“if a computer can solve a thirty-year old math problem in a weekend because it’s a math problem, should we…make more problems math problems”
Yes! I’ve had the exciting and uncomfortable realization recently that almost anything in the world can be converted into if/then statements if you’re willing to spend the time encoding your human decisions like that. And then it’s just a question of:
- Can you break each individual step into a simple enough decision than an LLM can make it?
- Can you write a script that strings those decisions together in the right order and with enough checks and balances to not veer off-course midway through?
- Can you afford the token bill?
- Can you live with the knowledge that your own human experience, knowledge, and creativity was ultimately reducible to a string of 1s and 0s?
yeah, I can't help but have the slightly uncomfortable feeling that we're all sort of in a race to figure out out how to turn all our problems into Moneyball (or really, high-frequency trading) problems, and we just don't really realize it yet. And in ten years, when a few people figure that out, we'll all be sitting around wondering how we didn't see it.
I think this is actually one of the few right use of AI: crack the hard problems that humans cant solve but have clear expectation with verifiable math. Maybe "curing cancer" will no longer be a joke but a reality with the right use of AI like this.
At the start of all of this, AI curing cancer felt ridiculous to me, but now, I gotta say, it doesn't seem that crazy, for exactly this reason. Surely, assuming we make it that long, give people 1,000 years, and we would've figured out how to cure cancer. And AI seems like it's just a way to compress that into a much shorter timeline.
And what if AI figures out that most cancers are caused by chronic exposure to certain things (which by and large we already know, e.g. lung cancer and smoking) -- will we then ban these things (e.g. lead in paint), or are we looking for some kind of magical injection so that we can keep smoking? What if the things we crave are made in a way that gives *other people* cancer -- will we ever care?
Righteousness is not a math problem; it is a behavior change -- and it is much simpler than a math problem (i.e. just cease from doing or contributing to evil).
yeah, I mean, I don't really have a lot of optimism that AI (or any huge product that ultimately has to make a lot of money) makes us capital-B Better people. But, if we're all running around giving everyone cancer, it doesn't seem bad to have better ways to cure people of it. Or really, I think my view is people are going to be people, just as they have been for thousands of years. We might as well give everyone ways to make their lives better along the way.
Nevertheless, I am more leaning towards to still progress *with better moral education* paired up with the advancement of tech. IMHO this is the problem - the tech goes too fast while the ethic and moral of people are not catching up.
Are we trending upward? Have you looked at the world lately? The herd has no idea where it is going, and the shepherds are greedy dogs which keep devouring the sheep and can never have enough, and cannot understand: they all look to their own way, every one for his gain, from his quarter.
Woe to the shepherds that feed themselves! Shouldn't they first feed the flocks?
Woe unto them that call evil good, and good evil; that put darkness for light, and light for darkness; that put bitter for sweet, and sweet for bitter! Woe unto them that are wise in their own eyes, and prudent in their own sight! Woe unto them that are mighty to drink wine, and men of strength to mingle strong drink: Which justify the wicked for reward, and take away the righteousness of the righteous from him!
I think one of my core beliefs is basically this ta-nehisi coates bit from this old post, that people are fundamentally the same moral character as they've always been, and all that matters is the system and social pressure you put around them. That could be education, or religion, or like, draconian Singapore laws, but ultimately, people are people, and the only thing that changes them is external pressure and norms.
> Are we trending upward? Have you looked at the world lately? The herd has no idea where it is going, and the shepherds are greedy dogs which keep devouring the sheep and can never have enough, and cannot understand: they all look to their own way, every one for his gain, from his quarter.
it depends on the length of the scope - if we are just looking for the next 5-10 years, probably nope. it is due to the transitional pain of AI; if we look for the next 50-500 years, then yes, we are trending upward.
Funny that every example here comes with free wrong answers. A failed counterexample costs nothing, so the loop gets a million swings; the moment a test needs a wet lab or a real customer, the swings aren't free anymore and the loop slows way down.
