Page 98 - Nanotechnology an introduction

Examining again Figure 8.3, it can be asserted that both putative results of mixing slightly sticky cubelets together are organized, but most people
would not hesitate to call the structure in (b) better organized than that in (a). Evidently there is some meaning in the notion of “good organization”,
even though it seems difficult to formulate an unambiguous definition. Can a system spontaneously (automatically) change from a bad to a good
organization? This would be a reasonable interpretation of “self-organization”, but has been proved to be formally impossible [10]. Consider a
device that can be in any one of three states, A, B or C, and the device's operation is represented by some transformation, e.g.,

Now suppose that we can give an input f into the device, and that the output is determined by the value of f, e.g.,

Spontaneous (automatic) operation means that the device is able to autonomously select its input. The different possible input values are here
represented by a subscript indicating the state of the device on which the input now depends. However, this places severe constraints on the actual
operation, because f (B) (for example) is impossible; only f (A), f (B) and f (C) are possible, hence the operation necessarily reduces to the
A
B
C
A
simple transform, lacking any autonomy:

Any change in f must therefore come from an external agent.