The output of the process (a working machine) is provably equivalent. So you (and pg in one of his essays) conclude that the patent rules should be equivalent.
However, the purpose of patents is to promote progress by motivating people to invent. So what matters is the input to the process, i.e. the human activity that eventually leads to a working machine.
The patent system was designed for human activities that involve so much time and effort that people might not do them without an additional incentive, i.e. temporary monopoly. Picture 18th-century mechanical engineering. Building several different designs of a machine to see which works best would be a monumental task. It would be much easier to search the patent database and find something someone else invented, and cheaper to license it from them.
Imagine for a moment what would happen if you gave everyone a machine such that you could simply drop a diagram of a mechanical invention into it, and out the other end comes a working implementation. That would totally change the game. Invention would require much less effort. Everyone would be doing it without consulting the patent database, and the huge influx of inventors would overwhelm the patent office, making it impossible to find which inventions in the flood of incoming applications are novel and nonobvious.
This is what happened with software. Millions of people have these magic machines on their desks and in their backpacks and briefcases. No patent incentive is needed, just as none is needed for mathematics.
However, the purpose of patents is to promote progress by motivating people to invent. So what matters is the input to the process, i.e. the human activity that eventually leads to a working machine.
The patent system was designed for human activities that involve so much time and effort that people might not do them without an additional incentive, i.e. temporary monopoly. Picture 18th-century mechanical engineering. Building several different designs of a machine to see which works best would be a monumental task. It would be much easier to search the patent database and find something someone else invented, and cheaper to license it from them.
Imagine for a moment what would happen if you gave everyone a machine such that you could simply drop a diagram of a mechanical invention into it, and out the other end comes a working implementation. That would totally change the game. Invention would require much less effort. Everyone would be doing it without consulting the patent database, and the huge influx of inventors would overwhelm the patent office, making it impossible to find which inventions in the flood of incoming applications are novel and nonobvious.
This is what happened with software. Millions of people have these magic machines on their desks and in their backpacks and briefcases. No patent incentive is needed, just as none is needed for mathematics.