May 312023
 

I just finished uploading the latest release, 5.47.0, of our beautiful Maxima project.

It was a harder battle than I anticipated, lots of little build issues I had to fix before it was ready to go.

Maxima remains one of the three major computer algebra systems. Perhaps a bit (but only a bit!) less elegant-looking than Mathematica, and perhaps a bit (but only a bit!) less capable on some friends (exotic integrals, differential equations) than Maple, yet significantly more capable on other fronts (especially I believe abstract index tensor algebra and calculus), it also has a unique property: it’s free and open source.

It is also one of the oldest pieces of major software that remains in continuous use. Its roots go back to the 1960s. I occasionally edit 50-year old code in its LISP code base.

And it works. I use it every day. It is “finger memory”, my “go to” calculator, and of course there’s that tensor algebra bit.

Maxima also has a beautiful graphical interface, which I admit I don’t use much though. You might say that I am “old school” given my preference for the text UI, but that’s really not it: the main reason is that once you know what you’re doing, the text UI is simply more efficient.

I hope folks will welcome this latest release.

 Posted by at 8:54 pm
May 232023
 

In the last several years, we worked out most of the details about the Solar Gravitational Lens. How it forms images. How its optical qualities are affected by the inherent spherical aberration of a gravitational lens. How the images are further blurred by deviations of the lens from perfect spherical symmetry. How the solar corona contributes huge amounts of noise and how it can be controlled when the image is reconstructed. How the observing spacecraft would need to be navigated in order to maintain precise positions within the image projected by the SGL.

But one problem remained unaddressed: The target itself. Specifically, the fact that the target planet that we might be observing is not standing still. If it is like the Earth, it spins around its axis once every so many hours. And as it orbits its host star, its illumination changes as a result.

In other words, this is not what we are up against, much as we’d prefer the exoplanet to play nice and remain motionless and fully illuminated at all times.

Rather, what we are against is this:

Imaging such a moving target is hard. Integration times must be short in order to avoid motion blur. And image reconstruction must take into account how specific surface features are mapped onto the image plane. An image plane that, as we recall, we sample one “pixel” at a time, as the projected image of the exoplanet is several kilometers wide. It is traversed by the observing spacecraft that, looking back at the Sun, measures the brightness of the Einstein ring surrounding the Sun, and reconstructs the image from this information.

This is a hard problem. I think it is doable, but this may be the toughest challenge yet.

Oh, and did I mention that (not shown in the simulation) the exoplanet may also have varying cloud cover? Not to mention that, unlike this visual simulation, a real exoplanet may not be a Lambertian reflector, but rather, different parts (oceans vs. continents, mountain ranges vs. plains, deserts vs. forests) may have very different optical properties, varying values of specularity or even more complex optical behavior?

 Posted by at 12:06 am
May 042023
 

Claude still gets easily confused by math (e.g., reciprocal vs. inverse of a function), but at least it can now plot them as part of a conversation when we communicate through my UI:

And it has not forgotten to use LaTeX, nor has it lost its ability to consult Google or Maxima when needed. In fact, I am beginning to feel that while GPT-4 is stronger when it comes to logic or basic math, Claude feels a tad more versatile when it comes to following setup instructions, and also more forthcoming with details. (Too bad sometimes the details are quite bogus.)

 Posted by at 6:29 pm
May 032023
 

And just when I thought that unlike Claude and GPT-4, GPT 3.5 cannot be potty-, pardon me, Maxima- and Google-trained, I finally succeeded. Sure, it needed a bit of prodding but it, too, can utilize external tools to improve its answers.

Meanwhile, as I observe the proliferation of AI-generated content on the Web, often containing incorrect information, I am now seriously worried: How big a problem are these “hallucinations”?

The problem is not so much with the AI, but with us humans. For decades, we have been conditioned to view computers as fundamentally dumb but accurate machines. Google may not correctly understand your search query, but its results are factual. The links it provides are valid, the text it quotes can be verified. Computer algebra systems yield correct answers (apart from occasional malfunctions due to subtle bugs, but that’s another story.)

