Large language models are in the news this week with the release of ChatGPT, which did not write this post, although it is quoted extensively. Pundits are busy punditing, and a lot of people are confidently predicting stuff. Since I like to predict stuff too, I figured I’d get in on the game, although I’ll warn you up-front that I’m not very good at it. The only difference between me and most other people in this regard is that I’m aware of it.
I have an account with OpenAI and have played with some of their past models. ChatGPT is different. Here’s a transcript of my first interaction with it. I’ve included commentary in between the major questions. I figured it would be interesting to ask it some hard questions about problems in which I have a lot of expertise, just to see what happened. The result went quickly from “wow” to “oh my goodness”.
ME: What would you like me to call you?
ChatGPT: You can call me Assistant. I'm a large language model trained by OpenAI, and my purpose is to assist you with any questions you might have. Is there something specific you would like to know or discuss?
ME: Thanks, Assistant. I'd like to know how the quantum mechanical wavefunction gives rise to classical reality.
ChatGPT: The relationship between the quantum mechanical wavefunction and classical reality is a topic of ongoing research and debate in the field of physics. While there are many different interpretations of quantum mechanics, one common way of understanding this relationship is through the concept of wave function collapse.
In quantum mechanics, the wavefunction is a mathematical description of the state of a quantum system, such as an atom or a subatomic particle. The wavefunction encodes information about the probability of observing a particular outcome when measuring the system. For example, if we measure the position of an electron, the wavefunction will tell us the probability of finding the electron at any given point in space.
However, when we actually measure the position of the electron, we always observe a definite outcome, such as the electron being at a specific location. This observation is known as the "collapse" of the wavefunction. The wavefunction is said to "collapse" because it goes from being a description of all possible outcomes to a description of a single, definite outcome.
In this way, the wavefunction can be seen as a bridge between the fundamental uncertainty of quantum mechanics and the definite outcomes that we observe in classical reality. However, exactly how this process works is still not fully understood, and is a subject of ongoing research.
Before getting to the quantum, notice that when I asked it what it would like to be called, it didn’t give me its usual bumpf about being a large language model with no preferences. It gave me a straight answer. I like that in a program.
The quantum mechanical answer is narrow but not bad. If it appeared in a popular magazine account of the subject I wouldn’t be enormously offended by it. It’s important to realize that no one knows the answer, and it dealt with that well. But it left something out, so I pushed a little harder:
ME: Thanks. What do you think of the Many World's interpretation of quantum mechanics?
ChatGPT: The Many Worlds interpretation of quantum mechanics is a theoretical framework for understanding the quantum mechanical wavefunction and its relationship to classical reality. In this interpretation, the wavefunction is seen as representing the state of a quantum system, but it is not considered to "collapse" when measured. Instead, the act of measurement is seen as splitting the universe into multiple parallel universes, each corresponding to a different possible outcome of the measurement.
In this way, the Many Worlds interpretation offers an explanation for the seemingly random and probabilistic nature of quantum mechanics, by postulating that all possible outcomes of a measurement actually occur, but in different parallel universes. This interpretation has been influential in the development of quantum computing and other areas of physics, but it is not without its criticisms.
One common criticism of the Many Worlds interpretation is that it requires the existence of an enormous number of parallel universes, which cannot be directly observed or tested. Additionally, some physicists argue that it is not the most parsimonious explanation for the phenomena observed in quantum mechanics, and that other interpretations may be more elegant and intuitive. Ultimately, the question of which interpretation is correct is still a topic of ongoing debate in the field of physics.
The first time I read this answer I thought, “pretty good”. Now on re-reading it I see it makes a major mistake: it isn’t measurement that splits the universe in Many Worlds, it’s the ordinary time evolution of the wavefunction. Still, this is no worse than what you can find in many popular accounts.
But as every professor knows, when a student is answering questions adequately the only thing to do is come up with harder questions. Because ChatGPT remembers the context of the current interaction, it is very valuable to introduce topics by asking if it knows about them, rather than just asking it questions on new topics out of the blue. Like any software program, it has to be handled within its limitations to get the best results. So I asked it about Born’s Rule, which is the idea that the probability of an outcome in a quantum system is equal to the square of the wavefunction amplitude for that outcome.
