Steven D'Aprano wrote:
software*is* mathematics
No it isn't.
Yes, it is.
(If the machine is particularly
simple -- you might be able to exactly simulate a lever in pure
mathematics, but simulating, say, a nuclear bomb or a dialysis machine in
mathematics is more of a challenge...)
I do not disagree with your frustration over what may or may not be
simulated by mathematics, within a computer, but that is to
misunderstand the thrust of the argument. Essentially what you are
saying is that because it is difficult to simulate in software what is
evident in pure mathematics that software is somehow not mathematics...
if I have understood what you are saying here, then you are absolutely
incorrect. If I have misunderstood you, please clarify.
We are not talking about what can or can not be simulated--- much
less how difficult those simulations might be. The argument is much much
simpler than that... please do not over complicate this.
What it is that software does is to extend human thought and
process over symbol across a machine ALU (the von Neumann funnel). The
machine ALU is the medium *only* for the natural and obvious expression
of mathematics (relationship over symbol) carried about in the human
mind yet extended and expressed across the registers and switches of the
machine, rather than markers and white-boards (or black-boards and
chalk, if you're as old as I am).
Software is comprised of nothing more nor less than mathematics;
the human tools of thought and process, relationship over symbol,
expressed across the domain of switches and registers in the processor's
ALU.
This is the part of the argument that Geremy will loath and despise
perhaps even more than you do... that what software is comprised of
resides at the very heart of the CPU itself... that which we call the
von Neumann funnel--- the ALU. It does not matter in the least what is
being simulated (H bomb, or word-processor, or spread-sheet, or life
automata) no software ever ever ever ever does anything other than
logically manipulate registers of bits (ones and zeros) on and off at
very high speeds (that's it, nothing more and nothing less). All of this
is mathematics, and nothing more nor less.
Even addition in the ALU is not computation... it is logical
manipulation of 1s and 0s with a bitwise exclusive (xor) function across
the register with carry. Whalla, ADD. All logic operations in the ALU of
all CPUs are comprised of logical manipulations (algorithms) designed to
simulate higher and higher types of functions; regardless of what is
simulated, at the core and heart of the CPU is nothing more nor less
than logical algorithm(s) expressing relationship over symbol by
"software". In fact, the software itself is some of the logical
manipulation --- in other words, the software itself is processed in
precisely the same ways.
Again:
Mathematics *is not* software.
Software *is* mathematics.
kind regards,
m harris
--
http://mail.python.org/mailman/listinfo/python-list
