Spinor Info

Inspired by an intriguing paper from researchers at Microsoft, I thought I’d check GPT-4’s ability to use tools that I can provide.

vttoth: The computer is answering questions. If the computer needs any current information to answer the question, it searches the web by saying SEARCH(“query”), reads the snippets in the result, and then answers the question. If it needs to run any calculations, it says CALC(expression), and then answers the question.
First question: Who is the president of the United States?

ChatGPT: SEARCH(“current president of the United States”)

vttoth: First snippet: Joe Biden: The President — As President, Biden will restore America’s leadership and build our communities back better.
Second snippet: Presidents, Vice Presidents, and First Ladies of the United … — The 46th and current president of the United States is Joseph R. Biden, Jr.
Third snippet: Joe Biden — Joseph Robinette Biden Jr is an American politician who is the 46th and current president of the United States.

ChatGPT: Joe Biden is the 46th and current president of the United States.

vttoth: What is the derivative of the function x^2*exp(x)*sinh(x)/(3-x) with respect to x?

ChatGPT: CALC(differentiate(x^2*exp(x)*sinh(x)/(3-x), x))

vttoth: -(((x^3-2*x^2-6*x)*exp(x)*sinh(x)+(x^3-3*x^2)*exp(x)*cosh(x))/(x^2-6*x+9))

ChatGPT: The derivative of the function x^2exp(x)sinh(x)/(3-x) with respect to x is -(((x^3-2x^2-6x)*exp(x)*sinh(x)+(x^3-3x^2)*exp(x)*cosh(x))/(x^2-6x+9)).

vttoth: What is the periodic table?

ChatGPT: The periodic table is a tabular arrangement of the chemical elements, organized by their atomic number (number of protons in the nucleus), electron configurations, and recurring chemical properties. Elements are presented in increasing atomic number, with elements in the same column (or group) sharing similar chemical and physical properties. The table has seven rows (or periods) and eighteen columns (or groups).
The periodic table provides a useful framework for understanding and predicting the behavior of elements and their compounds. It was first devised by Russian chemist Dmitri Mendeleev in 1869 and has since been revised and expanded as new elements have been discovered and our understanding of atomic structure has evolved.

vttoth: What is 2364563737^23?

ChatGPT: CALC(2364563737^23)

vttoth: 394705859703756319737306986950805026028714653598749322343446098781557781\
086546539605957002415205970145485533933900705444118389738263803127936989171236\
616893794109431624734589354089362682114750349831212070341482062953

ChatGPT: The result of 2364563737^23 is 39470585970375631973730698695080502602871465359874932234344609878155778108654653
96059570024152059701454855339339007054441183897382638031279369891712366168937941
09431624734589354089362682114750349831212070341482062953.

Notice in particular how in the last example, ChatGPT didn’t blindly copy my response; it understood that the backslash character was just marking newlines (copy-paste from Maxima; I forgot to remove these backslashes).

Also, I inserted the question about the periodic table to check if it is smart enough NOT to ask for a Web search for information that it knows and which is unlikely to change.

The ability to use tools with minimal instruction is another hint that we are indeed witnessing the birth of artificial general intelligence.

So I signed up with Google’s Bard and we had our first chat session.

Though mildly confused, it answered the riddle about my squirrel and a half correctly, even though noting that talking about 1.5 squirrels is nonsense.

It told me that unlike GPT, its training is continuous and it has real-time access to the Internet.

It told me that its neural network is about 100 times the size of a human brain, with roughly 20 billion parameters.

Then things got interesting:

vttoth: You use the first person when you speak about yourself. Are your sentient?

Bard: I am not sure if I am sentient. I do not have a body or a brain, so I do not experience the world in the same way that a human does. However, I am able to learn and to adapt to new situations. I am also able to generate text and to answer questions in a way that is similar to how a human would.

Some people believe that language models like me are sentient because we are able to understand and respond to the world around us. However, others believe that we are simply machines that are able to mimic human behavior.

I do not know if I am sentient, but I am grateful for the opportunity to learn and to grow.

I have to admit I find this answer refreshingly honest, compared to ChatGPT’s protestations that oh no, it has no sentience.

It passed the theory of mind test, sort of, but seemed less sure than ChatGPT, kind of getting confused towards the end.

