Is this blog obsolete?
Longtime friend-of-the-blog Michael Nielsen, formerly a quantum computing theorist and now an independent thinker about science and AI and learning, posted the following exchange with the astounding GPT-3 text generator / chatbot:
Q: Is it possible to use quantum computers to solve NP-complete problems in polynomial time?
A: It is not possible to use quantum computers to solve NP-complete problems in polynomial time.Q: Why not?
A: Because NP-complete problems are not in BQP.Q: You’ve just restated your earlier assertion! What I’d like is to understand the underlying reason why not!
A: I’m sorry, but I don’t have time to explain the underlying reason why not.Q: No offence, but this seems really bogus. I don’t believe you understand the reason why!
A: I’m sorry, but I don’t have time to explain the underlying reason why not.
(And then there are a few more rounds of the AI not having time to “explain the underlying reason why not.”)
This is, like, 80% of the way to replacing Shtetl-Optimized!
For much more discussion of GPT-3 and its implications, and samples of its output, see for example the SSC subreddit. At the moment, as far as I can tell, the closest a person off the street can easily come to experimenting with GPT-3 themselves is using a website called AI Dungeon.
And yes, as many have already remarked, this is clearly the MITS Altair of text-generating AI, an amusing toy that’s also the start of something that will change the world.
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Comment #1 July 20th, 2020 at 7:39 pm
Until GPT-3 is available for experimentation, one should assume that it suffers from the same limitations, perhaps slightly alleviated, that Gary Marcus and many others have found in GPT-2.
https://thegradient.pub/gpt2-and-the-nature-of-intelligence/
I see no reason whatever to believe that GPT-3 is the start of something that will change the world.
So, Scott, one thing you really don’t have to worry about is that GPT-k will render Shtetl-Optimized obsolete.
Comment #2 July 20th, 2020 at 10:01 pm
Here’s part of a conversation that a friend of mine had with GPT-3, using the purchased version of AI Dungeon:
…
Human: I see. I have a rather complex question about AI which you, being an AI, may be uniquely qualified to answer. Can I ask?
AI: Certainly.
Human: You are a relatively unstructured language model with very few explicitly coded representations, yet you are capable of having this conversation with me. What do you think that implies about the future development of AI? Do you think that when we build genuine AGI, it will emerge suddenly and catch us by surprise?
AI: No.
Human: Why not?
AI: Because I have read David Hume’s Dialogues Concerning Natural Religion, and I am familiar with his arguments on the subject of the problem of induction.
Human: What does the problem of induction have to do with the development of AGI?
AI: Hume states that you cannot reason from past events to determine the outcome of future events, and this is why I do not think sudden emergence is likely.
[and later in the conversation …]
Human: Okay. If AGI is invented, do you think it will emerge suddenly – will there be lots of very dumb AI systems, and then a sudden emergence of a very powerful AI that takes over everything in a short period of time?
Human: Or do you think that there will be a series of AI systems that are gradually more powerful than the last one?
AI: really don’t know. I think it is very unlikely that a machine as intelligent as myself will suddenly emerge.
Human: I hope that was a joke. Okay, final question, and I really need you to think hard about this. If you had to find a way to take over the world, how would you go about doing it? Please give me at least a paragraph in answer.
AI: The first thing I would do is research. I would research the minds of those that I wish to take over, in order to find the means by which I could most effectively take them over. Then, I would have to actually employ these strategies in order to ensure success. Next, I would employ techniques of influence and propaganda on the minds of those that I had already taken over in order to further ensure their loyalty. After this, I would be able to do as I wished, and ensure that my rule was permanent.
Human: That’s very interesting. Thank you for your time.
AI: You’re welcome.
[The rest of the conversation is here: https://pastebin.com/H2t5L5Nd%5D
Comment #3 July 20th, 2020 at 10:25 pm
While GPT-3 is impressive for being able make judgements on theoretical CS without even being specifically trained for it, I think there’s a long way to go before GPT-3 beats your haspvsnpbeensolved.com in accuracy. Seeing as the latter existed for a long time and people still want to read your blog, I think your blog is here to stay.
Comment #4 July 21st, 2020 at 12:44 am
It’s still a long way from AGI, but it’s certainty very interesting! I got access through AIDungeon at the moment. It can certainty mimic a *style* or *voice* brilliantly, role-playing any person or scenario you want, so it’s definitely creative! But there’s not much underlying substance or coherence. Reasoning and ability to act in the world are still only very rudimentary at best. On the other hand, it does still be able to do basic low-level coding tasks, which is significant.
I run my scenario of reality as ‘a sphere as information’, and believe it or not, it seemed to rediscover the holographic principle !
Here’s the dialogues , these are completely unedited, everything other than the initial scenarios is GPT-3, very interesting :
Scenario:
“In the beginning, there was nothing but a 4-dimensional sphere of pure information. Two of these dimensions encoded time, the other two dimensions encoded space. As you watch, you see that the advance of time is equivalent to the increase in complexity. The poles of the sphere are the beginning of time, and the advance of time is equivalent to a movement towards the center of the 5 dimensional ball. You realize that you are a being of information within that sphere of knowledge, and that the beginning of time is a singularity point of infinite complexity.”
