Beyond Church/Turing Computing

[Carl Hewitt]

The following is excerpted from  https://papers.ssrn.com/abstract=3603021

[Church 1931] developed the lambda calculus and [Turing 1936] developed Turing Machines, which are based on the following:

 

An isolated individual human is provided with means to incrementally obtain paper and pencils without limit. Computation begins by providing the human with paper input that includes particular instructions how to proceed. No further input and output is allowed during the computation. Furthermore, the human is not allowed any outside communication. If the human finishes the instructions, then a single output on paper occurs and the computation terminates.

 

Alternative paradigms included the following: 

Large-scale astronomy calculations and resulting catalogues were the work of teams of women ably captained by Williamina Fleming, who discovery of the first white dwarf and the Horsehead Nebula among other notable achievements. [cf. Geiling 2013] One of the team, Antonia Maury was one of the greatest contributors developing the field of morphology of stellar spectra. 

In the face of widespread hostility, teams of Wrens (female Naval Officers) operated large-scale simulations in that discovered ways to defeat U-boat attacks that were crippling Britain. The simulations were then used to train ship commanders in use of the discoveries with the help of radar. Directed by scripts, the simulations were enacted on a large floor where each 10-inch square represented one nautical mile. From behind white sheets designed to limit their line of sight as at sea, British ship commanders worked under tight time constraints for each step of a simulation to maneuver and attack submarines. While British ships were outlined in conspicuous white chalk, the U-boats were marked in green, rendering them invisible. Some of the scripts were reenactments of actual battles that had recently occurred. Other scripts were used to try out new tactics. The Wrens played as the German team, kept time, marked ship movements, and sometimes gave advice to the British captains, which was not appreciated until the captains realized that the Wrens were extremely knowledgeable although they had never been in a real battle. None of the Wrens received official public recognition for their contributions.

Alternative computing paradigms were not developed in foundations of computing. Instead, the Church/Turing Thesis was widely accepted to the effect that the lambda calculus and Turing Machines captured all of computation. However, as shown next in this article, the Church/Turing thesis does not hold for digital computation

Regards,

Carl

https://professorhewitt.blogspot.com/