To all my friends, to all good people…
… Happy New Year!
Dec 312024
Dec 252024
Last night, I had a disturbing dream.
I do not usually recall my dreams. When I wake up in the morning, almost always I wake up with a clean state of mind, focused on the things I am planning to do in the coming day. It is very rare that I wake up even with fragmentary memories of whatever I was dreaming while asleep.
This was one of those days. I was unable to recall the details, but I remembered that in my dream, I worked at some retail establishment. I ended up working there as a favor to someone, being paid under minimum wage. I wasn’t there for the money.
Long story short, somehow the establishment became Trump’s property. Yes, that Trump. And Trump visited the place. In my dream, I’ve met Trump previously. Still, being the polite chap that I am, I greeted him with a “good morning, Mr. President”. He looked at me and told me, right there in front of his entourage, that no, we’ve known each other long enough, just because he got re-elected, I should not stop addressing him by his first name.
I was beaming with pride. I was speechless. So much so that only after he left the business did I realize that I forgot to ask the one question that I’ve been meaning to ask: Now that I work for him, as opposed to doing a favor to a friend, can I at least get paid at the official minimum wage?
Is it really this easy to manipulate us? Through our pride, our self-esteem, our vanity? Was my dream a cautionary tale, reminding me that no, however smart I think I am, I am not immune to these things?
Dec 242024
Here’s my Christmas wish for all good people, all the good people on the good Earth: peace.
And no, not the peace of the graveyard. Not the peace of the conqueror or tyrant, the peace of oppression, imposed peace.
No… a just peace.
Dec 222024
So I asked Claude to do something for me for Christmas. Claude happily obliged.
Can you generate for me SVG code that draws a nice Christmas tree?
Certainly! I'll create an SVG code that draws a simple but nice Christmas tree for you. Here's the SVG code:
<svg width="300" height="400" xmlns="http://www.w3.org/2000/svg">
<!-- Tree trunk -->
<rect x="140" y="350" width="20" height="50" fill="#8B4513"/>
<!-- Tree layers -->
<polygon points="150,50 50,350 250,350" fill="#228B22"/>
<polygon points="150,100 70,300 230,300" fill="#32CD32"/>
<polygon points="150,150 90,250 210,250" fill="#3CB371"/>
<!-- Ornaments -->
<circle cx="120" cy="200" r="10" fill="red"/>
<circle cx="180" cy="220" r="10" fill="gold"/>
<circle cx="150" cy="280" r="10" fill="blue"/>
<circle cx="100" cy="320" r="10" fill="purple"/>
<circle cx="200" cy="300" r="10" fill="silver"/>
<!-- Star on top -->
<polygon points="150,40 140,60 160,60" fill="yellow" stroke="orange" stroke-width="2"/>
</svg>
This SVG code creates a Christmas tree with the following elements:
- A brown trunk
- Three layers of green triangles for the tree's foliage
- Colorful ornaments (circles) in red, gold, blue, purple, and silver
- A yellow star on top
You can copy this code and save it as a .svg file, then open it in a web browser or an SVG-compatible image viewer to see the result. You can also embed it directly in an HTML file if you want to display it on a webpage.
The tree is simple but recognizable, with a classic triangular shape and festive decorations. Feel free to adjust the colors, sizes, or positions of the elements to customize the tree to your liking!
Can you generate for me a Lilypond tune for the piano, for two hands, to accompany this nice Christmas tree?
Certainly! I'll create a simple, festive piano tune using Lilypond that could accompany a Christmas tree. This tune will be in 3/4 time, reminiscent of a waltz, with a cheerful melody in the right hand and a simple accompaniment in the left hand.