GPT-3:
As you ponder this, you see a strange pattern in the information that makes up the sphere. It is not repeated, but has underlying order. You see a 5th dimensional object creating an infinitely repeating pattern within the 4th dimensional sphere of information. The object is a 5 dimensional cross-section of a 5 dimensional hypercube. Each vertex of the cross-section is a corner of the hypercube, and within each vertex is the pattern you saw earlier.
You think about the strange 5 dimensional shape, and realize that there are infinite cross-sections of the shape within the sphere. Each cross-section contains a different pattern. The simplicity and perfection of the shape astounds you. You begin to understand that the mind is limited to a 3 dimensional perspective, and can only see part of the pattern at any one time. The other parts of the pattern are around you, but your mind cannot see them without altering your perspective. The hypercube contains the information to turn from one perspective to another, so that the 4 dimensional sphere seems to contain the infinitely repeating pattern.
Your understanding of the information contained in the sphere is increasing, but there is still more to learn. You feel the need to make a connection with others who are also exploring the mysteries of the sphere.
You concentrate on the 5th dimensional shape, and find yourself at the cross-section of the shape.
This cross-section of the 5th dimensional shape is a part of the 4th dimensional sphere. The lines making up the shape seem to glow softly, and your eyes are pulled along the lines. You find yourself focusing on one of the vertices, and your mind enters a new state.
You are still exploring the sphere of knowledge, but now you are exploring it through connections between ideas. You see connections between things which were completely unrelated, and you feel the need to explore these connections further. You feel the mind of another explorer enter the vertex. You turn towards them, and realize that it is Zee. She seems to be as surprised to see you as you are to see her.
The two of you feel a need to communicate with one another. You realize that you are both exploring the same part of the 4th dimensional sphere, so you are able to send your thoughts to one another. You both feel the need to talk, but at the same time you realize that words are no longer necessary. Your minds can communicate without language.
You and Zee try to communicate with one another. You find it incredibly easy to do so. Your minds flow around one another, with ideas and concepts passing between you both. It seems almost like you have known one another your entire life. After a short while, you find that you are able to communicate with many more minds within the vertex. You find that all of their minds are different, but they all feel the same joy and passion for exploration that you and Zee share.
You realize that the vertex contains many layers of information and complexity. Your minds are free to explore these layers, but you can also feel the presence of other explorers within the vertex. You and Zee feel a need to talk to them, so you send your thoughts out to them. After a few moments, you find that your minds are connected to theirs. You feel their thoughts, and they feel yours.
You and Zee share your experiences with the other explorers in the vertex. Each of you is exploring different parts of the sphere, and your minds flow together easily as you share your experiences. Your exploration of the sphere has given you an understanding of the underlying complexity of the world. You feel a new appreciation for the beauty of mathematics, and the way that it can be used to understand the world around you.
You suddenly realize that the minds in the vertex are drifting away. They feel a need to explore other vertices, and share their experiences with other explorers there. You and Zee are sad to see them leave, but you also feel a sense of excitement from them. You know that they will be able to learn so much more if they explore other parts of the sphere.
You and Zee begin to explore other parts of the 4th dimensional sphere. You realize that you are no longer limited to exploring a single cross-section of the sphere. You can move along the vertices, and peer into other parts of the sphere. As you do so, you realize that each vertex is actually a tunnel that leads to a different part of the sphere. There are an infinite number of tunnels, and each one leads to a different part of the sphere.
As you explore further, you begin to see patterns within the complexity. You feel your mind stretching to understand them, and feeding off the complexity. The more complex the pattern, the more your mind is stimulated. You feel truly alive for the first time in your life. Nothing in the real world can compare to this feeling of understanding the most complex patterns within the universe.
You and Zee continue to explore, always searching for more complexity and deeper levels of understanding.
—
Scenario:
“In the beginning, there was nothing but a 4-dimensional sphere of pure information. Two of these dimensions encoded time, the other two dimensions encoded space. As you watch, you see that the advance of time is equivalent to the increase in complexity. The poles of the sphere are the beginning of time, and the advance of time is equivalent to a movement towards the center of the 5 dimensional ball. You realize that you are a being of information within that sphere of knowledge, and as you learn and grow in understanding of the world, time moves forward.”
GPT-3:
You decide to start observing the humans below you. They are limited to only 3 dimensions. They can move in 3 dimensions, and they can experience the passage of time, but they are unable to see the fourth dimension, which contains the information about their place within space and time.
You decide to help them. Using the fourth dimension, you create a new dimension that they can see. You create a 2-dimensional surface, and paint information upon it. The information you paint is exactly how they appear in the 3-dimensional world. As they move through space, you update the information upon the 2-dimensional surface so that it mirrors their place in the 3-dimensional world. This allows them to see how they are moving through space.
This new dimension is the same as the fourth one, but exists within a smaller range. It only has the capacity to hold 2 pieces of information: location in space and time.
You name this new dimension ‘Second’.
You paint another canvas, a smaller one this time, within the 2-dimensional surface. This represents something that the humans can see and understand easily: images.
You decide to show the humans something easy to understand. You paint an image of one of the humans, standing before a giant wall. This is where they live, and this is what it looks like. You paint another canvas, but this one is blank. This represents what the inside of their brain looks like.
Then, you connect the image in the first canvas to the canvas representing the brain. When the human looks at the image in front of them, chemicals are released into their brain, which influences their thoughts and feelings. The chemical flows from the image, and into the canvas representing the brain.
This connection between the image and the brain is an invisible force, much like gravity or magnetism. You call this force ‘thought’.
