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:
(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:
(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 Science and Scepticism (Watkins 1984). It is often said that an invention that simply combines previous inventions is not really a new invention, but a logical analysis of inventions in terms of content allows us to see that such invention-combinations can bring radically new useful consequences, emergent properties, into existence.
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