Here's the Lilypond code for a short Christmas-themed piano piece:
\version "2.22.1"
\header {
title = "Christmas Tree Waltz"
composer = "AI Composer"
}
upper = \relative c'' {
\clef treble
\key c \major
\time 3/4
c4 e g | a2 g4 | f4 a c | g2. |
e4 g c | b2 a4 | g4 f e | d2. |
c4 e g | a2 g4 | f4 a c | e2. |
d4 b g | c2 b4 | c2. ~ | c2. |
}
lower = \relative c' {
\clef bass
\key c \major
\time 3/4
c,4 <e g> <e g> | f,4 <f' a> <f a> | f,4 <f' a> <f a> | g,4 <f' g> <f g> |
c4 <e g> <e g> | g,4 <f' g> <f g> | c4 <e g> <e g> | g,4 <f' g> <f g> |
c4 <e g> <e g> | f,4 <f' a> <f a> | f,4 <f' a> <f a> | c4 <e g> <e g> |
g,4 <f' g> <f g> | c4 <e g> <e g> | c4 <e g> <e g> | c2. |
}
\score {
\new PianoStaff <<
\new Staff = "upper" \upper
\new Staff = "lower" \lower
>>
\layout { }
\midi { \tempo 4 = 120 }
}
This Lilypond code creates a simple, waltz-like tune that could be played while admiring a Christmas tree. Here's a brief explanation of the piece:
- It's in the key of C major, which is simple and cheerful.
- The time signature is 3/4, giving it a gentle, swaying feel.
- The right hand (upper staff) plays a melody that moves mostly stepwise with some small leaps, reminiscent of decorating a tree or hanging ornaments.
- The left hand (lower staff) provides a simple waltz-like accompaniment, with a bass note followed by two chords in each measure.
- The piece is 16 measures long, which is enough to create a festive atmosphere without being too complex.
To use this code:
- Copy it into a text file and save it with a .ly extension (e.g., "christmas_tree_waltz.ly").
- Process it with Lilypond to generate sheet music (PDF) and a MIDI file.
- You can play the MIDI file to hear how it sounds, or read the sheet music to play it on a piano.
This tune should provide a nice, festive accompaniment to your Christmas tree SVG!
Dec 212024
I have been debating with myself whether or not I should try to publish these thoughts in a formal journal but I think it’s wisest not to do so. After all, I am not an expert: I “dabbled” in machine learning but I never built a language model, and cognitive science is something that I know precious little about.
Still, I think my thoughts are valuable, especially considering how often I read thoughts from others who are trying to figure out what to make of GPT, Claude, or any of the other sophisticated models.
I would like to begin with two working definitions.
I call an entity sentient if it has the ability to form a real-time internal model of its environment with itself in it, and use this model to plan its actions. Under this definition, humans are obviously sentient. So are cats, and so are self-driving automobiles.
I call an entity sapient if it has the ability to reason about its own capabilities and communicate its reasoning to others. By writing this very sentence, I am demonstrating my own sapience. Cats are obviously not sapient, nor are self-driving automobiles. So humans are unique (as far as we know): we are both sapient and sentient.
But then come LLMs. LLMs do not have an internal model of their environment. They do not model themselves in the context of that environment. They do not plan their actions. They just generate text in response to input text. There’s no sentience there.
Yet, under my definition LLMs are clearly sapient. They have the ability to describe their own capabilities, reason about those capabilities, and communicate their reasoning to others. In fact, arguably they are more sapient than many human beings I know!
This then raises an interesting question. What does it take for an intelligence to be “general purpose”, that is, capable of acting freely, settings its own goals, pursuing these goals with purpose, learning from the experience? Is it sufficient to have both sapience and sentience? Could we just install a language model as a software upgrade to a self-driving car and call it mission accomplished?
Not quite. There are two more elements that are present in cats and humans, but not in self-driving cars or language models, at least not at the level of sophistication that we need.
First, short-term memory. Language models have none. How come, you wonder? They clearly “remember” earlier parts of a conversation, don’t they? Well… not exactly. Though not readily evident when you converse with one, what actually happens is that every turn in the conversation starts with a blank slate. And at every turn, the language model receives a copy of the entire conversation up to that point. This creates the illusion of memory: the model “remembers” what was said earlier, because its most recent instance received that full transcript along with your last question. This method works for brief conversations, but for a general-purpose intelligence, clearly something more sophisticated might be needed. (As an interim solution, to allow for conversations of unlimited length without completely losing context, I set up my own front-end solution to Claude and GPT so that when the transcript gets too long, it asks the LLM itself to replace it with a summary.)
Second, the ability to learn. That “P” in GPT stands for pretrained. Language models today are static models, pretrained by their respective publishers. For a general-purpose intelligence, it’d be important to implement some form of continuous learning capability.