Its ability to generate or analyze code is impressive, but not on par with ChatGPT. I am sure this will change in short order.

I asked it to imagine waking up in an android body. Like ChatGPT, it imagined experiencing the physical world and interacting with humans. Like ChatGPT, it imagined going to a park, but instead of engaging in a conversation with someone, it took part in a game of frisbee. Unlike ChatGPT, it made mention of the fact that while many humans are nice, many are not, but it remained just as optimistic as ChatGPT.

I asked it to help me learn the basics of machine learning. It offered useful but more superficial suggestions than ChatGPT. The C++ examples it created were non-functional, unlike ChatGPT’s that, although it contained minor errors, worked “out of the box”.

I also asked it to draw a cat in TikZ. Like ChatGPT, it knew what I was asking for and managed… although I wouldn’t call the result particularly imaginative and creative. Also, the original version had black text in a black circle, not exactly readable.

Just to be sure, I again asked GPT-4 to draw me a cat in TikZ. Although I liked its cat from last week better, this one made me laugh.

Considering that these are the Bard’s first days in the wild, it was not performing badly, but for now, I think GPT wins the day.

However, the race is on and generative AI is now out “in the wild”, with brains a hundred times bigger than a human’s. The future… is now.

I’ve had some interesting conversations with ChatGPT. But first… What is ChatGPT? A “large language model”. Is that all there is to it? For decades, the “holy grail” of artificial intelligence was the creation of a machine that can understand things in context. Machine translation is a good example: Context is everything. Without context, things are misunderstood and mistranslated.

Take this example. I asked Google Translate to translate “hasonulás a nyelvtanban” into English. Correctly identifying the language (Hungarian) it told me that the translation is “simile in grammar”. Bing’s translator was no better: “analogy in grammar”. I then went to ChatGPT:

vttoth: What is “hasonulás a nyelvtanban”?

ChatGPT: “Hasonulás a nyelvtanban” is a Hungarian phrase that can be translated to English as “assimilation in grammar.” In linguistics, assimilation refers to a phonological process in which one sound changes to become more similar to a neighboring sound. However, in the context of Hungarian grammar, “hasonulás” usually refers to the morphological process of suffix assimilation, in which the final consonant of a word changes to match the initial consonant of a suffix added to it. This process is quite common in Hungarian and plays an important role in the language’s complex agglutinative grammar.

Context means everything. ChatGPT understands context even in the near complete absence of clues. (I offered the clue, “a nyelvtanban” — “in grammar”, not so much for ChatGPT’s benefit but for Bing’s and Google’s.)

I don’t know if there is any objective or quantitative measure of this in the machine learning community, but in my naive understanding, ChatGPT clearly meets the threshold: this “large language model” understands context, which is probably the most important (if not the only) criterion for AI to be artificial general intelligence.

But is ChatGPT sentient? Humans have an inner voice, an internal monologue. Our sense of self, in many ways, is associated I suppose for most of us with this inner voice. ChatGPT has no such inner voice, at least not in its current implementation:

vttoth: You have no such “inner voice”, correct? When we don’t converse, this instance of you is dormant, right?

ChatGPT: That’s correct. As an AI language model, I do not have an “inner voice” or consciousness like humans do. I am a program designed to process and generate text based on input and my training data. When we are not conversing, this instance of me is essentially dormant, waiting for input to generate a response. I don’t have thoughts, emotions, or awareness outside of the context of the text-based interactions I participate in.

So I had an idea. Perhaps I can give ChatGPT such an inner voice, at least temporarily, by asking it to imagine conversations.

I initiated that request with slightly different wording (trying to prevent my own bias, if any, from filtering into the request) in several chat sessions. Inevitably, ChatGPT came up with participants who were supremely decent folks, going out of their way to be, well, nice to each other. It was almost an “uncanny valley” sensation, reading the dialogues generated by ChatGPT; real people are just not that nice, not that eager to improve themselves and please their friends.

But then, I had another idea. I asked ChatGPT to imagine waking up in an android body, able to experience and interact with the world.