Yeah, that's another way to think about putting the problem in a box, I suppose. It means the problem has to fit in the box, and it means need to be able to cheaply mess around in the box.
I generally like your thinking and in this case you point to "restructure data to be more suitable to an LLM" and "change how we write code so that it's optimized for a machine" - I really liked both of those articles/sets of thinking of yours. But in this case, I came across a different set of thinking on the Jacobian conjecture subject (I'm in the "what?" camp unfortunately) - but its conclusion is very different - AI is best where the solution is easily verifiable (the Jacobian conjecture solution was confirmed by Tao very quickly), and that societal problems take years to know whether the solutions really work. Anyways, that was stated much better by Carlo Iacono - here - https://hybridhorizons.substack.com/p/ai-gets-good-where-the-world-can
Yeah, someone else mentioned that another part of this is that this only works on problems that are free to test, which seems right. A machine that can develop a million hypotheses isn't all that useful if it takes us forever to test all of them. So "making it a math problem" needs to solve that too, where you can make it something testable as well.
True, though people seem to have a lot of capacity to turn seemingly non-math problems into math ones. A lot of finance; sports; a lot of entertainment; tons of small businesses that have been PE-ified - they aren't pure math proofs, but they've gone from being run by small spreadsheets to huge models. This seems like it could push us towards a lot more of that.
The thing with science is that at the frontier, there is no model for the phenomena being experimented on, that's why the experiments need to be made. So scientific unknowns can't be turned into math for the AI to puzzle through. I expect AI to stall out on revolutionizing science.
For true frontier stuff, sure? But it does seem like there's a lot of stuff to be found in the gaps of what we don't know, and this kind of brute research could fill those in a lot faster? I wouldn't consider these sorts of math problems frontier (or a lot of drug development as all that frontier-y), but it seems like it could be really useful all the same?
A math problem can be solved without ever leaving the computer. Can any scientific gap be filled in entirely inside a computer? Filling in a scientific gap needs empirical validation.
I wouldn't think so, though that's kind of the point - if you can solve the problem by putting it in a computer, I'd think there'd be a lot of effort to figure out how to rephrase more problems so that they can mostly be put in the computer.
in combination with genuine, rapid progress from these machines.
Taking our highly complex, often pre-linguistic and tacit understandings of the world and creating meaningful and effective math-shaped versions of those understandings (while exercising appropriate fear and judgement regarding the inevitable risks of the Procrustean bed) so that it can then be worked through by a machine. This is a skillset that can definitively be trained and requires effort, craft and domain-specific expertise.
Interesting article. I recall Nassim Taleb arguing in Antifragile that many important innovations have originated from brute trial and error. Smart theory doesn’t precede the breakthrough, but follows it.
At least in a lot of corporate contexts, that does seem to be where a lot of "discoveries" come from. Someone tries a thing, it works, and then a bunch of theories get developed as to why the market needed that thing, or that message, or whatever. Creating the opportunity to have these sorts of accidents seems as important as having a grand theory about what you're doing.
Brute force calculation reaches exponential walls surprisingly fast when navigating combinatorial trees. Understanding why chess remains hard reveals deep truths about search, intuition, and representation. Explored that dynamic here:
“if a computer can solve a thirty-year old math problem in a weekend because it’s a math problem, should we…make more problems math problems”
Yes! I’ve had the exciting and uncomfortable realization recently that almost anything in the world can be converted into if/then statements if you’re willing to spend the time encoding your human decisions like that. And then it’s just a question of:
- Can you break each individual step into a simple enough decision than an LLM can make it?
- Can you write a script that strings those decisions together in the right order and with enough checks and balances to not veer off-course midway through?
- Can you afford the token bill?