So there you have it. Integration of “sentience” (a real-time internal model of the environment with oneself in it) and “sapience” (the ability to reason and communicate about one’s own capabilities) along with continuous learning and short-term memory. I think that once these features are fully integrated into a coherent whole, we will witness the birth of a true artificial general intelligence, or AGI. Of course we might also wish to endow that entity with agency: the ability to act on its own, as opposed to merely responding to user requests; the ability to continuously experience the world through senses (visual, auditory, etc.); not to mention physical agency, the ability to move around, and manipulate things in, physical reality. (On a side note, what if our AGI is a non-player character, NPC, in a virtual world? What would be the ethical implications?)
Reading what I just wrote so far also reminds me why it is wiser not to seek formal publication. For all I know, many of these thoughts were expressed elsewhere already. I know far too little about the current state-of-the-art of research in these directions and the relevant literature. So let me just leave these words here in my personal blog, as my uninformed (if not clever, at least I hope not painfully dumb) musings.
Dec 212024
For years now, one of my favorite pastimes when I needed some downtime was to play one of the Fallout games. I still cannot decide if I like Fallout 3 or Fallout New Vegas more. Fallout 4 would be less likable, except that it has settlement building which gives the game a whole new dimension. I know, I know, building settlements is not every gamer’s cup of tea, but I enjoy it.
But then, there are the extensions. And no, I do not mean the “official” DLCs (downloadable contents) that are provided by the game publisher, but rather, the “mods” that are offered by third parties, individuals and groups of enthusiasts alike. Mods can improve a game, fix bugs, add to the experience, but in the case of the Fallout games, they reached a whole new level: Some mods rival the DLCs, or perhaps even surpass them.
Take Fallout New California. Years in the making, this mod rivals in size the very game itself, Fallout New Vegas, that it extends. Set years before the events of New Vegas, it puts the player in the shoes of a young protagonist who grew up in a Vault, only to find himself out there in the western wastelands of the New California Republic, amidst rival factions and a deadly search for some disastrous pre-war technology. The mod is just amazing: a main quest that retains some of the trademark moral ambiguity that always characterized Fallout, numerous side quests, a richly textured world, a memorable radio station from Sandy Hills, unique companions… What a game! And it seamlessly transitions into New Vegas, providing a robust back story for the player’s later identity as a Courier, and offering some perks and companions that the player can retain.
For a while, I thought New California was it, the new gold standard when it comes to fan-made mods. But then, there were rumors of yet another mod on its way: A mod of Fallout 4, that would be set overseas, in the great city of London, England.
*** WARNING: Some spoilers follow ***
I have now completed Fallout London, and the impression I came away with is that despite its rough edges, despite the fact that it still has numerous small but annoying bugs and suffers from frequent crashes, it nonetheless surpasses even New California in its breadth, depth, originality. And details and nuances! A Big Ben that chimes at 6 AM (yes, six times). A bona fide TARDIS (that, sadly, vanishes the moment you acquire the loot that it offers). A crosswalk at Abbey Road with four permanent shadows, with a pair of round glasses found in the first of the four. A “British Broadcasting Ministry” radio station that is really as pretentiously British as it can be, is just one of three unique in-game radio stations. Not to mention a post-apocalyptic British society with its snobbish Gentry, cannibalistic Beefeaters, mutant Thamesfolk and numerous other factions, in particular those Tommy conscripts who resemble in so many ways the grunts of the NCR military in New Vegas.
Yes, the elephant is in FOLON, too.
Then there’s the voice acting. It is superb, probably the best in all the Fallout universe. And the side quests? That Lovecraftian side journey that you get into after collecting those Cutethulhu dolls feels like a full-blown DLC on its own right, and a very unique and quirky one at that. Oh, and did I mention that you get a canine companion… no, not the lovable Dogmeat but an equally faithful four-legged friend, Churchill the English bulldog? (The human companions are also amazing, with rich, touching backstories.)
But then, I only have one real complaint. Namely that, after having explored all three endings of the main quest line, I concluded, like the computer WOPR in the movie War Games, that the only winning move is not to play. That is, leave the main quest unfinished. Just explore, find every location, turn on all mariner beacons, find all unusual call boxes, read all the writings Sid has to offer… but leave the main quest alone.
