1. Forum
  2. Usenet
  3. COMP.AI.PHILOSOPHY

  • =?UTF-8?Q?Re=3A_Clarification_of_Linz_=C4=A4_Description_=5B_Are_we_th?

    From Don Stockbauer@21:1/5 to olcott on Tue Oct 5 05:48:11 2021
    On Saturday, October 2, 2021 at 4:02:13 PM UTC-5, olcott wrote:
    On 10/2/2021 3:15 PM, Ben Bacarisse wrote:
    Richard Damon <Ric...@Damon-Family.org> writes:

    On 10/2/21 12:34 PM, Ben Bacarisse wrote:
    olcott <No...@NoWhere.com> writes:

    M applied to wM means: The TM described by wM applied to w.
    <snip>
    if M applied to wM does not halt
    is translated into

    The TM described by wM

    I.e. M

    applied to wM does not halt

    You got it right this time. I think the w above is just a typo.


    The q0 wM w ⊢* qn

    is the specification of H, not H^.

    H is applied to wM w as an input.

    Yes, but that's not what I'm talking about. (And when I say he got it right I juts mean it's not technically wrong. It's still a silly way to put it.)

    I'm talking about this line:

    ||| M applied to wM means: The TM described by wM applied to w.

    I don't think he intended to write that lone w, but the whole digression is peculiar so goodness knows what he meant.


    w is the arbitrary finite string that H deals with.
    wM is the TM description finite string that Ĥ deals with.

    But later on he does not use the same "translation", just a pointless renaming of M as "[t]he TM described by wM":

    ||| if M applied to wM does not halt
    ||| is translated into
    |||
    ||| The TM described by wM applied to wM does not halt

    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
    Transitioning to Ĥ.qn is based on this decision: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
    The fact that Ĥ halts on input ⟨Ĥ⟩
    does not contradict the fact that the input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ never halts.

    This is apparently too difficult for you to understand.

    It is very very difficult and cannot be understood until after every
    single detail of the actual complete computation has been studied.

    No one ever does this. The x86utm C/x86 version is as close as anyone
    has ever come to studying every single detail of the essential algorithm.

    Most people simply dismiss it as impossible on the basis that they
    falsely believe it is a contradiction.
    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre minds." Einstein

    And a good example of a mediocre mind is Olcott.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)