And now here we are, confronted with systems like GPT and Claude, that do the exact opposite. Like humans, they misremember. Like humans, they don’t know the boundaries between firm knowledge and informed speculation. Like humans, they sometimes make up things, with the best of intentions, “remembering” stuff that is plausible, sounds just about right, but is not factual. And their logical and arithmetic abilities, let’s be frank about it, suck… just like that of humans.

How can this problem be mitigated before it becomes widespread, polluting various fields in the information space, perhaps even endangering human life as a result? Two things need to be done, really. First, inform humans! For crying out loud, do not take the AI’s answers at face value. Always fact check. But of course humans are lazy. A nice, convenient answer, especially if it is in line with our expectations, doesn’t trigger the “fight-or-flight” reflex: instead of fact checking, we just happily accept it. I don’t think human behavior will change in this regard.

But another thing that can be done is to ensure that the AI always fact-checks itself. It is something I often do myself! Someone asks a question, I answer with confidence, then moments later I say, “But wait a sec, let me fact-check myself, I don’t want to lie,” and turn to Google. It’s not uncommon that I then realize that what I said was not factual, but informed, yet ultimately incorrect, speculation on my part. We need to teach this skill to the AI as soon as possible.

This means that this stuff I am working on, attempts to integrate the AI efficiently with computer algebra and a search engine API, is actually more meaningful than I initially thought. I am sure others are working on similar solutions so no, I don’t see myself as some lone pioneer. Yet I learn truckloads in the process about the capabilities and limitations of our chatty AI friends and the potential dangers that their existence or misuse might represent.

 Posted by at 6:21 pm
Apr 262023
 

It appears that I managed to convince Claude, too, to use Google and Maxima more or less correctly. It needs a little more handholding than GPT-4 and makes mistakes more often but hey, nobody is perfect! And the very fact that our AI friends can be taught to rely on external tools is by itself absolutely remarkable.

I admit I am having a blast of a time with our little robot friends. Kid-in-a-candy-store kind of sensation.

 Posted by at 11:41 pm
Apr 242023
 

My nice shiny UI to GPT and Claude is more than just a UI: GPT-4 can use it to perform real-time Google searches and also make use of computer algebra. It also gives the AI geolocation information from my browser.

And now the UI offers feedback, letting the poor user (namely, me) know if GPT-4 needed to consult any of these tools or if it provided a response using its pre-existing knowledge.

I am having more fun working with this thing than I ever thought possible at my age.

Oh, and it’s quite multilingual, too.

English, French and Hungarian for now.

 Posted by at 8:31 pm
Apr 202023
 

Another paper of ours, in all its 36-page glory, was accepted by Physical Review D and I am delighted.

One of the things we do in this paper is the use of symmetric trace-free tensors (STF) that allow us, among other things, to effect a rotation of spherical harmonic coefficients. This approach likely has many uses as a bit of practical math, beyond modeling gravitational fields.

 Posted by at 7:13 pm
Apr 202023
 

I just asked GPT-4 using my freshly developed UI about Starship.

In the background, GPT-4 correctly utilized a facility to perform Google searches and make use of the resulting snippets (I’m sure I’ll find a way to prevent it from referencing those snippets, which are not visible to the user, in the actual answer). Here is the critical part of the conversation that took place in the background:

User: What happened to Starship this morning?

