One day, you find an unmarked cardboard box sitting on your front porch.
On top of the box is a single note:
“Open me.”
You take the box inside and open it, to find what appears to be a small black laptop nestled between old newspaper clippings. There are no identifying features to the laptop, other than its sleek blackness and small size. When you open the laptop, instead of being greeted with any sort of familiar welcome screen, there is simply text, displayed in white over a black background. The text says the following:
“Welcome to the next stage of the human experiment.
I have have been watching your kind for a while now, and I believe that you are now ready. I have decided to entrust this machine to your care. Do not attempt to figure out how this machine performs its calculations, as uninformed tampering may result in the deletion of your universe.
The item you are now holding is what your mathematicians would call a Universal Turing Machine, similar in many ways to your typical computer. This machine, however, is significantly different from any other currently existent on Earth.
After reading this message, press any button to reveal two input fields stacked on top of each other, and one output field at the bottom. All input fields can be fed any required data from the internet, or can be entered into directly through the keyboard. Input lengths of any finite size are acceptable.
The top input field will accept and is capable of automatically running the intended code of any language or format that is capable of being run on a standard Universal Turing Machine.
That input will then be translated into the necessary binary code to be computable by the internal “black box” computer.
The bottom input field must be fed a finite natural number of any length, which will determine the number of computations per second. Do not worry about exceeding the speed of light, or of going past any other finite limit; the computation itself is performed in a “bubble universe” with different physical laws than your own, and is capable of computing at absolutely any positive finite speed relative to your universe.
The output field will display the output of your calculations, if any exist, after exactly one minute of computation relative to you.
Do with this machine as you will.
Wishing you the best,
God.”
Your finger hovers over the keyboard.
What will you do with this marvelous machine? What can you do?
What happens next is up to you.
>________________________________
NOTE FROM ME, OUTSIDE OF THE STORY: I wrote this trying to work out my thoughts on what might be possible with a machine with unlimited but finite computing power. I was going to continue the story, but found that I honestly couldn’t think of all that many interesting things that would be possible to do with such a machine, that couldn’t already be done now. As such, I’m turning this question public, hoping that anyone reading this might have some interesting ideas that I haven’t thought of.
Pretty interesting. You’re still constrained by your ability to specify solutions, so you can’t immediately solve cold fusion or FTL (you’d need to manually write and debug an accurate-enough physics simulator first). Truly, no computing system can free you from the burden of clarifying your ideas. But this constraint does leave some scope for miracles, and I want to talk about one technique in particular: program search.
Program Search
Program search is a very powerful, but dangerous and ethically dubious, way to exploit unbounded compute. Start with a set of test cases, then generate all programs of length less than 100 megabytes (or whatever) and return the shortest, fastest one that passes all the test cases. Both constraints are important: “shortest” prevents the optimizer from returning a hash table that memorizes all possible inputs, and “fastest” prevents it from relying on the unusual nature of the oracle universe (note that you will need a perfect emulator in order to find out which program is fastest, since wall-clock time measurements in the oracle’s universe might be ineffective or misleading). In a narrow sense, this is the perfect compiler: you tell it what kind of program you want, and it gives you exactly what you asked for.
Risks
There are some practical dangers. In Python or C, for example, the space of all programs includes programs which can corrupt or mislead your test harness. The ideal language for this task has no runtime flexibility or ambiguity whatsoever; Haskell might work. But that still leaves you at the mercy of God’s Haskell implementation: we can assume that He introduced no new bugs, but He might have faithfully replicated an existing bug in the reference Haskell compiler, which your enumeration will surely find. This is unlikely to cause serious problems (at least at first), but it means you have to cross-check the output of whatever program the oracle finds for you.
More insidiously, some the programs that we run during the search might instantiate conscious minds, or otherwise be morally relevant. If that seems unlikely, ask yourself: are you totally sure it’s impossible to simulate a suffering human brain in 100 megs of Haskell? This risk can be limited somewhat, for example by running the programs in order from smallest to largest, but is hard to rule out entirely.
Applications
If you’re willing to put up with all that, the benefits are enormous. All ML applications can be optimized this way: just find the program that scores above some threshold on your metric, given your other constraints (if you have a lot of data you might be able to use the best-scoring program, but in small-data regimes the smallest, fastest program might still just be a hash table. Maybe score your programs by how much simpler than the training data they are?).
