The Myth of 'the Myth of Hypercomputation'

ness and Approximations Thursday, June 9, 2011 Abstractness and Approximations • This rather absurd attack goes as followsness and Approximations • This rather absurd attack goes as follows Thursday, June 9, 2011 Abstractness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully.ness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. Thursday, June 9, 2011 Abstractness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully.ness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Thursday, June 9, 2011 Abstractness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully.ness and Approximations • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Thursday, June 9, 2011 • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Abstractness and Approximations Thursday, June 9, 2011 • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Abstractness and Approximations • Going by the same argument: Thursday, June 9, 2011 • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Abstractness and Approximations • Going by the same argument: • Since Turing computers can’t be realized fully, Turing computation is now another “myth.” Thursday, June 9, 2011 • This rather absurd attack goes as follows 1. Even Turing machines are abstract models that can’t be implemented fully. 2. Therefore, no other more powerful model can be implemented fully. Abstractness and Approximations • Going by the same argument: • Since Turing computers can’t be realized fully, Turing computation is now another “myth.” • The problem is that Davis fails to recognize that a lot of th hypercomputational models are abstract models that no one hopes to build in the near future. Thursday, June 9, 2011 Necessity of Noncomputable Reals Thursday, June 9, 2011 Necessity of Noncomputable Reals • Another point in Davis’ argument is that almost all hypercomputation models require Physics to give them a Turing-uncomputable real number. Thursday, June 9, 2011 Necessity of Noncomputable Reals • Another point in Davis’ argument is that almost all hypercomputation models require Physics to give them a Turing-uncomputable real number. • This is false. Quite a large number of hypercomputation models don’t require non-computable reals and roughly fall into the following categories Thursday, June 9, 2011 Necessity of Noncomputable Reals • Another point in Davis’ argument is that almost all hypercomputation models require Physics to give them a Turing-uncomputable real number. • This is false. Quite a large number of hypercomputation models don’t require non-computable reals and roughly fall into the following categories • Infinite time Turing Machines Thursday, June 9, 2011 Necessity of Noncomputable Reals • Another point in Davis’ argument is that almost all hypercomputation models require Physics to give them a Turing-uncomputable real number. • This is false. Quite a large number of hypercomputation models don’t require non-computable reals and roughly fall into the following categories • Infinite time Turing Machines •  Thursday, June 9, 2011 Necessity of Noncomputable Reals • Another point in Davis’ argument is that almost all hypercomputation models require Physics to give them a Turing-uncomputable real number. • This is false. Quite a large number of hypercomputation models don’t require non-computable reals and roughly fall into the following categories • Infinite time Turing Machines •  Kieu-type Quantum Computation Thursday, June 9, 2011 Science-based Arguments: A Meta Analysis of Davis and friends Thursday, June 9, 2011 Science-based Arguments: A Meta Analysis of Davis and friends The Main Case Science of Sciences Part 1: Chain Store Paradox Part 2: Turing-level Actors Part 3:MDL Computational Learning Theory CLT-based Model of Science