decoration decoration
Stories

GROKLAW
When you want to know more...
decoration
For layout only
Home
Archives
Site Map
Search
About Groklaw
Awards
Legal Research
Timelines
ApplevSamsung
ApplevSamsung p.2
ArchiveExplorer
Autozone
Bilski
Cases
Cast: Lawyers
Comes v. MS
Contracts/Documents
Courts
DRM
Gordon v MS
GPL
Grokdoc
HTML How To
IPI v RH
IV v. Google
Legal Docs
Lodsys
MS Litigations
MSvB&N
News Picks
Novell v. MS
Novell-MS Deal
ODF/OOXML
OOXML Appeals
OraclevGoogle
Patents
ProjectMonterey
Psystar
Quote Database
Red Hat v SCO
Salus Book
SCEA v Hotz
SCO Appeals
SCO Bankruptcy
SCO Financials
SCO Overview
SCO v IBM
SCO v Novell
SCO:Soup2Nuts
SCOsource
Sean Daly
Software Patents
Switch to Linux
Transcripts
Unix Books

Gear

Groklaw Gear

Click here to send an email to the editor of this weblog.


You won't find me on Facebook


Donate

Donate Paypal


No Legal Advice

The information on Groklaw is not intended to constitute legal advice. While Mark is a lawyer and he has asked other lawyers and law students to contribute articles, all of these articles are offered to help educate, not to provide specific legal advice. They are not your lawyers.

Here's Groklaw's comments policy.


What's New

STORIES
No new stories

COMMENTS last 48 hrs
No new comments


Sponsors

Hosting:
hosted by ibiblio

On servers donated to ibiblio by AMD.

Webmaster
Not Quite | 277 comments | Create New Account
Comments belong to whoever posts them. Please notify us of inappropriate comments.
Not Quite
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.

[ Reply to This | Parent | # ]

Real computers : Turing machine
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.
-----------------------
Fiction must be plausible. Reality just has to happen.

[ Reply to This | Parent | # ]

Not Quite
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.

[ Reply to This | Parent | # ]

Not Quite - random generators
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.

[ Reply to This | Parent | # ]

The answer is ... a Turing Machine
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 | # ]

Not Quite
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 :-

  1. Lambda Calculus is not really mathematics
  2. VN machines don't really do Lambda Calculus
  3. 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.

[ Reply to This | Parent | # ]

I said software, not computers.
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 | # ]

Groklaw © Copyright 2003-2013 Pamela Jones.
All trademarks and copyrights on this page are owned by their respective owners.
Comments are owned by the individual posters.

PJ's articles are licensed under a Creative Commons License. ( Details )