Tau manifesto and the more general problem of notation optimization?

Discussion in 'Physics & Math' started by Secret, Sep 13, 2014.

  1. Secret Registered Senior Member

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    299
    So just today I accidentally came across this
    http://www.tauday.com/tau-manifesto

    After read through the entire article on why tau=2pi is more natural choice (note I did not agree what the author said that natural =true=correct, and you cannot really define something as correct provided it is not pseudomathematics, since they could all be correct if it matches what we know), I started to have a question

    Because in his article, he mentioend another guy who claimed pi/2 is more natural than 2pi and pi, as usual for my thinking style of like to generalise things with perfectionism

    Say if we have
    \(new \hspace{1mm} notation =n\times old \hspace{1mm}notation\)
    where n is a number
    ====================
    Questions:
    1. Is there exists an algorithm that can quantify the degree of simplication of a formula or expression of a new notation compared to an old notation?
    2. If 1 is true, then for the simplest case, is "counting the no. of specious factors of <insert number>" a good way to quantify the simplicity?

    tl:dr
    3. what is the commonly accepted standard of quantifying the simplicity of a formula of one convention vs another. In other words, how do we know in general that a formula is "simple and elegant?"?
     
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  3. Aqueous Id flat Earth skeptic Valued Senior Member

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    whoa that started getting really nutty. I bailed out when I realized how it goes on and on and on.

    That person is crazy, and not very good in math. It makes no difference whether you relate C to D or r. Math is a language, and we are free to move the words around to suit whatever we are trying to say. He seems to think the number 2π is magic, but it's not. It can be divided by 2! Everyone recognizes that π is a special number, but so are its multiples. And there is no great insight to be gleaned from 2π that is not already evident from π. If anything, the significance of π is that it represents half of a period and 2π represents a full period. He went into great detail trying to show how often 2π shows up in common formulas, but he failed mention that in part this stems from integrating over the full period. That was when I gave up. It all looks so pointless.
     
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  5. Aqueous Id flat Earth skeptic Valued Senior Member

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  7. Secret Registered Senior Member

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    So when given a notation, how do we quantify the degree of insight it can provide compared to another notation, so as to determine which notation is the more natural or convenient choice?
     
  8. exchemist Valued Senior Member

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    12,454
    We don't bother. Notation in the equations of science is that established by tradition and thus commanding a wide degree of understanding. It's the same in music: why do we have 5 lines on a stave and why do we have whole tones between some lines and spaces but semitones between others? Tradition, that's why. (In Gregorian chant, written with neumes, it is 4 lines).

    New notations are sometimes developed that greatly simplify expressions that would otherwise become long and repetitious, e.g. Dirac's bracket notation in QM, but such new notations only really take off when a lot of people find them helpful.

    In other words, it seems to me it is mixture of accident and qualitative collective judgement, rather than any kind of quantitative analysis.
     

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