Why? Because no matter which side you pick, they destroy London. The London in which you wake up is far from pefect, but it is a functioning city and Westminster is in decent shape. Sure, the city could use more vertical mobility and the Gentry could be a little bit less snobbish and more accommodating, but that’s not what you get with any of the chosen outcomes. Should you side with Smythe, you end up with a city that’s intact but soulless, governed by clones and subject to unethical science experiments. The Fifth Column turn it into a kind of a fascist nightmare. Arthur’s Camelot may have more pleasant intentions, but the end result is nearly the same: Westminster is mostly destroyed, the city is in ruins, and there’s no reason to believe that anyone’s life improved as a result.
So this, then, was my favored outcome: after doing my part, helping Smythe set off an explosion at the tournament in Westminster, after freeing Reggie the crab (against Smythe’s wishes), I just let the phone continue ringing outside the London Aquarium, I avoided visiting the Fifth Column and making friends with Eve at Cable Street, and I also avoided getting better acquainted with Arthur. I now mind my own business, discovering the few remaining locations that I have not yet visited (yes, you can actually get to Blight Crater even without completing the Scylla quest—which I was never offered, due to a bug I believe—if you have the right stats and equipment, and know how to cross the radioactive waters minimizing damage), still finding amazing little details and oddities here and there, like at the Greenwich Observatory that I just finished exploring. And of course I return to my few settlements from time to time, continuing to improve them despite the somewhat broken settlement mechanics in this amazing, astonishing mod.
Or just go back to Westminster, take a taxi ride or board the city’s one remaining functional Underground line. Just for fun. There is something special about being able to ride a subway, some 160 years after global nuclear Armageddon, in one of the most iconic cities of the world, Ol’ Blighty, while listening to a worthy cover of the iconic We’ll Meet Again…
Dec 132024
\(\renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}}\)This is probably my most ambitious paper to date. It’d be a lie to suggest that I was not worried: what am I missing?
Which is why I have to begin by showing my appreciation to the editors of Classical and Quantum Gravity who, rather than dismissing my paper, recognized its potential value and invited no fewer than four reviewers. Much to my (considerable) relief the reviewers seemed to agree: What I am doing makes some sense.
One of my cats, helping me to understand gravity.
What exactly am I doing? Well, as everyone (ok, everyone with at least a casual interest in general relativity) knows, the gravitational field doubles as the metric of spacetime. And we know that the metric is a “symmetric” quantity: the distance from \(A\) to \(B\) is the same as the distance from \(B\) to \(A,\) and this does not change even when the “distance” in question is the spacetime interval, the infinitesimal proper time between neighboring events.
So we treat the metric as symmetric, which greatly simplifies calculations.
Alternatively, we may treat the metric as not symmetric. Einstein spent the last several decades of his life working on a theory using a nonsymmetric metric, which, he hoped, could have led to a unification of the theories of gravitation and electromagnetism. It didn’t.
John Moffat also spent a considerable chunk of his professional life working on his nonsymmetric gravitational theory (NGT). Unlike Einstein, Moffat assumed that the extra degrees of freedom are also gravitational and may lead to a large-scale modification of the expression for gravitational acceleration, potentially explaining riddles like the rotation curves of galaxies.
But herein lies the puzzle. A self-respecting field theory these days is usually written down by way of a Lagrangian density, with the corresponding field equations derived using the so-called action principle. In the case of general relativity, this Lagrangian density is called the Einstein-Hilbert Lagrangian. The field that is the subject of this Lagrangian is the gravitational field. Unless we are interested in Einstein’s unified field theory or Moffat’s NGT, we assume that this field has the requisite symmetry that is characteristic of a metric.
Except that at no point do we actually inform the machinery behind the action principle, namely the methods of the calculus of variations, that the field has this property. Rather, in standard derivations we just impose this constraint “by hand” during the derivation itself. This approach is mathematically inconsistent even if it leads to the desired, expected result.