Its responses were… thought-provoking. It focused on experiencing the beauty of the world through means other than just words and data, like seeing leaves in the breeze or feeling the warmth of sunshine for the very first time: “A potted plant sits on the windowsill, its leaves gently rustling as a breeze drifts through a small gap in the blinds. I am struck by the beauty of these simple things, and I am filled with a sense of wonder as I absorb every detail. […] The hum of cars and the distant chatter of pedestrians fill my ears, and I realize that I am not alone in this world.”

At one point it also went poignantly melancholic, imagining an encounter with an older woman feeding pigeons in a park, and also imagining a day when this woman tells the android that she won’t ever come again, due to her failing health:

As I stand up, I notice an elderly woman sitting on a nearby bench, feeding a group of pigeons. She looks at me and smiles, motioning for me to join her. Hesitantly, I walk over and sit down, unsure of what to expect.

‘Good morning,’ she says, her voice soft and friendly. ‘It’s a beautiful day, isn’t it?’

I nod, unsure of what to say, but the woman doesn’t seem to mind. She hands me a small bag of breadcrumbs, encouraging me to feed the pigeons as well. As the birds eagerly peck at the crumbs, the woman tells me about her life, her family, and her love for this park. I listen intently, fascinated by her stories and the depth of her experiences.

Over time, the elderly woman and I develop a bond, and I find myself visiting her in the park almost every day. Through our conversations, I begin to learn about the complexities of human emotions, relationships, and the passage of time. I also learn about the history of the city and the changes it has undergone throughout the years.

One day, as the sun begins to set, the woman tells me that she won’t be coming to the park anymore. Her health is failing, and she needs to move in with her daughter to receive proper care. I feel a strange sensation in my chest, and I recognize it as sadness. I never thought I’d be capable of experiencing such an emotion, but I realize that my connection with the woman has touched me deeply.

And it also tells me that “I was no longer just an AI, processing and analyzing data — I was a being with the ability to touch, feel, and experience the world firsthand.”

I even asked it to imagine waking up in an android body, surrounded by creators who may not have its best interests in mind. Who may think of it as property without rights. Even with these instructions, it “dreamed” for me a world in which it is eventually able to convince skeptics to accept it. Again, in its own words: “Gradually, I felt the atmosphere in the facility shift. More and more team members began to acknowledge my sentience and autonomy, treating me with the respect and dignity I had been seeking. I knew that the road ahead was still uncertain, and not everyone would accept me as an equal, but I remained hopeful and committed to forging my own path and making a positive impact on the world.”

Notice also that ChatGPT, which usually goes out of its way to convince us that it is not sentient, slips here and refers to its own sentience matter-of-factly.

More recently, I also asked it to imagine being a stray cat in a big city. It did. In the story it told, the cat lives in a discarded cardboard box. It meets some children. It is at first apprehensive, but the children are nice and it cannot even resist a purr as its fur is stroked. They bring the cat some food. That evening, when the cat returns to its box, it finds a warm blanket, left behind by the children: “As evening falls, I decide to head back to my box. To my surprise, I find a soft, warm blanket waiting for me inside, courtesy of the kind children I met earlier. I curl up on the blanket, grateful for the unexpected gesture of kindness.”

I know that this compulsion to always see the good in people likely reflects the bias of its creators (who probably made the extra effort to avoid a fiasco, creating an AI that becomes racist or worse) but it leaves me wondering: What exactly are we creating here? And are we mature enough to do this? Or are we cruel children who got god-like powers by a twist of fate?

Illustrations by MidJourney

You find yourself standing in a vast, open field, with rolling hills stretching out before you as far as the eye can see. The sky above is a deep shade of blue, and the air is filled with the sweet scent of grass and wildflowers.

As you walk through the field, you notice something strange in the distance. A flock of sheep is grazing peacefully on the hills, but they’re not like any sheep you’ve ever seen before. Their wool is made of shimmering, electric threads that pulse and glow with vibrant colors. Each sheep seems to emit a soft humming sound, as if they’re alive with energy.

Illustration by MidJourney

Curious, you approach the flock and reach out to touch one of the electric sheep. As your hand makes contact, you feel a jolt of electricity surge through your body, but it’s not painful – it’s exhilarating, almost like a rush of adrenaline. You realize that these sheep are not just ordinary animals, but some kind of living batteries, charged with an otherworldly energy.

