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

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

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

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"

Hi, gang!

For two particle systems, the application of quantum mechanics and a change of

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 - r2The 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"