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That's not what I mean.

If I use a calculator to find a logarithm, and I know what a logarithm is, then the answer the calculator gives me is perfectly useful and 100% substitutable for what I would have found if I'd calculated the logarithm myself.

If I use Claude to "build a login page", it will definitely build me a login page. But there's a very real chance that what it generated contains a security issue. If I'm an experienced engineer I can take a quick look and validate whether it does or whether it doesn't, but if I'm not, I've introduced real risk to my application.

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Those two tasks are just very different. In one world you have provided a complete specification, such as 1 + 1, for which the calculator responds with some answer and both you and the machine have a decidable procedure for judging answers. In another world you have engaged in a declaration for which the are many right and wrong answers, and thus even the boundaries of error are in question.

It's equivalent to asking your friend to pick you up, and they arrive in a big vs small car. Maybe you needed a big car because you were going to move furniture, or maybe you don't care, oops either way.

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Yes. That is the point I was making.

Calculators provide a deterministic solution to a well-defined task. LLMs don't.

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Furthermore, it is possible to build a precise mathematical formula to produce a desired solution

It is not possible to be nearly as precise when describing a desired solution to an LLM, because natural languages are simply not capable of that level of precision... Which is the entire reason coding languages exist in the first place

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