Turing machine/Genz: e.g. instructions that correspond to a certain position can only be: Print 0.
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: a proof is therefore dependent on natural laws.
>Proofs, >Provability, >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 within a 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)(1): David Deutsch 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.
1. David Deutsch(1997). The Fabric of Reality. London: Viking Adult.
Gedankenexperimente Weinheim 1999
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002