It's the idea of an implementation that is patented, not the implementation of an idea.
This is particularly obvious when it comes to software patents as the entire process being patented concerns the manipulation of abstract information, which places even the implementation of the idea squarely in the realm of ideas. Even if that patent office requires the software to be "embodied" in some general-purpose computer before granting the patent, the patent covers the abstract data-manipulation algorithms even when they are reimplemented in different software running on a completely different kind of computer—which puts the lie to the idea that this "embodiment" has any relevance at all to the patent.
A true but useless statement. An idea is not patentable. An idea implemented in a computer program is.
Not according to EPC art52.2 (in Europe).
And not according to Alice jurisprudence (in the US).
But the patent lobby, including the patent offices, are at work trying to destroy those.
USA does blur the lines with its broad software patents and business method patents. But we in Europe have software patents to, they're just for inventions, not ideas.
This post is my personal opinion and does not relate to my employment.