# Quantum Mechanics and Self-Replicating Machines

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"
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snipped-for-privacy@aol.com.pif ( Doug Goncz ) wrote:
<snip>

<snip>
Just curious what your definition of "self-replicating" is, and where that definition came from. Is anything other than the machines you mentioned here included in the self-replicating entity that you envision? How much assistance or work by an external agent, and what degree of pre-processing of raw materials and energy sources, can be utilized while still meeting the qualifications for self-replication?
Bert
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Which is also my question. I think Doug and I might have discussed this once before. I have an axiom that and entity (not a machine but something with and using it's own volition and knowledge) cannot create something equal to or certainly not greater than itself. Interestingly though a machine I believe can replicate itself, just as DNA does.
John
Please note that my return address is wrong due to the amount of junk email I get. So please respond to this message through the newsgroup.
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(Same question as Bert)

Probably did, right here, during the drill press days.

The finite problem of this class is the work envelope problem: If a BP mill table is 5 feet long, and it slides back and forth 4 feet 4 inches, how the hell do you replicate it? Answer: By self-guiding the rough work through the mill without moving the table, feeding it like a table saw. How do you make the jig to guide the work? With a lathe, mill, and whatever else is needed, which you assume you have.
The indentification I have mentioned prevents the SRMT from running away uncontrolled. The machine has no initiative and is manually controlled. It can't run away unless the operator goes mad.

I think in this case, I am the RNA or transcriptase, and the machine is the DNA. Ambient thermal energy and enzyme reactions drive DNA replication. A continuous flow of reliable nuclear electric energy drives the reproduction of the SRMTs, but only as they are needed by the growing and increasing colony population.
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"
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[ ... ]

But a combination of a human and a machine can create a greater machine. In particular, things like the layout of a modern CPU chip, and the generation of the masks is a task for which a human is poorly suited, but a computer (another CPU) is ideally suited, as long as the human sets some design parameters. Things like word size, number of registers, the style of logic used in adders and multiply/divide circuits, and similar parameters.
Even the early Motorola 68000 (one of the first serious 16/32-bit chips) had approximately 68000 devices fabricated in the chip. I have no idea where today's crop is, but certainly well beyond that. Just the time taken for a human to do all that layout, let alone to make sure that it is error-free, boggles the mind.
Machine tools, of course, are much simpler (until you get into CNC, where you need a CPU again). Where they stretch the envelope is in the quest for greater accuracy.

Certainly the combination of a human and one or more machines can do so.
Enjoy,         DoN.
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Well past 20 million I believe. Things have come a long way since your Commodore 64 ;)
Tim
-- In the immortal words of Ned Flanders: "No foot longs!" Website @ http://webpages.charter.net/dawill/tmoranwms
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Oh right, Altair. Couldn't think of it so threw in a generic old thing ;)
Tim
-- In the immortal words of Ned Flanders: "No foot longs!" Website @ http://webpages.charter.net/dawill/tmoranwms
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This is my first postulate: that the property of self-replication is transitive when the machine tool and operator are considered as a working unit, together. But:

I call this the self-designing, self-upgrading ability of our existing digital computers. However they do not actually self-reproduce. The machine tools we have can be loaded by robots and produce parts, like they do in Japan, automatically, but the generation of circuit lithography patterns, the lithography itself, and the manufacture and use of integrated circuits in appropriate (DIP, flip-chip) packaging, and the integration into the CNC machine tools that make parts is all a scale-up process.
It means you have to outthink the work envelope limitation not just once or twice, but dozens of times, in a cascading series of manifestations, bringing the technology from nanoscale to human scale. Through that "filter" the "self" which is being "replicated" becomes a hideously complex series of interlocking technologies, not subject to theoretical analysis, AFAIK.

Yes, computers do the complex finite tasks well, but this thread is about theory. They are great for designing the geodesic domes on Mars, but we are going to have to build them ourselves.

You mean circuitry can provide accuracy and precision? Yes, it can. So can care and concentration.
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"
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"DoN. Nichols" wrote: ...

A minor correction here -- the F00F bug was protection-related,* nothing to do with FP, so a separate FP chip wouldn't have made a difference. -jiw
* " The F00F bug received its name from its instruction encoding F0 0F C7 C8. This instruction encoding maps to a LOCK CMPXCHG8B EAX instruction. CMPXCHG8B compares 64-bit memory contents with the contents in EDX and EAX." "Instead, the Pentium processor locks up and freezes the entire computer when it encounters this instruction." - from a web page re F00F
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What's your definition of an entity? Seems there are programs (or could be) capable of creating equal, and perhaps better programs.
Dave

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Sounds like the mechanical version of a (software) virus...

email I get.

