I have 2 questions regarding algorithm "tangibility".
Let me give an example. Suppose I had this great algorithm for music processing, and at the heart of the algorithm is this special set of mathematical formulas I put together for the purpose of superior music processing.
Now, my understanding is that algorithms, including those based on math, are "abstract ideas" or something "intangible", and cannot be patented UNLESS disclosed with details of a computational hardware implementation of said algorithms, at which point the entire system (the algorithm + its hardware implementation) becomes tangible, and thus patentable.
Question 1: Regarding the tangibility issue, does it mean that the patent office/courts/legal system need me to demonstrate that the algorithm can indeed be implemented by some 'physical' means? Can this really be the entire issue? Those guys are just too dumb to realize that algorithms are almost always implementable by some computing hardware? (be it a PC, the cloud, HPC, FPGA, etc).
Question 2: Ok, so suppose I went ahead and disclosed a "tangible" system made of both a (mathematical) algorithm and the hardware to implement it with, but since it's almost inconceivable to cover every possible hardware implementation of the same algorithm, my lawyer didn't properly cover the aspect of, say, an FPGA implementation of my algorithm. But, other than this little mishap, the patent was issued without any troubles.
Now consider the following situation: Someone created a "system" made of the CORE algorithm disclosed in my patent but they used an FPGA to implement it! Does this count as infringement? Yes/No?