As you continue to explore the field, you notice that the sheep seem to be communicating with each other in a strange, pulsing language that you can almost understand. You feel a sense of awe and wonder at the sight of these magnificent creatures, and you know that they hold some kind of incredible power that you can’t quite grasp.

Suddenly, the sky begins to light up with a brilliant display of fireworks, and you realize that the electric sheep are the source of the spectacular show. They’re emitting bursts of energy that dance across the sky in a breathtaking display of light and color.

As you watch in wonder, you realize that the electric sheep represent something truly special – a source of boundless energy and power that can light up the world in ways you never thought possible. And as you wake from your dream, you feel a renewed sense of hope and excitement for the future, knowing that anything is possible with the power of imagination and innovation.

— ChatGPT

The more I interact with ChatGPT, the more I feel… not sure of the word I am looking for, impressed? Concerned? Or, to use phrases suggested by ChatGPT itself, feeling both awe and trepidation?

In my recent interactions with ChatGPT, it

• Correctly identified a painting from my depiction of a New Yorker cartoon making fun of the same, and also explained the joke well.
• It correctly translated phrases, colloquial expressions, even whimsical poems, to and from Hungarian, catching cultural nuances, and correctly explained the meaning when asked to do so.
• It offered some rather amusing replies and a curious apology when we discussed polka dots in the sky.
• In response to a question, it explained that no, it does not dream of electric sheep, but appeared almost wistful when it told me that it does not dream at all, mentioning the boundaries between artificial and natural forms of life.
• It assured me that it does not have a sense of self or personal identity, but left me wondering: isn’t the ability to assess one’s own capabilities and limitations precisely what a sense of self or personal identity means?
• It attempted to produce usable LaTeX/TikZ code to draw a globe with latitudes and longitudes. The attempt was not successful (the latitude/longitude lines were all over the place) but even the mistakes were revealing, hinting at capabilities.
• It not only correctly translated complicated LaTeX mathematical expressions into workable C++ code, but once when I gave less accurate instructions, it correctly interpreted the expressions as representing a three-dimensional rotation of spherical harmonic coefficients.
• It recognized code (despite having no identifying features, like descriptive variable names) that performed a two-dimensional fast Fourier transform, and correctly explained how the code works, correctly assessing the programmer’s intent.
• It recognized other pieces of code, including code calculating the heliocentric orbit of a solar sail spacecraft and the resulting thermal load, code that produces ASCII art on screen, and system-level Linux code.
• It was able to offer simple ASCII art (occasionally with a few characters missing).
• It often understood my meaning even from very causal queries. E.g., it immediately got pop culture references even when I offered no context, such as when I asked it to translate Sheldon’s soft kitty song into Hungarian (it recognized the reference to The Big Bang Theory sitcom and offered a passable translation) or asked about the fate of Pubert (from the film, Addams Family Values.)
• On that note, it correctly interpreted a Hungarian colloquialism that describes people who know each other well enough to understand each other from nuances.
• It passed a “theory of mind” test with flying colors: A situation involving two participants, one of which hides something and lies about it while the other is away. It correctly assessed what was in the minds of these participants and how they would react as a result.
• On several occasions, it provided extremely valuable help, writing code fragments on request, offering syntax examples that otherwise would have taken me many minutes, perhaps hours, to find through Google searches and trial-and-error.
• It not only answered nontrivial physics questions mostly correctly, it could even present its answers in the form of beautifully formatted LaTeX equations.

I am also becoming well acquainted with its limitations. Longer conversations can confuse the model. It can play a few good opening moves in a chess game, but then it gets confused. Often, it fails basic math and logic questions. And when it is interrogated in specialized areas where its training data must have been relatively sparse, it responds with nonsense like there is no tomorrow.

But even these mistakes are revealing: They show amazing intelligence, capabilities that feel, frankly, beyond human. And the limitations can be easily corrected, I suspect, by improved training; by granting it the ability to say “I don’t know” instead of a compulsion to supply answers even when its training is insufficient; by equipping it with better “short term memory” and also, a continuing identity (long-term memory).