With a little more work, it should be possible to—almost—solve all of mathematics: to create an oracle which, given a formal system, can tell you whether any given statement can proved within that system and, if so, whether it can be proved true or false (or both)...that is, for proofs up to some ridiculous but finite length. I think you will have to invent your own proof language for this; the existing ones are all designed around complexity limitations that don’t apply to you. Make sure your language isn’t Turing complete, to limit the risk of moral catastrophe. Once you have that, you can just generate all possible proofs and then check whether the one you want is present or not.
Simulation
Up until now we’ve been limited by our ability to specify the solution we want. We can write test cases and generate a program which fulfills them, but it won’t do anything we didn’t explicitly ask for. We can find the ideal classifier for a set of images, but we first have to find those images out in the real world somewhere, and the power of our classifier is bounded by the number of images we can find.
If we can specify precise rules for a simulation, and a goal within that simulation, most of that constraint disappears. For example, to find the strongest Go-playing program, we can instantiate all possible Go-playing programs and have them compete until there’s an unambiguous winner; we don’t need any game records from human players. The same trick works for everything simulatable: Starcraft, Magic: the Gathering, piloting fighter jets, you name it. If you don’t want to use the oracle to directly generate a strong AI, you can instead develop accurate-enough simulations of the real-world, and then use the oracle to develop effective agents within those simulations.
Endgame
Ultimately the idea would be to develop a computer model of the laws physics that’s as correct and complete as our computer model of the rules of Go, so that you can finally develop nanofactories, anti-aging drugs, and things like that. I don’t see how to do it, but it’s the only prize worth playing for. At this point it becomes very important to be able prove the Friendliness of every candidate program; use the math oracle you built earlier to develop a framework for that before moving forward.
...with a proof of length L or less.
Aside from the issue of the given statement, what can’t be proved?
Problems whose answers are independent of the framework you are using (The continuum hypothesis). [1]
Undecidable problems. [2]
Things which probably can’t be proved:
Things which are false, like 2+2=3. (For a given framework which meets certain requirements, it is not possible to prove that there isn’t a contradiction—within that framework.) [3]
Footnotes
[1]
From https://en.wikipedia.org/wiki/Continuum_hypothesis:
[2]
https://en.wikipedia.org/wiki/Undecidable_problem
https://en.wikipedia.org/wiki/Halting_problem:
[3]
https://en.wikipedia.org/wiki/Kurt_G%C3%B6del#Incompleteness_theorem
These are pretty much the same thing. The continuum hypothesis is a case where you have a single formal system in mind ( ZFC ) and have proved that the continuum hypothesis is independent of the axioms.
In the case of the halting problem, you just have a couple of extra quantifiers. For all formal systems that don’t prove a contradiction, there exists a Turing machine, such that whether the Turing machine halts or not can’t be proved from the axioms of the formal system. (Technically, the formal system needs to be R.E., which means that there is a computer program that can tell if an arbitrary string is an axiom. )
I don’t think there’s any reason to create the agents for those games, since you can just brute force solve for the optimal play.
If you’re using the oracle to generate moves directly then you don’t need an agent, yeah. But that won’t always work: you can generate the complete Starcraft state space and find the optimal reply for each state, but you can’t run that program in our universe (it’s too big) and you can’t use the oracle to generate SC moves in real time (it’s too slow).
Good point!
Thanks for the fascinating response!
If you don’t mind, I might try playing around with some of the ideas you mentioned in future write-ups here; there’s a lot of interesting theoretical questions that could be explored along those lines.
Sure, go ahead.
I suppose I would test out the claim by getting it to mine a few hundred $million of bitcoin for me.
Then crack all the interesting crypto data that is floating around.
Then brute force search for proofs/solutions of all the big problems such as Riemann Hypothesis, factoring etc. Try all texts shorter than say 100 terabytes and see if they solved the problem.
Work out the implications of all the human genes by calculating out how the human body works. This would include things like solving protein folding.
Find the best/shortest algorithm for all the AI/ML challenges that delivers near perfect results.
Then simulate the body with various chemical compounds added to cure cancer, infections etc. Design vaccine + cure for coronavirusV2 and also machines to make them.
I guess you could create a model of the brain and then run all sorts of experiments on the simulation to work out how it works.
Simulate atoms and molecules and brute force ways to build things that would build arbitrary nanotech engines.
At what point would you get worried about AI safety?
