Large Language Models Are Neurosymbolic Reasoners

Various attempts at feeding their output back in to check itself have shown marked improvements in accuracy.

> if you model a geometric, g : Real -> Real with computable, c : Int -> Int then there are gaps at arbitrarily high precisions, say p (eg., p = delta(g, c) at (x, t))

Nobody takes "computable approximation to g: R -> R" to mean "a computable function c: R* -> R" where R is the computable reals. There are many mathematical issues with this caused by self-referential programs (realised by Turing himself in "On Computable Numbers"). Typically you would model it as "c: R* x Q -> R*" where Q is a rational describing your desired precision, right?

> Since 10^BIG are required, "delta(g, c) I'm not sure what you mean by this - the computable approximation "c" is deterministic essentially by definition. If you mean "in order to remain within some bound of g" I can kinda see what you're saying but in that case you can interleave computations with smaller and smaller precisions (the "Q" I mentioned) in order to work around that issue, right? It won't be efficient, but it will certainly be computable.

> Refences: Look for physical church-turing, church-turing thesis, non-det and det in chaos theory, non-det in classical mechanics, physical interpretations of the reals -- this will be in postgrad work, it wont be in popsci books.

Thanks! I don't know much chaos theory, I'll have a look around for a good textbook.

Edit: I just want to say - you have a pretty wild way of writing that makes it hard for me to tell if you're a crank or not. Either way, reading your posts here has given me a ton of food for thought =) what's your background?

1 yr medicine, 6 yr physics, 4 yr debating union, 20 yr c programming, 20 yr love of political and stand up comedy, 15 yr software eng, 10 yr data scientist, 15 yr python, 22 yr informal & formal philosophy, 8 yr data sci & software consult/coach to finance/defence/... and maybe soon, 4 yr PhD AI & HCI

Of those, you may decide which is the most relevant to my writing style. The amount of theatrics and irony in a live delivery might change the interpretation.

Replacing R with Q is just replacing it with (Int, Int) -- so be it. My claim concerns whether CM assumes determinism (it does) and therefore requires infinite precision, any gap whatsoever that goes missing means P(t_next|t_now) You might say this indicates reality doesnt follow CM, and so that CM is wrong and (some now less hegemonic views) of QM are correct -- reality isnt deterministic.

Fine, but QM makes the situation worse. Since it's linearity now under threat: we would not be able to compose QM systems linearly if the wavefns didnt have infinite dim.

One important assumption here is that we ought take the explicit and implicit assumptions of physics as given as our starting point, ie., Prior(Physics) = High, and Posterior(NotPhysics|Physics) = Low.

So the dialectical burden is on the "computationalists" to show that there is a workable theory of physics, at every level which preserves either (1) the assumptions of physics; or (2) motivates why those assumptions are wrong non-circularly.

Given the premise on priors above, the argument, "physics is wrong because reality is computational" is both circular and unpersuasive (this doesnt mean its wrong, just that no reason has been presented).

You think that reality is a pattern, and that properties obtain from configurations. Eg., that, of course, we can transmute gold into lead. Alchemy.

The problem with this is that the patterns have semantics, a pattern of wood does not have the same properties as a pattern of lead. The pattern isnt the important bit.

If you want to turn hydrogen into lead you first have to fire up a star and wait a very very long time, and as protons and electrons bundle up in every more complex configurations interactions between them come to dominate their properties... so that lead is nothing at all like hydrogen.

What is the only known element that enables "weak polymerisation", ie., adaptive self-replication at the molecular level: carbon.

What are the properties of all intelligent systems known to science? They're organic.

Why? This is no coincidence. In order to think, you have to grow -- self-replicate at every level from the cellular to organs, tissues... the material placitity of the machine that holds your thoughts has to itself adapt its structure to that of your body (the device which explores the world).

Now, should we expect hydrogen to do that? No. Silicon? No. Why would we? Ah, only because we loath the idea of being apes, and of oozing.. our biological disgust instincts tell us to run far away from it. How more beautiful if, like in genesis, we can fashion man out of clay and breath in life.

but alas, we arent clay; nor will clay ever think or desire or want.. clay cannot take impressions of the world without becoming an impression. It cannot adapt.

"The pattern isn't the important bit."

I was taking pattern as the electrical impulses in the brain. Which I would say is everything when it comes to thought and thinking.

Human Neurons are just Calcium Voltage potentials. Just like weights in a NN.

Yes. The human brain neurons are far more complicated than that. There is a lot of chemical soup of hormones and modulators that factor into the voltage potentials. What you eat can impact gut, that impacts how many neurotransmitters are produced, that impact when a neuron fires, that is experienced as a mood, etc.... SO yes, the human brain cannot be separated from the body.

There is some entity, brain+body. And it so happens that it is made from Carbon . And we call things based on Carbon to be 'organic' and it can re-produce so we call it 'alive'. These are just definitions, that we have assigned to things.

Just like a CPU can't be removed from it's power supply and keep working. There is a 'system' and it has 'parts'.

That doesn't mean, we can't model a brain to a degree close enough that you couldn't tell an AI and Human apart.

I'm just saying, that when we do reach that point, then we'll be forced to realize the AI also has an internal subject experience, and is 'conscious', or we'll have to acknowledge that humans do not.

It will be either/or.

Humans and AI are both conscious, have internal subjective experience. or Neither do. And if neither do, then humans really are just hallucinating their inner experience, but not in control. Humans are also deterministic. Nothing special.

I see from your other posts, that you seem to be putting a lot of faith in Chaos Theory or Quantum Mechanics as some underlying explanation. To give humans the special sauce.

I'd just say, introducing randomness, does not make a system un-determined. That there is a lot of randomness in our 'chaotic' body, does not imbue it with agency. Randomness != Agency.

Edit: I like the clay example. I'd say that is like the NN that goes through training, then released, but the model is static. Doesn't get updated. Eventually these AI's will learn as they go and be continually updating.