I think that is precisely relevant to the topic of the article.
Invention is all about synthesis, not analysis.
I am not sure
where you are going with this. As far as I know a patent is not granted on the
manner by which an invention is derived. Subject matter is the work product, it
is the machine, process, composition of matter or article of manufacture, or it
is the improvement thereof. What if the work product of your synthesis is math?
What if the work product is abstract? You need analysis to find out whether this
is the case. Whether the the engineer has derived the invention by analysis of
synthesis is not the issue.
Thus, this problem perfectly fits into
your paradigm. It's all about mapping one set of symbols into another and back
to the original.
Point taken. I have missed that on the first
reading of your comment. I have left a better answer in another
comment.
The invention of algorithms that perform such mappings is
where synthesis and invention takes hold. No amount of analysis can come up with
perfect codes, and you can't say that these codes occur in nature. They are
invented by humans. And that is where your adoration of the Turing machine
ceases to be relevant, and the point at which your arguments about why computer
programs should not be patentable cease to be persuasive.
First I
don't adore Turing machines, I use them in arguments when I think they are
relevant.
Second my argument in this article doesn't rely on Turing
machines. When you say my argument is not persuasive are you really discussing
the argument in this article? If you assume the article relies on Turing
machines you and I may not discussing the same argument.
Third why should it
matter whether the algorithm is developed by analysis or synthesis? This is not
the test for subject matter patentability. The manner the invention has been
derived is not relevant.
Fourth abstract mathematics doesn't occur in nature
but it is still abstract. This whole paragraph about algorithms apply as is to
other form of contents. You are not distinguishing algorithms about symbolic
codes from contents.
But there is absolutely nothing in any theorem
that tells you what algorithm to use for the mapping.
Why is that
relevant? Besides there should be a theorem showing a particular algorithm will
work as expected and other theorems showing they work at such and such degree of
performance. To the extent that theorems are relevant your statement is
misleading. It leaves an impression that there are no theorems about the
algorithms when this is not the case.
Moreover, the particular
algorithm may not be useful if it takes longer to perform the coding and
decoding than is available to transmit and receive the data.
So
what? There are infinitely many values of pi. It takes forever to compute them
all. But if you compute the volume of a cylinder, say an oil drum, you need to
use pi because the formula refers to it. If you want the calculation to be
useful you must use only a finite number of decimals of pi. That doesn't make an
arithmetical calculation using an approximate value of pi non math. The same
could be said of any algorithm.
Finding out the volume of an oil drum is
useful. Utility doesn't distinguish math from non math. It doesn't distinguish
contents from non contents.
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