It’s been a while since I last presented to the world our cat, Master Rufus.
World, please meet Master Rufus.
May 282022
May 252022
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.
May 232022
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.
May 092022
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.
May 062022
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.
Apr 192022
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.
Apr 132022
Acting as “release manager” for Maxima, the open-source computer algebra system, I am happy to announce that just minutes ago, I released version 5.46.
I am an avid Maxima user myself; I’ve used Maxima’s tensor algebra packages, in particular, extensively in the context of general relativity and modified gravity. I believe Maxima’s tensor algebra capabilities remain top notch, perhaps even unsurpassed. (What other CAS can derive Einstein’s field equations from the Einstein-Hilbert Lagrangian?)
The Maxima system has more than half a century of history: its roots go back to the 1960s, when I was still in kindergarten. I have been contributing to the project for nearly 20 years myself.
Anyhow, Maxima 5.46, here we go! I hope I made no blunders while preparing this release, but if I did, I’m sure I’ll hear about it shortly.
Apr 122022
Our work on the Solar Gravitational Lens, complete with some diagrams created by yours truly, now made it onto TikTok.
@toknerdytome Solar Gravitational Lens #learnontiktok #tiktokpartner #science #space #astrotok #alien #nasa #physics #astronomy #technology ♬ Interstellar- Main Theme – Geek Music
How about that.
Mar 292022
For the first time in my life, I exercised my right as a Hungarian citizen and voted.
Before I left Hungary, voting was pointless: my choice was the Hungarian Socialist Workers’ Party or else. The “or else” meant nothing.
More recently, I didn’t feel it kosher to participate in elections in a country where I do not reside and do not pay taxes. Then again, thanks in part to the current government, a great many Hungarian citizens who do not reside in Hungary or pay taxes there have gained the right to vote… so perhaps it’s not unethical for me to do so as well.
So I did.
Incidentally, the Parliament building in Budapest is quite an impressive edifice.
Mar 242022
Between a war launched by a mad dictator, an occupation by “freedom convoy” mad truckers, and other mad shenanigans, it’s been a while since I last blogged about pure physics.
Especially about a topic close to my heart, modified gravity. John Moffat’s modified gravity theory MOG, in particular.
Back in 2020, a paper was published arguing that MOG may not be able to account for the dynamics certain galaxies. The author studied a large, low surface brightness galaxy, Antlia II, which has very little mass, and concluded that the only way to fit MOG to this galaxy’s dynamics is by assuming outlandish values not only for the MOG theory’s parameters but also the parameter that characterizes the mass distribution in the galaxy itself.
In fact, I would argue that any galaxy this light that does not follow Newtonian physics is bad news for modified theories of gravity; these theories predict deviations from Newtonian physics for large, heavy galaxies, but a galaxy this light is comparable in size to large globular clusters (which definitely behave the Newtonian way) so why would they be subject to different rules?
But then… For many years now, John and I (maybe I should only speak for myself in my blog, but I think John would concur) have been cautiously, tentatively raising the possibility that these faint satellite galaxies are really not very good test subjects at all. They do not look like relaxed, “virialized” mechanical systems; rather, they appear tidally disrupted by the host galaxy the vicinity of which they inhabit.
We have heard arguments that this cannot be the case, that these satellites show no signs of recent interaction. And in any case, it is never a good idea for a theorist to question the data. We are not entitled to “alternative facts”.
But then, here’s a paper from just a few months ago with a very respectable list of authors on its front page, presenting new observations of two faint galaxies, one being Antlia II: “Our main result is a clear detection of a velocity gradient in Ant2 that strongly suggests it has recently experienced substantial tidal disruption.”
I find this result very encouraging. It is consistent with the basic behavior of the MOG theory: Systems that are too light to show effects due to modified gravity exhibit strictly Newtonian behavior. This distinguishes MOG from the popular MOND paradigm, which needs the somewhat ad hoc “external field effect” to account for the dynamics of diffuse objects that show no presence of dark matter or modified gravity.
