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Comment by teiferer | Hacker News Reader

> 5.5 is excellent and leaves very little to be desired.

Hm, that may have to do with (faking) confidence. I've often enough with 5.5 still run into cases where it confidently explained something, at the surface it kinda made sense, but the more I dug and verified, the more it became apparent that it was entirely wrong with the most crucial core concepts. It has gotten to a point where you really need a domain expert though to realize this, which makes it tough for using it in areas where you are not an expert and don't have easy access to one either.

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In a world of short videos, shallow reads, and now quick answers from LLM's it is easy to accept truth without verifying before moving on to the next thing. I was running into similar cases where the confidence was there but the answer was wrong, and as the article suggests, math separates correctness and understanding, so I thought it would be a great area to test where hallucinations still exist in the models. I made a test on large prime numbers where the LLM's couldn't know the answer and we can easily check the factors it produces to verify if it faked it. Nearly 75% of GPT-6 Luna were faked with a false factor when given a hard number with no tools.

You point at the exact problem here: people are so used to arguing from ignorance, they don't even notice.

Verification isn't knowledge. Far from it. You can verify statements without knowing why they're true. Variants of that concept are e.g. used in cryptology.

You need humans to truly understand (to know the context) in order to make correct judgements. Without actually knowing the context, you have no way to compare.

An infallible oracle tells Archimedes that the speed of light in vacuum is ~1.08 billion kilometers per hour. Archimedes, with the iron age tools and methods at his disposal, might be able to verify this and make some use of it himself. Maybe. In any case, what he has gained is knowledge itself.

The same goes for our own time. A powerful AI can tell us things at the edge of what we can grasp -- or beyond what we can grasp -- and it would nevertheless be knowledge that we possess. We can work to verify it, we can have it explained to us as though we were schoolchildren, or we can simply accept it as a static fact of the natural world.

In truth, we're going to have to learn to coexist with minds that are more powerful than ours. At least in some respects, if not in all respects. The good scenario is that they share information with us, and we receive it however we can. "Head in the sand" and "mutual disdain" are bad outcomes.

No, you're wrong.

You might want to look up the actual definition of knowledge. It's a pretty interesting topic in epistemology really, far from your simplistic take.

You already live in coexistence with minds more powerful than yours. Society works in a way that you never need to notice that, those minds taking care of things beyond your grasp for you.

The downside of that "convenience" is you developing an over-simplified bubble-view of the world, rendering you prone to arbitrarily hazardous misjudgements.

Here, you align foolishly with interests that cannot possibly be your own. Namely, exploiting scientific knowledge for personalized monetary gain on an unsustainable scale.

When a tiny group of people hogs essentially all scientific knowledge, that renders you what?

Your idea of being graciously provided with some "basic income" or whatever is blind copium. You would live as livestock at best, to be discarded as useless whenever your masters see fit.

The dictionary definition says that knowledge is information gained by study -- i.e., in the very vast majority of cases, by being told. What's your definition? Come on, humor me.

The rest of your post is excessively emotional and off-target.

Perhaps be more thoughtful regarding the "dictionaries" you use? The words you use become the borders of your world.

How does random data differ from "information you gained by study"? Let alone from "what you're being told"? How do you possibly notice?

Other people cannot force you to gain true knowledge. It has to be earned by putting in the necessary effort. Its value is manifold, starting with not gullibly falling prey to other's interests.

I don't think the social problems you listed can be solved by redefining knowledge to your convenience - they can play that game better than you can. The definition of knowledge in this context is simply that which describes reality. And the person you're replying to was correct in saying that the thing gained from the oracle was knowledge itself, even though they've not considered the epistemological nuances.

It's not me who's "redefining knowledge to my convenience". You weirdly succumb to "them" doing that and come to wrong conclusions.

Merely claimed "descriptions of reality" lack the crucial property of truth. The description has to actually fit reality, or it's mere fantasy. It has to be exhaustive, or it remains a facade, leaving you blind to what lies beneath.

When you don't actually know whether it does any of that, you're merely a believer, entirely dependent on your "oracle" and its slave in effect.

Not caring about nuance leaves you open to exploitation, among other things.

The oracle is infalliable in the toy scenario. That was asserted as an axiom. To us who are god's eye observers of the toy universe, we already know that whatever the oracle says necessarily fits reality in that universe.

But I understand what you mean. Suppose I am Archimedes in there. I don't have access to the axiom, so I don't know if what the oracle told me is true until I can verify it myself. So verify I will. This is what is being done with AI-written proofs IRL. Humans may not be able to internalize the proofs, but we can internalize the programs which verify the proofs. So we do know the proofs are correct, or rather, as correct as the verifier programs.

You could have explained why he was wrong before injecting your opinions into the discussion.

He's wrong because the epistemological formula is the justified true belief. The infallible oracle simply gave Archimedes a true belief, the needed justification, sensors that can actually give meaning to the precise number, would take hundreds of years to develop. Archimedes would have to sit there with the oracle and develop modern physics together before the oracle can be said to have given him knowledge.

And AI won't have given us any actual knowledge until it can fit its findings into the mathematical establishment. I forget who it was that said that society doesn't know anything until you can teach it to a room-full of undergrads, but that's about right.

And you will have to actually show your intellectual work before your arguing here will actually accomplish your goal of sounding smart.

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