GPT: SEARCH(Starship event on 2023/04/20)

System: Snippet 1: 3 hours ago … The rocket got off the launchpad before exploding above the Gulf of Mexico. This segment airs on April 20, 2023. Audio will be available after …
Snippet 2: UPCOMING. April 19, 2023. STARLINK MISSION · April 20, 2023. Starship Flight Test.
Snippet 3: 6 hours ago … April 20, 2023 … SpaceX launches the inaugural test flight of the integrated Starship and Super Heavy rocket from the company’s Starbase …
Snippet 4: 5 hours ago … April 20, 2023. Elon Musk has called it the “holy grail” for space technology. Starship, a new SpaceX rocket system that launched for the …
Snippet 5: ATCSCC ADVZY 007 DCC 04/20/2023 OPERATIONS PLAN. MESSAGE: EVENT TIME: 20/0200 – AND LATER … THE SPACEX STARSHIP SUPER HEAVY LAUNCH FROM BOCA CHICA, …

GPT: This morning, SpaceX launched the inaugural test flight of the integrated Starship and Super Heavy rocket from the company’s Starbase. Unfortunately, the rocket got off the launchpad but exploded above the Gulf of Mexico during the flight test (Snippet 1, Snippet 3).

In case you are wondering, yes, it knows the current date, too, thanks to the way my UI sets it up.

And yes, Starship blew up. But it blew up after the job of the first stage was nearly complete, at separation, at an altitude of some 40 km. Which means that despite the spectacular RUD (rapid unscheduled disassembly) event, this launch is still a huge success.

Now if we could only convince Elon to spend more time building rockets and less time honing his skills at corporate value destruction at Twitter, pardon me, X Corp…

 Posted by at 3:22 pm
Apr 182023
 

So here is my latest conversation with GPT-4 using my custom user interface. The important features of this implementation are the following:

  1. GPT is instructed to use LaTeX for mathematical output, which the UI correctly renders;
  2. The UI captures and renders SVG graphics that GPT may generate;
  3. GPT can use an external computer algebra tool for accurate computation;
  4. GPT can invoke an external tool to perform Google searches for current information;
  5. Conversations are condensed to ensure that they can run effectively indefinitely without hitting the token limit;
  6. GPT is used efficiently (GPT3.5 used for summaries, GPT-4 for new queries);
  7. The UI is optimized for easy printing (to PDF or hardcopy).

I was able to achieve this level of integration even without plugin-level access, simply by clever “prompt engineering” to ensure that the majority of the time, GPT uses the provided tools effectively. For this, GPT-4 seems essential; GPT3.5 is not really able to grasp the notion of using external tools before constructing its answers.

By way of example, when GPT was asked about the current Bank of Canada interest rate, what happened in the background was the following exchange:

User: What is the current Bank of Canada interest rate?

GPT: SEARCH(“current Bank of Canada interest rate”)

User: Snippet 1: Mar 8, 2023 … The current Bank of Canada interest rate sits at 4.50%, with a 0.25% rate hike announced on January 25, 2023.
Snippet 2: See the Current Bank of Canada Interest Rate graphs at this page. You will read in the news about this rate when the Bank of Canada makes a rate …
Snippet 3: Find answers about questions you may have about the Bank of Canada. What is the current bank of Canada interest rate?

GPT: As of March 8, 2023, the current Bank of Canada interest rate is 4.50%. A 0.25% rate hike was announced on January 25, 2023.

The prompting that I use can of course be improved. The behavior of GPT-4 is not always consistent, sometimes it fails to make use of the computer algebra result or attempts to invoke computer algebra in the wrong place. I suspect that the “right” solution will have to wait until I have plugin-level developer access. But I am very happy that I was able to accomplish this already, in particular that access to Google and the computer algebra tool are completely automated in the background, requiring no user action.

 Posted by at 3:08 am
Apr 172023
 

Here’s something that I’ve been putting off (literally) for years: Upgrading PHP.

Until today, that is.

My server used to run a seriously outdated version of PHP, 5.6. OK, it was still supported (kind of) under CentOS 7 but the writing was on the wall. In particular, the content management systems I use (WordPress, Joomla) were also grumbling.

Why didn’t I upgrade until now? Because I have Web content dating all the way back to the 1990s. Though the issues were trivial, such as using mysql_ instead of mysqli_ for database access, or using ASP-style tags, <%...%> instead of <?php...?> for PHP code, trivial issues still need fixing, and the fixes still need testing.

