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Math Help - Transitive vs. Substitution

  1. #16
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    Quote Originally Posted by ThePerfectHacker View Post
    They are all useful.
    Examples,
    1)Einstein found a way of describing space through "Differencial Geometry", a math topic which probably had no application until then.
    2)In Quantum Mechanics, Homotopy groups appear, another supprising application of pure math.
    3)Mathematical Logic can sometimes be applied to computer science.
    ...
    Now, if all these people had your approach and said, well, let me never use it. That will never had happened.

    As I said, the is a standard math, all mathematicians learn.

    You should first learn these different fields of math first before you can complain about them and say they are useless.
    And who uses "Differential Geometry"? "Homotopy"? <-----what is that.

    What about the Math we learn and use, that is not standard Math? It's sub-standard Math? Nope. The Math of your kind is like language only. It's use is only for your kind. Our Math is the, uh, "universal" Math. Everybody, including your kind (I think), understands and uses our kind of Math.

    Oh, I don't complain about your kind of Math as I don't complain about Greek, Chinese, Afghan languages.

    ----------------------------
    "1)Einstein found a way of describing space through "Differencial Geometry", a math topic which probably had no application until then."

    Whoa! Have you not said Einstein is not a Mathematician?
    Last edited by ThePerfectHacker; February 16th 2007 at 11:21 AM.
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  2. #17
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    Quote Originally Posted by ticbol View Post
    Have you not said Einstein is not a Mathematician?
    No Einstein was not a mathemation.

    The story was that Einstein had an idea about the curvature of space time. However, he was a physicist. The concepts of Differencial Geometry were beyond his mathematical skills to understand. Therefore, he got help from somebody that he was friendly with while still in college. It was Marcel Grossman. From what I read, Grossman taught Einstein the necessary math needed to create his spacetime theory. Even after Einstein had the necessary mathematical knowledge he still was not able to fully arrive at the conclusions. This time Einstein got help from somebody else (this time a physicist) who knew this topic well, Schwarzschild.
    Then after all of that, Einstein finally completely his theory. However, it was not "rigorous" enough and some people had trouble accepting it at first.
    Now, imagine, Einstein did study Diffferencial Geometry at a mathematical level, rather than on how to apply it, he would have been more succesful in doing his work, and perhaps, not requiring help from other people because his mathematical theory knowledge will assit him.

    ..... And much of the credit of course goes to one of my favorite mathemations, Riemann. Without him, Differencial Geometry would not exist, and the mathematics behind relativity will not exist. And Einstein would only have been famous for the photoelectric effect rather than relativity. Again, if Riemann had your approach, none of this would have happened.

    What about the Math we learn and use, that is not standard Math? It's sub-standard Math?
    Calculus, is not really used by mathemations. Of course, they know it, but they do not use it in the work that they do. They use an analouge called, Analysis.

    If it is the applications, that you care about then:
    Quote Originally Posted by Wikipedia
    Although much mathematics is not immediately useful, history has shown that eventually applications are found.
    .

    I have a sense, that you despise advacned mathematics is because you do not know it.
    Last edited by ThePerfectHacker; February 16th 2007 at 11:46 AM.
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  3. #18
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    Quote Originally Posted by ticbol View Post
    I am a mathematician, or I know Math too much. Not the way you know Math.
    Mine is useful or is based on reality. Not on dreams.

    Theorems? Definitions? Those are for you and your kind. I use any of those only if they are useful in real life.
    At least one working definition of a mathematician is someone
    who has proven a new theorem, or produced a new proof of an
    existing theorem.

    Under this definition if you have proven a theorem then you are a
    mathematician if not you are not.

    RonL
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  4. #19
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    Quote Originally Posted by ThePerfectHacker View Post
    No! But they are very well familar with the pure side as well. I was not saying there is something wrong with applying, I was saying that everyone who does math today is familar with the abstract concepts, they decipher them into applied problems. But! You do not have a quantum field physicist who is considered a mathemation.
    I think you might find that Paul Dirac was considered a mathematician, as
    is Roger Penrose.

    RonL
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  5. #20
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    Quote Originally Posted by ticbol View Post
    And who uses "Differential Geometry"?
    Physicists I think you will find.

    RonL
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  6. #21
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    Quote Originally Posted by CaptainBlank View Post
    Physicists I think you will find.
    But I am sure that they use the primitive type of Differencial geometry. Not the Graduate Math level. But anyway, I would love to buy a book on the simpler phsyics version of it, at least get to learn something but the time I start leaving DG it will be much easier.
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  7. #22
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    Quote Originally Posted by ThePerfectHacker View Post
    But I am sure that they use the primitive type of Differencial geometry. Not the Graduate Math level. But anyway, I would love to buy a book on the simpler phsyics version of it, at least get to learn something but the time I start leaving DG it will be much easier.
    If you believe that then I suggest you look up Weinberg's "Gravitation and Cosmology." Whereas it is definitely NOT a Math text, the level of the Differential Geometry is also NOT second class. (In fact, I get the distinct sense that he had to tone it down so that us mere Physics grad students could understand what he was talking about.)

    -Dan
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  8. #23
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    [QUOTE=ThePerfectHacker;39611]No Einstein was not a mathemation.

