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Happy New Year

  1. Dec 29, 2004 #1


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    Happy New Year - reply to Lubos


    Let us welcome the International Year of Physics! There is a
    poster on the wall in the corridor here, saying "Help make 2005
    another miraculous year".

    Well, I don't know that I can do much - but one can try.

    I've posted here, because it takes days for my posts to appear on Strings.


    Shuzan held out his short staff and said: "If you call this a
    short staff, you oppose its reality. If you do not call it a
    short staff, you ignore the fact. Now what do you wish to call
    Zen koan

    In classical (Boolean) logic the law of the excluded middle

    [tex]U \vee \neg U = \textrm{true}[/tex]

    holds. Consider the following examples of its failure.

    1. The collection of subspaces of a Hilbert space [itex]\mathcal{H}[/itex] forms an algebra under intersection [itex]\wedge[/itex] and [itex]U \vee V[/itex] the smallest subspace containing both U and V. [itex]\neg[/itex] is the orthogonal complement (hence the need for inner product). False is the zero subspace and true is the full
    space [itex]\mathcal{H}[/itex].

    2. The open sets of the two dimensional sphere under the
    operations of intersection and union, with [itex]\neg U[/itex] the
    interior of the complement (it can't be the complement because
    that's not an open set). False is the empty set, and true the
    whole sphere.

    This second example is interesting because it describes the two
    sphere as a category (with an arrow between open sets when there
    is an inclusion) which underlies the sheaf of germs of analytic
    functions...anyway, think of it as the celestial sphere of an
    observer in GR and it turns up in twistor theory.

    One might also consider the axiom of choice. The 'local' version
    of this also forces Booleanness on one's logic.

    So we're going to have to be rather careful with which mathematics
    we use if we want a description of the quantum world that is
    sophisticated enough to describe decoherence, for instance.

    As far as I understand it (correct me if I'm wrong, Lubos) String
    theorists are quite keen on twistors at the moment, but they do
    not address these questions.

    Kea :cool:
    Last edited: Dec 29, 2004
  2. jcsd
  3. Dec 31, 2004 #2
    I would have preferred your post to start and end in 'Happy 2005 everyone!'
  4. Dec 31, 2004 #3
    Sad, but true: A retarded greeting such as "Happy 2005! Einstein rawks! luv y'all" would have yielded much more meaning to me. :(
  5. Dec 31, 2004 #4


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    Happy 2005 everyone!!!

    Einstein RAWKS!!!!

    Luv y'all!!! ('specially our neice, recon :biggrin:)
  6. Dec 31, 2004 #5


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    It won't be 2005 in the Pacific Time Zone for another 8 hours, but either way: Happy New Year, everyone!
  7. Dec 31, 2004 #6

    Ivan Seeking

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    Happy New Year everyone!!!
    Einstein meows!.

    [he's my cat]
  8. Jan 1, 2005 #7
    Am I the only one who reset my watch to the exact time at 12:00?
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