Information Technology Reference
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does not create new alphabetical letter types by stringing together more and more
existing letters—new types must be introduced from outside the system. This is
typically carried out by an external agent. Likewise, in our computer simulations,
we set up a space of variables and their possible states, but the simulation cannot
add new variables and states simply by traversing the simulation-states that we have
previously provided.
These ideas bear directly on fundamental questions of computational creativity.
What are the creative possibilities and limitations of pure computations? Exactly
how one defines “computation” is critical here. In its more widely used sense, the
term refers to any kind of information-processing operation. Most often, the issue
of what allows one to distinguish a computation from a non-computational process
in a real-world material system is completely sidestepped, and the term is left loose
and undefined. However, in its more precise, foundations-of-mathematics sense, the
term refers to concrete formal procedures that involve unambiguous recognitions
and reliable manipulations of strings of meaningless symbols. It is this latter, more
restrictive, sense of computation as formal procedure that we will use here. For
practical considerations, we are interested in computations that can be carried out in
the real world, such as by digital electronic computer, and not imagined operations
in infinite and potentially-infinite realms.
2
In these terms, pure computation by itself can generate new combinations of sym-
bol primitives, e.g. new strings of existing symbols, but not new primitive symbols
themselves. In order for new symbol primitives to be produced, processes other than
operations on existing symbols must be involved—new material dynamics must be
harnessed that produce new degrees of freedom and new attractor basins that can
support additional symbol types. To put it another way, merely running programs
on a computer cannot increase the number of total machine states that are enabled
by the hardware. In order to expand the number of total machine states that are avail-
able at any given time, we must engage in physical construction, such as fabricating
and wiring in more memory.
There was a point in the history of computing devices at which self-augmenting
and self-organising physical computational devices were considered. In the early
1960s, when electronic components were still expensive, growing electronic logical
components “by the pound” was contemplated:
2
Popular definitions of computation have evolved over the history of modern computing (Boden
2006
). For the purposes of assessing the capabilities and limitations of physically-realisable com-
putations, we adopt a very conservative, operationalist definition in which we are justified in calling
an observed natural process a
computation
only in those cases where we can place the observable
states of a natural system and its state transitions in a one-to-one correspondence with those of
some specified deterministic finite state automaton. This definition has the advantage of defining
computation in a manner that is physically-realisable and empirically-verifiable. It results in clas-
sifications of computational systems that include both real world digital computers and natural
systems, such as the motions of planets, whose observable states can be used for reliable calcula-
tion. This finitistic, verificationist conception of computation also avoids conceptual ambiguities
associated with Gödel's Undecidability theorems, whose impotency principles only apply to infi-
nite and potentially-infinite logic systems that are inherently not realisable physically.
