A really simple abstraction in mathematics is that of numeric basis (e.g. base 10) for representing numbers. Being able to use the symbol 3 is much more useful than needing to write III. Of course, numbers themselves are an abstraction- perhaps you and I can reason about 3 and 7 and 10,000 in a vacuum, but young children or people who have never been exposed to numbers without units struggle to understand. Seven… what? Dogs? Bottles? Days? Numbers are an abstraction, and Arabic digits are a particular abstraction on top of that.

Without that abstraction, we would have insufficient tools to do more complex things such as, say, subtract 1 from 1,000,000,000. This is a problem that most 12 year olds can solve, but the greatest mathematicians of the Roman empire could not, because they did not have the right abstractions.

So if there are abstractions that enable us to solve problems that were formerly impossible, this means there is something more going on than “hiding information”. In fact, this is what Dijkstra (a mathematician by training) meant when he said:

The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise

When I use open(2), it’s because I’m operating at the semantic level of files. It’s not sensible to think of a “file” at a lower level: would it be on disk? In memory? What about socket files? But a “file” isn’t a real thing, it’s an abstraction created by the OS. We can operate on files, these made up things, and we can compose operations together in complex, useful ways. The idea of a file opens new possibilities for things we can do with computers.

I hope that explanation helps!

Under the assumption that the input data is properly formatted you can generate machine code. This is however an abstraction which can fail as nothing forces a user to input valid files.

So we have an abstraction without any encapsulation.