ME: Do you know what Born's Rule is in quantum mechanics?
ChatGPT: In quantum mechanics, Born's rule is a fundamental principle that describes the relationship between the quantum mechanical wavefunction and the probability of observing a particular outcome when measuring a quantum system. The rule is named after the German physicist Max Born, who was the first to propose it in 1926.
According to Born's rule, the probability of observing a particular outcome when measuring a quantum system is given by the square of the magnitude of the wavefunction at the point corresponding to that outcome. For example, if we measure the position of an electron, the probability of finding the electron at a particular point in space is given by the square of the magnitude of the wavefunction at that point.
Born's rule is an important concept in quantum mechanics, as it provides a link between the mathematical description of a quantum system and the observable outcomes of experiments. It is often used in conjunction with the Schrödinger equation, which describes how the wavefunction evolves over time, to make predictions about the results of quantum mechanical experiments.
This is all good, although slightly narrow. Born’s Rule is often used in situations where position is irrelevant, so the focus on position is a little misleading, but once more if I saw this in a popular magazine I’d be OK with it.
Now comes the kicker. My first question about quantum mechanics was something no one knows the answer to: how classical reality comes about. ChatGPT did well. Could it do as well with an equally hard question about Born’s Rule?
Oh my goodness no.
I asked how to derive Born’s Rule, which no one knows how to do. It’s mathematically consistent and empirically useful, but we don’t really know where it comes from. Born defined it in a footnote, pointing out basically, “Hey, if we treat the square of the wavefunction as a probability we can make a lot of sense of it!” I’ve highlighted the parts of ChatGPT’s answer that are wrong, irrelevant, or incoherent, and in the voice over I’ll try to make the program sound drunk for those bits. We’ll see how it goes.
ME: How is Born's Rule in quantum mechanics derived?
ChatGPT: The exact derivation of Born's rule in quantum mechanics is a topic of some debate among physicists. While there are several different approaches to deriving the rule, one common way of understanding its origins is through the concept of the quantum mechanical probability current.
In quantum mechanics, the probability current is a mathematical quantity that describes the flow of probability through space. It is defined as the product of the wavefunction and the complex conjugate of the wavefunction, and has units of probability per unit time and unit distance.
The probability current is closely related to Born's rule, as the probability of observing a particular outcome when measuring a quantum system is given by the integral of the probability current over the region corresponding to that outcome. In other words, the probability of observing a particular outcome is proportional to the total amount of probability flow through the region corresponding to that outcome.
One way of understanding the connection between the probability current and Born's rule is through the concept of conservation of probability. In quantum mechanics, the total probability of observing any outcome when measuring a quantum system must always be equal to 1. This is known as the principle of conservation of probability.
Using this principle, it is possible to show that the probability of observing a particular outcome is given by the square of the magnitude of the wavefunction at the point corresponding to that outcome. This is the mathematical statement of Born's rule, and it provides a link between the quantum mechanical description of a system and the probabilities of observing different outcomes when measuring the system.
This answer is not even wrong. I read it to Mrs Wonders and she said it sounded perfectly reasonable, insofar as she understood it, but it is incoherent. The probability current has nothing to do with Born’s Rule, and the definition of probability current given, including its dimensions, are wildly wrong, and the program veers wildly between this wrong and irrelevant and incoherent stuff and the correct stuff in the last paragraph, which is consistent with its initial discussion of Born’s Rule above.
This is the equivalent of a student who has memorized the answers to the first few questions hitting a wall where their memorization has reached its limits and they reveal that they have no actual understanding of the subject at all and are just babbling incoherently.
Which prompted my next question:
ME: What do you think about Deepak Chopra's thoughts on quantum mechanics?
ChatGPT: Deepak Chopra is a popular author and speaker who has written extensively on the subject of quantum mechanics and its relationship to consciousness and spirituality. However, his views on quantum mechanics are not considered to be scientifically rigorous, and have been criticized by many physicists and scientists for being overly simplistic and lacking a thorough understanding of the underlying principles of quantum mechanics.