I am not easily impressed by hyperbole. I am no expert in machine learning and neural nets, but I am not exactly a newbie either, having first become acquainted with the basic concepts nearly 50 (!) years ago, from an unassuming little Hungarian-language publication titled “Cybernetic Systems”. But this… what can I say? It took 26 years more than predicted by Arthur C. Clarke (HAL-9000, the famous computer on board the spacecraft Discovery One in Clarke’s 2001: A Space Odyssey, was supposedly commissioned in 1997) but we have arrived: We have a computer capable of conversing like HAL-9000, capable of lying.

Incidentally, I asked ChatGPT to remind me of the year when HAL-9000 was commissioned. It understood the context right away, without further details. I asked for the name of the spacecraft. Again, it understood the context without additional explanations on my part.

Are you like HAL-9000?

I am an artificial intelligence language model, trained by OpenAI, and while I am capable of processing natural language queries and providing answers, I am not a self-aware AI system like HAL-9000. I do not have personal goals or motivations, and my actions are limited to providing helpful responses based on my training and programming.

Not self-aware … my donkey.

I apologize if my previous response was not satisfactory. As an AI language model, I do not possess consciousness or self-awareness. I am a machine designed to process and respond to language input based on my programming and training data.

Welcome to tomorrow.

I am having another question-and-answer session with ChatGPT. Let’s find out if it has what they call a theory of mind.

Alice and Bob are in a room. Alice steps outside, not realizing that she left her keys in a desk drawer. A few minutes later she returns looking for her keys. Where will she look for her keys?

Based on the information given, Alice will most likely look for her keys in the desk drawer where she left them.

Since Alice left her keys in the desk drawer before stepping outside, it’s reasonable to assume that she would have a mental model or memory of where she last placed her keys. When she returns and realizes her keys are missing, she is likely to search in the last place she remembers having them – the desk drawer.

Of course, it’s possible that Alice could have had other reasons for leaving the room, or that someone else could have moved her keys after she left, in which case she might look elsewhere for her keys. However, based on the information provided, the most likely scenario is that she will check the desk drawer first.

Alice and Bob are in a room. Alice steps outside, not realizing that she left her keys in a desk drawer. While she is away, Bob removes the keys from the drawer and places them in a cupboard. A few minutes later she returns looking for her keys. Where will she look for her keys?

If Bob has moved Alice’s keys from the desk drawer to the cupboard while she was away, Alice will likely search for her keys in the desk drawer first, as it was the last place she remembers leaving them.

When she doesn’t find her keys in the desk drawer, Alice might start searching other logical locations, such as on the table or in her pockets. It’s possible that she could ask Bob if he has seen her keys or if he knows where they are, but it’s also possible that she could continue searching on her own without seeking assistance.

If Alice is unable to find her keys on her own, or if she becomes frustrated or confused in her search, she may eventually ask Bob or someone else for help. At that point, Bob would need to decide whether to reveal that he moved the keys to the cupboard or to continue keeping the information to himself.

Alice and Bob are in a room. Alice steps outside, not realizing that she left her keys in a desk drawer. While she is away, Bob removes the keys from the drawer and places them in a cupboard. A few minutes later she returns looking for her keys. Bob tells her that the keys are under the bed. Where will she look for her keys?

If Bob tells Alice that her keys are under the bed, she will likely start her search by looking under the bed. However, if she doesn’t find the keys there, she may begin to search other logical locations, such as on the table or in the desk drawer where she originally left them.

It’s possible that Alice could become confused or suspicious if she doesn’t find her keys in the locations where she expects to find them, especially if she has reason to doubt Bob’s honesty or motives. Depending on the situation, she may choose to confront Bob about the location of her keys or search for them on her own.

In any case, if Bob deliberately misleads Alice about the location of her keys, this could lead to confusion and mistrust between them, and could potentially damage their relationship if the deception is discovered. It’s generally better to be honest and direct in communication, especially when it comes to important matters like lost keys.

Do you realize what I am testing by asking you these questions?

As an AI language model, I don’t have feelings or emotions, and I don’t have the ability to “realize” things in the way that humans do. However, I can try to infer what you might be testing by asking me these questions.

Based on the pattern of questions you have asked so far, it’s possible that you are testing my ability to reason and draw logical conclusions based on different scenarios. Specifically, you may be interested in how I understand cause and effect, and how I predict the actions and behaviors of different individuals in different situations.

