Re: limit speed of computation - Digital vs. Quantum

From: Kent Paul Dolan (xanthian_at_well.com)
Date: 10/13/04

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    Date: Wed, 13 Oct 2004 18:57:56 +0000 (UTC)

    "Paul Chapman" <paul@igblan.free-online.co.uk> wrote:

    > Is it possible to construct an infinite graph
    > where each vertex has at most n neighbours, such
    > that *all* vertices are t steps away from
    > O(exp(t)) other vertices?

    > If such a graph is constructible, and DP will
    > admit that the universe might be a general
    > verticular automata based on this topology rather
    > than the limited topology of a
    > (finite-dimensional) CA, then DP and QC would once
    > again be compatible.

    Probably navigations done with such assumptions are
    fraught with dangerous shoals. I don't know enough
    about graph theory, much less infinite graph theory,
    to comment meaningfully, but I am just _dandy_ at
    noticing those who can. A recent extremely dragged
    out discussion between one person trying to navigate
    by what was "intuitively obvious" about graphs when
    extended to infinite graphs, and a whole newsgroup
    who knew that wasn't working for the OP (because he
    was using his intuitional "findings" to derive
    results well known to be not merely subtly false but
    "obviously nonsense"), just recently wrapped up in
    comp.theory, on a topic so similar it might contain
    your answer.

    Useful cautionary tutorial articles from that thread
    are these by Tim Peters [who has annoying habits of
    his own, work past the "<wink>"s without vomiting,
    if possible; people who choose to insult other
    people deliberately and maliciously rather than to
    do the harder work to conduct discussions without
    insults, shouldn't simultaneously try to pretend
    that being insulting isn't their exact intention,
    with cutesy text decorations]:

    http://groups.google.com/groups?selm=R5adnTP0EPYGCMXcRVn-uw%40comcast.com

    http://groups.google.com/groups?selm=6ZydnY67xsz_fcXcRVn-iA%40comcast.com

    http://groups.google.com/groups?selm=qN2dnZmOmf3NTsTcRVn-pQ%40comcast.com

    http://groups.google.com/groups?selm=O7-dnT2wspA-QcHcRVn-jw%40comcast.com

    http://groups.google.com/groups?selm=gvednU9u_Pfn38PcRVn-iw%40comcast.com

    The whole thread starts here, is quite educational
    in a strange sense, and has contributions from
    several other cluefull commentators, but trying to
    survive the OP's deliberate and intransigent
    stupidity without exploding is a labor suitable for
    a deity-descended person like Hercules [I failed at
    the task multiple times, but then, I have a well
    documented temper-control problem on Usenet, and am
    besides a devout atheist]:

    http://groups.google.com/groups?selm=fa69ae35.0409221823.682ae186%40posting.google.com

    HTH

    xanthian. 

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