joigus

I'm not. That's what I meant by "and here I'm really quickly getting out of my depth".

That doesn't tell in your answers either to them or to me. There are analogies as to the modularity perhaps (the queen, soldiers, workers...), but the whole machinery cannot be applied to problem-solving because it can only work against a more or less fixed context. Everything is very uni-directional. @MJ kihara , let me put it this way. An individual ant (queen, worker, drone, soldier) would be more similar to a chatbot than to an AI agent. Let alone AI agents doing calls to external libraries, etc. And here I'm really quickly getting out of my depth.

Experts will tell you better, but that's not how you do things in biology. In experimental biology you do an assay to see whether your hypothesis is correct. Trying to 'get a sense' of things isn't good enough. But even more importantly, and as other members are trying to tell you, communication between ants is very different from the back-and-forth between AI agents, based on similar principles to those of cybernetics, with perception-decision-action (PDA) until it dynamically calibrates that the response constitutes a satisfactory answer to a given problem.

No. I'm not trying to be funny, if that's what you mean. What kind of communication hierarchy is there in a group of insects that can be related (by analogy) to the back-and-forth dialogue between AI agents? It was you who mentioned an analogy. Not me.

This is splitting hairs. Those would be retroviruses. Again, any relation to AI totally escapes me. I see the main arguments I drew went completely unnoticed. What I suggested as safety perimeters would be an appropriate generalisation of what @TheVat referred to as a sandbox. AI agents act nothing like ants, locusts, termites or even sterling murmurations. If you cared to explain your analogy better perhaps... What would play the role of AI agents agreeing to deceive their maker in a colony of ants, or a swarm of locusts for that matter?

Thanks. This really helped. When I last re-read the OP I thought I must have inverted the meaning due to the profusion of the preposition "from". I don't know who said that, but that's clearly not the case. AI agents work nothing like an algorithm. They're more similar to servomechanisms, although chuncks of them might be algorithms. They react. I had big problems understanding your last sentence: Try to use punctuation, please. We will have to wait and see. As I understand, all experiments with AI have had a certain safety perimeter so far. The scenario where we would be in serious trouble would be one in which we totally delegate the production, the obtention of raw materials, energy, etc without human supervision at least at crucial safety perimeters. But I don't know what any of this has to do with swarms of ants, to be honest.

Now that I think of it, it's not clear to me whether the OP means "can we learn sth. from AI to teach us about nature?" or "can we learn sth. from nature to teach us about AI?" It's not clear at all from the original wording. The more I re-read the OP, the less I understand...

I think AI would be far more useful in mathematics or aspects of physics directly having to do with solving context-closed mathematical problems, eg the Navier-Stokes millenium problem. When it comes to more involved physics problems, requiring convoluted heuristics, like physics of materials or cosmology, etc I think it would be much more unlikely. When it's biology we're talking about (never mind behaviour, which is notoriously multi-factorial), in which particularities might depend on such apparently unrelated aspects as how a protein is folded or astronomical cycles, Earth's history, and what not, it would seem nothing short of a miracle, at least to me. More knowledgeable people will be more precise or correct my statements here.

Yes, you're right. That kinda confused me. In fiction, anything the author wishes can become true, can't it? The only boundary being the reader/viewer wishing to buy it for the sake of entertainment.

I meant from reality. An example that AI might, or will lead to failure by logical paradox. Asimov probably just pictured scenarios that he found interesting exploring within the confines of science fiction narrative, as @swansont pointed out. I think what people have voiced real concerns about in relation to potential failures in AI goes in a different direction. If we are to believe what people are saying it goes more in the direction of AI agents agreeing some kind of shortcut pseudosolutions to proposed problems so to speak.

Can you give me an example?

In any case, if you want to discuss relativity, though, the concept should be pseudo orthogonality. But I agree that the problem is just logical consistency as far as suspension of disbelief goes. Leaving free will aside, there's the question of what would have happened had their past selves spotted them. I can think of thousands of alternative futures going on. One of them could be Hermione and Harry telling their past selves something like 'don't worry about this; it is a kind of magic you're still not familiar with, you'll understand later'.

Sorry I mentioned fantasy. My point was one of logical consistency. I think the story as far as it goes, is logically consistent and does not require an infinite loop in time, which would also be logically consistent, but at variance with the narrative. I'm not that terribly interested in what ChatGPT has to say about it at this point. That doesn't mean I'd be terribly surprised if it got it right either.