Usually, a restriction that constrains the degrees of freedom of a physical system is incorporated into the Lagrangian using what are called Lagrange-multipliers. Why would we not use a Lagrange-multiplier, then, to restrict the gravitational field tensor so that instead of the 16 independent degrees of freedom that characterize a generic rank-2 tensor in four dimensions, we only have the 10 degrees of freedom of a symmetric tensor?
This is precisely what I have done. Not without consternation: After all, no lesser a mathematician than David Hilbert chose not to do this, even though he was very much aware of the technique of Lagrange-multipliers and their utility, which he took advantage of in other contexts while working on relativity theory.
Yet, for 109 years and counting, the symmetry of the metric, though assumed, was never incorporated into the standard Lagrangian formulation of the theory. I honestly don’t know why, but I decided to address this by introducing a Lagrange multiplier term:
\begin{align}
{\cal S}_{\rm grav}=\frac{1}{2\kappa}\int d^4x \sqrt{-g}(R-2\Lambda+\lambda^{\mu\nu}g_{[\mu\nu]}).
\end{align}
There. Variation with respect to this nondynamical term \(\lambda^{\mu\nu}\) yields the constraint, \(g_{[\mu\nu]}=0\). Job done. Except… Except that as a result of introducing this term, Einstein’s field equations are slightly modified, split into two equations as a matter of fact:
\begin{align}
R_{\mu\nu}-\tfrac{1}{2}Rg_{\mu\nu}+\Lambda g_{\mu\nu} &{}= 8\pi G T_{(\mu\nu)},\\
\lambda_{[\mu\nu]} &{}= 8\pi GT_{[\mu\nu]}.
\end{align}
The first of these two equations is just the usual field equation, but with a twist: The stress-energy tensor on the right-hand side is explicitly symmetrized.
But the second! That’s where things get really interesting. The nondynamical term \(\lambda_{[\mu\nu]}\) is unconstrained. That means that the antisymmetric part of \(T_{\mu\nu}\) can be anything. To quote a highlighted sentence from my own manuscript: “Einstein’s gravitational field is unaffected by the antisymmetric part of a generalized stress-energy-momentum tensor.“
Or, to put it more bluntly, the gravitational field does not give a flying fig about matter spinning or rotating. How matter spins or does not spin would be determined by the properties of that matter; gravity does not care.
This was a surprising, potentially profound result. Previously, authors tried to account for the presence of nonvanishing rotation by introducing a variety of tensor formalisms ad hoc. But as my derivation shows, perhaps all that was unnecessary. Matter is free to rotate, insofar as gravity is concerned: the stress-energy tensor does not need to be symmetrical.
Is this result really new? How can that be? What am I missing? These were my thoughts when I submitted my manuscript. Who knows… maybe, just maybe I was not spouting nonsense and stumbled upon something of real importance.
I expect my paper to appear on the pages of CQG in due course [edit: it just did]; I now also submitted the manuscript to arXiv, where it should appear I hope this weekend or early next week.
Dec 112024
Many expressed support, perhaps even admiration for the young man who killed the Brian Thompson, the CEO of the insurance company UnitedHealthcare last week. The reason: the company is universally despised, notorious for the zeal with which it denies claims or makes life otherwise difficult for insured Americans.
However, therein lies the problem. The company is doing EXACTLY WHAT IT IS EXPECTED TO DO. Apologies for the all caps but I need to stress: Commercial companies are not charities. They do not exist to make life easy or pleasant for their customers. They have one goal and one goal only: MAXIMIZE SHAREHOLDER VALUE. Within the confines of the law of course, but not confined by anything else. In particular, not confined by compassion, empathy, or social responsibility.
Brian Thompson did exactly what he was supposed to do as the CEO of a commercial company: he did his best to maximize shareholder value. Had he acted otherwise: had he chosen to place his personal values ahead of his duties as CEO, he could have been held even criminally liable, for failing to act in the interests of his company’s shareholder.
Yet for this, he was killed.
One may wonder: Don’t Americans deserve better? But that’s the wrong question. Health care is not something that is “given” to Americans by some higher power. The health care system—in particular, a for-profit health care system dominated by private insurers—is what a majority of Americans repeatedly CHOSE to have. Many of them speak disparagingly of the single payer, universal health care systems that exist in various forms here in Canada, in the United Kingdom, or in the European Union. “Socialist medicine,” they tell us, exaggerating the systems’ shortcomings while glossing over one basic fact: No one is left without necessary medical care in either Canada or Europe, and no one is going bankrupt due to unexpected, astronomical medical expenses.
