So, the reason I think the argument on Turing completeness matters here, is that if we accept that an LLM and a brain are both Turing complete, then while you're right that there can be Turing complete systems that are so different in performance characteristics that some are entirely impractical (Turings original UTM is an example of a Turing complete system that is too slow for practical use), if they are both Turing complete the brain is then both an existence-proof for the ability of Turing machines to be made to reason and gives us an upper limit in terms of volume and power needed to achieve human-level reasoning.

It may take us a long time to get there (it's possible we never will), and it may take significant architectural improvements (so it's not a given current LLM architectures can compete on performance), but if both are Turing complete (and not more) then dismissing the human ability to do so is

It means those who dismiss LLM's as "just" next token predictors assuming that this says something about the possibility of reasoning don't have a leg to stand on. And this is why the Turing completeness argument matters to me. I regularly get in heated arguments with people who get very upset at the notion that LLMs can possibly ever reason - this isn't a hypothetical.

> And vice versa. While Deutsch tends to claim that humans will be able to run any computation that ASI will run in the future, I would claim that to the extent a human is able to act as Turing Complete, such computations may take more than a lifetime and possibly longer than the time until the heat death of the universe.

If you mean "act as" in the sense of following operations of a Turing-style UTM with tape, then sure, that will be impractically slow for pretty much everything. Our ability to do so (and the total lack of evidence that we can do anything which exceeds Turing completeness) just serves as a simple way of proving we are Turing complete. In practice, we do most things in far faster ways than simulating a UTM. But I agree with you that I don't think humans can compete with computers in the long run irrespective of the type of problem.

Ok, so it looks like you think you've been arguing against someone who doubt that LLM's (and similar NN's) cannot match the capabilities of humans. In fact, I'm probably on the other side from you compared to them.

Now let's first look at how LLM's operate in practice:

Current LLM's will generally run on some compute cluster, often with some VM layer (and sometimes maybe barebone), followed by an OS on each node, and then Torch/TensorFlow etc to synchronize them.

It doesn't affect the general argument if we treat the whole inference system (the training system is similar) as one large Turing Complete system.

Since the LLM's have from billions to trillions of weights, I'm going to assume that for each token produced by the LLM it will perform 10^12 FP calculations.

Now, let's assume we want to run the LLM itself as a Turing Machine. Kind of like a virtual machine INSIDE the compute cluster. A single floating point multiplication may require in the order of 10^3 tokens.

In other words, by putting 10^15 floating point operations in, we can get 1 floating point operation out.

Now this LLM COULD run any other LLM inside it (if we chose to ignore memory limitations). But it would take at minimum in the order of 10^15 times longer to run than the first LLM.

My model of the brain is similar. We have a substrate (the physical brain) that runs a lot of computation, one tiny part of that is the ability that trained adults can get to perform any calculation (making us Turing Complete).

But compared to the number of raw calculations required by the substrate, our capability to perform universal computation is maybe 1 : 10^15, like the LLM above.

Now, I COULD be wrong in this. Maybe there is some way for LLM's to achieve full access to the underlying hardware for generic computation (if only the kinds of computations other computers can perform). But it doesn't seem that way for me, neither for current generation LLM's nor human brains.

Also, I don't think it matters. Why would we build an LLM to do the calculations when it's much more efficient to build hardware specifically to perform such computations, without the hassle of running it inside an LLM?

The exact computer that we run the LLM (above) on would be able to load other LLM's directly instead of using an intermediary LLM as a VM, right?

It's still not clear to me where this is not obvious....

My speculation, though, is that there is an element of sunk cost fallacy involved. Specifically for people my (and I believe) your age that had a lot of our ideas about these topics formed in the 90s and maybe 80s/70s.

Go back 25+ years, and I would agree to almost everything you write. At the time computers mostly did single threaded processing, and naïve extrapolation might indicate that the computers of 2030-2040 would reach human level computation ability in a single thread.

In such a paradigm, every computer of approximately comparable total power would be able to run the same algorithms.

But that stopped being the case around 10 years ago, and the trend seems to continue to be in the direction of purpose-specific hardware taking over from general purpose machines.

Edit: To be specific, the sunk cost fallacy enters here because people have been having a lot of clever ideas that depend on the principle of Turing Completeness, like the ability to easily upload minds to computers, or to think of our mind as a barebone computer (not like an LLM, but more like KVM or a Blank Slate), where we can plug in any kind of culture, memes, etc.