3 ms·

In an entirely mechanistic nonprobabilistic universe, where state C always follows state B, which always follows state A, etc, then if State X ever equals a pri

In an entirely mechanistic nonprobabilistic universe, where state C always follows state B, which always follows state A, etc, then if State X ever equals a prior state, say state B, then the universe enters into an infinite loop. A-B-C-D-X-C-D-X...

tempestn 9y ago
That's true, but why is it important?
- dotancohen 9y ago
  No big bang, no great crunch, Pantera will have more live shows, etc.
- SubiculumCode 9y ago
  As constructed, it is true. But important? Probably not. Even if the universe was total mechanistic, and should be described as a series of discrete states, the probability of ever entering into identical states would be very near zero, except perhaps in some hypercooled state, or something. am not sure that the laws o thermodynamics would even allow that to happen. But I am no physicist..just a dude, who had a thought.
posterboy 9y ago
I think most people wouldn't assume a discrete nature of finite state changes as I take from your comment. A cauchy series for example orbits around a limit point. Fixed states would be enumerated by Natural numbers that are extensionally defined in set theory for example as ( 0 ), [ 1, ( 0 ) ], { 2, [ 1, ( 0 ) ] }, ... Be 0 the empty set, then this is the Von Neumann construction [1]. This is a very tangible notion that represents a total order. So a state is a sequence of inputs and the natural number represents the recursion depth of the successor funtion (succ). But the complexity of that function alone is less than NP, so it would not have arbitrary consequences, so cycles would be the least of a problem. A P-adic numbers field Q_p on the other hand isn't even well ordered. Or Pi, it contains many different fixed length versions of itself in its remainder. [1] https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_construction https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_con... [2] https://en.wikipedia.org/wiki/Mealy_machine https://en.wikipedia.org/wiki/Mealy_machine

tempestn 9y ago

That's true, but why is it important?

dotancohen 9y ago
No big bang, no great crunch, Pantera will have more live shows, etc.
SubiculumCode 9y ago
As constructed, it is true. But important? Probably not. Even if the universe was total mechanistic, and should be described as a series of discrete states, the probability of ever entering into identical states would be very near zero, except perhaps in some hypercooled state, or something. am not sure that the laws o thermodynamics would even allow that to happen. But I am no physicist..just a dude, who had a thought.

posterboy 9y ago

I think most people wouldn't assume a discrete nature of finite state changes as I take from your comment. A cauchy series for example orbits around a limit point. Fixed states would be enumerated by Natural numbers that are extensionally defined in set theory for example as ( 0 ), [ 1, ( 0 ) ], { 2, [ 1, ( 0 ) ] }, ... Be 0 the empty set, then this is the Von Neumann construction [1]. This is a very tangible notion that represents a total order. So a state is a sequence of inputs and the natural number represents the recursion depth of the successor funtion (succ). But the complexity of that function alone is less than NP, so it would not have arbitrary consequences, so cycles would be the least of a problem. A P-adic numbers field Q_p on the other hand isn't even well ordered. Or Pi, it contains many different fixed length versions of itself in its remainder. [1] https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_construction https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_con... [2] https://en.wikipedia.org/wiki/Mealy_machine https://en.wikipedia.org/wiki/Mealy_machine