575,478 research outputs found
The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability
In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed. Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theory plus the axiom of choice. This is, surely, seriously disturbing from a computation point of view. Therefore, in this paper, I seek to locate a foundation for analog computing in exhibiting some tentative dualities with results that are analogous to those that are standard in computability theory. The main question, from the point of view of economics, is whether the Phillips Machine, as an analog computer, has universal computing properties. The conjectured answer is in the negative.Phillips Machine, Analogue Computation, Digital Computation, Computability, General Purpose Analogue Computer
Information Compression, Intelligence, Computing, and Mathematics
This paper presents evidence for the idea that much of artificial
intelligence, human perception and cognition, mainstream computing, and
mathematics, may be understood as compression of information via the matching
and unification of patterns. This is the basis for the "SP theory of
intelligence", outlined in the paper and fully described elsewhere. Relevant
evidence may be seen: in empirical support for the SP theory; in some
advantages of information compression (IC) in terms of biology and engineering;
in our use of shorthands and ordinary words in language; in how we merge
successive views of any one thing; in visual recognition; in binocular vision;
in visual adaptation; in how we learn lexical and grammatical structures in
language; and in perceptual constancies. IC via the matching and unification of
patterns may be seen in both computing and mathematics: in IC via equations; in
the matching and unification of names; in the reduction or removal of
redundancy from unary numbers; in the workings of Post's Canonical System and
the transition function in the Universal Turing Machine; in the way computers
retrieve information from memory; in systems like Prolog; and in the
query-by-example technique for information retrieval. The chunking-with-codes
technique for IC may be seen in the use of named functions to avoid repetition
of computer code. The schema-plus-correction technique may be seen in functions
with parameters and in the use of classes in object-oriented programming. And
the run-length coding technique may be seen in multiplication, in division, and
in several other devices in mathematics and computing. The SP theory resolves
the apparent paradox of "decompression by compression". And computing and
cognition as IC is compatible with the uses of redundancy in such things as
backup copies to safeguard data and understanding speech in a noisy
environment
Introduction to the Phillips Machine and the Analogue Computing Tradition in Economics
In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed.
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