I agree, but as a software engineer this gives me pause because I keep trying to insist on coding standards but I’m unable to come up with a compelling reason why it matters. Ostensibly the reason we cared about things like DRY and code quality was so that it would be easy to understand and easy to maintain and easy to make changes to later. But it now seems like a shared understanding of the codebase is less important than ever, and it’s more about shoveling requirements in without breaking any existing functionality.
Is a well tested slopfest better? That seems to be the conclusion for mathematics, so why not software too?
IMO it's still a problem with LLMs; we still have to build in a way that makes it easier for an LLM to make changes later and arguably it's the same things that made software development easier for humans. IME LLMs tend to not know how to do that for themselves and instead just amplify/copy patterns that already exist.
If an LLM can't pave the way for itself then ultimately shared understanding is required to take advantage of LLMs in the first place.
Would you personally vouch, at your job, for the importance of proper assembly coding standards?
I read a lot of assembly.
Certainly scopes vary, but in my line of work i define memory layout and how this data will be processed myself - thus it's great a compiler might do that, but the result of the computation will not change.
Now in comparison giving an LLM specs ... i a) cannot be sure what the computation will be b) it might be something else on another run.
We already have countless examples of such filling up the arXiv, written by hacks long before LLMs started writing proofs. No one cares about them. You might as well build a box blasting radio static into the void. You could save a lot of electricity that way.
I believe Terry Tao when he says the bottleneck will no longer be the writing of proofs, it’ll be everything else: reading them, reviewing, publishing, and teaching from them. A bunch of proofs that nobody reads are of no use to anyone.
Why is it so hard to imagine we can build tools to think thoughts we can't comprehend?
If there's commercial value, I think it's inevitable. We don't fund mathematicians because it's cute when they understand a problem, but because their work tends to have applications with commercial value. The value can be captured without understanding the details.
It depends on what exactly you mean by "commercial value commensurate with the costs involved" but I'd volunteer the 3G/4G/5G specifications and the other documentation required to implement the mobile network protocols. 5G is currently sitting at over 50,000 pages and it's one of the reasons Qualcomm/Broadcom/Apple are the only ones who can realistically make a mobile radio.
I don't think there is a single human to whom more than a few thousand pages would be comprehensible at a time except for the occasional genius.
If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text. That dissemination of knowledge is what provides the value, not the mere existence of the text. If that person forgets or dies before they can share their knowledge then it will be lost.
We have many examples of this from history: ancient texts written in a lost language. These texts provide us with no value until the day they can be deciphered, unless you count linguistic puzzle-solving as a virtue.
If there exists a text which only an AI can understand, that AI can communicate their key conclusions to others, even if that doesn't help them with the original text.
The only difference here is the amount of meat involved. Perhaps tossing a few steaks on the server racks could help with that.
Because, again, I can point to hundreds of examples of texts where nobody but the author understands it, and they're only giving summarized "commandments" that you should follow if you want good results.
If I told you "don't use spin locks, call futex instead", do you think have gained an understanding of the Linux scheduler?
Yes, because I already knew what schedulers are, what spinlocks are, and if I want to know what futex is I can go look it up. Comprehension is within my grasp.
Your original claim, which you’ve repeatedly distanced yourself from (by trying to use comprehensible examples) but won’t admit to, was about incomprehensible stuff. That is, text that no human could possibly understand, ever.
You’re repeatedly engaging in intellectual dishonesty rather than simply admit that “human comprehension probably will continue for the foreseeable future”, which is really not a controversial idea at all.
For what it's worth, we've known about BSCCO for nearly 40 years, and we still don't have a great physical understanding of how it works, thought we made decent progress in 2022.
All we know is that if we melt the right rocks together, we get a superconductor that works in some mysterious way that we can't explain. We know it's not Cooper pairs.
I can see there is no further productive discussion to be had with you at all. I bid you good day.
[1] https://www.merriam-webster.com/dictionary/incomprehensible
With the definition you seem to want to use, it's impossible for anything to be incomprehensible, and therefore it's tautological that there's no incomprehensible LLM output: nothing at all is incomprehensible.
Do you have an example of anything incomprehensible? Anything at all? Even the things that Gödel would say are inaccessible could, in theory, become accessible: we just don't know with absolute certainly that the mathematics it was based on got all the axioms right, though we see no errors now.
How's your understanding of Schroedingers "An Undulatory Theory of the Mechanics of Atoms and Molecules"? You seem to be using the results of it as applied to semiconductor engineering just fine. And, I promise you, most semiconductor engineers haven't read it in full, they just accepted the results as passed on by several layers of teacher.
I have a paper on routing algorithms, which I have attempted to read to my cat. I don't think my cat retained much, but they seem to be enjoying the cat food that got delivered using the results.
I'd suggest that we're going to be a lot closer to the cat than the author of the paper when AI takes off.
All the stuff you've listed is understood by some person, and that understanding is the source of its value.
Now that we've cleared that up, can you furnish an example that satisfies the original claim of incomprehensibility and value?
Anyways, people benefitted greatly from Newton's laws of gravity, even though we still don't have a quantum-compatible set of laws for it. The laws of gravity are still incomprehensible for people, but the approximation that we've observed is still immensely valuable.
You keep falling back on "incomprehensible for some people" but that wasn't the claim. It was about a text which is incomprehensible in principle; that is, utterly impossible for any human to ever understand.
