Matrix exponential question

Discussion in 'The Cesspool' started by Vkothii, Oct 7, 2008.

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  1. Guest254 Valued Senior Member

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    If you could talk more about Borel measures, it has the potential to be even better!
     
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  3. rpenner Fully Wired Valued Senior Member

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    The problem with learning at the purely syntactic level is that small missteps lead to gross semantic errors and that different syntax is used by practically every author, especially in different fields.

    I just finished Anathem by Neal Stephenson, which is the subject of an xkcd strip. The novel has some fun, and has some elements of math as magic which was explored in Rudy Rucker's Mathematicians in Love (likewise classified as "Science Fiction"). But it does has a great deal of made-up words for this world of monastic avout and includes a glossary. (Because, and this is a point, the connection between words and their meanings are flexible, context-sensitive, and vary between authors.)

    For your amusement:
     
    Last edited: Oct 17, 2008
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  5. Vkothii Banned Banned

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    The probability of getting someone who is convinced everything is a mathematical abstraction, to talk about measurement or measure theory, isn't what I want to find out.
    I'm already reasonably convinced that someone who can't distinguish between a mathematical representation and real information content won't be able to give any real advice. Because they think real means mathematically precise and consistent.

    Borel's measure is currently of interest in some areas of QIS. All I've done is THINK, about how the symbols \( \mu, B \) can REPRESENT other things. How \( \mu \) is also a measure, how \( B \) can mean a basis, a real physical basis for a measurement. Then discovering that B is the first letter of some dude's name, called Borel.

    And I forgot about how some math-wits like to have one foot nailed firmly to the floor.
     
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  7. Guest254 Valued Senior Member

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    You have, quite literally, no clue what measure theory entails, do you?
     
  8. Vkothii Banned Banned

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    I have no clue what you think it entails, no.

    So you're now going to tell me measure theory has nothing to do with measuring, right?
     
  9. Guest254 Valued Senior Member

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    Have you even tried to google "measure theory"? Come on, you must have done at least that much.
     
  10. Vkothii Banned Banned

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    Have you?
    Please establish some facts. Do you have a hammer handy?
     
  11. Guest254 Valued Senior Member

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    I teach courses with measure theoretic content. My experience allows me to deduce you haven't got the first clue about measure theory.
     
  12. Vkothii Banned Banned

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    And my experience allows me to deduce you haven't got a second clue, about anything.

    You aren't very good at communicating, for example. You appear to believe a channel has only got one end.
    Since you teach theory, do you have a theory of what an information channel is?
    Perhaps we could start with the building blocks, and work our way up to the sandcastle part?

    While you try that, I can tell you how you're just guessing, you must have cheated, you know nothing, etc etc.

    Speaking of measure theory, do you know if quantum information has any "measure theoretical" aspects?
    You might be aware that classical measurement and quantum measurement are sort of "different"?

    If I posted some stuff from someone's Ph.D. thesis, about that very thing (i.e. quantum measurement), which appears to use a Borel measure. would that be "interesting"? "Algorithmic Information Theoretic Issues in Quantum Mechanics", a paper that uses Borel-Cantelli's Lemma, whatever the hell that is.

    You're going to laugh, but I have this idea the paper is about measuring something - usually that implies information and information has content, a representation, and a way of getting from somewhere to somewhere else. If it didn't it would not be information.
     
    Last edited: Oct 18, 2008
  13. rpenner Fully Wired Valued Senior Member

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  14. Vkothii Banned Banned

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    Let's hear(?!) the man.

    Does that paper nonetheless, use the thing or not (the B word)?
    Is this Ph.D. any good at math, surely our resident expert can point to the drastic blunders and totally false assumptions, in less than 5 minutes?
    Or this load of rubbish:
     
    Last edited: Oct 18, 2008
  15. Vkothii Banned Banned

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    So why would someone bother to apply a magnetic potential, how come an electron has a x-axis, where did it get it from?

    Sorry to get all pedantic on your ass, but if the context is complex Hilbert space (of which there are two obvious clues to, in the sentence), then it most certainly is valid. Any symbols are, as long as they're defined. 1 and 0 are the standard, and for the classical basis of measurement. OK then?

    I mean for FS, here's what the thing says:
    "The basis of three-bit strings 000, 001, ..., 111 is known as the computational basis, and is often convenient, but other bases of unit-length, orthogonal vectors can also be used."
    I ask about the dimensions of a complex space, you assume I'm talking about integers, WTF? It's almost getting desperate.

    It's complex dimensionally, it scales as the number of discrete states - wavefunctions. A classical circuit is a manifold that scales in complexity as the number of discrete 'operators' or 'functionals' on it increases. It has a single complex dimension, but evolves linearly in 3 [time] dimensions, right?
    So there's an algebra with dimensions of 'complex state index' - a C*-algebra or somesuch. I don't think I need to know about it beyond what sort of logic circuit you can build.
    Which is where things appear to part company with math-aware types here, because the view of a circuit is fundamentally different, and you have to understand how. not necessarily all about why - just how. It's about getting some insight without having to do postgrad math (as Mr Lloyd indicates - not a reqmn't).
     
    Last edited: Oct 18, 2008
  16. temur man of no words Registered Senior Member

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    OMG please stop
     
  17. Vkothii Banned Banned

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    Stop what FFS?
     
  18. Vkothii Banned Banned

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    Do you agree with this statement? Or is there something too abstract about it, perhaps, is that it? Can you point out the bleedingly obvious flaw for me?
    What's with a measurement basis? Is the reset-view a problem?
    What is the geometry or topology, and what transforms it? How do we push the right button?
    Uh huh, but guess what else? They do in practice too..
     
  19. Guest254 Valued Senior Member

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    And now he's moved onto \(C^*\)-algebras. Wonderful.
     
  20. AlphaNumeric Fully ionized Registered Senior Member

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    No, 1 and 0 are the symbols put within the bra or ket figures which are the standard ways of representing elements in quantum mechanical Hilbert spaces. You have to have the \(| \phantom{o}\rangle\) or \(\langle \phantom{o}|\) around the 0 and or 1 otherwise you don't know if it's a member of the Hilbert space V or its dual V*.
    If I had the time, the inclination and felt really vindictive I'd start rambling about \(\mathfrak{g}\) values 1-forms in G-bundles, liberally throwing in opinion/comments about Clifford algebras, Grassman algebras, Pink Floyd's seminal album 'Dark Side of the Moon' and why people really can't believe it's not butter.

    It'd be about as valid and coherent as Vkothii's posts after about page 3 of this thread.
     
  21. Guest254 Valued Senior Member

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    Ha!
     
  22. Saxion Banned Banned

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    Oh shut up, and let the boy do his work.
     
  23. Vkothii Banned Banned

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    You should do some work on this little detail, to start, young man.

    You have just made the totally false assumption, that 0 and 1 cannot represent Hilbert spaces.
    Of course they can, so you just failed that question.
    Any two symbols can, any two at all (you can make up your own). Assuming the 0 and 1 are always restricted to integers, is one great big incorrect assumption. Ha Ha.

    And tell that other f-wit to read up something about quantum measurement, find out what a Borel measure is.
     
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