Correct, ideas are abstract. Mathematics (including computer science) is abstract. If you invent a new math, or a new piece of software, it is abstract and thus non patentable.
If you invent a new piece of hardware, it's concrete. The ideas embodied are abstract. If you came up with hardware that works differently in a concrete way (e.g. you figured out how to use carbon in place of silicon, opening the door to entirely new categories of manufacturing) then it would be potentially patentable. Your methods would be concrete methods involving substances which are not abstract.
I would argue (playing devil's advocate in favor of software patents) that a new /piece of/ software is decidedly not abstract, it is concrete and it has an abstract part that is (in the US today) patentable.
What's not patentable is "old idea, now on a computer for the first time" -- covering any implementation of "old idea" that nobody thought to put on a computer before, "but on a computer." That's clearly abstract. It's not an implementation. There are no implementation-specific details to put in the patent as claims (they would have to stand up to the obviousness test either individually or as a group). With nothing new except "on a computer" or "on a mobile device" it's not novel or specific and therefore not patentable.
I'm actually not going to argue the point "now if you HAD a specific implementation" because I'm not sure I actually believe in patents (or more specifically software patents) at all, but I do believe that even without a patent: if you have some source code that your competition doesn't, and you made it... and they acquire it somehow without getting a license, there are already copyright laws that protect you (so long as you can establish your own original ownership of that work) if they should decide to rip it off wholesale.
If you invent a new piece of hardware, it's concrete. The ideas embodied are abstract. If you came up with hardware that works differently in a concrete way (e.g. you figured out how to use carbon in place of silicon, opening the door to entirely new categories of manufacturing) then it would be potentially patentable. Your methods would be concrete methods involving substances which are not abstract.
HTH