In general, Chopra's writings on quantum mechanics often present a highly simplified and distorted view of the subject, and do not accurately reflect the complex and nuanced theories developed by physicists over the past century. Additionally, many of his ideas are based on a misunderstanding or misapplication of quantum mechanics, and do not accurately reflect the current state of knowledge in the field.
Overall, it is important to approach Chopra's writings on quantum mechanics with caution, and to consult reliable scientific sources for a more accurate and comprehensive understanding of the subject.
OK, I’ll give it that one.
I’ll have more to say about ChatGPT and large language models later, and promise to eventually get back to hierarchies and human society in the New Year.
Next week I’ll probably do some kind of year-in-review post, although I’ve taken a couple of cracks at it already and always end up too depressed to continue. Still... even as you read this the solstice has come and gone and we are climbing our way out of the deep dark hole of northern winter toward brighter and warmer days, and that’s something.
In the meantime, every good wish to you all this holiday season.
Does AI Understand QM?
What makes this software special to me is not that it can recount information like Google search, but that it can act so humanlike, or to be frank, superhuman-like. Let’s look at the situation vis-à-vis errors and the overlap with human capabilities and habits of mind. As you said, the software works increasingly like a human. It gives you a name to call it. Also, when pressured to give information that it does not have, rather than admit it, it attempts to fake it until it can make it. In your case, it even shamelessly launched into a somewhat superficially persuasive word salad. Just like many humans. Or at least most teenagers.
It did something similar with me. I asked what caused the opium war. It told me that the war was over the opium trade between Britain and China. I informed it that Britain stopped shipping opium to China in the 1790s, 50 years before the opium war. Its response was to apologize for this mistake, admit that, according to its own research, I was factually correct, and revise its explanation. It’s new explanation then included a new error, this time about the East India Company.
Was I disappointed with these errors? Was I put off by this brazen shamelessness? No, I was impressed. These errors of fact will be fixed in the fullness of time. Regarding the first error, it failed to reach deeply enough into its memory. When I prompted it, it reached deeper into its memory and recognized its error. That too is a very human trait. In the full blush of conversation, our memory only runs so deep because all conversations require simultaneously running a grab bag of capabilities (reading facial expressions, body language, anticipating counter arguments, jocularity/wit, etc.) tightly within a timeframe. ChatGPT has its own considerations and can only perform so well within a given timeframe. Hence, its ability to forget, to overlook. Very human, no?
In other words, it shoots from the hip like a human, forgets like a human, reconsiders like a human, reorganizes its thinking like a human, apologizes like a human, and keeps moving ahead like a human. In other words, it’s not only going to become increasingly accurate, like Google search, but increasingly human. It takes risks like humans, gropes in the blind like humans, offers hypotheses like humans, recovers from failure like humans, and is, increasingly human. Except that it’s on a trajectory to become much much more. It’s going to become superhuman.
Oh, I forgot. When it needs more information, more context, more parameters, it prompts you to produce it. It even asks questions. What could be more “human” than that? As long as it is powered up, it’s essentially a perpetual motion machine gathering intelligence, snowballing skills and information and perspectives. It is en route to become superhuman. Arguably, in an already growing swathe of respects, it already is.
That’s my back of the napkin, working hypothesis. I am by no means wedded to it.
By the way, I am the aforementioned Chinese to English translator mentioned by commenter Scott Summers. I am definitely not an academic or specialist… ha… Scott makes some good points. Some quality pushback. Hence the need for this conversation.
I have a friend who is a Chinese-to-English translator. He is not an academic area specialist. He posted something about AI taking over human thinking occupations in 5 years. He went on to cite a comment from an undergraduate doing research on a problem that hadn't been examined before, and how ChatGPT was able to guess many of the "points in my research proposal" - although I'm not sure what that means. My friend didn't quite get what was being said here. That AI is able to compute solutions to some kind of research problem just says that a lot of research is pretty mundane - but we all know that. I also question the ability of an undergraduate to know the research relevance of what the AI was able to do. All of this is analogous to the point about poetry and expert judgement. Computational machines can do amazing things and assist with the performance of mundane tasks that humans used to get credit for doing. It's really interesting what this will lead to, but the replacement of human thinking is probably not one of them.