Comment by chongli
2 days ago
You've moved the goalposts. The original claim was about producing mathematics that are in principle impossible for any human to understand.
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?
You asked for examples, for a technology that we're still building. Maybe you can see the issue with that?
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.
No, I gave you a lot more leeway than that. Take any utterly incomprehensible piece of writing from the entire history of civilization and demonstrate its value.
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.
His examples work fine but you aren't accepting them because they don't confine to your paradox.
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)
4 replies →
Can you give me an example single piece of writing that the author didn't claim they understood? I don't think that any utterly incomprehensible writing exists.
If you want examples where nobody but the author understands it, examples are a dime a dozen.
5 replies →
Nothing is in principle impossible to understand. It just takes too long, is inconvenient and/or economically unviable.
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?
There are plenty of artifacts that, if not impossible for humans to understand, then at least no human has ever completely understood. To start with, the universe as a whole. Despite that, we are able to choose legible pieces of it to model and perform useful actions from.
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.
One person need not completely understand something for it to have value; it's sufficient for there to exist a shared understanding.
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).
So, what you're asking for is an example of someone extracting value out of something that is fundamentally irreducible random noise?