Copyright quite literally protects the act of copying or reproducing a work protected by copyright. And you are technically entering into something akin to an end user licensing agreement when you buy a book, the only difference being that the EULA is incorporated into law on an international basis through reciprocal copyright treaties.

So if scan a book you are making a copy. In some copyright jurisdictions this is allowed for individuals under a private copying exception - a copyright opt out, if you like - but the important thing is private use. In some jurisdictions there is also a fair use exception, which allows you to exploit the rights protected by copyright under certain circumstances, but fair use is quite specific and one big issue with fair use is that the rights you are exploiting cannot result in something that competes with the original work.

Other acts restricted by copyright include distribution, adaptation, performance, communication and rental.

So if you copy a book, digitize it, and write a program to analyze the word frequencies it contains you may, in some jurisdictions but not all, be allowed to do this.

If you’re doing it locally on your own machine you are simply copying it. If you do it in the cloud you are copying it and communicating the copy. If you copy it, analyze it and train an AI model on it that could be considered fair use in certain jurisdictions. Whether the outputs are adaptations of the training data is a matter of debate in the copyright community.

But importantly if you commercialise that model and the resulting outputs compete with the copyright protected material you used to train, your fair use argument may fail.

So when you buy a book you are actually party to what is effectively a licence granted by the copyright holder, albeit it to the publisher. But as the end user of the book you are still restricted in what you can do with that copyright protected work, through a universal end user licence encoded in law.