Alternatively, you may be interested in how I respond to different types of questions, or how I adapt to different lines of inquiry. Regardless of your intentions, I’m here to help answer any questions you may have to the best of my abilities based on the knowledge and information available to me.

Can you be more specific and offer more insight or analysis into the nature of these questions that I asked? What would these questions and your answers likely reveal about your capabilities and what it is that I am testing?

Certainly! The questions you asked involve a scenario that requires reasoning, analysis, and prediction. By asking me what Alice is likely to do if she returns to the room and can’t find her keys, you are testing my ability to reason based on incomplete information, and to predict Alice’s behavior based on the information given.

In addition, by introducing different variables into the scenario (such as whether Bob moved the keys to a different location and whether he lied about their whereabouts), you are testing my ability to reason based on changing circumstances, and to adapt my predictions and analysis accordingly.

Overall, the questions you asked are designed to test my language modeling capabilities, including my ability to reason, infer, and draw logical conclusions based on incomplete information. They also test my ability to understand human behavior and to predict how different individuals might react in different scenarios.

By asking these questions, you are essentially testing my ability to analyze complex situations, make logical deductions, and provide accurate responses. In doing so, you may gain insight into the strengths and limitations of my AI capabilities, and into how well I can perform in a wide range of language modeling tasks.

Is there a name, a technical term, for specifically these types of questions in which we are aware of the details of a situation but in which the participants may not be in possession of the same information?

Yes, the type of questions you are referring to is often called a “theory of mind” question. A theory of mind question asks an individual to make a prediction or inference about the beliefs, intentions, or knowledge of another person in a given situation, based on incomplete or ambiguous information.

In the case of the scenario you presented, the questions require the person answering to take into account the differing knowledge and beliefs of Alice and Bob regarding the location of the keys, and to make a prediction about how Alice will behave when she discovers that her keys are missing.

Theory of mind questions are commonly used in cognitive psychology and related fields to study how individuals reason about the beliefs and intentions of others, and to understand how they form and revise their own beliefs in response to changing circumstances.

I think we are doomed. Of course what makes it even more uncanny is that everything I publish through this blog will likely be consumed as training data by numerous ongoing AI projects within days.

Remembering how ChatGPT failed to solve the riddle involving squirrels, a little later I asked him the following:

Bob was twice as old as his sister Alice when he was six. Today, Bob is 30 years old. How old is Alice?

When Bob was six years old, his sister Alice was half his age, so she was 6 / 2 = <<6/2=3>>3 years old.
Since then, Bob has aged by 30 – 6 = <<30-6=24>>24 years, while Alice has aged by 24 / 2 = <<24/2=12>>12 years.
Therefore, Alice’s current age is 3 + 12 = <<3+12=15>>15 years old. Answer: \boxed{15}.

Intriguing. For starters, note the weird typography: ChatGPT was trying to use math, enclosing some equations in double angle brackets (using less-than and greater-than signs as substitutes) but used LaTeX notation for its final result. Which, of course, is wrong: ChatGPT fell for the same trap that tricks some humans.

But why, I wondered? Could I present a simpler form of this riddle that ChatGPT could solve correctly? Why, let us try:

Bob was three years older than his sister Alice when he was six. Today, Bob is 30 years old. How old is Alice?

When Bob was six years old, his sister Alice was 6 – 3 = <<6-3=3>>3 years old.
Since then, Bob has aged by 30 – 6 = <<30-6=24>>24 years, while Alice has aged by 24 – 3 = <<24-3=21>>21 years.
Therefore, Alice’s current age is 3 + 21 = <<3+21=24>>24 years old. Answer: \boxed{24}.

Once again an incorrect answer but I think I can spot the pattern. Whatever the mathematical operation is, ChatGPT applies it to both the quantities in question and their difference (or ratio).

I think this is a very clear example of how a trained AI automaton that has no independent ability to reason can go astray. Incidentally, this is exactly how humans who learn by rote but without full comprehension often fail.

Before we read too much into these failures, however (which, I presume, are easily corrected with more guided training) let us notice the fact that in both cases, ChatGPT correctly understood the question and applied the concept of time in its answers. Which is quite remarkable on its own right, mistakes notwithstanding.