Re: Flibble's Law

On 4/18/25 5:01 PM, Mr Flibble wrote:

On Fri, 18 Apr 2025 15:08:55 -0400, Richard Damon wrote:
 

On 4/18/25 3:00 PM, Mr Flibble wrote:

Flibble's Law:
>
If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

>
>
Why?
>
Especially when the question is "Is the behavior of the process
infinite?"
>
The issue is that fundamentally, knowledge must be based on finite
processes, as we can't do infinite analysis and do anything with the
answer.
>
Knowing that a process will be infinite, allows us to not waste all of
our time on something that won't get us an answer.
>
The basic result of all this sort of proof, is that there are cases
where we can't ever know for certain if we are on a wild-goose-chase
that will never give a result, or we are on a path that WILL give a
result eventually if we persist long enough.
>
Knowing that there ARE Wild-Goose-Chases as fundamental properties of
systems lets us plan better for what to do.
>
We KNOW we can't be perfect in all we do, so we accept realistic
results, and try to keep improving.

 It is about playing the game by the rules of the game:

Right, and the rules of the game say deciders must answer in finite time or they aren't deciders.
Possible inputs might be programs that do not halt, but will run forever, and possible never repeat an exact state, and the decider, to be a correct decider, must detect this in finite time.

 If Busy Beavers are allowed an INFINITE tape in the context of the Halting
Problem then Simulating Halt Deciders are allowed INFINITE resources.
 /Flibble

Sure, they can use as much tape as they want, they just can't use infinite time.
Note, Busy-Beaver is about detecting if a program IS a busy beaver, some possible inputs will be non-halting with infinite growth, and these need to be rejected, and rejected in finite time.