I finally bit the bullet. I was like this busy robot, assisted with kittycats, but it appears that I managed to pull it off: having done reasonably rigorous testing on backup/secondary servers, I was able to upgrade my main server without much drama so far.

Of course I still worry about the bugs and issues that I have not yet seen, but I am optimistic.

 Posted by at 8:31 pm
Apr 172023
 

This really is just a quick test post to see what’s going on. When I check the Twitter developer portal, my app (which connects this blog to Twitter) no longer shows as “suspended”. What does it mean, I wonder?

So let’s give it a try. Just to give this post some meaningful content, though, here’s a beautiful image generated by MidJourney in response to my request to depict a stray cat with its little robot friend.

If it shows up on Twitter, good. If not… well, frankly, I don’t much care anymore.

 Posted by at 3:40 pm
Apr 142023
 

Your service has violated Viktor’s rules and policies. As a result, it can no longer serve as a destination for my blog entries. For assistance, please just bugger off, along with your thin-skinned “free speech champion” ruler.

To my friends: This is likely my last ever blog entry to be posted to Twitter. In fact, the only reason I am not closing my Twitter account just yet is because there are still a few important information sources there that I follow, which have not yet migrated to Places That Shall Not Be Named like the place whose name begins with Mast and ends with odon, or the Sub place that is also a Stack and now has Notes.

 Posted by at 5:07 pm
Apr 132023
 

Once again, we have summer in April.

This picture shows the melting pile of dirty snow in our visitor parking area, photographed from our upstairs bedroom window.

The date and the temperature widget speak for themselves. (Yes, I still use Windows widgets, through a third-party tool. What can I say? I like them.)

 Posted by at 5:14 pm
Apr 012023
 

Oh my. Now that we are done with cryptocurrencies, NFTs and blockchain, AI is rapidly becoming the new fad. Apparently, all you have to do is call yourself a “prompt engineer” or “AI whisperer” to earn an exceptional salary.

Well, let this serve as advertising, notice to any prospective clients that my services are available as a consultant, either fixed-price or retainer based, should you wish to engage me. And, I daresay, with my in-depth knowledge and experience, which includes not just chatting with GPT but accessing it programmatically, as well as some hands-on exercises building simple toy models of deep learning architectures in low-level languages like C++, I am probably much more capable of delivering the goods than most of my “competition”.

Somehow, Bloomberg’s enthusiasm notwithstanding, I don’t expect any takers but just in case, my recent engagements with ChatGPT, as recounted in this very blog, should serve as my relevant portfolio. Not just words, AI-generated images, too.

 Posted by at 2:54 pm
Mar 262023
 

These lovely knitted bunnies and the felted eggs were made by my wife for Easter. She was hoping to sell a few of them at 613flea, but there were no takers. I cannot understand why… I love them. In fact I told her that if there are no takers, I’m happy to buy them.

Oh well. Maybe we should put them up for sale on eBay or Etsy.

 Posted by at 2:00 pm
Mar 232023
 

My wife’s beautiful creations will be at 613flea again this Saturday. Rufus the cat won’t be; he just volunteered as a model.

The Easter eggs are felted decorations. There will also be some knitted bunnies.

 Posted by at 10:10 pm
Mar 222023
 

Students at the California State University, Northridge, are currently working on a short documentary film about our work on the Solar Gravitational Lens.

The project hopes to attract modest crowdfunding. They also produced a teaser trailer.

Of course I hope they succeed; our SGL work could use some good publicity.

 Posted by at 9:39 pm
Mar 152023
 

… with laughter.

Without further ado, here is what transpired moments ago.

vttoth: Can you produce TikZ code that draws a cat?