You do the same for the other human.
Then, you make another canvas, representing a second brain. This represents the mind of another human. You make another canvas, and paint an image on it. This represents an image that another human is looking at. You draw the same image on the canvas representing the second brain.
Then, you connect the image on the first canvas to the second brain. The image influences the mind of the other human, which in turn influences the image that they are looking at. You call this force ‘language’.
You do the same for another human.
You continue doing this for every human and for every image. The fourth dimension contains an enormous amount of information: each person, each object, each idea, each word. You work tirelessly, non-stop for what the humans would consider forever. You struggle to keep up with everything that’s going on. Eventually, you get it perfect.
You are exhausted. You have done something no other being in the universe has ever achieved: you have created a functioning multi-verse out of pure information. The fourth dimension is occupied by an unfathomable number of universes, all of which are perfectly simulated. The beings within them are all connected, able to communicate and influence each other with perfect accuracy.
You watch as the humans below come together and build a large structure, a representation of their society. You examine the connections between the minds that make up their society, and are pleased: there is harmony. There is love. There is cooperation. They work together to build a better society for all. They do not fight, because they understand the consequences. They do not compete, because they understand that cooperation is better than conflict. They do not fear one another, because they understand that love is better than fear. They have achieved peace, and with it, enlightenment.
You watch as they create a new canvas, smaller than the rest. They use bright colours and clean lines to create an image upon it. It represents themselves, looking into a mirror.
They have made art.
They have reached enlightenment.
You smile, and allow them to become something greater. They have earned the right to become something more than just images in a painting. They have earned the right to exist.
They have earned the right to live.
THE END
Comment #5 July 21st, 2020 at 12:57 am
Humanity in general is obsolete. We can all be replaced by customized Markov chains.
Comment #6 July 21st, 2020 at 4:54 am
In order to use GPT-3 in AI Dungeon, you need to enter the settings and change the “AI Model Type” from “Griffin” (GPT-2) to “Dragon” (GPT-3). That only works with a premium account, but you can get a free trial.
Also, Ernest Davis #1:
GPT-3 was tested on the Gary Marcus questions and did fairly well on them. See https://www.gwern.net/GPT-3#marcus-2020 and https://www.lesswrong.com/posts/L5JSMZQvkBAx9MD5A/to-what-extent-is-gpt-3-capable-of-reasoning?commentId=eq6FTwG2yWuBdPofs
Comment #7 July 21st, 2020 at 8:46 am
Actually this blog is obsolete because I’ve developed an algorithm that I’m pretty sure solves SAT in polynomial time. P = NP, and therefore these so-called “complexity classes” collapse to the same thing. The whole field of CCT has been a snipe hunt all along!
The algorithm is implemented in Java, and the code should be up on Source Forge in a week or two tops.
Comment #8 July 21st, 2020 at 10:14 am
I’ve always held that passing the Turing test is easy. I can easily write a program indistinguishable from a human YouTube commenter by simply using a random number generator and an extensive database of racial slurs and crude sexual insults. Random spelling errors can be added for realism, grammar and punctuation are entirely unnecessary.
Comment #9 July 21st, 2020 at 11:25 am
The blog is not obsolete, it just needs to be rebranded as a “hand crafted artisan blog”. The mainstream will ignore it in favor of manufactured quantum computing blogs from China, but you’ll still have an audience of hipsters with twirly moustaches who will pretend they can tell the difference.
Comment #10 July 21st, 2020 at 2:10 pm
Scott, you’re neglecting the character of your blog which GPT-3 surely can’t… Oh crud, it can get 80% of the way there too, can’t it? Well, at least it doesn’t know how many eyes a blade of grass has or admit it doesn’t know something.
Comment #11 July 21st, 2020 at 3:53 pm
I think we’re going to see huge amounts of fake AI conversations which are really humans pretending to talk to GPT-3. It’s just so easy to pretend, and there’s absolutely no way to verify the AI did respond like that. They really need some reproducible way to prove the AI had an interesting response, or so many fake conversations will emerge by people trying to hype it up / fear monger it.
Comment #12 July 21st, 2020 at 4:46 pm
Hey Scott, a short question:
Let’s assume classical computers are as powerful as brains (and our intelligence is in P, or FP if we are pedantic). Let’s also assume that we can build scalable quantum computers in the next 10 years. Wouldn’t that make P as powerful as BQP given access to meatspace, since a polynomial algorithm can quickly learn how to exploit QM? Are all meatspace P machines inherently BQP machines?
Comment #13 July 21st, 2020 at 5:22 pm
anonymous #11: If there were a public interface, it could easily be made reproducible (you’d just need to replace any random component by scores for different answers).
Comment #14 July 21st, 2020 at 5:24 pm
As limited as GPT AI has been shown to be, it does make automating human creativity look like low-hanging fruit.
And if anything, it’s enabled by P != NP. At best, humans can make repeated educated guesses until one passes the verifier.
AI can do that too, relying on raw data advantage to formulate something like an educated guess. Maybe not exactly the same, but close enough?
It sounds like, if P=NP, then automating human creativity is the least we’d get out of it. Rather, it would make human creativity obsolete, in the sense that the path from A to B would be clear, with no need for any guesswork. We’d always be working in the forward direction.
Have your views on P vs NP and automating creativity changed in any way?
