XPost: comp.theory, comp.ai.philosophy   
   From: NoOne@nospicedham.NoWhere.com   
      
   On 12/16/2020 7:48 PM, Kaz Kylheku wrote:   
   > On 2020-12-17, olcott  wrote:   
   >> On 12/16/2020 6:21 PM, Kaz Kylheku wrote:   
   >>> If Halts is really a pure function of two arguments, and it generates a   
   >>> hierarchy of UTMs, then every call to Halts with the same two arguments   
   >>> must generate exactly the same hierarchy of UTMs, and come to exactly   
   >>> the same conclusion when it examines that hierarchy.   
   >>>   
   >>   
   >> According to your reasoning the chairman of the board of a corporatation   
   >> is at the same place in the corporate hierarchy as the janitor.   
   >   
   > You're forgetting that the hierarchy here is infinitely recursive due   
   > to precise self-embedding: invocations of Halts(X, Y) contain   
   > invocations of Halts(X, Y).   
   >   
      
   No you are forgetting that the pinnacle of the otherwise infinite   
   simulation hierarchy cuts off the subsequent simulations as soon as it   
   has seen enough of their execution trace to decide that it would be   
   otherwise infinite.   
      
   We are talking about an actual program that actually executes one step   
   at a time. Every time Halts executes it creates a process context that   
   has its own registers memory and stack. It then executes its input as a   
   separate virtual machine within this process context.   
      
   Then H_Hat executes Halts again and yet another process context is   
   created to execute yet another virtual machine. Every time this occurs   
   the number of process contexts and virtual machine increases to some   
   finite number.   
      
   > So for the corporation analogy not to be a strawman, we have to make   
   > the corporation likewise infinitely nested, and we have to have   
   > identical copies of the janitor and chairman at various levels.   
   >   
      
   Infinity is cut off at three.   
      
   >> The first invocation of Halts() is the pinnacle of the hierarchy and   
   >> every invocation after that is subordinate to the preceding one.   
   >   
   > Every recursive invocation is indistinguishable.   
      
   Bullshit each one has a unique process ID.   
      
   > Just like the suffix of   
   > an infinite list of identical ducks is exactly the same as the original   
   > list.   
   >   
      
      
   --   
   Copyright 2020 Pete Olcott   
      
   "Great spirits have always encountered violent opposition from mediocre   
   minds." Einstein   
      
   --- SoupGate-Win32 v1.05   
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