**Kinematic
Self-Replicating Machines**

**©
2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.**

Robert A. Freitas Jr., Ralph C. Merkle, *Kinematic Self-Replicating Machines*,
Landes Bioscience, Georgetown, TX, 2004.

**B.2 Some Limits to Assembler
Scalability**

This particular molecular assembler architecture may be scaled to larger or smaller sizes. There are, however, limits to the extent that the present architecture can be scaled without modification. Perhaps the most significant limit as size increases is the error rate. At some point, the assumption that a complete replication cycle can be completed with a modest probability of any error during the entire cycle will no longer be practical. The first concern would likely be the error rates in the relatively simple feedstock binding sites, which require feedstock that is, by present standards, very pure. As the total atom count in the design increases, and as a consequence the number of feedstock molecules that must by cycled through the intake mechanisms increases, the error rates of these mechanisms must be reduced. At some point, this would require adopting a more complex intake mechanism, adopting the strategies proposed by Drexler [208] (his Section 13.2.2) for a multi-staged cascade system that would be able to tolerate feedstock impurities while still delivering feedstock molecules to the assembler interior with a low overall probability of error.

With further increases in size, a point will be reached where radiation damage can no longer be neglected. Error detection and correction mechanisms would be required to insure correct system function. The current design assumes that the entire assembler can be discarded if a single error occurs – which is feasible only if the overall probability of an error is low. As size increases, the probability of a radiation-induced error will approach certainty, and the simple approach of discarding the entire assembler in the event of a single error will fail. While more sophisticated error isolation and correction strategies are feasible [208, 213], these lie outside the scope of the present analysis.

Another limit at even larger sizes in the scaling continuum
is that the ratio of the surface area of the materials transport wall or the
piston end wall to the volume of the device (or to the number of atoms per device)
falls inversely with increasing linear dimension of the device (the Square-Cube
law; Freitas [228], p. 172). This makes it
progressively more difficult for a sufficient quantity of power and materials
to pass through the two YZ walls during a fixed replication time, thus limiting
the ability to up-scale this specific architecture at significantly larger dimensions
(though numerically the present design is far from these limits). The problem
of feedstock bottleneck can be dealt with by increasing the input area exposed
to the feedstock solution using “multiple thin sheets which have binding
sites on their surfaces” [213] or by
increasing the surface area of the intake by adopting a folded surface (Drexler
[208], his Section 14.3.1.b) much as the gut
has villi which greatly increase the surface area available for absorption of
nutrients (Freitas [228], his Section
8.2.3). In this manner, convergent assembly could produce finished assemblies
at least 1 m^{3} in size [213] (Section
5.9.4).

At the smaller end of the scaling continuum, the probability of error in signal detection via the pistons that provide power and control scales [208] as ~exp(-L). This source of error increases rapidly in importance as device dimension L decreases, thus limiting our ability to downscale this design to significantly smaller dimensions. In addition, stiffness scales adversely with size, resulting in poorer ability to control positional uncertainty using smaller positional devices. While this source of error only increases linearly with smaller size, it will also limit scaling of the present architecture.

Last updated on 1 August 2005