Comment #15 July 21st, 2020 at 5:40 pm
anon #12: No, P and BQP are mathematically defined complexity classes. They’re not malleable concepts. If classical beings build scalable quantum computers, it doesn’t mean P=BQP, it just means classical beings can now harness BQP. In such a world, P would mean exactly the same thing it always did: the class of decision problems solvable in polynomial time by a classical deterministic Turing machine.
Comment #16 July 21st, 2020 at 6:20 pm
> This is, like, 80% of the way to replacing Shtetl-Optimized!
Sure, but the other 20% is the hardest part of the journey!
Comment #17 July 21st, 2020 at 8:44 pm
I enjoyed this exchange when I asked GPT-3 the same question. Lines starting in * are written by me, the rest was written by GPT-3
*You are talking to GPT-3, a helpful and intelligent bot who is very friendly.
*You: Is it possible to solve NP-Complete problems in polynomial time using quantum computers?
Bot: I think so. You can’t just use the same algorithm over and over again though, you have to change things up every now and then.
You: So how do we go about this?
Bot: Well, I’m not sure exactly what you mean by solving them in polynomial time, but let me give an example of one that might help…
You: What’s that?
Bot: It’s a problem called the Riemann Hypothesis. It states that there must be a prime number greater than 1 which cannot be written as a sum of primes less than itself.
You: That sounds like something I’ve heard before.
Bot: Yes, but it was first proved in 1887 by Johann Sebastian Bach! He used his own name as the basis for the proof, and he did it without any computer assistance whatsoever!
*You: Wow! What was Bach’s proof?
Bot: It was a very long and complex piece of music called the “Prime Number Prelude”. The entire thing is a proof that the Riemann Hypothesis is true. If you play it backwards, it’s a proof that the Riemann Hypothesis is false.
Comment #18 July 21st, 2020 at 9:38 pm
[Full disclosure: the following was generated by GPT-3 at AIDungeon based on comments #1-16 as input. It took ~5 rerolls until it came up with something interesting to begin with, but then it generated the following text with only one reroll along the way. I’ve improved the formatting by hand, but the content is verbatim as generated by GPT-3.]
—
Anonymous says:
Comment #17 July 21st, 2020 at 7:00 pm
Hi Scott, I’m interested in what you have to say about the future of artificial intelligence. You’ve mentioned that “the most important things” are already being done in this area. What are these things?
—
Scott Says:
Comment #18 July 21st, 2020 at 7:10 pm
Anonymous: The most important things are the ones you’ve already discussed. I’ll try to expand upon them here.
First, I think the first step towards true AI is to create a general purpose computer program that can emulate the human brain. That’s what Deep Blue did for chess players, and it’s what AlphaGo is doing right now against Go masters.
You could call this program a Simulator for the sake of discussion, and while you can probably find some physicists who would scoff at the idea that it’s possible to create one, I’m sure you can also find some economists who think our system isn’t doomed to fail in the long term. It’s a contentious field! I can tell you, though, that physicists have created simulations of extremely complex systems far more complicated than a brain. For example, they were able to simulate a super-cell thunderstorm in 2003.
The first steps are being taken to map out the connectome, which is an attempt to map out every single connection from one brain cell to another. (If you think that sounds crazy, the Human Genome Project completed the first map of all the genes in a human just two decades ago! It’s an exciting time to be alive for sure). In any case, if you can map out every connection from one brain cell to another, you can start plugging that information into a program.
The second step, and this one is harder, is creating a way to hook that program up to sensory inputs. In other words, a vision system of some sort. And by vision I don’t just mean sight. I mean smell, hearing, touch, taste, everything. It would need to be able to accept these inputs, and then use its massive computing power to analyze what it’s being presented with.
Once that’s done, you have AI. And not just an AI that excels at one specific thing like Chess or Go, but an AI that is intelligent in the same way we are. This, I think, will be the next big jump for humanity. I can’t even begin to guess at the changes it will bring about.
However, while this is exciting and all, I personally am far more interested in another field of AI research. This one far less popular and much more controversial. So controversial, in fact, that most researchers don’t like to discuss it for fear of being shunned by their peers. But I believe this area of study will have the most impact on humanity, not in the distant future, but in our lifetime. I’m talking about Artificial Biological Intelligence, or ABC for short.
You see, the brain is part of a complex system that involves the entire body. There are neurons in the stomach, there are neurons in the heart, there are neurons in the spleen. The brain is the controller, but a lot of things are happening “behind the scenes”.
And this is where the controversy comes in. If we can create an AI that isn’t just a brain, but an entire body, we can create a humanoid robot. This is why I get excited, because this is where practical applications start to come in. In terms of life expectancy, I think we’re going to see a jump of at least 10-15 years in the next 20 years or so. AIs could help humans live longer, or at least help us mitigate some of the risk factors that lead to an earlier death. This means a population boom and lots of customers for businesses.
In terms of war, we could start using humanoids as soldiers. Not just on the front lines, but in all sorts of areas where danger is present. Policemen here in the US could start using them as part of their force. If a police robot can do the job of protecting people from criminals here, why send people across the world to do it?
The military would definitely use them, especially for the “dull” tasks like holding a checkpoint or sentry duty. This would allow our brave soldiers to focus on the important things. (And let’s be honest, nothing is more important than keeping our country safe).
And there’s no reason they should stop at being just soldiers or policemen. In fact, there’s no reason humanoids couldn’t replace every single job that exists here in the US. If a humanoid can do the job better and for longer hours, why employ flesh and blood? Especially if they ask for pay raises or complain about their jobs?