- Can you live with the knowledge that your own human experience, knowledge, and creativity was ultimately reducible to a string of 1s and 0s?
yeah, I can't help but have the slightly uncomfortable feeling that we're all sort of in a race to figure out out how to turn all our problems into Moneyball (or really, high-frequency trading) problems, and we just don't really realize it yet. And in ten years, when a few people figure that out, we'll all be sitting around wondering how we didn't see it.
It's all arbitrage, all the way down.
Literally what we have done for thousands of years.
Societal problems plus writing become bureaucracy
Plus rhetoric become logic problems
Plus steam become logistics problems
Plus computing become control problems
We mold society to our tools, not to people.
Yeah, agreed; I had a very old post about this, at least on a smaller scale, about how we typically fit what we do around the tools we have: https://benn.substack.com/p/the-product-is-the-process
I think this is actually one of the few right use of AI: crack the hard problems that humans cant solve but have clear expectation with verifiable math. Maybe "curing cancer" will no longer be a joke but a reality with the right use of AI like this.
At the start of all of this, AI curing cancer felt ridiculous to me, but now, I gotta say, it doesn't seem that crazy, for exactly this reason. Surely, assuming we make it that long, give people 1,000 years, and we would've figured out how to cure cancer. And AI seems like it's just a way to compress that into a much shorter timeline.
And what if AI figures out that most cancers are caused by chronic exposure to certain things (which by and large we already know, e.g. lung cancer and smoking) -- will we then ban these things (e.g. lead in paint), or are we looking for some kind of magical injection so that we can keep smoking? What if the things we crave are made in a way that gives *other people* cancer -- will we ever care?
Righteousness is not a math problem; it is a behavior change -- and it is much simpler than a math problem (i.e. just cease from doing or contributing to evil).
yeah, I mean, I don't really have a lot of optimism that AI (or any huge product that ultimately has to make a lot of money) makes us capital-B Better people. But, if we're all running around giving everyone cancer, it doesn't seem bad to have better ways to cure people of it. Or really, I think my view is people are going to be people, just as they have been for thousands of years. We might as well give everyone ways to make their lives better along the way.
I see your point Benn, and I am with you there.
Nevertheless, I am more leaning towards to still progress *with better moral education* paired up with the advancement of tech. IMHO this is the problem - the tech goes too fast while the ethic and moral of people are not catching up.
Somehow I got reminded with this book: The Rational Optimist (https://www.amazon.de/Rational-Optimist-How-Prosperity-Evolves/dp/0007267126). The point is: while it may look grim in the shorter period of time, in longer run we are actually trending upwards. Hence: "Rational Optimist".
Are we trending upward? Have you looked at the world lately? The herd has no idea where it is going, and the shepherds are greedy dogs which keep devouring the sheep and can never have enough, and cannot understand: they all look to their own way, every one for his gain, from his quarter.
Woe to the shepherds that feed themselves! Shouldn't they first feed the flocks?
Woe unto them that call evil good, and good evil; that put darkness for light, and light for darkness; that put bitter for sweet, and sweet for bitter! Woe unto them that are wise in their own eyes, and prudent in their own sight! Woe unto them that are mighty to drink wine, and men of strength to mingle strong drink: Which justify the wicked for reward, and take away the righteousness of the righteous from him!
I think one of my core beliefs is basically this ta-nehisi coates bit from this old post, that people are fundamentally the same moral character as they've always been, and all that matters is the system and social pressure you put around them. That could be education, or religion, or like, draconian Singapore laws, but ultimately, people are people, and the only thing that changes them is external pressure and norms.
https://benn.substack.com/p/it-is-the-internet
> Are we trending upward? Have you looked at the world lately? The herd has no idea where it is going, and the shepherds are greedy dogs which keep devouring the sheep and can never have enough, and cannot understand: they all look to their own way, every one for his gain, from his quarter.
it depends on the length of the scope - if we are just looking for the next 5-10 years, probably nope. it is due to the transitional pain of AI; if we look for the next 50-500 years, then yes, we are trending upward.
It is a matter of scope.
