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Authored by: StormReaver on Tuesday, October 09 2012 @ 04:28 PM EDT |
> Turing Machines don't include things like network, hard disks, keyboards,
and displays.
Those are entirely irrelevant. The software puts numbers into particular
locations within those devices, and the devices then interpret those numbers.
Software and hardware are two entirely separate realms.
Software is obviously, painfully obviously, nothing but math. It's like arguing
whether concrete is hard.
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- Not Quite - Authored by: Anonymous on Tuesday, October 09 2012 @ 05:08 PM EDT
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Authored by: Imaginos1892 on Tuesday, October 09 2012 @ 04:48 PM EDT |
I have such a model right here in front of me -- it's called
Fedora 17. If it were not such a model, it would be unable
to run reliably on a real, physical computer that includes
asynchronous events such as you describe.
Since it has run reliably for over 7 months, handling every
condition it has encountered during that time, it is a
sufficiently detailed model. QED.
Every digital computer is a finite state machine. Every state
transition can be replaced by an Exclusive-OR operation.
Everything that goes on inside the computer, including
every computer program that has ever been or can ever be
written, can be replaced by a sequence of Exclusive-OR
operations. It's all math.
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Fiction must be plausible. Reality just has to happen.[ Reply to This | Parent | # ]
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Authored by: Anonymous on Tuesday, October 09 2012 @ 04:48 PM EDT |
All you have to do to show that software is mathematics is tolook at the
instruction set of any computer. The arithmetic, test, and logic instructions
are indisputably math. Is copying values between registers and memory math? It
is not what I usually think of as math, but I could not argue the point.
Then we have the questions:
Is all math unpatentable?
Are all chemical reactions unpatentable?
Is all physics unpatentable?
About an hour ago, I was looking at a patent for an improvement in lenses. It
was optics, which is a branch of physics. The claims gave formulas for
calculating distortion, which is math.
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Authored by: Anonymous on Tuesday, October 09 2012 @ 07:16 PM EDT |
> Even the random number generators built into modern CPUs violate the Turing
model (at least they do if they are real random number generators.)
It is impossible to create a perfect random number generator using only
software. The ones inside CPUs etc. utilise hardware to generate a random event
the software then uses as input to the generation process, resulting in a number
of the appropriate magnitude. The hardware is necessary. Hence patentable.
All software random number generators are actual pseudorandom, repeating a fixed
(albeit lengthy) sequence. Software is mathematics. Hence unpatentable.
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Authored by: Anonymous on Tuesday, October 09 2012 @ 09:40 PM EDT |
If you do not understand this then I suggest you take "Introduction to
Computer Theory". I did as a freshman in college. It is hard to condense
approximately 800 pages and a semester long class in an itty bitty post.
Suffice it to say, computers were developed to make an actual Turing
Machine. Memory is equivalent to the Turing Machine tape and the only input
and output to a CPU is memory.
A hard drive or removable drive is called secondary or tertiary memory for a
reason. A display is nothing more than a matrix of numbers which is in turn
nothing more than memory. A network is just a string of numbers, individual
computers have a network address which makes it ... drum roll .. just memory.
In fact in today's world it seems to me that the first inventor of computers
could have patented the computer and prevent all Turing machines from being
created without their specific approval.
If you do not believe me than research the various technologies, especially the
digital devices. After all a digital device is a device of just ones and zeroes.[ Reply to This | Parent | # ]
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Authored by: JonCB on Tuesday, October 09 2012 @ 10:32 PM EDT |
I don't think this has actually been proven. At
least I've never
seen a proof. Most people point to a Turing
Machine and claim that's good
enough.
Personally i think the claim via Turing Machine is a
bit
harder to make. The claim I usually see (and personally
agree with) is
that anything computable via our current(and
earlier) standard of Von Neumann
computing machines(our
current standard of Desktop, Laptop, Phone and tablet
PCs
are all Von Neumann style computing machines, Quantum
Computers may be
different) is equivalent to Lambda Calculus
and Lambda Calculus is a
mathematical notation describing
computation. Note that it IS generally
accepted within
mathematics and computer science(if unprovable due to the
halting problem) that Turing Machines and Lambda Calculus
are equivalent and
that everything that you can compute in
one you can compute in the
other.
There are three principle arguments i have seen made to
counter this assertion :-
- Lambda Calculus is not really
mathematics
- VN machines don't really do Lambda Calculus
- Lambda
Calculus doesn't do hardware
If you accept the first argument
then you are saying that
the mathematics experts that have published
mathematical
papers (even so recently as within the last 12 months) that
talk
about lambda calculus don't know what they're talking
about. In that case i'd
ask you to have a bit of respect for
the experts in their own field. If there
was any controversy
on whether lambda calculus was part of mathematics then
there would be a paper somewhere that contests it's
applicability. Until you
can at least show some evidence
this controversy exists, this argument is
without
foundation.
If you believe the second argument then i would
respond that
, while you are possibly correct, for this argument to be
persuasive to me you would have to describe what the
difference between this
case (i.e. taking Lambda Calculus
and translating it into machine code for
execution on a CPU)
and the already accepted case of performing an equation on
a
calculator (i.e. taking an algebra equation and translating
it into a series
of button presses that can be executed on a
calculator) are.
Finally
to answer the third argument, even assuming the
point is true (and i don't
believe that it universally is),
if you examine the hardware's effect from the
CPU's view
(e.g. i/o lines on clock, hardware interrupts etc...) it IS
perfectly describable by lambda calculus. This would
certainly imply that the
method of interfacing hardware to
the CPU certainly IS patentable subject
mater, and i'm kinda
good with that. However this simply does not imply that
the software instructions are not equivalent to lambda
calculus and therefore
mathematical.
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- Not Quite - Authored by: jesse on Wednesday, October 10 2012 @ 11:20 AM EDT
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Authored by: Anonymous on Wednesday, October 10 2012 @ 04:14 AM EDT |
The fact is that *software* is pure math.
And it generally doesn't take into account the actual physical behavior of the
hardware, not in detail; it deals with an abstract model of the hardware.
Even in the very rare case where the software deals with true low-level hardware
details, *the non-math part is in the hardware*. The software is still just
math.[ Reply to This | Parent | # ]
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