|Turing-Machine: is a model by A.M. Turing (A.M. Turing, “On Computable Numbers, with an application to the decision-making problem”, Proceedings, London Mathematical Society, 230-265 (1936)), which reproduces the process of character manipulation according to simple rules and thus makes it possible to investigate. A Turing machine can, in principle, calculate everything which is calculable. See also model, formal language, system, computability, decidability, holding problem, Church Turing Thesis._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Turing machine/Genz: e.g. instructions that correspond to a certain position can only be:
Move the tape one square to the right
Move the tape one square to the left
If there is a 1 in the square, go to statement i
If there is a 0 in this square, go to the statement i
And that is all there is to it.
Logic/Mathematics/Physics/Genz: if the laws of physics were different, it might be impossible to build a Turing machine.
N.B.: it might be impossible to calculate the sum of two numbers!
Proof/Genz: is therefore dependent on natural laws.
Initial conditions/Initial states/nature/Genz: in nature there are countless initial states. But a training machine could not list them all, because it could not represent them all differently.
Initial conditions/initial states/nature/Genz: in nature there are countless initial states. But a Turing machine could not list them all, because it could not represent them all differently.
Holding Problem/Non-Hold-Theorem/Genz: Could it be that a future physics (other than ours) allows to do infinite calculation steps in finite time?
Turing machine/Genz: a possible world in which more is possible than the logic allows could not be simulated by a Turing machine.
Genz: Thesis: I do not see that it has to be the case that in the updated world every sequence has to be simulated by a Turing machine.
David DeutschVsGenz: (The Fabric of Reality): assumes that everything in the actual world can be simulated by a Turing machine. From this he deduces that the universe collapses, because an infinitely growing universe cannot be simulated by a Turing machine.
GenzVsDeutsch: reversed: the answer to the question of the ultimate fate of the universe, based on physical facts, will also determine whether this fate can be simulated by a Turing machine._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Gedankenexperimente Weinheim 1999
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002