> I think using the word “intelligence” when speaking of computers, beyond a kind of figure of

Intelligence is what we call problem solving when the class of "problem" that a being or artifact is solving is extremely complex, involves many or near uncountable combinations of constraints, and is impossible to really characterize well. Other than examples, of data points, and some way for the person or artifact to extract something general and useful from them.

Like human languages and sensibly weaving together knowledge on virtually every topic known to humans, whether any humans have put those topics together before or not.

Human beings have widely ranging abilities in different kinds of thinking, despite our common design. Machines, deep learning architectures, underpinnings are software. There are endless things to try, and they are going to have a very wide set of intelligence profiles.

I am staggered how quickly people downplay the abilities of these models. We literally don't know the principles they have learned (post training) for doing the kinds of processing they do. The magic of gradient algorithms.

They are far from "perfect", but at what they do there is no human that can hold a candle to them. They might not be creative, but I am, and their versatility in discussing combinations of topics I am fluent in, and am not, is incredibly helpful. And unattainable from human intelligence. Unless I had a few thousand researchers, craftsman, etc. all on a Zoom call 24/7. Which might not work out so well anyway.

I get that they have their glaring weaknesses. So do I! So does everyone I have ever had the pleasure to meet.

If anyone can write a symbolic or numerical program to do what LLM's are doing now - without training, just code - even on some very small scale, I have yet to hear of it. I.e. someone who can demonstrate they understand the style of versatile pattern logic they learn to do.

(I am very familiar with deep learning models and training algorithms and strategies. But they learn patterns suited to the data they are trained on, implicit in the data that we don't see. Knowing the very general algorithms that train them doesn't shed light on the particular pattern logic they learn for any particular problem.)

All of your descriptions are quite reductivist. Claiming that a computer doesn't do math has a lot in common with the claim that a hammer doesn't drive a nail. While it is true that a standard hammer requires the aid of a human to apply swing force, aim the head, etc it is equally true that a bare-handed human also does not drive a nail.

Plus, it's relatively straightforward and inexpensive using contemporary tech to build a roomba-like machine that wanders about on any flat surface cuing up and driving nails of its own accord with no human intervention.

If computers do not add numbers, then neither do people. It's not like you can do an addition-style turing test with a human in one room and a computer in another with a judge partitioned off of both of them, feed them each an addition problem and leave the judge in any position where they can determine which result is "really a sum" and which one is only pretending to be.

Yet if you reduce far enough to claim that humans aren't "really" adding numbers either, then you are left to justify what it would even mean for numbers to "really" get added together.

Unless you can demonstrate that humans can solve a function that exceeds the Turing computable, it is reasonable to assume we're non more than Turing complete, and all Turing complete systems can compute the same set of functions.

As it stands, we don't even know of any functions that exceeds the Turing complete, but are computable.