Because whats inside our minds is more than mathematics, or we would be able to explain human behavior with the purity of mathematics, and so far, we can't.
We can prove the behavior of LLMs with mathematics, because its foundations are constructed. That also means it has the same limits of anything else we use applied mathematics for. Is the broad market analysis that HFT firms use software for to make automated trades also intelligent?
Note that what you claim is not a fact, but a (highly controversial) philosophical position. Some notable such "non-computationalist" views are e.g. Searle's biological naturalism, Penrose's non-algorithmic view (already discussed, and rejected, by Turing) and of course many theological dualist views.
Your reasoning is invalid.
For your claim to be true, it would need to be provably impossible to explain human behavior with mathematics.
For that to be true, humans would need to be able to compute functions that are computable but outside the Turing computable, outside the set of lambda functions, and outside the set of generally recursive functions (the tree are computationally equivalent).
We know of no such function. We don't know how to construct such a function. We don't know how it would be possible to model such a function with known physics.
It's an extraordinary claim, with no evidence behind it.
The only evidence needed would be a single example of a function we can compute outside the Turing computable set, which would seem to make the lack of such evidence make it rather improbably.
It could still be true, just like there could truly be a teapot in orbit between Earth and Mars. I'm nt holding my breath.
I mean some people have a definition of intelligence that includes a light switch, it has an internal state, it reacts to external stimuli to affect the world around it, so a light switch is more intelligent than a rock.
Leaving aside where you draw the line of what classifies as intelligence or not , you seem to be invoking some kind of non-materialist view of the human mind, that there is some other 'essence' that is not based on fundamental physics and that is what gives rise to intelligence.
If you subscribe to a materialist world view, that the mind is essentially a biological machine then it has to follow that you can replicate it in software and math. To state otherwise is, as I said, invoking a non-materialistic view that there is something non-physical that gives rise to intelligence.
No, you don’t need to reach for non-materialistic views in order to conclude that we don’t have a mathematical model (in the sense that we do for an LLM) for how the human brain thinks.
We understand neuron activation, kind of, but there’s so much more going on inside the skull-neurotransmitter concentrations, hormonal signals, bundles with specialized architecture-that doesn’t neatly fit into a similar mathematical framework, but clearly contributes in a significant way to whatever we call human intelligence.
> it all rests on (relatively) simple mathematics. We know this is true. We also know that means it has limitations and can't actually reason information.
This was the statement I was responding to, it is stating that because it's built on simple mathematics it _cannot_ reason.
Yes we don't have a complete mathematical model of human intelligence, but the idea that because it's built on mathematics that we have modelled, that it cannot reason is nonsensical, unless you subscribe to a non-materialist view.
In a way, he is saying (not really but close) that if we did model human intelligence with complete fidelity, it would no longer be intelligence.
Any model we can create of human intelligence is also likely to be incomplete until we start making complete maps of peoples brains since we all develop differently and take different paths in life (and in that sense it's hard to generalize what human intelligence even is). I imagine at some point someone will come up with a definition of intelligence that inadvertently classifies people with dementia or CTE as mindless automatons.
It feels like a fool's errand to try and quantify intelligence in an exclusionary way. If we had a singular, widely accepted definition of intelligence, quantifying it would be standardized and uncontroversial, and yet we have spent millennia debating the subject. (We can't even agree on how to properly measure whether students actually learned something in school for the purposes of advancement to the next grade level, and that's a much smaller question than if something counts as intelligent.)
Don't we? Particle physics provides such a model. There is a bit of difficulty in scaling the calculations, but it is sort of like the basic back propagation in a neural network. How <insert modern AI functionality> arises from back propagation and similar seems compared to how human behavior arises from particle physics, in that neither our math nor models can predict any of it.
>Because whats inside our minds is more than mathematics,
uh oh, this sounds like magical thinking.
What exactly in our mind is "more" than mathematics exactly.
>or we would be able to explain human behavior with the purity of mathematics
Right, because we understood quantum physics right out of the gate and haven't required a century of desperate study to eek more knowledge from the subject.
Unfortunately it sounds like you are saying "Anything I don't understand is magic", instead of the more rational "I don't understand it, but it seems to be built on repeatable physical systems that are complicated but eventually deciperable"
Your first sentence is a non-sequitur. The fact that we can't explain human behavior does not mean that our minds are more than mathematics.
While absence of proof is not proof of absence, as far as I know, we have not found a physics process in the brain that is not computable in principle.