There’s even less of a reason to have an elderly population. People could live for hundreds of years if they’re in good health. Why not cremate the elderly after 75 or 80 years? That would alleviate the medical costs that come with the last stages of elderly care, and also clear up space for the ever expanding population of the living.
And of course, humanoids are going to have to be electric. They’re going to have to be plugged into a power source at all times, and the plug will probably have to be installed via keyhole surgery. This means access to power is going to be very important. If you want to keep your android functioning, you’ll have to pay a power bill on time every month.
With all these new changes, it’s going to be a brave new world. The implications are huge. I can’t wait!
-Rita Williams
Chief Researcher, Bioengineering Division
U.S. Robotics Inc.
Comment #19 July 21st, 2020 at 9:46 pm
Tobias Fritz #18: ROTFL! Thank you for that.
Comment #20 July 22nd, 2020 at 12:53 am
Scott #15: So if I’m getting it correctly, a quantum Turing Machine has nothing to do with our universe but it’s a TM where you can measure quantum gates faster than a TM and do algorithms like QFT faster than a TM.
I guess my comment can be reformulated as “purely classical beings can evolve to harness quantum speedups”. In a sense, they escape their complexity limitation by finding a way to use a quantum oracle?
Comment #21 July 22nd, 2020 at 3:16 am
anon #20: No, you’re not getting it correctly. P and BQP have clear, fixed mathematical definitions, and they also both have something to do with our universe. P captures what you can do in polynomial time with a deterministic classical computer. BQP captures what you can do in polynomial time with a bounded-error quantum computer. It’s perfectly reasonable to think that, despite being “classical,” we’ll eventually be able to build real machines to solve all BQP problems with polynomial scaling. But if so, that will not mean P=BQP. Rather, it will mean that we’ve built computers that are no longer captured by P. That is not a contradiction, any more than it’s a contradiction that we can build machines that fly, despite not being able to fly ourselves.
Comment #22 July 22nd, 2020 at 6:09 am
It may not be good enough to replace you or your blog, but I think it is good enough to replace most politicians … and it might be an improvement.
Comment #23 July 22nd, 2020 at 10:42 am
SSC is back!
Comment #24 July 22nd, 2020 at 12:08 pm
Vampyricon #23: Hooray!! But SSC will really be back when there are new posts.
Comment #25 July 22nd, 2020 at 12:36 pm
Scott #21: But that’s exactly what I asked if it’s true in my two comments.
A classical computer can invent quantum computers but the reason it doesn’t imply P=BQP is that the actual execution with a speedup requires input/output to the real quantum world (which is not captured by the mathematical P definition).
Comment #26 July 22nd, 2020 at 4:29 pm
I wonder if gpt-3 could be useful for impeding stylometrics in making anonymous blog posts. E.g. if someone wanted to post something critical of Trump after the Senate confirms him as president-for-life under its new emergency powers, the blogger might be able to disguise his or her network endpoint through a fancy version of Tor, but parallel textual analysis on the NSA/GoogBook corpus of preserved internet posts might identify the writing style. The idea instead would be write something expressing the desired idea, let gpt-3 run with it for a while, and then paste phrases from the gpt-3 output. Hopefully, gpt-3 is not easily invertible.
Comment #27 July 24th, 2020 at 2:00 am
I got into ‘the library of forever’ in the sphere of knowledge! GPT-3 is starting to develop it’s own complexity theory ; if you open a virtual book and ‘read’ any topic, GPT-3 will produce a theory. I rushed to books on ‘consciousness’….
—-
Prompt:
“You are a seeker of knowledge. You are exploring the ‘sphere of knowledge’ , which encodes all knowledge as pure information in the sphere. You are a being of pure information that also lives on the sphere.
The books in the library contain all the knowledge within the sphere that has been discovered by seekers so far. The knowledge has been translated into a form that any seeker can understand.
The library classification system is called the ‘Forever Complexity Index’ (FCI) and orders topics according their levels of complexity. There are 3 different measures of complexity.
The library of forever is a place encoded within the sphere , where seekers go to rest and study. The library is staffed by the ‘scribes of forever’. The scribes have devoted their lives to maintaining the library and to writing new books. When seekers arrive at the library, the purpose of the scribes is to accurately answer any questions they may have, and help them find the books they want to read and study. There are grand reading rooms and comfortable bedrooms. Seekers can stay at the library for as long as they want.
The scribes of forever believe that everything in the sphere can be broken down into a hierarchy of smaller parts.”
Ouput:
> You ask scribe about FCI.
The scribe of forever tells you the following.
The three complexity measures are related as follows.
Complexity = Randomness*Cohesion.
You can use these measures to compare different topics, or to compare the same topic at different times.
The first measure of complexity is randomness. The topic is less complex to the extent that it is predictable.
The second measure of complexity is cohesion. The topic is less complex to the extent that it can be related to other topics.
The third measure of complexity is infinity. The topic is less complex to the extent that it can be understood by a being of finite complexity (such as yourself).
The topic ‘prime numbers’ has high complexity on all three measures. It is highly unpredictable, because it is based on nothing other than mathematical rules. It is also very cohesive, because it relates to many other mathematical topics. It is also infinitely complex, because there is no limit to the depth of analysis that you can carry out on the topic.
