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But, logical reasoning is the very foundation of mathematics | 758 comments | Create New Account
Comments belong to whoever posts them. Please notify us of inappropriate comments.
But, logical reasoning is the very foundation of mathematics
Authored by: Tkilgore on Sunday, October 14 2012 @ 01:58 PM EDT
You say:

"Software is about solving practical real world problems and in doing so
the ability to use logical reasoning is useful as is on occasions mathematical
algorithms but writing a software program is not performing mathematics."

Here are a few words about the distinction which you are trying to draw, from
someone who has taught mathematics in a university for over 35 years, has
produced a fair share of original research on the side, and has also written
some software.

You attempt to distinguish between "logical reasoning" and
"mathematical algorithms." Sorry, but in fact there is no distinction.


In fact, all "mathematical algorithms" depend utterly and totally upon
a chain of "logical reasoning" which was used in the development of
the algorithm and which often must be applied yet again by the careful user of
the algorithm in order to make sure it is being used correctly.

As a very down-to-earth example, consider the development of
the theory of convergence and divergence of infinite series and the development
of computational methods for expressing hard-to-compute functions in series
form. When this is done, there is also such a thing as the "interval of
convergence" and to use such a series expansion for a function outside of
its interval of convergence is most exceedingly invalid. If real-world
consequences depend upon the output of the calculation, such misuse can
literally endanger lives. But the existence of these computational procedures
and the understanding of their limitations, too, depends in the first place on
"logical reasoning." The fact that too many students taking
second-year calculus can not and do not want to understand what I just said is
one of those unfortunate facts of life. Fortunately for the safety of the rest
of us, most of such students who survive that calculus course anyway are not
wanted by the departments of engineering, either.

To this mathematician, therefore, attempts to draw distinctions between
"logical reasoning" and "mathematical algorithms" are quite
amazing. Your arguments seem to boil down to something like this:

Software is not mathematics. Software depends in part upon mathematics, to be
sure, in that it uses "mathematical algorithms" some of the time. But
software also depends upon "logical reasoning" so in its nature
software is not mathematics. It is agreed that mathematics is not patentable,
but software is different because it uses "logical reasoning" in
addition to "mathematical algorithms."

The problem is that mathematics also depends totally upon "logical
reasoning" even to the extent that no "mathematical algorithm"
can even be developed or safely used without the application of "logical
reasoning." Thus, if software is considered patentable because it contains
"logical reasoning" in addition to "mathematical algorithms"
it follows that _all_ "mathematical algorithms," which are without
exception developed by the use of "logical reasoning," are also
patentable. Nevertheless, it is generally agreed that mathematics is not
supposed to be patentable (except on those occasions when some mathematics has
been patented anyway, but that is a different topic).


[ Reply to This | Parent | # ]

You are confusing math and arithmetic.
Authored by: Anonymous on Monday, October 15 2012 @ 03:05 AM EDT
I take it you're not an actual theoretical mathematician.

Every piece of software is pure mathematics.

Now, if your software is attached to unique hardware which you invented (some
special antenna, perhaps), or you've discovered a unique and undocumented way of
using hardware (such as making an old hard drive "crawl" across the
floor), then you might have a patentable combination. But it's patentable
because of the *hardware*.

The vast majority of software is using an off-the-shelf computer for exactly the
purpose for which the hardware designers intended it to be used, and is not
patentable.

[ Reply to This | Parent | # ]

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