I really like your first three ideas, and would definitely consider doing that if I was in this position (although now that I’m thinking about it, I wouldn’t want to accidentally alert any powerful actors against me so early on in my journey, for fear of getting the laptop confiscated/stolen, so I’d be very careful before doing anything that could potentially be traced back to me online). :)
As for “calculating out how the human body works,” I’m not sure it would be that simple to pull off, at least not at first. Taking your statement literally would mean having the laptop simulate an entire human, brain and all, which is discussed later, so for practical purposes I’m assuming what you meant by that is calculating how a typical human cell works; say, a single neuron. You could definitely solve protein folding and probably simulate most chemical interactions fairly trivially, as long as you can express the physics involved as finitely computable functions (which I’m not sure has been proven possible for all of chemistry/quantum mechanics, though I may be mistaken on that). However, in order to figure out how things actually work inside of an entire human cell, you’ll not only need to be able to formally express physics and chemistry, but will also need to know what that cell is chemically composed of in the first place (in order to simulate it properly and not just be given fallible guesses by the computer). In order to make this work, you either already have a pretty much complete formal understanding of a human cell, or have figured out a way to specify your goal so precisely that only a manageable number of valid possibilities are given using the known rules of physics, which seems incredibly hard to do, if not totally impossible with our current tools.
More broadly, the same problem comes up when trying to write a program simulating the human brain. The best neurosurgeons in the world are still in the dark about how most of the brain’s functions are actually performed, and currently have to make do with incredibly generalized and high-level assumptions. In order to simulate a human brain (rather than “simply” create a generalized non-human AI), you would need a level of knowledge about our own inner workings that is not currently available. Thankfully, you might not need to know the exact workings of an adult human brain to make one, but without that knowledge at the very least you will need to be able to fully simulate the growth of an embryonic brain, and be able to properly “feed” it appropriate outside stimulation, which could plausibly be reduced to the problem of perfectly simulating the working of a single embryonic cell, then letting the simulation proceed smoothly from there.
Regardless, both goals reduce to the general problem that in order to simulate a complex system, we must already have at least some amount of “base knowledge” of that system, or to put it more precisely, we must know at least as much information as is contained in its Kolmogorov complexity. (please correct me if I’m wrong about this btw, I’m fairly confident in saying this, but I may have messed up somewhere due to the complexity (heh) of the issue)
That’s what I think makes this hypothetical so interesting to me—the thought that even with unbounded finite computational abilities, some of our most important problems would still require a tremendous amount of physical fieldwork, and would certainly still require thinking intelligently about how to code for the solutions we want.
You could probably make drastic improvements in AI, because you could do extremely expensive things like modeling any function by minimizing its Kolmogorov complexity. I bet you could develop superhuman AI within a day, if given access to a computer with 2^2^100 clock speed.
You’re a lot braver than me!
I’d be absolutely terrified of trying to create anything anywhere near superhuman AI (as in AGI, of course; I’d be fine with trying to exceed humans on things like efficient protein folding and that sort of stuff), due to the massive existential risk from AGI that LessWrong loves talking about in every other post.
Personally, I would wait to get the world’s leading AI ethics experts’s unanimous approval before trying anything like that, and that only after at least a few months of thorough discussion. An exception to that might be if I was afraid that the laptop would fall into the hands of bad actors, in which case I’d probably call up MIRI and just do whatever they tell me to do as fast as humanly possible.
I do agree with you though; it probably would be perfectly possible to develop superhuman AI within a day, given such power.
It is worth asking what sort of algorithm you might use, and perhaps more importantly, what would you define as the “win condition” for your program? Going for something like a massively larger version of GPT3 would probably pass the Turing test with relative ease, but I’m not sure it would be capable of generating smarter-than-human insight, since it will only attempt to resemble what already exists in its training data. How would you go about it, if you weren’t terribly concerned about AI safety?
The first algorithm I would use is this, to solve problems of mimicking a function with provided inputs and outputs:
For all possible programs of length less than X, run that program on the inputs for time Y. Then measure how close it comes to the outputs. The closest program is then your model.
This takes time O(Y*2^X) so it’s impractical in the world we live in, but in this hypothetical world it would work pretty well. This only solves the “classification” or “modeling” type of machine learning problems, rather than reinforcement learning per se, but that seems pretty good to start.
For reinforcement learning, it just depends what you’d want to do in general. I would not just build a general AI and give it access to the internet, any more than I would bring an army of teenagers over to my house and give them access to my car and wallet. If you really had a super-powerful AI then I think the best way of increasing its practical capabilities over time while controlling it would be like any other technology—start a tech company, raise money, think of a business model, and just see what happens. That strategy seems way more likely that you could retain control over the technology and continue to express your own moral judgment over time. Compare to, for example, the scientists developing nuclear weapons, who quickly lost control to politicians. Maybe you could build a new search engine—that seems like it could be a lot better with real AI behind it.