I Think I Just Broke a Glass into an Infinite Number of Pieces

Discussion in 'General Math' started by mimus, May 4, 2008.

  1. mimus

    mimus Guest

    At least, I swept up at least twice as much glass as could possibly have
    been in the original.

    And that's only possible if you do an infinite decomposition of the
    object, as exemplified by the Tarski-Banach ball.

    Maybe this is a sign I should mop my kitchen-floor.

    Will I need an infinite mop?

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13

    I wonder what I have been up to.

    < _Beyond Apollo_
     
    mimus, May 4, 2008
    #1
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  2. mimus

    Tim Weaver Guest

    Yes, if you have a mobius shaped floor.
    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 4, 2008
    #2
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  3. mimus

    mimus Guest

    Mobius strips are usually finite.

    Just unbounded.

    Neener.

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13

    "The math is easy," said Chaos.

    < _Thief of Time_
     
    mimus, May 4, 2008
    #3
  4. mimus

    Tim Weaver Guest

    By the time you get back to where you started, it's dirty again. Infinite
    mopping. Of course, you could try to find a mop that mops an infinite area
    in one go.
    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 5, 2008
    #4
  5. mimus

    Jim Langston Guest

    Yes, but then you'd need an infinite amount of water to mop the infinite
    amount of floor, and since an infinite amount of water would take up an
    infinite amount of space there'd be no room for the floor to begin with.
     
    Jim Langston, May 5, 2008
    #5
  6. mimus

    mimus Guest

    What if it was N-water and an N+1-floor?

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13

    Given a manifold M with a submanifold N, N can be knotted in M
    if there exists an embedding of N in M which is not isotopic to N.
    Traditional knots form the case where N = S1 and M = S3.

    < Deep wisdom from on high (Wikipedia)
     
    mimus, May 5, 2008
    #6
  7. mimus

    Tim Weaver Guest

    Mr. Jim Langston's argument is moot. He's basically complaining about elbow
    room.
    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 5, 2008
    #7
  8. Not if you use my special non-molecular zero viscosity high quality
    water. Put the xy plane horizontal and put a drop of this stuff on the
    origin and it just spreads and spreads. No point in the plane will
    remain un-wetted, whether or not that's a word.

    --Lynn
     
    [Mr.] Lynn Kurtz, May 5, 2008
    #8
  9. Only if you forget to take your shoes off.


    --
    Lorrill Buyens
    MHM: 9x1; Smeeter: #21; WSD: #3; Gutter Chix0r: #19
    Alcatroll Labs; Sex, Drugs and Rock 'n' Roll Division

    "dsysm, its sooooo smooth and clesr."
    - Dave Hillstrom's ringing endorsement of mead, in
    aav3f
     
    Lorrill Buyens, May 6, 2008
    #9
  10. mimus

    Tim Weaver Guest

    I mop naked.
    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 6, 2008
    #10
  11. Infinite amount of TMI, d00d.


    --
    Lorrill Buyens
    MHM: 9x1; Smeeter: #21; WSD: #3; Gutter Chix0r: #19
    Alcatroll Labs; Sex, Drugs and Rock 'n' Roll Division

    "dsysm, its sooooo smooth and clesr."
    - Dave Hillstrom's ringing endorsement of mead, in
    aav3f
     
    Lorrill Buyens, May 8, 2008
    #11
  12. mimus

    Tim Weaver Guest

    Yes, infinite. Correct.
    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 8, 2008
    #12
  13. mimus

    Aratzio Guest

    It is a metaphor.
     
    Aratzio, May 8, 2008
    #13
  14. mimus

    Peter Webb Guest

    Technical note: Mobius strips have a single boundary.

    (Are you the same mimus who also hangs around politics groups and deflates
    idiots?)
     
    Peter Webb, May 12, 2008
    #14
  15. mimus

    mimus Guest

    ok fine.

    (As soon as I read that, my head tried to encompass an unbounded Moebius
    strip and couldn't do it.)
    No, that's my evil twin.

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13
    It's the Peterson kid dressed as an iguana!

    < _Bloom County Babylon_
     
    mimus, May 12, 2008
    #15
  16. mimus

    Peter Webb Guest

    Well ...

    Imagine the width of the Mobius strip was infinite. You would then have a
    surface that was unbounded in both directions, finite in one direction and
    infinite in the other - sort of like a cylinder, but its not. Nor is it a
    Klein bottle or cross-cap. It can't be embedded in R^3 as it self
    intersects. But it is a reasonable interpretation of an "unbounded Mobius
    strip", whatever its real name is (if it has one).
     
    Peter Webb, May 12, 2008
    #16
  17. mimus

    mimus Guest

    <squint>

    A single-sided infinite plane or saddle or a single-sided sphere, is
    what it looks to me like what we're lookin' at, yes it does. Yes.

    I think Klein bottles cheat with that penetration business-- tearing is a
    no-no in algebraic topology, even though that's how you make a Moebius
    strip, and also in a sense how they work up the matricial representation
    of one, swapping connection-points or vertices in the matrix representing
    an ordinary strip or tube.

    http://www.kleinbottle.com

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13

    Given a manifold M with a submanifold N, N can be knotted in M
    if there exists an embedding of N in M which is not isotopic to N.
    Traditional knots form the case where N = S1 and M = S3.

    < Deep wisdom from on high (Wikipedia)
     
    mimus, May 12, 2008
    #17
  18. mimus

    Tim Weaver Guest

    Speaking of Klein bottles, Cliff Stoll gave an interesting talk last year at
    TED. He did eventually break out a Klein wine bottle.


    --
    Tim Weaver

    "Usenet is like a herd of performing elephants with diarrhea - massive,
    difficult to redirect, awe-inspiring, entertaining, and a source of mind-
    boggling amounts of excrement when you least expect it."

    - Gene Spafford, 1992
     
    Tim Weaver, May 12, 2008
    #18
  19. mimus

    mimus Guest

    I love his _The Cuckoo's Egg_, as agonizing as that epic was, not least
    for his new tennis-shoes at the time (nuked); someone on rasfw recently
    recommended _Silicon Snake-Oil_ as well.

    --


    smeeter 11 or maybe 12

    mp 10

    mhm 29x13

    Here is the World.

    < _Gravity's Rainbow_
     
    mimus, May 12, 2008
    #19
  20. <THWACK>

    --
    dave hillstrom mhm15x4 zrbj
    "i believe that the word "fuckhead" has become so wide spread and
    nearly meaningless as to qualify as a metavariable, similar to "foo"
    and "bar". and that it should uphold the responsibilities and enjoy
    the privileges of the new office. here here!!"
    -dave hillstrom
     
    dave hillstrom, May 12, 2008
    #20
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