The Critical Rationalist Vol. 01 No. 02 ISSN: 1393-3809 26-Nov-1996
7 Conclusion
5 The Special Economic Status
of Objective Knowledge:
Resources and Inventions as World 3 Objects
(60) Before I conclude this paper, I must discuss the relevance of Frank Tipler's fascinating argument for indefinite economic growth to my own argument.
(61) Tipler argues that life and hence economic growth can continue forever (Tipler & Barrow 1986, Tipler 1994). Carbon based life-forms like ourselves are doomed eventually in the extremely high temperatures to be encountered at the approach to the final singularity in a closed universe. However, our successors--highly sophisticated, self-reproducing computers--will colonize the whole of space and will effectively undergo an infinite amount of economic growth and experience before the singularity.
(62) Tipler accepts that growth rates within the present epoch are limited by physics, but thinks that most predictions of physical limits have ignored economics and thus grossly underestimated the potential for economic growth. Following Simon, Tipler assumes that economic production is equivalent to the production of services, but Tipler adds that each of these units of service are in turn equivalent to the production and transfer of amounts of information. Thus the limits of economic growth are the limits of the growth of knowledge: the amount of information that can be read, stored and processed.
(63)
Tipler says: "Information processing is
constrained by the first and second laws of
thermodynamics. These laws imply that the amount of
information that can be processed at a given
temperature T is 
where E is
the energy available for processing, 
is the
natural logarithm of 2, and k is Boltzmann's
constant. Now any temperature T that we can use is
greater than the background radiation, which is 3
degrees on the Kelvin scale, and if we limit
ourselves to operations on the Earth, the greatest
available energy is 
, where M is the
mass of the Earth."
(Tipler 1988, pp. 4-5) Thus even life
based on steady state economies is doomed, if it
remains confined to the Earth. But life need not be
confined to the Earth, since there is the possibility
of expanding into and beyond the solar system using von
Neumann probes. In any case, Tipler points out, this
relationship between energy and information processing
allows for a one hundred-billion-fold increase in
economic wealth before we reach the physical limits of
the Earth. This estimate is based on the assumption
that we can increase economic wealth at the same rate
as we increase the speed of our computers.
(64) Tipler argues that what is important to future self-conscious intelligent life will be subjective time, measured in terms of the number of thoughts experienced, not what physicists call proper time, that measured by atomic clocks. Tipler identifies thought with information processing of high speed computers. Tipler argues that indefinite economic growth is possible in a closed universe only if an infinite amount of information can be processed before the end of time. This is possible if the rate of information processing increases to infinity before the big crunch. This, Tipler argues, is possible. The required energy for the information processing is obtained from the differential speeds at which different regions of the universe will collapse, a phenomenon known as sheer.
(65) However, there is an important qualification. If this information processing is done on a finite state machine, then eventually it will start to repeat itself: no new thought would be possible. This information processing must be conducted on an infinite state machine. To supply this machine, Tipler conjectures that life, taken as a whole, can be regarded as an infinite state machine; but Tipler fails to explain how. I conjecture that the body of scientific knowledge provides the basis for an infinite state machine. The unfathomable information content of theories provides the "infinite tape" for the Turing machine. Stated more generally, the possibility of thinking an infinite number of new thoughts is made possible by World 3. It must be born in mind that there are two senses of "information" here. Tipler's "information" is the engineer's conception of actually encoded information (Shannon and Weaver), existing as realized distinct states of matter/energy, such as on-off electrical states in a computer. The "Logical content" and "information content" of say, scientific theories, are mostly unencoded, existing as only potential information in the engineer's sense. In some places Tipler explicitly identifies knowledge and information. But the above analysis of the unfathomable content of scientific theories makes it important to distinguish between knowledge and information. Tipler's bold and fascinating argument is thereby reinforced.
7 Conclusion
5 The Special Economic Status
of Objective Knowledge:
Resources and Inventions as World 3 Objects
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