Doug,

This is a kool idea, as many of your posts are (even drill press abuse). I
have two comments - 1. you have not shown proof that "two of everything" or
even "two of anything" is the smallest number required and 2. I think
replication without evolution is undesirable.

Early man used sticks and stones as tools. Everything we currently have
(good and bad) has evolved from those simple beginnings. So I suggest that
the minimum number of anything is very close to zero. Send McGiver to Mars
with a Swiss Army Knife (and an unlimited supply of bicycle spokes and boot
laces) and by the time you get there, you'll have to hunt for a place to
park your shuttle between the Bridgeports.

Now project that evolutionary capacity to a capability that may be available
in ideal environments and simple replication of current technology may even
be undesirable. Grow your lathe ways from a single diamond crystal - now
your iron machine tools are as desirable as the barber's leeches. Evolve
some more and now you can generate any product by selectively ADDING
molecules of the appropriate type to the proper location - why machine by
chip REMOVAL? When your razor gets dull, it can be sharpened by replacing
the displaced molecules not by abrading until a fresh edge is exposed.

Machine tool self-replication is an excellent philosophy exercise - and that
brings me to the next level of evolution. Perhaps we don't really need
THINGS as instances of matter, we can just THINK them and therefore don't
actually need to perform an actual task or build a particular device to know
the cosmic truth. We think through the problems, then we know that we can
build that 42-shot-simiautomattic-revolver with each part perfectly heat
treated and accurate to a couple of milliangstroms. Now that we know, we
don't have to actually build it to prove our knowledge or skill. (Made you
think about some old westerns, didn't it?)

Just some ideas to think about.

Bruce

" Doug Goncz " wrote in message
...
This one was rejected as too speculative for sci.physics.research.


Hi, gang!

For two particle systems, the application of quantum mechanics and a
change of
variable allow the separation of the problem into "one concerning only the
centre of mass of the system, and another which describes the behavior of
a
particle of mass mu under a potential V(r)." (Alistair I. M. Rae, Quantum
Mechanics, John Wiley and Sons, New York, 1981, p. 189.

If you have a small machine shop with two lathes, two mills, two surface
grinders, two cylindrical grinders, and two of every other machine tool
needed,
and duplicate tooling, than taken as a system of 2v machine tools, the
system
is capable of self-replication. (The foundry is a separate thing. Don't
worry
about it.)

This does not contradict the finding of Wigner in "On the impossibility of
self-replication" in "The Logic of Personal Knowledge" because the
machinist,
an agent not included in Wigner's analysis of structures growing in a
nutrient
"sea", is self-replicating (alive).

I assert that a properly trained machinist inherently knows how to operate
such
an array to self-replicate, given time, because the machinist is a living,
self-replicating being, but special training in the theory of
self-replication
may help. It may take generations to acheive it if it is done one machine
part
at a time, but a theoretical solution might be achieved in one machinist's
lifetime, and a computer calculation might be a matrix operation that
would
complete in seconds, or days. Once stated, the theoretical basis can be
taught,
in context, to students at the appropriate level of instruction in mere
minutes.

v is finite and may be 2, for a small shop, or up to around 7.

If n is 1, we have a pair of self-replicating machine tools and then can
consider a growing population of them. This idea of growth doesn't work in
an
array very well because it's constrained to pairs of machine tools.
Multiple
pairs of machines. It's rather over constrained. In particular, cross
pairings
start to get all, well, complicated.

If we start with an large enough array of pairs of machine tools ( a fully
equipped shop) then the array is "universal", able to construct any
product of
industry, and in theory, can be reduced to a single pair of identical,
universal self-replicating machine tools: the Holy Grail of Mechanical
Engineering.

Goncz's Postulate is : "You Need Two of Everything"

If and only if you start with a pair of universal self-replicating machine
tools, then each tool in the growing population is indistinguishible from
(functionally identical to) its fellow, so every possible pairing in a
population is a valid pairing in which one machine may reproduce a part of
the
other and there are no cross pairings to get in the way. In other words,
the
population gets busy, starts growing faster, and we get more and more of
the
little devils. And then exclusion principles, entanglement, and other
interesting properties will probably start showing up.

If we can accomplish this, the cost of guns, if not butter, should fall,
producing new wealth for all to share.

For a system of two particles with position vectors r1 and r2, and with
mass
m1= m2, we form the center of mass of the system, bold R, and the
relative
position bold r:

bold R = ( m1*r1 + m2*r2 ) / ( m1 + m2 ) and
bold r = r1 - r2


The center of mass of a circular machine tool array in full assembly is
fixed,
the position vector magnitudes are constant, but the mass of each machine
tool
is distinct, and it may vary as one only of each pair is disassembled to
relase
an internal part for replication by the array.

So the wave function of this system will in general be a function of the
masses
of the particles. That is, if a machine tool's current mass is m.r, and
its
fully assembled mass is m.t, then m.r = m.t, and by reference to a chart,
m.r
indicates the state of disassembly.

So what I have done is to ignore spin (or a hiden variable) like Rae does
on p.
188, and instead of

psi (r1, r2, r3, ..., rn, t)

I write

psi (m1, m2, m3, ... mn, t)

to describe the state of an array of n = 2*v machine tools, one pair of
each
of v types, and

| psi (m1, m2, t) | ^ 2 d (something)

to describe the probabilities related to transistion between states of
disassembly in a pair of self-reproducing universal machine tools, or the
probability that the array will be in a particular state at a particular
time.
I guess you could go with dm where d (something) is written, because m is
multiple and analogous to r. Then dm would be something like the
"sloppiness"
of disassembly, relating to the probability that pair could self-replicate
in a
messy shop. That seems reasonable.

In a circular array in polar coordinates, the position vector magnitures
ri are
constant relative to the center of position, while in a multiparticle
system,
and in particular, systems of _indistinguishible_ particles, the masses mi
are
constant, all equal.

I find this similarity striking and have attempted to form new variables
for
use in describing the state of an circular array of indistinguishible
(functionally interchangeable) machine tools by transposing the roles of m
and
r, forming a new variable.

Let's look at a two machine system with one machine in partical
disassembly.
The first analogy is to the relative position bold r.

bold m = m1 - m2

This is the mass difference, directly related to the amount of work needed
to
achieve bold m = 0, which would seem to be associated with the most stable
states Usually bold m = 0 is associated with m1 = m2 = mt. If we impose
the
rule that only one of the pair may be disassembled at a time, then bold m
= 0
is the most stable state, the state in which universal construction is
available for use.

Now, bold M is a bit tricky. The moments above the virgule seem reasonable
and
add OK, but putting the sum of the positions below them gives:

bold M = (r1*m1 + r2*m2) / (r1 + r2)

Moment divided by distance is mass. What I'd like here, by analogy to the
center of mass above, bold R, is still like the location of the center of
mass,
something like the location of the center of imbalance, that is, the point
around which the system, while imbalanced, is centered.

The analogy is breaking down.

Should I just keep bold R and deal with the center of mass or is there
something I've missed?

The moments above the virgule, while listed in the other order, still sum
to a
moment. And there's really only two choices for the denominator: the sum
of the
masses, or the sum of the positions.

Help!


Yours,

Doug Goncz
Replikon Research (via aol.com)

Nuclear weapons are just Pu's way of ensuring that plenty of Pu will be
available for The Next Big Experiment, outlined in a post to
sci.physics.research at Google Groups under "supercritical"