more precise, someone broke a large part of the Internet in Canada. The network of Rogers has been down since about 4:30 this morning. When I woke up, I saw several e-mails from my own server complaining about its failure to connect to remote hosts; I also saw an e-mail from our family doctor’s office informing us that their phone lines are down and what to do in case of a medical emergency.

The fact that a major provider can have such a nationwide outage in 2022 is clearly unacceptable. Many are calling for the appropriate regulatory agencies to take action, and I fully approve.

In my case, there are backups and backups of backups. I am affected (we have no mobile data, and my highest-bandwidth network connection is down) but the outage also offered an opportunity to sort out an issue with network failover.

But I find it mind-boggling that more than 9 hours into the outage, Rogers still has no explanation and no ETA.

And now I accidentally hit Ctrl-Alt-Del while the KVM was connected to my main server instead of the device that I was trying to reboot. Oh well, no real harm down, the server rebooted cleanly, I just feel stupid.

All in all, this Friday is shaping up to be a rather unpleasant one. And here I thought I was looking forward to a nice, quiet, productive day.

There are a few things in life that I heard about and wish I didn’t. I’m going to mention some of them here, but without links or pictures. If you want to find them, Google them. But I am mindful of those who value their sanity.

• In a famous experiment, a researcher subjected rats to drowning. Rats that were previously rescued tried to stay afloat and took longer to die than those who weren’t. Hope changed their behavior.
• There was an old Chinese method of execution: literally cutting the condemned in half at the waist.
• Japan’s wartime bioweapons and chemical warfare research facility, the famous Unit 731, was so horrific, Auschwitz-Birkenau is probably like a happy summer camp in comparison (and not because Mengele was nice).
• Touch a tiny fraction of a milligram of dimethylmercury for more than a few seconds even while wearing a latex glove, and you will almost certainly die a horrible death months later, as your body and mind irreversibly deteriorate. (Someone once said that the very existence of something evil like Hg(CH3)2 is proof that there’s no God, or at least not a benevolent one.)

There may be a few other similarly unpleasant tidbits, but I can’t recall them right now, and that’s good. Mercifully, our human memory is imperfect so perhaps it is possible to unlearn things after all. (Or, perhaps I am hoping in vain, like those unfortunate rats.)

I have a color laser printer that I purchased 16 years ago. (Scary.)

It is a Konica-Minolta Magicolor 2450. Its print quality is quite nice. But it is horribly noisy, and its mechanical reliability has never been great. It was only a few months old when it first failed, simply because an internal part got unlatched. (I was able to fix it and thus avoid the difficulties associated with having to ship something back that weighs at least what, 20 kilos or more?)

Since then, it has had a variety of mechanical issues but, as it turned out, essentially all of them related to solenoids that actuate mechanical parts.

When I first diagnosed this problem (yes, having a service manual certainly helped), what I noticed was that the actuated part landed on another metal part that had a soft plastic pad attached. I checked online but the purpose of these plastic pads was unclear. Perhaps to reduce noise? Well, it’s a noisy beast anyway, a few more clickety-click sounds do not make a difference. The problem was that these plastic pads liquefied over time, becoming sticky, and that caused a delay in the solenoid actuation, leading to the problems I encountered.

Or so I thought. More recently, the printer crapped out again and I figured I’d try my luck with the screwdriver one more time before I banish the poor thing to the landfill. This time around, I completely removed one of the suspect solenoids and tested it on my workbench. And that’s when it dawned on me.

The sticky pad was not there to reduce noise. It was there to eliminate contact, to provide a gap between two ferrous metal parts, which, when the solenoid is energized, themselves became magnetic and would stick together. In other words, these pads were essential to the printer’s operation.

Inelegant, I know, but I just used some sticky tape to fashion new pads. I reassembled the printer and presto: it was working like new!

Except for its duplexer. But that, too, had a solenoid in it, I remembered. So just moments ago I took the duplexer apart and performed the same surgery. I appear to have been successful: the printer now prints on both sides of a sheet without trouble.

I don’t know how long my repairs will last, but I am glad this thing has some useful life left instead of contributing to the growing piles of hazardous waste that poison our planet.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Not very profound or insightful, is it.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Move over, general relativity. Solar gravitational lens? Meh. Particle physics and the standard model? Child’s play.

Today, I had to replace the wax ring of a leaky toilet.

Thanks to this YouTube video for some useful advice, helping me avoid some trivial mistakes.