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| Authored by: PolR on Monday, October 15 2012 @ 01:11 AM EDT |
Symbols and notation are not mathematics, they are the expression
of
mathematics.
This is incorrect. Textbooks of mathematical
logic and computation theory are explicit about this. In mathematical logic the
definition of what is a mathematical proof explicitly states that it is a series
of formulas where the notion of formula is defined as a series of symbols
complying with a certain syntax. Theorems are proven on the mathematical
properties of proofs based on this definition. In computation theory a Turing
machine has a tape where symbols are written on it. The computation is a
manipulation of these symbols. Lambda-calculus is operations on strings of
symbols complying with a certain syntax. All models of computations are
manipulating symbols in a way or another. This is how they are defined in
textbooks of mathematics.
Perhaps you should read on formal languages. There is such a thing as a part of mathematics about
symbols and notations.
you started with a conclusion and
then
sought the evidence from a body of works drawn over the most tumultuous
of
centuries with regards to the meaning of mathematics and then you over
valued
notation (which you call symbols) to prove that software is
unpatentable
mathematics.
This is incorrect. I have used the parts of
mathematics which are the foundations of computer science. This is the correct
procedure. The mathematical sources are accurate and they support the
conclusion.
Patentable chemical processes also have a notation and
obey rules which
are described mathematically. Is chemistry
mathematics?
The chemical processes are not mathematics. But
perhaps the notation may be a formal language in the sense given above. I have
not examined the question so I don't know.
And you overlooked my
other point, hardware and software are
equivalents. You can interchange
them.
I didn't overlook anything. I invited you to read the
article. Did you read it? You can't say I have overlooked something if you
haven't read it.
[ Reply to This | Parent | # ]
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- good grief.. - Authored by: Anonymous on Monday, October 15 2012 @ 04:07 PM EDT
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| Authored by: Anonymous on Monday, October 15 2012 @ 09:41 PM EDT |
Hardware and software are not equivalent but yet they are. It depends on what
you are referring to as hardware and software.
Can algorithms written on paper compute another algorithm next to it?
Software is an algorithm. Hardware implements logic which calculates an
algorithm, software. As such they are not equivalent.
Another use of the term hardware is the logic gates and configuration
implementing a specific algorithm. An example would be an MP3 decoder
circuit in an MP3 player. That algorithm is equivalent to software. The
hardware logic gates are not equivalent to software.
Thus it would be more accurate to state the "hardware is equivalent to
software" as "An algorithm can be stated as software or as a
configuration of
logic gates exemplified as an electrical circuit. An electrical circuit is by no
means the only hardware that can implement said logic gate configuration."
Not quite as catchy though.[ Reply to This | Parent | # ]
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