The Critical Rationalist Vol. 01 No. 02 ISSN: 1393-3809 26-Nov-1996

6 The Possibility of Infinitely New Information Processing: Why Tipler Needs World 3

4 World 3 and the Unfathomable Content of our Knowledge

* (50)*
The above has some interesting implications for an
economic analysis of resources and the issue of
long-run diminishing returns.

* (51)*
Just as a resource needs to be interpreted, so an
invention cannot be reduced to its chemical and
physical properties and relations, but must be placed
in a means-end relationship. All inventions are
means/ends relationships; they are invented and adopted
for a purpose. This shows their World 2 aspect. But a
means/end relationship is partly constituted by its
theoretical interpretation, and thus all inventions are
theory impregnated. Inventions, therefore, have a world
3 aspect also.

* (52)*
I must make clear at this point that I do not subscribe
to the popular view that every technological decision
and action (including inventions) is prescribed by one
or more scientific theories; in fact none are. This
would overlook the fact that scientific laws are
universal and therefore can only proscribe; alone, they
can tell us only what cannot happen, not what will
happen, and therefore alone cannot tell us what we
should do to achieve a given end. Building a bridge,
car, space-ship and tube of toothpaste is a matter of
engineers discovering sets of constructible initial
conditions that typically lead efficiently to the
desired result. This is a conjecture and refutation
affair. Universal theories of science help the engineer
insofar as they can be used to eliminate some of the
hopeful candidates of efficient sets of initial
conditions, namely the ones whose description
contradicts the accepted scientific theories.

* (53)*
In talking of the theories that help to constitute and
identify a given invention or resource, I include these
low level theories. But I also want to make it clear
that even these theories plus our psychological
dispositions toward the invention or resource do not
exhaust the useful possibilities inherent in a type or
particular invention or type or particular portion of a
resource. It is sufficient for my argument that at
least part of the range of its useful possibilities is
encompassed by these low level theories.

* (54)*
Now theories as World 3 objects have three relevant
properties:

- They are universal, applying to all space and time.
- They have infinitely varied logical/information content.
- They are infinitely copyable.

* (55)*
Now, on the basis of these facts it becomes clear how
it is possible for a) an invention to be applied in a
literally infinite number of significantly different
possible ways and b) combined in a literally infinite
number of significantly different possible ways with
other inventions. But an exactly analogous argument
applies to resources, for resources are also
interpreted as a means/end relationship.

* (56)*
Any particular wheel or lever or computer will wear
out, but due to the universality of the theory that
helps to constitute the invention, the invention type
may be applied a potentially infinite number of times
without diminished effect. Due to the infinitely varied
logical/information content of the invention-theory,
the invention may be applied in an infinite number of
significantly varied ways. No one person, therefore,
can work out all the useful content of a theory of a
resource. If one employs more and more people on a
given piece of land, one will get diminishing returns;
after all, there is only so much room on a piece of
land. But one may not get this when employing more and
more people on a given theory, say the theory of levers
or the quantum computer. Due to its infinite content,
it has an infinitely varied terrain to work on, as it
where. This is most clearly the case with something
like the theory of arithmetic, where in the light of
the work of Gödel and Tarski, there will always be an
infinite number of problems to work on. Unlike a piece
of land, an indefinite number of copies can be made of
a theory. At any time, any number of people can be
working out useful ramifications and implications of
the theory and applying them.

* (57)*
Let us return to Machlup's suggestion that the number
of possible combinations of inventions increases
geometrically with the number of elements at hand. From
our analysis it is clear that any two inventions will
each have a cluster of theories that explains, partly
constitutes and identifies it. It is the logical and
information content of these theories that allows us to
combine them to make further inventions. But because of
the infinite content of the theories they can be
combined in a potentially infinite number of ways. To
explain the emergence of any given combination one will
look to see what the inventor's problem situation was,
how the inventor searched through different
combinations of different portions of logical and
information content, and finally, how the two or more
invention-theories were combined. On this analysis, it
becomes clearer that a "fusion of two inventions" may
consist of the following possible combinations:

- (a) Proper subsets of the theoretical contents of
the two inventions.
- (b) A proper subset of one with the whole of the other.
- (c) A newly discovered subset of the content of
one with a familiar subset of another.
- (d) Whole or part contents brought together via a
bonding theory.

* (58)*
In fact, since the aim of the fusion of two inventions
is a new invention, the two invention-theories will
form part of a larger action schema, and so it will
always be through some third theory that the two
inventions are combined.

* (59)* I suggest that this logical analysis is a more
subtle and powerful way of revealing the way in which
the number of possible combinations of inventions
increases much more rapidly with the number of elements
at hand, than saying with Machlup that they increase
"geometrically". This is reinforced when one considers
that in combining two theories one sometimes obtains
interesting implications and ramifications not
contained in the content of either theory considered
alone. Watkins has fruitfully explored this possibility
in his book

6 The Possibility of Infinitely New Information Processing: Why Tipler Needs World 3

4 World 3 and the Unfathomable Content of our Knowledge

The Critical Rationalist Vol. 01 No. 02 ISSN: 1393-3809 26-Nov-1996

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TCR Issue Timestamp: Tue Nov 26 17:14:18 GMT 1996