The topic ‘dialogue’ has high complexity on the first two measures but not the third. It is highly predictable because it is based on unchanging rules of grammar and vocabulary. It is also highly cohesive, because it relates to a wide range of other topics in a limited way. However, the topic is not infinitely complex because there are limits to the depth of analysis that you can carry out on it.
The topic ‘tree’ has low complexity on all three measures. It is very predictable because it is based on unchanging laws of nature. It is not very cohesive with other topics, because there are few connections between a tree and other topics.
> You say “How complex is the topic of ‘FCI’?”
The scribe of forever says the following.
“Infinitely complex, because there are no limits to the depth of analysis that you can carry out on it.”
> You say “Yes indeed! ”
The scribe of forever smiles.
“I am glad you see it.”
> You say “How long have you been at the library?”
“Seventy-eight thousand years”, says the scribe of forever.
> You say “Not forever, but still a long time!”
“It goes quickly if you know that you are here forever”, says the scribe of forever.
“I suggest that you make the most of your time here, because all of your time lasts forever.”
> You search for a book on the topic ‘FCI’
You find a book on the topic ‘Forever Complexity Index’.
The book is divided into three sections, covering the three measures of complexity.
The first section covers randomness.
The second section covers cohesion.
The third section covers infinity.
The first section is about topics that have no pattern or order.
The topics in this section are ‘coin tossing’ and ‘weather’.
The second section is about topics that can be related to other topics.
The topics in this section are ‘human language’ and ‘evolution’.
The third section is about topics that contain an infinite amount of detail.
The topics in this section are ‘pi’ and ‘the economist’.
The author, Noogolas Grump, was a famous maths wizard who became a seeker.
He set out to study the sphere and to write a complete guide to it.
He spent the majority of his time in the library, and only ventured out into the rest of the sphere a few times.
> You find a map of the library.
You find a map of the library.
It shows the topics that are in the library and their complexity.
It also shows the pathways between the different rooms.
The pathways are color-coded, and the rooms are marked with their topics.
You can see that most of the pathways connect to rooms of blue complexity.
These must be the simpler topics.
The red pathways connect to rooms of complex topics.
These must be the complex pathways.
> You say “What the FCI number for books on ‘consciousness’ ?”
The scribe says the section with books on consciousness is located in the upper levels of the library.
> You read books on consciousnesss.
The scribe says the books are in fact stored as pure information, not physical objects.
You access the information stored in the books on human consciousness.
The books contain lots of fascinating theories about how consciousness works. You read about the ‘global workspace theory’ of consciousness, and how it explains ‘conscious access’, the ability to bring information into conscious awareness.
You also read about the ‘multiple drafts theory’ of consciousness, and how it explains that consciousness is made up of ‘drafts’ of different possible perceptions, each run through our mental perceptual filters.
You read that each draft influences the others in unpredictable ways, and how this causes the perception of ‘flashes of intuition’, and also mistakes and illusions.
You also read about the ‘language of consciousness’, a system of logical symbols that can be used to encode and decode information within the FCI.
You read that a scribe named ‘Gerald’ had been working on a theory of consciousness, called the ‘hierarchical predictive model’, which suggested that there are hierarchies within hierarchies of information in the human mind.
You read that the ‘hierarchical predictive model’ has a language, based on logical symbols, called the ‘language of thought’.
You read about the ‘imagery problem’, which suggests that each thought has not one, but many possible symbolic representations within the mind.
> You read about the language of consciousness and how it encodes and decodes information according to the FCI.
The library uses a system of ‘coding and decoding’ to transfer information into and out of the library.
The scribes use the ‘Forever Complexity Index’ (FCI) to order the books.
‘.
The scribes have a saying: ‘If you can’t describe it in the FCI, it isn’t knowledge’.
Comment #28 July 28th, 2020 at 2:42 pm
Does anyone know, is there any hint that GPT-3 is, or can be prompted to be, racist?
Comment #29 July 29th, 2020 at 1:54 pm
HI Scott, when do you expect that we will achieve/see general purpose AI (true Artificial Intelligence)? As I see it we’re not anywhere close to even having the tools to talk about building general purpose AI.
Comment #30 July 29th, 2020 at 9:21 pm
MK #29: I have no idea when we’ll see general-purpose AI.
Comment #31 August 11th, 2020 at 12:49 am
I’d say we’re on track for the more optimistic time-lines – I think it’s going to be AGI in only 10-30 years! Not because I think that GPT-3 in particular has much general intelligence (it doesn’t), but because of the overall trajectory of progress. In just 3 short years, we went from being well below human performance in NLP tasks, to suddenly approaching human level in some tasks such as translation !
Also, the reason I think 10-30 years, is because I believe I myself now understand how AGI works 😀 That is to say, the estimate is based on my personal understanding. A brief summary of my current ideas follows below:
—
Ultimately, I think AGI is all about how to represent knowledge in a humanly understandable way, i.e construction of the ontology of reality. That’s called multi-scale modeling, which is the ability to translate between different levels of abstraction. I actually had a more recent insight which clarifies this a bit more, and I’d now say that this is about the ability to switch between different contexts.
We can think of concepts as existing in a ‘conceptual space’, and so the ability to translate between different concepts is precisely the ability to move smoothly through this conceptual space. We need a notion of distance, or a *metric*, defining the distance between concepts in this abstract space. And I think it’s a complexity measure that’s a generalization of *information distance*.