Mar 032022
This beautiful creature was my Mom’s canine, who went by the name Labi.
I use the past tense because unfortunately, Labi is no more. He died a few hours ago. He was 13.
I know, I know. This is a very minor tragedy with all that’s going on in the world right now. But even minor tragedies are devastating to those who experience them first-hand.
Our first cat, Marzipan, taught us a lesson. Do not grieve death; celebrate life. It’s been almost 22 years since Marzipan’s life was cut short by illness, and every time we think about him, we smile. He continues to bring happiness to our lives even this many years after his death.
I’ll have to tell my Mom that this will also be true for Labi. Years from now, every time she thinks about him, she will smile, remembering all the love and all the mischief. Life, even a brief life, triumphs because it exists.
Jan 112022
My name is not the rarest, but also not terribly common. I never met another Viktor Toth in person, but over the years, I came across a few and I’ve at least been in close contact with one.
The first Viktor Toth I read about as a teenager was featured with his girlfriend in some silly magazine for young Pioneers in then-communist Hungary.
Around the same time, I also read about a Viktor Toth in a small town in Hungary, who butchered his unfortunate wife with an axe. Yikes!
When I came to Ottawa, Canada, I was surprised to learn that there was already a Victor Toth in the local phone book. I never met him, but I did end up working with a gentleman who knew him.
It was still relatively early in the Internet era when I first searched for my own name, in the context of the small Hungarian town of Visegrad where I once lived. Much to my surprise, I found a Viktor Toth but it wasn’t me. It was a Hungarian astronomer who organized a conference that happened to take place in that small town. (Much later, he and I got in touch and even collaborated a little, contributing an article to a Hungarian popular science magazine about the future of radio astronomy in the country.)
There is a Viktor Toth who is an internationally renowned jazz saxophonist; unfortunately the type of improvisation-based modern jazz he plays is not my favorite subgenre, but he seems very well regarded.
And finally, there’s the Viktor Toth who recently put his pet rat into a virtual reality harness and had him play Doom. For the record, the only rat I own is this one, and he definitely doesn’t play Doom:
Dec 312021
Y’all heard the joke: twenty-twenty-two,
It will be just like twenty-twenty, too.
But I really hope it will not be so.
We really just can’t give it another go.
Dec 242021
Although we are not religious, we celebrate Christmas.
And I still cannot think of a better way to celebrate Christmas than with the words of the astronauts of Apollo 8, and the sense of awe they felt when they became the first human beings ever in the history of our species to be completely cut off from Mother Earth, when their spaceship disappeared behind the Moon.
Earthrise from Apollo 8
Re-emerging, they read passages from the Book of Genesis to their audience, with Frank Borman concluding with the words:
[G]ood night, good luck, a Merry Christmas – and God bless all of you, all of you on the good Earth.
To me, this is the most beautiful Christmas message ever.
Dec 242021
For the record: The Viktor Toth who has recently become quite popular on YouTube by placing his pet rat into a virtual reality harness and letting him play Doom is not me.
Even if I were inclined to do such an experiment with a live animal (I am not) it would be one of my cats, and the retro game of choice would be Duke Nukem.
You see, I was never really a fan of Doom.
Nov 202021
I kept staring at my calendar.
November 20. November 20. Why is this date memorable?
Then it suddenly popped into my mind. My father was born exactly 115 years ago, on November 20, 1906, in what was then Austria-Hungary, in the fine city of Temesvár, today known by its Romanian name as Timișoara.
He passed away in the fall of 1985, not long before I left Hungary.
Nov 142021
I am sure everybody had people like my friend Ken in their lives: People who, often by pure chance, played a major role in shaping our lives at critical turning points. When I came to Canada in 1987, I met several people who opened doors for me, offered me opportunities when I needed them most, or simply rewarded me with their friendship.