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David Peterson wrote:

A compiler, for example...
More useful examples are things like learning systems; there are systems that develop a program expressed as a series of rules. It runs tests against past data in which each rule is assessed for how much it helped, and bad rules removed, and good rules duplicated and variations tried. Solutions evolve automatically.
A spectacular case in point... some group decided to use an FPGA (programmable digital logic chip; you feed in setup instructions to tell it what gates to wire to what, more or less), along with an evolving engine like that above, to evolve a circuit to work out the frequency of a train of pulses. The FPGA was too small (not enough gates) to contain the circuit you'd get if you designed it by hand.
Sure enough, it soon came up with a working design... but the way it had managed to do better than what was thought to be the theoretical capacity of the chip was that it wasn't using them just as digital logic gates any more. It had gates wired back into themselves in unstable feedback loops, using their analogue characteristics (which you steer clear of in digital design!). Which was fine - but as soon as the temperature changed, the chip's analogue characteristics shifted and the circuit stopped working :-) They'd trained it in a stable temperature environment, so it had evolved to need that...

ABS
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The vision came to me during the intense self-examination typical of the first two years in college, right after high school. I postulated "I am this body" in defiance of those who would have me "be" an engineering, a student (although I was and remain one), or, in particular, a salesman.
During my summer selling high school level study aids (a two volume dictionary set) I became strongly identified with the sales company, due to the usual cult like experience of door-to-door sales. After all, I said, "Hi! I'm Doug Goncz, and I'm just another one of those XXXX BOOK salesman. Y'all don't shoot 'em out here, do ya?" more than 1000 times, with enthusiasm. But when I came back to MIT, there was trouble, so I rebelled. I became a pip, an unknown.
During that rather adolescent phase, I did latch on to the idea that the individuals in any organization identify with the group. Like being all you can be in the Army. So when I learned that machine tools already were capable of self-replication, but that they were still mass-produced (partly, and in any case a product of industry), I theorized that if identity meant what I though it meant, it would be important for the machinist to identify with the machine, to be close to it, to feel it and know it, in order for self-replication to proceed.
I'd learned about the power of exponential growth. We have only about 2^32 people on this planet, so if a machine could be replicated in a month, in 32 months, everyone could have one. And a fork, a bowl, and something to eat. It was a very idealistic notion.
But all of us here know our machines well, and I think it's not too far out to say that a team assigned with reducing a set of pairs of machine tools to their most compact configuration has to be tightly knit.
Why would anyone want to do it. Well, due to transportation costs, and now that we have learned how to make hydrocarbons from CO2 and water, and extract minerals from rock with supercritical CO2, we're almost ready to colonize Mars, and we will HAVE to bring a "fully equipped machine shop" with us. It'll be expensive enough just to transport the people!
It's the only place we can reach where SRMTs are required. And so that is where I am bound, and have been since 1979.
Thus the experiments with cross vise, drill press, collet indexer, and four jaw chuck in 1995, in pairs.

The only source possible, since the energy requirements for synthesis are extreme, is nuclear. I can't go NUPOC. I'm too old to serve 20 years before the age of 55. So I have to go NASA. Solar cells actually do not self-replicate. Solarex tried it at their Rockville plant, near here. It wouldn't come off.
Electronics technology is self-designing, and thus Moore's Law, but it is not self-replicating.
The only thing I've left out of the QM analysis is the foundry. With unlimited available power, the foundry is not a problem.
Just as they leave out "spin" in QM in order to build a foundation for multiparticle systems which includes spin later in the analysis, I am leaving out the foundry for now, but will include it later.
The bookeeping of self-reproduction is the same as taking an order for a typewriter that comes with two free ribbons, an additional paid ribbon, a space bar, and a spare backspace key. It's done with an invertible quantity matrix, lower triangular, in technological order, inverted, and multiplied by the demand vector. I've seen the power of Mathcad doing this sort of thing, and it truly is amazing, so much faster than Excel on the same data....
I'm the guy who likes to bang out the lowest and highest notes on the piano just to see what they sound like together.
Wigner's paper analyzed exactly what Bert has asked, considering a machine or rather configuration of matter floating in a "nutrient sea" of components, which could be fundamental ingredients or parts ready to be final-assembled, and concluded it was impossible for the configuration to replicate in finite time with available ambient thermal energy. But Wigner himself was SR. So by identifying the machine with the operator, we transfer the SR property of the operator to the machine. Transisivity is a powerful theoretical tool that can do things like prove FLT. Or prove simply that if a=b and b=c, then a=c.
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"
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OK, a few more questions and comments:
snipped-for-privacy@aol.com.pif ( Doug Goncz ) wrote:

...<snip of historical prelude and thoughts on identity>

Yes, isn't idealism great? I'm guessing that at the time you weren't too concerned with the concomitant exponential growths in the amount of steel required for all those machines, the amount of associated equipment and energy to mine and process the raw materials for that steel, and the amount of energy consumed by the machines during replication.
Unfortunately, even a sub-exponential growth in the population of us "self-replicating" humans is beginning to create problems due to resource scarcity. But that's a whole different topic.

...
I get the impression that, analogies to quantum mechanics notwithstanding, the primary (or only?) requirement for having pairs of machines is so that one machine can serve as a model or blueprint while the other is actually being used for making parts. If that's the case, why not add a pantograph (or other 2-D duplicating device) into the mix and then replace one of each pair of machines with a set of drawings or specifications? That would save you quite a bit of weight (and expense) on your trip to Mars.