Every writing must be comprehensible to at least the author, regardless of whether it has commercial value or not. If I hit the keyboard a few times, I've created writing, but it doesn't mean anything. It is just gibberish and without meaning, so there is nothing to try to comprehend. So if there is something to be comprehended, then at minimum the author should know it.
Therefore what you keep claiming is the only refute of your argument of "an [...] incomprehensible [...] writing" is actually a paradox, and cannot be disproved itself. However "humans comprehending things" is not a paradox, which means that your specific request to beat your paradox is not actually related at all.
His examples disproving the non-paradox version of your challenge (writing incomprehensible to folks other than the original authors) are sufficient to disprove your statement, as he gave examples of both people not comprehending human made and 'God' made writing (the universe/gravity)
His original claim amounts to creating an AI that takes its place above humans as some kind of electronic God, delivering edicts to humanity that we cannot comprehend, but which somehow have value to us. It's unskeptical, pseudo-religious nonsense.
The age of humans comprehending things is coming to an end [1]
Look at it this way. AI has destroyed humanity at chess for decades now. That doesn't mean we have placed AI above humans in the general sense.
You have basically totally fabricated what you thought the other person was saying.
If you want examples where nobody but the author understands it, examples are a dime a dozen.
Understanding == Value
If a mathematician produces something incomprehensible then it has no value. It's meaningless. Indistinguishable from random noise.
An AI which produces incomprehensible text is producing no value. We didn't need to spend trillions of dollars on LLMs to figure that out. Markov chains can do that job perfectly well.
Again, do you believe that there are documents, of any value, that humans don't understand?
Maybe an LLM could help you notice what I was saying, since it's clearly beyond at least one human's comprehension!
There is no value in an undeciphered document until understanding is achieved, just as a lode of gold ore in some asteroid orbiting a distant star has no value until we can fly there and extract it.
If an LLM can help us understanding something then it was not incomprehensible, by definition.
I don’t find it hard at all to imagine that an AI comes up with a fundamental proof applicable to physics which results in some widget we can now produce that would otherwise not have been produced yet nobody takes the time to fully comprehend why it works. Somebody could, in principle, devote their lives to it and possibly get it, but for what purpose?
This will shift your argument--that doesn't count! etc., to the point where it's by construction unsatisfiable and vacuous. And it doesn't matter: an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
No, that is the entire point. If it is an algorithm which accomplishes something useful, then it is intelligible as such. That which is incomprehensible cannot be understood even in part, so it provides no value as a bit of knowledge (unless you're looking for a strong random number source, I suppose).
"Not many people understand some things fully" is so massively different from "the human mind is incapable of understanding some things that AI will understand for us"
The best I can do is things that are incomprehensible to nearly everyone, but still provide value. There's a small leap of imagination to consider an author that understands it and can show others how to leverage results without understanding be mechanical rather than biological.
Paul Krugman (1998): predicted the internet’s economic impact would be no greater than the fax machine’s.
The 1876 Western Union memo dismissing the telephone as having too many shortcomings, and the banker telling Horace Rackham not to invest in Ford because the automobile was a novelty.
We are in good company!
Mathematicians have never been known to communicate their ideas very clearly.
Regardless, even that target llms will likely win - an llm will likely be more efficient at teaching me string theory than a professor in a room with 463 other students.
The llm is the shared understanding.
And at this level, while there are anecdotical exceptions, mathematicians have always been pretty decent (with their conferences, workshops, paper publications, international collaborations, ...).
So, it does not mean "teaching the subject", it means "creating a human network of people that share the understanding". LLM can be useful at telling a human, but you still need a human. The point of Tao is not that LLM is not good at providing explanations, it is that "providing explanations" is not the contribution to science, "the human network" is. It's like saying "LLM are great cook, they generate tons of food in space", but the point of having cooks is so that people can eat food and not die. Having LLM generating mathematical proofs is as useless as having LLM generating food that no one can access: the point was never to "generate proofs" or "generate food", the point was "creating a shared human understanding" or "eating the food so human can survive".
I get that there is a cultural benefit to keeping it alive. Just like we ideally want the languages represented at the universities.
But keeping humans in the loop does not appear to be necessary in order to call it science, and certainly not in order to have progress or dessiminate that progress.
I don't have a problem with people doing math. As long that we don't idiomatically hold on to that way of doing things.
I do, however, find it hard to belive that individual humans will play a big role from here and forward, in any scientific desciplines.
The point of Tao is that people see LLM providing "proofs" and are concluding that this is all that is needed to "have progress or disseminate that progress". That is the same mistake of thinking that "generating food" is all that is needed to "have people not dying of hunger".
The hard part of "have progress or disseminate that progress" is the human network. A fundamental point of this human network is that it generate trust, accountability and reliability. Generating "useful new theorem" is useless unless the society also built the trust around the theorem to distinguish it from a fake theorem.
Maybe in the future, we will have AI doing some part of it, but this is a totally different AI animal than the one we are able to have now, and people who think the current AI that we see now is able to do that have no understanding how it works. This is demonstrated by the facts in math: current AI is able to provide math proofs, and yet, a lot of human work is still needed to get progress out of current AI.
I would not bet that individual humans will still play a role as big as today in the future. Maybe AI will be different in the future, but the reality is that we don't have any indication if this is even possible.
Humans soon won't need it.