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.
2.1.4 Limitations of von Neumann's Cellular Automaton Model
Although the 29-state von Neumann cellular array system (including a replicating device consisting of many millions of cells [372, 373]) permits a more elegant mathematical approach to the problem of machine construction and self-replication, it is more difficult to envision an actual useful physical implementation of the process (compared, say, to the kinematic model of replication). The entire cell space enterprise proceeds in a highly constrained artificial environment, one which is very special despite some features relating in a general way to the natural world. For example, the movement of objects in space, a ubiquitous and familiar phenomenon in the real world, becomes a complex process of deletion of cell states at one location and re-creation of these states at some other location.
In von Neumann’s model, there is an assumption of synchronous behavior throughout the system. All cells, no matter how distant, are subject to change of state at the same instant, a property which would be difficult to implement in any practical large cell space. Indeed, the requirement of a source of clocking pulses violates the array symmetry which makes the cell space notion an attractive object for mathematical treatment.
It is also very difficult to design machines of interest which can be embedded in von Neumann’s cell array format. To make design and embedding easier, a higher-level machine design language would have to be created. It is likely that, rather than undertake that task, one would first redesign the underlying cell space properties to rid the system of the deficiencies already noted.
For instance, one might wish to introduce a new primitive cell state in the system to permit signals to cross without interference. A “wire-crossing” organ can be devised using only the original von Neumann primitive cell types, but this introduces an unnecessary complexity into the machine design process since the organ contains initially active cell states whose creation involves considerable extra care to avoid the propagation of spurious signals. This extra care is especially critical because the cell system, as von Neumann originally constituted it, is highly susceptible to signal errors. (He undoubtedly intended his probabilistic machine model to mitigate this sensitivity and fragility.)
Von Neumann’s cell space system has very limited capacity to detect the states of cells. It has some capacity to detect states, for this is required in the operation of the memory unit. But a machine cannot analyze an arbitrary encountered cell to determine what state it is in, thus cannot “read” the states of an encountered machine. This inability severely restricts the capacity of von Neumann-type cell-space machines to repair other machines or to attempt self-repair. Such limitations also are evident in the construction process, where the constructing machine must assume that the region in which a new machine is to be created consists entirely of elementary quiescent cells. Should this not be the case, there is no systematic and complete way to detect it. A machine can send destruction signals into cells to reduce them to the quiescent form. Unfortunately, in some cases one must know the state of the cell ahead of time in order to determine what destructive signal must be sent to destroy it.
Finally, all machines that can be produced in von Neumann’s cell space system are essentially information transactional devices. Even construction is, in this context, a form of information processing. Physical construction and material transformations can possibly be viewed as informational processes but, in a practical sense, the cell-space notion is far from providing a readily useful paradigm of actual manipulation and transformation of physical materials – that is, of kinematic self-replication.
Last updated on 1 August 2005