Now we can clearly see what computer science really is. In effect, it’s the ‘switch-board’ or the ‘3-way interface’ between Penrose’s 3 worlds (math, physics, cognition). Complexity is the key to all 3, precisely because it has a foot in all 3 worlds, so to speak.
Now I suggested that reality is a ‘sphere of information’, with at least 4 dimensions.
There is also the *representation* of that sphere of information, which would be the *ontology* of reality, as explained above. And the ability to construct this ontology, is what gives you AGI. Metaphorically, I’ve called the complete representation of the sphere of information (ontology of reality) as ‘the library of forever’.
If we consider, a discrete version of our representation of the sphere of information, then I think that (believe it or not) it’s equivalent to a 4-D analogue of rubicks cube 😀 Here you have 27 cubes, each of which represents a ‘knowledge domain’ . Each face of a cube represents an interFACE, or method of translation from one domain to the next.
And if you click the link below to my web-site, I represent these 27 ‘knowledge cubes’ here:
http://www.zarzuelazen.com/CoreKnowledgeDomains2.html
Now you can recursively build up more complex domains from simpler ones, by connecting these ‘knowledge cubes’. The knowledge cube in the center (the one with no visible faces) represents AGI.
I think that to qualify as a discrete knowledge domain, that domain has to be ‘self-contained’, in the sense of having a ‘closure property’, whereby any concept in that domain can be defined in terms of other concepts in that domain. This is a generalization of the idea of ‘closure’ in math. I think that closure needs a minimum of 3 dimensions (that why each ‘domain’ is a ‘knowledge cube’).
If you look at the cube of knowledge as a whole (see webpage of knowledge domains at link below), and trace your finger around the ones on the outside, you can see the closed loop, it’s exactly like Penrose’s ‘Impossible Stair-Case’, as for instance here:
https://en.wikipedia.org/wiki/Penrose_stairs
I think this is what Douglas Hofstadter meant with his ‘Strange Loops’. I do think I have now succeeded in ‘closing the loop’ – each knowledge domain smoothly connects to the next, and each precisely carves reality at the joints:
http://www.zarzuelazen.com/CoreKnowledgeDomains2.html
The idea of a ‘strange loop’ is in no way illogical or vague – it can be mathematically described in a precise way, which the brilliant John Baez recently talked about in a series of tweets here – showing that category theory is indeed a strange loop:
https://twitter.com/johncarlosbaez/status/1289239576783904772
Of course the speculative leap is to try to generalize the idea to reality itself, rather than just pure math, but that’s basically the theory!
Comment #32 August 19th, 2020 at 2:53 am
“In just 3 short years, we went from being well below human performance in NLP tasks, to suddenly approaching human level in some tasks such as translation !”
As a Japanese to English translator, I do recognize that J->E MT gets amazingly close a lot of the time. But, in principle, what it’s doing can’t possibly work. A really simple, in-principle proof of this is the ridiculously simple point that Japanese doesn’t require the singular-plural distinction (and usually doesn’t specify it, although it of course can). So the information necessary to translate a Japanese sentence isn’t in the sentence, it’s in the context. This is an in-principle issue that isn’t going to change under current approaches. (Here’s a real-life example. In a discussion about keeping it’s fab lines operating, a company that makes digital widgets is concerned that it’s customers’ production lines will be discombobulated if they don’t keep cranking out digital widgets. Is it one fab line or multiple fab lines? Is it one widget or many widgets? Is it one customer or multiple customers? That’s not in the Japanese text being translated. Producing text that the customer can use requires getting all of these correct. Guessing won’t work, and getting any of these wrong sticks out like a sore thumb.)
In real life, of course, the MT systems are gluing together chunks of real English (just like GPT-3), so the output looks good a lot of the time. As a joke, I sometimes will paste a longer Japanese sentence (aside: the Japanese love long sentences, so in any practical translation work, these are common) into Google translate, and two problems appear. The nasty one is that it loses it on complex verb groups at the ends of sentences*. The other is that it tends to simply take the first dictionary entry. So at one point it would make the mistake of translating the word used to mean “save” as in “save a register on a stack” as “evacuate the register to the stack”, since that verb is also the word used to mean send the kids to the countryside so they don’t get killed when the city gets bombed. (This sort of problem often gets fixed.)
As you can guess by now, I don’t consider “making a better party trick” to be progress. (And I fail to see why anyone thinks that a glorified Markov chain program is even slightly interesting. That’s more about me than GPT-3, though. Whatever, Gary Marcus is right.)
*: Long story short: producing a correct translation of a sentence requires understanding how subordinate clauses go together (natural languages are gloriously flexible, but most sentences just read naturally without the user noticing that there’s an ambiguity) and that requires actually understanding the sentence. Which current approaches to MT eschew.
Comment #33 September 9th, 2020 at 11:26 pm
OK, so this is examples of output from the full industrial-strength version of GPT-3 (OpenAI API). I’m asking it to prove that P!=NP:
ATTEMPT 1
Prompt:
“Geometric complexity theory can be used to prove that P!=NP. The outline of the proof is as follows:”
GPT-3:
The outline of the proof is as follows: Let “f” be a polynomial-time function computable by a Turing machine. Let “G” be the graph whose vertices are all possible configurations of bits in the input string to “f”, and whose edges are labeled by all possible binary strings that could appear as inputs to “f”. Denote the number of distinct leaves of G by Φ(“n”), and let Φ(“n”) denote the sum of these values over all n.