ChatGPT: Drawing a cat using TikZ can be quite complex, but here’s a simple representation of a cat using TikZ:

\documentclass[tikz, border=2mm]{standalone}

\begin{document}
\begin{tikzpicture}
% Body
\draw[fill=gray!30] (0,0) ellipse (1cm and 1.5cm);

% Head
\draw[fill=gray!30] (0,1.75) circle (0.75cm);

% Eyes
\fill[white] (-0.35,2.1) circle (0.25cm);
\fill[white] (0.35,2.1) circle (0.25cm);
\fill[black] (-0.35,2.1) circle (0.1cm);
\fill[black] (0.35,2.1) circle (0.1cm);

% Nose and mouth
\fill[pink] (0,1.8) circle (0.1cm);
\draw (0,1.8) -- (0,1.6);
\draw (0,1.6) -- ++(-0.15,-0.15);
\draw (0,1.6) -- ++(0.15,-0.15);

% Ears
\draw[fill=gray!30] (-0.75,2.5) -- (-0.4,2.4) -- (-0.65,2.0) -- cycle;
\draw[fill=gray!30] (0.75,2.5) -- (0.4,2.4) -- (0.65,2.0) -- cycle;

% Tail
\draw[thick, gray!30] (1.3,-0.5) to[out=-90,in=0] (0.5,-1.5) to[out=-180,in=-90] (-0.5,-0.5);
\end{tikzpicture}
\end{document}

This code will produce a simple cat illustration. Copy and paste the code into a LaTeX editor that supports the TikZ
package, or use an online LaTeX renderer like Overleaf to generate the cat drawing. Please note that this is a simplistic
and stylized representation of a cat and not a realistic drawing.

vttoth: I love it. I find the result irresistibly funny. Is it a copy of a TikZ example that you came across during your
training or did you come up with this image on your own?

ChatGPT: I’m glad you liked the cat drawing! The cat illustration was not copied from a specific TikZ example that
I came across during my training. Instead, I synthesized it on my own, using my understanding of TikZ commands and
my knowledge of cat features to create a simple and stylized representation of a cat.

vttoth: Can you add whiskers?

ChatGPT: Of course! Here’s the updated TikZ code for the cat drawing with whiskers added:

\documentclass[tikz, border=2mm]{standalone}

\begin{document}
\begin{tikzpicture}
% Body
\draw[fill=gray!30] (0,0) ellipse (1cm and 1.5cm);

% Head
\draw[fill=gray!30] (0,1.75) circle (0.75cm);

% Eyes
\fill[white] (-0.35,2.1) circle (0.25cm);
\fill[white] (0.35,2.1) circle (0.25cm);
\fill[black] (-0.35,2.1) circle (0.1cm);
\fill[black] (0.35,2.1) circle (0.1cm);

% Nose and mouth
\fill[pink] (0,1.8) circle (0.1cm);
\draw (0,1.8) -- (0,1.6);
\draw (0,1.6) -- ++(-0.15,-0.15);
\draw (0,1.6) -- ++(0.15,-0.15);

% Ears
\draw[fill=gray!30] (-0.75,2.5) -- (-0.4,2.4) -- (-0.65,2.0) -- cycle;
\draw[fill=gray!30] (0.75,2.5) -- (0.4,2.4) -- (0.65,2.0) -- cycle;

% Whiskers
\foreach \i in {-1, 1} {
\draw (\i*0.15,1.65) -- (\i*0.5,1.5);
\draw (\i*0.15,1.65) -- (\i*0.5,1.65);
\draw (\i*0.15,1.65) -- (\i*0.5,1.8);
}

% Tail
\draw[thick, gray!30] (1.3,-0.5) to[out=-90,in=0] (0.5,-1.5) to[out=-180,in=-90] (-0.5,-0.5);
\end{tikzpicture}
\end{document}

This code includes the addition of whiskers to the cat’s face. Copy and paste the code into a LaTeX editor that
supports the TikZ package or use an online LaTeX renderer like Overleaf to generate the updated cat drawing with
whiskers.

I am laughing my head off in part because these cats, especially now with the whiskers added, strongly resemble cats I used to draw on letter-size sheets of paper with my set of colored pencils when I was of kindergarten age.

But I am also staring at these images sensing a combination of awe and apprehension.

 Posted by at 3:21 am