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Comment by somenameforme | Hacker News Reader

A game move, no matter how remarkable, is just a recombination within a strictly defined domain. And LLMs can do some awesome things in these very tight and well defined domains, especially when there is a way for them to determine victory or score. But stepping outside of well defined domains and creating knowledge that does not directly derive from what is already known is where intelligence shines. We somehow created mathematics out of absolutely nothing. We looked at the world around us and simply 'though it up' as a child might say.

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No we didn't. We are very good at parallel construction, to come up with the clean implementation of what the maths can be, but most of the examples given here were extensions of thinking about physical problems.

Remixing Jazz tokens might never generate classical music, but an evolutionary algorithm using musical notes and basing its cost function on what humans seem to enjoy might still discover something similar or better. A transformer could then generate infinite versions of that discovery.

I think this is provably false by looking at the various semi-isolated primitive tribes. They think about the world endlessly, yet many have yet to invent even basic mathematics. Many lack even the concept of numbers. For instance one tribe [1] only has concepts a few, more, and a lot. And in reality that's all you would ever really need for real world usage, pre mathematics. Mathematics largely creates the problems that it's used to solve.

More interesting is that these tribes also tend to lack the ability to recall even basic quantities of things if it's more than 2. You can give them 5 balls, but they will have extremely poor recollection of the number after just a few moments. There's these countless things humans need to simply invent, from nothing, over and over to advance to the next technological era. It only seems like a natural application of logic in hindsight, because it actually works!

[1] - https://www.sciencedaily.com/releases/2012/02/120221104037.h...

> they are really only one or two groups

Of corse one in a million that some will fall into a different evolutionary path.

The number on the success side is statistically way too significant so you can't revolve anything with this one.

I am not sure this is in support of the thesis how human intelligence is superior: it actually took millions of humans to continue experimenting from what they've learned from humans who came before them.

I am not saying it's not superior (I do believe it is), just that this does not really support it.

Basically, a single human acting on its own during their single lifetime has almost zero chance of inventing mathematics (as evidenced by the tribed you mention, but also examples of children lost in woods and raised by animals).

The point of the example is that math does not just logically derive from observation of the natural world. The reason we, in modern times, might intuitively think otherwise is because it so beautifully describes much of the universe around us. Yet these descriptions, or even the possibility of their existence, are impossible to even begin to imagine until you have developed math itself. And the problems we might think of it as solving aren't really problems until it's invented. As the tribes show you don't even need the ability to perform basic counting to live and thrive as a people.

And yes, it's going to be a slow process. Human intelligence is not about speed. The capability to do simple arithmetic rapidly correlates with intelligence in humans, yet a calculator can perform said calculations many millions of times faster than the fastest human. Yet that of course doesn't mean said calculator is thus millions of times more intelligent. The question is how long would it take an LLM to discover mathematics starting from the same empty baseline? And, using current methods, the answer is quite simple: never.

This example shown human is not a ingredient involved in invention of math concept.

https://earthsky.org/earth/fish-can-do-math-cichlids-stingra...

Mathematics is not a parlor trick. It's a purely cognitive and abstract system which can be infinitely recursed upon itself to learn ever more which, seemingly by good fortune, happens to map onto many things in the real world. Once one learns addition, the concept of multiplication comes naturally. As does subtraction, at which point you quickly end up on the eery domain of negative numbers, and so on.

To see how silly these things are imagine somebody claiming to have taught mathematics to one of these numberless tribes by training them to pick a larger group of items when it's blue, and pick a smaller group of items when it's yellow. Somebody claiming that is teaching them math would obviously be looked at like an idiot. It's a circus trick - and a rather apt reflection of what passes for research now a days.

> infinitely recursed

Infinite recursion has to be implemented by iteration in the physical universe.

Tribes who count one, one and that one, and string theory aren't the only two possibilities. There are the ancient Egyptians in between, who basically discovered fractions while dividing bread [1].

[1] https://en.wikipedia.org/wiki/Egyptian_fraction

Whats to say if you gave an LLM a pre prompt conditioning for things like: Be curious, Explore the domain you exist in, Learn about your environment like your life depends on it, You are a social creature so when you find out information you like to share it, Being a social creature, the most practical tool for sharing ideas is language (these notions among many others are similar pre-conditions for humans behaviour, largely I imagine for survival, but in our case initially informed by emotion rather than language)

And then just feed it endless continuous video of the world from a persons perspective (ie, not just random jumps around scenes) How is that any different to the way humans developed our own theories and understanding on the universe we found ourselves in? Obviously a video feed isn't quite the same as having a myriad of senses like we have for interfacing with the world. But theres no reason to say newtons laws need touch or smell to be figured out (maybe that is a bad example for not requiring touch, being about mass and force, but you get the point). Learning language and understanding of the world from scratch might depend on having physcial interaction with the world, sure, but thats again just different sets of input training data that a multimodal model can make connections between if there were pressure to do so.

Then you simply prompt the LLM to define the laws it has observed in a way that can use language to transmit the idea. In the human equivalent, a "prompt" doesn't need to be (but can be) a direct question being asked. It could just be our urge to share ideas, an emotion perhaps that moves us to action. I don't want to go too far on this thought as it is pure speculation without serious scientific backing, but for the sake of the thought experiment with all this in mind you could even say that brains are much like an LLM that is in a constant state of training & updating, but also being "prompted" from our environment and biological feedback loops being fed in. I don't feel like this idea is even that controversial or remotely original.

The difference is that models of today are already trained on the corpus of human knowledge so they already know all of this instead of having to figure it out. But I don't really see an argument for why an LLM wouldn't be able to crystallise observed patterns into mathematical formulae if it had the appropriate influences that would encourage it to do so. Its just that we don't care to train them inefficiently. I imagine this will be tried in the near future though.

FYI there is "symbolic fitting" that crunch through all combination of equations to find the math equation for simple phycis laws. That seem to me is hackable, like inserting heuristics to speed up the process. That heuristics can be generated from LLM.

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