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Monday, January 29, 2007

Thought of the Day

Life is just a big Markov chain, whose stationary distribution is death.

13 comments:

  1. In life the future depends not only on the present, but also on the past. So life is not a Markov chain ;-)

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  2. It only depends on the present with a broad enough definition of state.

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  3. With broad enough definition of the present number of states is not fixed apriori. Hence it is not a markov chain.

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  4. So I guess life doesn't take place on a bipartite graph with no self-loops?

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  5. Scott, this is a family blog. We must cherish our innocence.

    Markov, for one, seems to have lived on...

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  6. Life is a random walk on a cycle

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  7. 1. What is the starting vertex?
    2. What is the kolmogorov complexity of this graph?

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  8. Phillip Pullman's trilogy His Dark Materials is an extended commentary upon this topic.

    Spoiler ahead: late in the third book, it is revealed that Jehovah is the bad guy, and Markov (in the role of "dust") is the good guy!

    The phrase "his dark materials" is from Milton:

    … Into this wilde Abyss,
    The Womb of nature and perhaps her Grave,
    Of neither Sea, nor Shore, nor Air, nor Fire,
    But all these in thir pregnant causes mix't
    Confus'dly, and which thus must ever fight,
    Unless th' Almighty Maker them ordain
    His dark materials to create more Worlds,
    Into this wilde Abyss the warie fiend
    Stood on the brink of Hell and look'd a while,
    Pondering his Voyage...

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  9. Phillip Pullman's trilogy His Dark Materials is an extended allegory upon this topic.

    Spoiler ahead: late in the third book, it is revealed that Jehovah is the bad guy, and Markov (in the allegorical role of "dust") is the good guy!

    The phrase "his dark materials" is from Milton:

    … Into this wilde Abyss,
    The Womb of nature and perhaps her Grave,
    Of neither Sea, nor Shore, nor Air, nor Fire,
    But all these in thir pregnant causes mix't
    Confus'dly, and which thus must ever fight,
    Unless th' Almighty Maker them ordain
    His dark materials to create more Worlds,
    Into this wilde Abyss the warie fiend
    Stood on the brink of Hell and look'd a while,
    Pondering his Voyage...

    ReplyDelete
  10. Gosh-golly, I'll keep this thread going, `cuz the topic IMHO is both interesting and important. Just as Wigner inquired as to the "the unreasonable efficacy of mathematics in explaining the physical world", isn't it equally interesting to inquire as to "the unreasonable efficacy of poetry in motivating mathematics"?

    To quote Milton again (from Book Two of Paradise Lost):

    ... Chaos Umpire sits,
    And by decision more imbroiles the fray
    By which he Reigns: next him high Arbiter
    Chance governs all. ...


    Crikey --- Milton's "Chaos by decision more imbroiles the fray" anticipates both Shannon's entropy measures and modern chaos theory pretty handily, doesn't it? In the year 1674 (!).

    To generalize Lance's question, why is there so much good mathematics in poetry? And what are your favorite examples? Now is the chance for all you Hunting of the Snark fans to start posting!

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  11. Just to chest-compress this cardiac-arrested topic one final time, IMHO a book in which several prominent mathematicians each discussed one poem, interpreting it in mathematical terms, would find many readers.

    Because isn't it true, that the associative structure of human cognition is such that a practiced ability to "see mathematics in poetry" would necessarily lead to improved ability to "see poetry in mathematics"?

    The latter skill, everyone believes is good!

    For example, here's an "easy" poetic fragment that applies broadly in mathematics:

    ------------

    Mending Wall
    Something there is that doesn't love a wall,
    That sends the frozen-ground-swell under it
    And spills the upper boulder in the sun,
    And make gaps even two can pass abreast.
    ...
    Before I built a wall I'd ask to know
    What I was walling in or walling out,
    And to whom I was like to give offense.


    -------
    Here's a somewhat harder one, from the Sung Dynasty, which Shing-Tung Yau especially commends to his students:

    Looking for her a thousand times
    In a crowd
    All of a sudden
    As I turned my head
    There she was
    Standing in the shades of fading lights

    ReplyDelete