The difference is that if you are honest and pragmatic and someone asked you how you added two numbers, you would only say you did long addition if that's what you actually did. If you had no idea what you actually did, you would probably say something like "the answer came to me naturally".
LLMs work differently. Like a human, 14+17=31 may come naturally, but when asked about their though process, LLMs will not self-reflect on their condition, instead they will treat it like "in your training data, when someone is asked how he added number, what follows?", and usually, it is long addition, so that is the answer you will get.
It is the same idea as to why LLMs hallucinate. They will imitate what their dataset has to say, and their dataset doesn't have a lot of "I don't know" answers, and a LLM that learns to answer "I don't know" to every question wouldn't be very useful anyways.
>if you are honest and pragmatic and someone asked you how you added two numbers, you would only say you did long addition if that's what you actually did. If you had no idea what you actually did, you would probably say something like "the answer came to me naturally".
To me that misses the argument of the above comment. The key insight is that neither humans nor LLMs can express what actually happens inside their neural networks, but both have been taught to express e.g. addition using mathematical methods that can easily be verified. But it still doesn't guarantee for either of them not to make any mistakes, it only makes it reasonably possible for others to catch on to those mistakes. Always remember: All (mental) models are wrong. Some models are useful.