No one can "conduct arbitrary arithmetic". It's a problem that goes to infinity and you're throwing it at humans who very much don't.
Even in your own mind, "5 + 25" and "7 + 27" take two different routes based on different pattern-matched heuristics. You don't have a single "universal addition algorithm". You have a bag of pattern-matching features, and maybe a slow unreliable fallback path, if you have learned any. Which is why "5000+5000" is trivial but "4523+5438" isn't.
The problem with your "theory" is a common one: it's utter bullshit. It says "here's what I think is true" but stops short of "why", let alone "why it fits reality better than the alternatives" or "here's what this theory allows you to do". It's like claiming that "all matter is phlogiston". It was entertaining when people were doing that in Ancient Greece, but by now, it's just worthless noise.
Pattern-matching is a faster shortcut that conserves energy. The "slow fallback" you denigrate is the logical reasoning process itself, and it is reliable given sufficient time and energy. My claim was certainly not that doing arithmetic quickly is fundamental to intelligence.
> but stops short of "why",
No, I rather explicitly stated how I think reasoning regulation happens as a result of the body's attempt to conserve energy in environments where complex reasoning does not meaningfully improve chances of survival, and allocates more energy in environments where complex reasoning does meaningfully improve chances of survival. That is the "why".
> "here's what this theory allows you to do"
What it allows us to do is achieve deterministic results after observing new conditions we've never seen before and reasoning about how those conditions interact to produce a final result. Our ability to build computers and spaceships is the direct result of reasoning applied acrossing many, many steps. LLMs cannot get even the first step correct, of correctly deducing Z from X + Y, and without that there is a fundamental difference in the capability to solve problems that can never be resolved. They can be special-cased to use a calculator to solve the first step, but this still leaves them incapable of solving any new logical exercise they are not pre-emptively programmed to handle, which makes them no different than any other software.
Pattern-matching is faster because it's the "normal" path that the human mind naturally takes. The "slow fallback" is an exception, and an optional one at that. There is quite a number of humans who would be able to solve 5+5 but not 4523+5438.
If human mind was based on logic, 20+80 and 54+39 would be equally as fast. As they are for a calculator. The calculator has a simple, fast, broadly applicable addition primitive based on pure binary logic. Humans don't.
In case of addition, LLMs work the same way humans do. They have "happy paths" of pattern-matching, and a slow unreliable "fallback path". They just have better "happy path" coverage than almost all humans do.
And your attempts at making your "theory" look any better than phlogiston are rather pathetic. I'm not asking you "what logic can do". I'm asking you "what your theory can do". Nothing of value.
Even in your own mind, "5 + 25" and "7 + 27" take two different routes based on different pattern-matched heuristics. You don't have a single "universal addition algorithm". You have a bag of pattern-matching features, and maybe a slow unreliable fallback path, if you have learned any. Which is why "5000+5000" is trivial but "4523+5438" isn't.
The problem with your "theory" is a common one: it's utter bullshit. It says "here's what I think is true" but stops short of "why", let alone "why it fits reality better than the alternatives" or "here's what this theory allows you to do". It's like claiming that "all matter is phlogiston". It was entertaining when people were doing that in Ancient Greece, but by now, it's just worthless noise.