On May 7, 9:08 am, Tim Williams wrote:
On May 6, 3:29 pm, James Arthur wrote:

Not that I need such precision. I've got the CNC bug[1], and I'm
thinking of ways to make things nice. Ways to make nice ways,
if you will.

[1] A CNC mill and a lathe, and the desire to make more of the same.

The lathe and mill are both Turing-complete machine tools, so that's
no problem. :-)

Crossposting to RCM, which I recall had someone madly interested in
something like "Godel's Theorem for Machinists"!

Tim

Well, if their true Turing machines, let them decide what material
they want to use.......isnt that the whole point of the Turing
Test?.......

On Wed, 06 May 2009 17:01:06 -0700, VK3BFA wrote:

On May 7, 9:08 am, Tim Williams wrote:
On May 6, 3:29 pm, James Arthur wrote:

Not that I need such precision. I've got the CNC bug[1], and I'm
thinking of ways to make things nice. Ways to make nice ways, if you
will.

[1] A CNC mill and a lathe, and the desire to make more of the same.

The lathe and mill are both Turing-complete machine tools, so that's no
problem. :-)

Crossposting to RCM, which I recall had someone madly interested in
something like "Godel's Theorem for Machinists"!

Tim

Well, if their true Turing machines, let them decide what material they
want to use.......isnt that the whole point of the Turing Test?.......

Different thing. Turing showed that after a certain level of
completeness, any machine could simulate any other machine (barring such
minor difficulties as execution time and storage space -- he was a
mathematician). So a computer (or computing language) that is Turing
complete can emulate any other computer (or translate into any other
language).

A "Turing complete" machine tool would presumably be one that can do all
the operations of any other machine.

--
http://www.wescottdesign.com

On Wed, 06 May 2009 20:52:51 -0500, Tim Wescott wrote:
On Wed, 06 May 2009 17:01:06 -0700, VK3BFA wrote:
On May 7, 9:08 am, Tim Williams ... wrote:
On May 6, 3:29 pm, James Arthur ... wrote:
Not that I need such precision. I've got the CNC bug[1], and I'm
thinking of ways to make things nice. Ways to make nice ways, if
you will.
[1] A CNC mill and a lathe, and the desire to make more of the same.

The lathe and mill are both Turing-complete machine tools, so that's
no problem. :-)

Crossposting to RCM, which I recall had someone madly interested in
something like "Godel's Theorem for Machinists"!

Perhaps this is a reference to Doug Goncz's Replikon Research
attempts at self-reproducing machines; but that has nothing to
do with Godel or Turing either, and instead is more like von
Neumann's self-reproducing automata or Quine's self-replicating
programs.

Well, if their true Turing machines, let them decide what material they
want to use.......isnt that the whole point of the Turing Test?.......

Different thing. Turing showed that after a certain level of
completeness, any machine could simulate any other machine [...]
So a computer (or computing language) that is Turing complete can
emulate any other computer (or translate into any other language).

Turing made a *conjecture* about universality, but did not prove
or show it, and nobody else has proved or shown it either.
Equivalence of computation via certain recursions, λ-calculus, and
Turing machines has been shown, as noted at first link below.

A "Turing complete" machine tool would presumably be one that can do all
the operations of any other machine.

Sounds right. Following links have details re these topics.
http://en.wikipedia.org/wiki/Church-Turing_thesis
http://en.wikipedia.org/wiki/Turing_test
http://en.wikipedia.org/wiki/Von_Neumann_universal_constructor
http://en.wikipedia.org/wiki/Quine_(computing)
http://en.wikipedia.org/wiki/Universal_Turing_machine

--
jiw