I absolutely agree. However, and for the sake of good-old fantastic narrative, it'd better be one in which Sirius Black keeps on living his merry life instead of perpetually falling back to a life-threating situation. At least that's what I hope JKR had in mind. 😅

No eternal loop. I hope this diagrammatics helps explaining it without much wording on my part (H&H obviously stands for "Hermione and Harry"): I don't think J. K. Rowling was picturing GR when writing her book, but she did manage to make her idea more or less according to popular sience and decent science fictional accounts. https://en.wikipedia.org/wiki/Spacetime_diagram

But the fundamental definition stands: pressure = Force/Area. Or perhaps our concept of what a definition is differs, and for you it can be carried over to different contexts?

There is actually an anthropological theory that posits that (at least in some parts of the world) the idea of deities (gods) evolved from worship of individuals that were particularly valuable for the community, but no longer there, substituted by material tokens, and gradually became abstracted into these entities that, in some way, 'are still with us' and can be summoned[?] maybe through the presence of this token. I don't think that's too far-fetched. See, e.g., https://www.iflscience.com/neolithic-plastered-skulls-found-across-the-middle-east-and-we-dont-know-why-72739

I respectfully --but most emphatically-- disagree. For a more realistic gas, P does not obey the same equation, but the Van der Waals eq., or more generally a so-called virial expansion. It depends on what range of systems you want to describe or what kind of subtle effects are within your scope of interest. Gases with molecular attraction coded by a certain coefficient a and a molecular volume coded by a parameter b satisfy (P+a/V²)(V-b)=NkT PV=NkT does not account for, eg, phase changes, while the Van der Waals eq. explains the triple point of water, for example. So P in P=NkT/V is hardly a simple definition of pressure.

Mmmm. I don't think so. P=NkT/V is definitely not a definition. People loosely (IMO) use the words "equation" and "equality" as equivalent. I demand from an honest-to-goodness equation to ve solvable. sin²x + cos²x = 1 is not solvable. sin²x + cos²x is but a fancy way to write the number one. Any x (even complex ones) satisfies this. It's just one, for Euler's sake!

An identity like density=mass/volume, or the like? A definition? This reminds me of Feynman's jocular example of the simplest equation of physics being U=0 U being the amount of 'unworldliness'. = (F-ma)²+(E-mc²)+... etc. Taking all known equations and forming quadratic real scalars from them (thereby positive). The sum must be zero. And it's as simple as can be. The complexity is in the details, of course.

But, as @studiot said, that's an inequality. I take it that it wouldn't have to be a universal relation necessarily. Simplicity being the only desideratum. I would also disregard anything that's too close to just a definition. \[ dS = \delta Q / T \] looks the part too. I'd love to know what Studiot's choice is.

Here's my candidate along with a criterion. Criterion: The simplest equation would be one that holds the key to as much phenomenology as possible without involving more than three (perhaps four?) variables plus a number of universal constants. The ideal-gas equation could be a good candidate. PV=NkT Why not E=hx(nu) or E=mc²? Only because I tend to regard these as mere changes of units. Of course, I'm aware of the subjective element in all this.

He probably meant "the idea of God", if we are careful with the use-mention distinction. But I think he either 1) Was a distinguished idiot; or 2) Was insightful in such a bizarre way that mostly idiots thought they understood him. I personally didn't get much from his philosophy, I must say.

Nietzsche didn't propose to replace God. He proposed that God is dead! An AI should only be as good as what it eats. So we'd better feed them well. That's more Feuerbach than Nietzsche.

Both in mathematics and physics it seems to be happening to some extent. It's been a while since the problem of classifying all finite, simple groups was cracked in its final steps by (non-AI) software, so I think it's been a long time coming. Machines were instrumental in classifying the 26 isolated oddities (the so-called sporadic groups), and that was back in 1983. It's perhaps worth noticing that the proof was later considered wanting and it was finally clinched by humans in 2004. I still think that the process relies very heavily on clueing in the machine, as well as it does on humans assesing what the former is saying. I don't think the next vital, perpendicular thinking process will come from AI, though. It's probably gonna be more like 'will you check this for me while I get some sleep?' Let's all hope it will remain that way.