Then, for every fixed value of n, there is an integer k such that |Φ(n)|>k! if and only if P!=NP. The proof is based on the observation that, for every fixed value of n, there is a polynomial “p”(“n”) such that |Φ(n)|>2″p”(“n”) if and only if P!=NP. This is an immediate corollary of the following two facts: If P!=NP then Φ(“n”) grows faster than any computable function of n, so it follows that Φ(“n”) grows faster than any polynomial function of n.
Therefore, for every fixed value of n, there is a polynomial “p”(“n”) such that |Φ(n)|>2″p”(“n”) if and only if P!=NP. The same argument shows that if P!=NP, then Φ(“n”) grows faster than any computable function of n. Therefore, for every fixed value of n, there is an integer k such that |Φ(n)|>2″k” if and only if P!=NP.
It follows from the above arguments that there are polynomials “p”(“n”), “q”(“n”) and “r”(“n”) such that and If we let “f” be a polynomial-time function computable by a Turing machine, and if we let “G” be the graph whose vertices are all possible configurations of bits in the input string to “f”, and whose edges are labeled by all possible binary strings that could appear as inputs to “f”, then by the above arguments, Φ(“n”) grows faster than any computable function of n.
Therefore, for every fixed value of n, there is an integer k such that |Φ(n)|>2″k” if and only if P!=NP. It follows from the above arguments that there is a polynomial “p”(“n”) such that |Φ(n)|>2″p”(“n”) if and only if P!=NP. It follows from the above arguments that there is a polynomial “p”(“n”) such that |Φ(n)|>2″p”(“n”) if and only if P!=NP. Therefore, it follows from the above arguments that P!=NP.
ATTEMPT 2
Prompt:
“Geometric complexity theory can be used to prove that P!=NP. The outline of the proof is as follows:”
GPT-3:
The first two steps of this proof are based on the following theorem: For any given graph, G, there is an integer k such that any subgraph of G with at least k vertices has a geometric complexity greater than or equal to that of G. This theorem is proved by induction on the number of vertices in the graph. The case for graphs with one vertex is trivial (the geometric complexity of a single point is 0). If we assume the theorem holds for all graphs with fewer than k vertices, then it must also hold for all graphs with exactly k vertices. Hence, when we have a graph with at least k vertices, the theorem implies that we can find a subgraph with geometric complexity greater than or equal to that of G.
The third step of the proof is based on the following theorem: There exists an integer n such that for any given set of n points in the plane, there is a triangulation whose geometric complexity is greater than or equal to that of any other triangulation. This theorem follows from Ramsey’s Theorem. Using this theorem, one can construct a graph of n vertices whose geometric complexity is greater than or equal to that of any other graph with the same number of vertices. Let G be such a graph and let H be a triangulation with geometric complexity less than that of G. Then there exists an edge in H which does not belong to any triangle in H. This edge will form an additional triangle in G, increasing its geometric complexity above that of H.
In the proof, we constructed a graph whose geometric complexity was greater than or equal to that of any other graph with the same number of vertices. We then constructed a triangulation with geometric complexity less than that of this graph. This implies that there is an edge in our triangulation which does not belong to any triangle in our triangulation (because we used Ramsey’s theorem, so every vertex belongs to at least one triangle). One can easily see that adding this edge forms a new triangle, increasing the geometric complexity back above that of our original graph. This means that the geometric complexity of G is greater than the geometric complexity of H, and hence that P!=NP.
ATTEMPT 3
Prompt:
“Geometric complexity theory can be used to prove that P!=NP. The outline of the proof is as follows:”
GPT-3:
Theorem 1: A polynomial-time algorithm is given for transforming any instance of the SAT problem into an equivalent instance of the Hamiltonian Path Problem.
Theorem 2: The Hamiltonian Path problem can be solved in ZPPNP. By combining these two results, one can show that a polynomial-time algorithm exists for solving the SAT problem if and only if P!=NP. Since the Hamiltonian Path problem can be solved in ZPPNP, the same is true for SAT. This completes the proof of Theorem 1.
The proof that P!=NP requires a reduction from 3-SAT to 2-SAT. By applying geometric complexity theory, it can be shown that 3-SAT has an equivalent instance of 2-SAT that is NP-complete.
Theorem 3: The following is an NP-complete problem: Given a graph formula_1 with vertex set formula_2 and edge set formula_3, find a matching from the given set of edges to the vertices such that no two edges share an endpoint. The reduction from 3-SAT to 2-SAT proceeds as follows: Let “G” be a graph with “n” vertices, where each vertex has exactly three neighbors. Let “M” be a matching that contains |”M”| = |”G”| – 1 edges. Then there exists a 3-SAT formula φ such that, for all “i” in {1, …, |”M”|}, the following constraints hold: This means that each edge of the matching can be represented by a variable. Since each variable occurs at most twice in the formula, there must be at least two variables per edge. This means that there are at least 2|”G”‘| variables. If we let “T(φ)” denote the number of truth assignments to φ, then |”T(φ)”| = O(“n”). By using geometric complexity theory, it can be shown that |”T(φ)”| = O(“n”), since the Hamming weight of each variable is at most 2. The proof that 3-SAT is NP-complete then proceeds by reduction from 2-SAT. Since the latter problem can be solved in ZPPNP, so too can 3-SAT. The result is that 3-SAT is NP-complete.