    Are you contradicting yourself? You cited Einstein as an example of "mathematicians" who founded "math something" that can be used. Then, again you said Einstein is not mathematician. Are you, uh, trying to bluff your way out of this trap?

    -------------------------
    Calculus, is not really used by mathemations. Of course, they know it, but they do not use it in the work that they do. They use an analouge called, Analysis.

    Yeah?
    This Forum exist. You believe that?
    In this Forum there are a lot of Calculus questions. You answered some of them.
    You consider yourself a "mathematician", so how do we see that?
    "You just answered Calculus questions, but you did not "use" Calculus."
    Or, " Your are not a mathematician because you are using Calculus in answering some questions here."

    Analyze those.

    ------------------------------------
    I have a sense, that you despise advacned mathematics is because you do not know it.

    I do not despise Advanced Math in the same way I do not despise Greek, Chinese, Afghan languages.
    Last edited by ticbol; February 16th 2007 at 09:31 PM.
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  9. #24
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    Quote Originally Posted by CaptainBlack View Post
    At least one working definition of a mathematician is someone
    who has proven a new theorem, or produced a new proof of an
    existing theorem.

    Under this definition if you have proven a theorem then you are a
    mathematician if not you are not.

    RonL
    Is that so? And who said that? Your kind of "mathematicians"?

    Biased?

    He-he-he.

    In some of the free IQ tests in the Internet, I was called a "mathematician" of some sorts after my answers were evaluated. I have not proven any theorem, so the group behind those IQ tests are lying?
    Zeez, that's a lame reasoning, okay, but, still there is sense to it because the people behind those IQ tests are supposed to be with Ph.D's in Math.
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  10. #25
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    Quote Originally Posted by CaptainBlack View Post
    Physicists I think you will find.

    RonL
    You only think that.
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  11. #26
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    Quote Originally Posted by ticbol View Post
    Is that so? And who said that? Your kind of "mathematicians"?

    Biased?

    He-he-he.
    Paul Erdös, for one:

    "A mathematician is a machine for turning coffee into theorems."

    It's not the definition used by professional societies, which in the UK
    appear to require a degree with substantial mathematical content, and
    an ongoing interest in Mathematics and/or Mathematics Education, as
    attested to by two or three referees of standing recognised by the
    society.

    In some of the free IQ tests in the Internet, I was called a "mathematician" of some sorts after my answers were evaluated. I have not proven any theorem, so the group behind those IQ tests are lying?
    or don't know what they are talking about, or are using language in a loose
    and informal manner.

    Zeez, that's a lame reasoning, okay, but, still there is sense to it because the people behind those IQ tests are supposed to be with Ph.D's in Math.
    I doubt may people "behind" IQ tests have PhD's in maths, but then that is my surmise
    which is no better informed that yours I suspect.

    RonL
    Last edited by CaptainBlack; February 17th 2007 at 12:05 AM.
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  12. #27
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    Quote Originally Posted by CaptainBlack View Post
    Paul Erdös, for one:

    "A mathematician is a machine for turning coffee into theorems."



    RonL
    Is Paul Erdos in your kind of "mathematicians/linguists" ?


    I doubt may people "behind" IQ tests have PhD's in maths, but then that is my surmise which is no better informed that yours I suspect.

    Well, go the web.tickle.com. If the PH.D thing there is not there anymore, there's something wrong with your computer.

    Oh, if you go there, maybe you may want to test your IQ too based on their, say, "The Classic IQ Test".

    Tickle.com is too "big" now. Not like before when they were still flashing it as pop-up on computers online. Anyway the "The Classic IQ Test" is now filed inside the "Popular Tests". Press the "see all" there, and look for the "The Classic IQ Test" inside the "PhD-Certified".
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  13. #28
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    Quote Originally Posted by ticbol View Post
    Is Paul Erdos in your kind of "mathematicians/linguists" ?


    I doubt may people "behind" IQ tests have PhD's in maths, but then that is my surmise which is no better informed that yours I suspect.

    Well, go the web.tickle.com. If the PH.D thing there is not there anymore, there's something wrong with your computer.

    Oh, if you go there, maybe you may want to test your IQ too based on their, say, "The Classic IQ Test".

    Tickle.com is too "big" now. Not like before when they were still flashing it as pop-up on computers online. Anyway the "The Classic IQ Test" is now filed inside the "Popular Tests". Press the "see all" there, and look for the "The Classic IQ Test" inside the "PhD-Certified".
    A PhD in Psychology is not the same thing as a PhD in Maths.

    RonL
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  14. #29
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    Quote Originally Posted by ticbol View Post
    Is Paul Erdos in your kind of "mathematicians/linguists" ?
    He is one of the most famous mathematicians of the last 100 years. Has has
    several biographies written about him in the few years since he died.

    And I don't know what you mean by my kind of mathematician. Like most
    mathematicians he solved interesting mathematical problems. Such solutions
    have been presented when possible in the form of proofs since at least the
    time of Euclid.

    RonL
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  15. #30
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    Quote Originally Posted by CaptainBlack View Post
    A PhD in Psychology is not the same thing as a PhD in Maths.

    RonL
    I see.
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