Why not combine electronics, machinery, and the requisite chemical processing equipment into a system that is truly self-replicating, and perhaps self-designing and self-evolving as well? That seems a much more intriguing problem, though perhaps not as amenable to analysis or near-term solution.
This seems as good a point as any to interject my personal bias against the term "self"-replicating as you use it. To me, that term suggests that the entity makes a replica OF itself BY itself (such as in the reproduction by a simple asexual organism), whereas your definition describes an entity that is employed to make a replica of itself under the guidance and manipulation of an external agent. For that matter, to the extent that your machine (or system of machines) is involved, it is not making a replica of itself per se, but rather is making a pile of replicas of its component parts, which must be subsequently assembled and adjusted by an external agent to yield the replica machine. Unfortunately, I can't at the moment think of a more appropriate or palatable term for such a process.

With unlimited available power, many problems go away!

Will you also include mining and other requisite operations, and the equipment needed for those operations? How do you account for the non-metallic components of the machines, such as the insulation on wiring and motor windings, or grease, or rubber belts or bushings?

I assume there are more constraints on the "nutrients" in this sea than is implied here. Otherwise, instead of the solution being impossible, it would be quite possible, and in fact trivial for certain sets of machines and nutrients.
In any case, this is quite a different problem than accomplishing the same end result with "unlimited available power" (and by extension, unlimited energy).

How so? Sexual reproduction doesn't produce a replica, at least not what I would think of as a replica. For that matter, neither does cloning -- it produces at most an entity with a replica of one's DNA. But the actual capabilities and attributes of a human "machine" are determined by so much more than DNA that it would be a stretch, IMO, even to say that mature identical twins are replicas of each other (except in very unusual circumstances), let alone a human and a clone that is 20 or 40 or 60 years younger.

Do you have any particular reason for believing that transitivity is a property of self-replication?
Bert
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Mathcad is one of my favorite programs. I'm suprised people don't use it more often, so much nicer than spreadsheets for so many things.
Dave
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Yeah, I hate when that happens, don't you?

The theoretical understanding reduces this problem to general principles guiding "what to do first" and "what to do next" that are subject to insufficient analysis and bookkeeping errors in the finite solution by finite methods. So the inventorying can self-check and self-repair by comparing a description of what's going on with the "wave function" that describes everything that can be known about what's going on, without actually knowing the wave function at every point in time.

You see, it's the difference between a woodworking shop and a machine shop.
The jig guides the tool; The jig guides the tool; Hi, ho, the Derry, Oh, The jig guides the tool.
In woodworking the work is fed into and THROUGH the power tool by hand, mostly, and in any case can be larger than the tool. Mostly a linear process. But what's going on is feature projection of an unusual kind.
GD&T teaches us that we need to screw a tap into a hole with a known fit and "project" the hole outwards to where the coordinate measuring machine, or one of us, can measure its location. The process of mathing a transmission and engine that have never met, using a plate between, is feature projection: The holes on the engine and the holes on the transmission are both projected onto the plate so the plate can serve as an adapter.
So what's happening when you rip the edge off a board, or mill a BP x axis table by sliding it through a custom fixture, is that the flat, linear surfaces on the table saw or on the rough table are projected to and at time same time averaged with the produced surface, which improves that surface. Then, that improved surface becomes the guide and what was the guide surface is run through, a little closer this time, to improve it. So progress is made and the work envelope problem is solved by unconventional use of whatever's available, which is what got us through WWII, with drill presses used as milling machines, and milling machines used as lathes, three shifts.

Yes, but that is a self-reproducing automaton, and I am only talking about manually guided machine tools capable of assisted reproduction, not autonomously reproducing machine tools proliferating with no antibiotics in sight.

Yes. It's my job.
In experimental machine work, we use both woodworking and metalworking machines and principles, and the Smithy Super Shop is an experimentalists's dream tool, though its potential for SR is unknown to me. In woodworking, you sometimes make a fixture for just one use. In metalworking, usually a fixture is built for mass production. Different paradigms. Same jig and fixture technology, though. Kinematic contraint.
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"
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<snip>

machines
tool,
sometimes
built
You might enjoy reading "Foundations of Mechanical Accuracy" by Wayne R. Moore if you haven't already.
Excellent treatise on the production of accurate machines by simpler - albeit more tedious - methods than self reproduction.
StaticsJason
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Doug, you'll be interested to see my use of jigging to build a part for my lathe....
using essentially woodworking techniques to make a metal travelling steady for the lathe so that I can (eventually) make leadscrews for the mill/surfacegrinder/whatever I get to next... the CNC surface grinder is high on mylist, just for fun...
swarf, steam and wind
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Hey Doug, thought of a MAG DRILL lately? it processes things much larger than itself and is self guiding after initial placement. one coudl easily use one to drill the holes in the raw part of another one, no matter how big it is...? maybe?
--
swarf, steam and wind

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Hell, by the time NASA realizes they need me, I'll be on the payroll!
And what could be more fun than a paid trip to Mars?
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"