@nini @tuban_muzuru @cinebox @ozeng @RosannaSibora
More importantly, you can build a mental model of how a calculator works and learn to use it correctly. They offload a specific step in a calculation.
And using calculators in class does harm children’s ability to do mental arithmetic, which is why they’re not introduced into classrooms until children are past the stage where mental arithmetic is important.
They also cause the ability to do long division, multiplication, and so on to atrophy. That normally doesn’t matter because these are not actually useful skills, the ability to understand when to use them is. Using a calculator helps learning once you get to algebra because it’s useful only for a handful of steps and those are not the important ones for what you’re learning. Using a symbolic algebra system would let the machine do all of the steps, but only up to a certain limit and you’re acquiring a skill that includes knowing how to formulate the equation, so using a symbolic algebra system will increase your abilities later.
And, at that point, the systems aren’t entirely deterministic. They have tactics that will try to solve equations in different ways and they will select between them based on heuristics. But to really get the most out of these systems you need to understand how the tactics work and when they will be useful, which is what you learned solving equations by hand. And, once you understand that, then they behave deterministically: if the heuristics don’t work, you can apply steps manually (still much faster than doing it by hand).
There is no equivalent for an LLM. It will generate a sequence of tokens that is a statistically plausible continuation of the sequence that you provide as a prompt. But that can vary wildly based on the random seed. It will also vary wildly based on which model you use. In contrast, any skill you learn on something like Matlab will transfer directly to something like GNU Octave.
The impossibility of theory building is what really sets LLMs apart. Humans recognise patterns even when there are no patterns and so people come up with a load of things that they throw into their prompts because they made things better in a few previous attempts and build religions around them but they aren’t mentally modelling how the LLMs work.