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Comment by AlexSW | Hacker News Reader

Seems like a calculator is a good example of a program which we would write even though it is entirely unsurprising; even if we needed nothing else on a computer we might invent it still?

It seems to me that we create computer programs not to surprise us but typically to do things very quickly or conveniently. Even a complex beast like Photoshop is reasonably unsurprising.

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The point is that the outputs of the calculator are fundamentally surprising, in the sense that if any individual programmer could easily know all the expected outputs in advance, they wouldn't need the calculator in the first place. Photoshop surprises us by calculating the precise location of millions of pixels based on relatively simple inputs like a handful of clicks on a screen. This logic does not apply to every single imaginable program, but it does apply to the non-trivial ones.

So "surprising" == anything not previously known? That's not the definition I'm used to. I might not know the exact answer to sqrt(10), but I wouldn't be surprised by the answer considering I already know it's between 3 and 4.

To add to the other answer, Shannon's information is also sometimes called "surprisal". And it doesn't describe only what is not known, but rather what can be predicted. So if you can predict new information, it has low surprisal, even if it previously wasn't known (with certainty).

It is Shannon’s definition.

Surprise == new information.

Lack of surprise == lack of new information.

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