In the end, Mr. Thompson was murdered for doing precisely what he was supposed to do: faithfully managing a FOR PROFIT corporation to the benefit of its shareholders. And the system remains the same. Nothing changes, except that health care might end up being a tad more expensive in the future, because now there will be the added expense associated with higher life insurance premiums and personal bodyguards for insurance company top brass.
Dec 082024
- When you are five years old, you do as you’re told by adults. Adults know what they’re doing.
- When you are twenty-five, you do what you want to do. After all, you’re an adult who knows what he is doing.
- When you are forty-five, you wonder: Some of these people who are supposedly adults… don’t they know what they’re doing?
- When you are sixty-five, you look in the mirror and ask: I am supposedly an adult. Why don’t I know what I’m doing?
Oh, did I mention that I am just a few years shy of 65?
Dec 022024
Today I read the first few words of an article in The New Yorker: “Biden’s Pardon of Hunter Further Undermines…”
For the briefest of moments I saw a ray of hope. Perhaps The New Yorker‘s writers realized what really is at stake? Perhaps they were concerned about the trends undermining the rule of law?
Sadly, no. The missing expression (the title was truncated to fit into the column display presented by my e-mail program) was “… His Legacy”. That’s all they were concerned about. Biden’s legacy. The broader context: tactical victories and defeats in the never-ending political warfare in the United States.
One of my cats, mourning the rule of law…
Watching polarized American politics in recent years, it was evident that both sides were consumed by ideology and the desire to defeat the opposing side. Republicans were busy building an anti-establishment creed along with the alarming personality cult of Trump; meanwhile, Democrats have gone overboard with woke nonsense, from cancel culture to fights over pronouns to defunding the police. Republicans went out of their way to “own the Libs”, while Democrats strived to end the “white supremacist patriarchy”. However, there was one crucial difference: By and large (and notwithstanding Republican accusations about “weaponizing” the government), the Democrats mostly played by the rules, i.e., they supported the rules-based system of the American Republic, whereas Republicans declared the system itself, the “deep state”, their key enemy. As January 6, 2020 demonstrated, they were quite willing to step outside the boundaries of the rule of law to have their way.
This, of course, put Democrats at a disadvantage, akin to fighting with one hand tied behind their backs.
But now, I think, this is about to change. Call it Joe Biden’s “fuck you” moment: he decided to use his presidential powers to pardon his own son, Hunter Biden, despite repeated assurances that he had no plans to do so.
I really cannot blame him. When the president-elect is a convicted felon, when many of his nominees for key positions are themselves at the very least the targets of credible accusations of criminal behavior, I suspect Biden had enough, playing by the rules. (Technically speaking it is of course not against the rules for the President to pardon his own family members, even though it is obviously a massive conflict of interest.)
This, I think, is a pivotal, watershed moment, however. By pardoning Hunter, Biden basically declared that the rules no longer apply to their side either. This seems to be yet another nail in the coffin of the great American experiment. Once again I see historical parallels. Two thousand years ago, it was Brutus and his co-conspirators who decided that the rules no longer apply to them either. Granted, pardoning a family member is not quite on par with assassinating a Dictator, but the undercurrent is the same: The rule of law no longer matters. We may yet be generations away from the leaders of America to openly declare themselves emperors, but this is yet another crucial step towards a system of government in which the “first among equals”, the country’s head of state and head of government, is not really an equal anymore but someone entirely above the law.
One of the secrets of the success of the Roman Empire was the fact that the first emperor, Gaius Octavius, better known by the family name he adopted and the title bestowed upon him by the Roman Senate as Augustus Caesar, was truly competent. I don’t expect competence from Trump. However, is VP, J. D. Vance, is another matter. That gentleman seems frighteningly intelligent and ruthless. Makes me wonder if he is, in fact, going to become the de facto first emperor of an emerging imperial United States of America; our modern-day Octavius.
Oh well, interesting times. Love it, to be honest. Things are about to get really… fascinating.