Computation theory automatically shows an algorithm is an
algorithm when it is written in a language that can only express
algorithms.
So what you have shown is that a computer program
is a program when it is run on a computer that can only execute programs. You
haven't described how to write a program for any particular purpose
I'll
refer you to Wikipedi
a as a reference because I don't have the time to look through my old
textbooks and other references. But in a similarly algorithmic field, it can be
shown using Shannon's information theorem that channel capacity has the
following property related to communicating at information rate R (where R is
usually bits per symbol). For any information rate R 0, for large enough N,
there exists a code of length N and rate ≥ R and a decoding algorithm,
such that the maximal probability of block error is ≤ ε; that is, it
is always possible to transmit with arbitrarily small block error. In addition,
for any rate R > C, it is impossible to transmit with arbitrarily small block
error.
In other words, it is possible to communicate over a channel, such as
a binary symmetric channel, with arbitrary reliability up to a certain rate at a
given signal to noise ratio, and above this rate, nothing gets through.
But
what information theory doesn't tell you is how to do so. In
other words, the theory does not tell you how to find an optimum code for
transmitting at the highest possible rate over the channel. Neither can your
assertions about Turing machines help me find a particular algorithm to solve a
particular problem. All we learn from your dissertation is that, if you write a
program that can be run on a digital computer, it is a program made up of
symbols and therefore is mathematics.
But it takes a lot of engineering and
invention to find practical, near-optimal digital codes for transmission of
information, particularly over many real-world channels. Have you ever had a
digital cell phone call dropped? Have you ever tried to pick up a DTV signal
over the air without signal drops or pixelation? Disregarding novelty and
obviousness (which are separate questions), are you prepared to say that
practical solutions to these problems do not qualify as patentable subject
matter?
So I suggest that your argument is still not persuasive even if we
assume everything that you say is all provably true.
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