Zuse came up with the idea earlier—around 1946-47, when he was in a village in Bavaria and his z4 computer was disassembled in a barn. As for the reception to the idea, he paraphrased Pauli’s comment on the reaction to quantum theory: “not that my idea was crazy; it was not crazy enough.”
Amazingly close to what I've been thinking this week!
If at the ultimate level everything is quantised then the universe is no more than very advanced number theory (in the sense that cellular automata are number theory).
There are an infinite no of natural numbers (integers) - the definition of Beth-0.
There are an infinite no of possible universes - also Beth-0.
There are Beth-1 combinations of natural numbers.
Beth-1 combinations is more than enough to generate all Beth-0 universes.
The halting problem: a computer is a finite state machine. It only has a finite number of states. The question is which will it hit first: one of the predefined "stop" states or a previously-visited state (leading to a loop). [Bit like the knight's tour on a chess board.]
If there are K possible states and H designated "stop" states, then the probabilty of stopping on the Nth cycle is... H/(K-N+1) and the probability of looping is N/(K-N+1)
Obviously this only gets difficult when K is very large, but the likelihood of looping increases with N whereas stopping always has the same probability.
Zuse came up with the idea earlier—around 1946-47, when he was in a village in Bavaria and his z4 computer was disassembled in a barn. As for the reception to the idea, he paraphrased Pauli’s comment on the reaction to quantum theory: “not that my idea was crazy; it was not crazy enough.”
Amazingly close to what I've been thinking this week!
If at the ultimate level everything is quantised then the universe is no more than very advanced number theory (in the sense that cellular automata are number theory).
There are an infinite no of natural numbers (integers) - the definition of Beth-0.
There are an infinite no of possible universes - also Beth-0.
There are Beth-1 combinations of natural numbers.
Beth-1 combinations is more than enough to generate all Beth-0 universes.
The halting problem: a computer is a finite state machine. It only has a finite number of states. The question is which will it hit first: one of the predefined "stop" states or a previously-visited state (leading to a loop). [Bit like the knight's tour on a chess board.]
If there are K possible states and H designated "stop" states, then the probabilty of stopping on the Nth cycle is... H/(K-N+1) and the probability of looping is N/(K-N+1)
Obviously this only gets difficult when K is very large, but the likelihood of looping increases with N whereas stopping always has the same probability.