Funny that every example here comes with free wrong answers. A failed counterexample costs nothing, so the loop gets a million swings; the moment a test needs a wet lab or a real customer, the swings aren't free anymore and the loop slows way down.
Yeah, that's another way to think about putting the problem in a box, I suppose. It means the problem has to fit in the box, and it means need to be able to cheaply mess around in the box.
I generally like your thinking and in this case you point to "restructure data to be more suitable to an LLM" and "change how we write code so that it's optimized for a machine" - I really liked both of those articles/sets of thinking of yours. But in this case, I came across a different set of thinking on the Jacobian conjecture subject (I'm in the "what?" camp unfortunately) - but its conclusion is very different - AI is best where the solution is easily verifiable (the Jacobian conjecture solution was confirmed by Tao very quickly), and that societal problems take years to know whether the solutions really work. Anyways, that was stated much better by Carlo Iacono - here - https://hybridhorizons.substack.com/p/ai-gets-good-where-the-world-can
Yeah, someone else mentioned that another part of this is that this only works on problems that are free to test, which seems right. A machine that can develop a million hypotheses isn't all that useful if it takes us forever to test all of them. So "making it a math problem" needs to solve that too, where you can make it something testable as well.
100%
But: math is a language for formal logic.
Code is a language for a certain type of deterministic action.
Life stuff will not be formalized in math and code. I think there’s another language shaping. Some kind of purified English maybe.
True, though people seem to have a lot of capacity to turn seemingly non-math problems into math ones. A lot of finance; sports; a lot of entertainment; tons of small businesses that have been PE-ified - they aren't pure math proofs, but they've gone from being run by small spreadsheets to huge models. This seems like it could push us towards a lot more of that.
Genius used to mean seeing the path. Now it may mean designing the search space.
The thing with science is that at the frontier, there is no model for the phenomena being experimented on, that's why the experiments need to be made. So scientific unknowns can't be turned into math for the AI to puzzle through. I expect AI to stall out on revolutionizing science.
For true frontier stuff, sure? But it does seem like there's a lot of stuff to be found in the gaps of what we don't know, and this kind of brute research could fill those in a lot faster? I wouldn't consider these sorts of math problems frontier (or a lot of drug development as all that frontier-y), but it seems like it could be really useful all the same?
A math problem can be solved without ever leaving the computer. Can any scientific gap be filled in entirely inside a computer? Filling in a scientific gap needs empirical validation.
I wouldn't think so, though that's kind of the point - if you can solve the problem by putting it in a computer, I'd think there'd be a lot of effort to figure out how to rephrase more problems so that they can mostly be put in the computer.
Really interesting discussion and framing.
Deeply hopeful for the future of work
in combination with genuine, rapid progress from these machines.
Taking our highly complex, often pre-linguistic and tacit understandings of the world and creating meaningful and effective math-shaped versions of those understandings (while exercising appropriate fear and judgement regarding the inevitable risks of the Procrustean bed) so that it can then be worked through by a machine. This is a skillset that can definitively be trained and requires effort, craft and domain-specific expertise.
Lots to meditate on. Thank you.
Interesting article. I recall Nassim Taleb arguing in Antifragile that many important innovations have originated from brute trial and error. Smart theory doesn’t precede the breakthrough, but follows it.
At least in a lot of corporate contexts, that does seem to be where a lot of "discoveries" come from. Someone tries a thing, it works, and then a bunch of theories get developed as to why the market needed that thing, or that message, or whatever. Creating the opportunity to have these sorts of accidents seems as important as having a grand theory about what you're doing.
Math is hard.
but not *that* hard, apparently.
Brute force calculation reaches exponential walls surprisingly fast when navigating combinatorial trees. Understanding why chess remains hard reveals deep truths about search, intuition, and representation. Explored that dynamic here:
https://gzambrano.substack.com/p/chess-is-simple-why-is-it-so-hard
Dear Chat GPT, write my blog in a crass rip off of the style of Matt Levine