Ken Bowman was one such person. A mid-level manager at Canada Post in 1989, he was running the little project that I joined. I needed the income badly as my previous contract work ended months prior and I was rapidly running out of money. But the project itself was also interesting, challenging even. Oh, and the machines were fabulous: IBM PS/2-70 workstations with very large (by the standards of the time) hard drives, high resolution color monitors, laser printers… Lovely work.
I worked there for about nine months, but the friendships proved lasting. Some time later, Ken joined the company that was set up by a couple of my teammates on this project. He led the business side of one of my favorite development projects, which involved not only a product catalog but also an engineering and load sizing component, with plenty of interesting physics.
Ken’s partner at this company had a long, difficult-to-spell last name. One day, they received personally addressed but otherwise identical pieces of junk mail. The partner’s name was spelled flawlessly. Ken’s? Not so much. The envelope just read “Kenowman”. Needless to say, this earned him the obvious instant nickname: from this point on, he was often called Obi wan Kenowman, or just Obi wan for short. He loved it.
Even after he retired, we stayed in touch. Whether it was the politics of the day, a reaction to one of my silly blog posts, or just a picture of his beautiful cat Cimarron, I received missives from him occasionally, mostly in the form of lengthy text messages. And before the pandemic changed the world, we also met from time to time. Seeing him in person, I was actually worried about his health: he lost a great deal of weight, more than what I’d consider healthy.
Ken with one of his grandsons, two elegant gentlemen in happier times.
Photo courtesy Hollis Bowman.
Sadly, it appears that my concerns were not unfounded. One morning a few days ago I received an e-mail from Ken’s daughter Hollis that her Dad was now in palliative care. And before I could even respond, a second e-mail arrived: her Dad passed away.
And just like that, another friend is gone. If I am counting it right, Ken is the fifth person who played an oversize role in shaping the first couple of years of my life here in Canada. Inevitably it makes me wonder, who’s next? (Let that be a plea to my remaining friends: please stay healthy and take good care of yourselves!)
For now, though, Ken, I’ll miss hearing your voice on the phone from time to time. I’ll miss getting text messages from you about the state of the world. I’ll miss pictures from you about your beautiful cat.
I’ll miss you. Thank you for having been a part of my life.
Nov 122021
In 1973, my Mom and I visited my aunt here in Ottawa. It was a remarkable journey for 10-year old me. The differences between Hungary, then firmly behind the former Iron Curtain, and Canada were… astonishing. (Let’s just say that this experience firmly inoculated me against any communist claims about building a better society.) The trip was equally impactful on my Mom, though of course she experienced it quite differently as an adult.
At the time, my Mom spoke very little English. So when my aunt and her husband decided to take her to a movie theatre to see the latest James Bond movie, the first one with Roger Moore in the title role, they assured her that they will provide a running translation.
Then the film began and they quickly found out that translation was not necessary after all. At least insofar as these opening shots were concerned.
To this day, we cannot stop laughing when we think back of this moment.
Nov 122021
Today, I saw a funny post on Quora about how to pet a rabbit. Apparently, rabbits should not be picked up (fragile skeletal structure, bones that break easily) and also hate it when their tail is touched. I was about to make a cheeky comment on pulling either a rabbit or a cat by the tail. But first I wanted to fact check something quickly on Google, and that’s when I came across this article about tail pull injuries that cats sometimes suffer.
Yikes!
I admit I pulled our cats by the tail every once in a while. It’s funny, but also effective when you need to pull a cat back when he’s about to run out of the house or do something he’s not supposed to do.
Except… Except that, as I now learn, cats’ tails get injured relatively easily, and the injury can be devastating, affecting the bundle of nerves that exit the spinal column, which control much of their lower body. The least devastating consequence is losing mobility of the tail, but the injury can also lead to paralysis of the hind legs and incontinence. In short, ruining a cat’s life.
I did not know this. I am glad I never inadvertently caused injury to one of our cats. But I will never pull a cat by the tail again.
Oct 212021
My beautiful wife will be selling her beautiful hats and scarves and other knitware at Lansdowne Park this Saturday, at this year’s last “613flea” outside event.
