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Thread: Mod 9

  1. #1
    Harmonic Guest

    Mod 9

    If you get a moment, you may like to have a look at some research I have been working on. I would be pleased if you would share it with other intelligent people in your network, as you see fit.
    http://archive.org/details/IntroductionToNoCoincidence
    http://archive.org/details/PrimeNumbers_986
    http://archive.org/details/Music-Mod9
    http://archive.org/details/Fibonacci-Mod9
    Other papers also available by clicking on my name on any one of these document titles.
    All the best
    Anthony

    Quote Originally Posted by Craig.Paardekooper View Post
    An Experiment in Mapping Evolution Using Proteins

    Background - The Characteristics of Proteins


    1. Proteins are mostly of a small size - 300 aminoacids long +- 200
    2. They have clearly defined boundaries
    3. They have specific functional attributes
    4. They have the same properties across all life forms - the proteins of microbes or higher eukaryotes (animals and plants) have roughly the same properties

    The small size of protein sequences makes them easy to analyse and compare using computer software.


    Method

    1. We obtain a list of all the basic proteins
    2. For each protein, we gather it's sequence from several species
    3. We determine the degree of alignment between these sequences
    4. We form an evolutionary tree



    Hypothesis

    If species evolved by random mutation then the degree of variance between protein sequences should be proportional to the time between now and when one species branched off from the other.

    Therefore we should expect that the degree of variance is directly proportional to the order of evolutionary emergence.

    What is more, the DEGREE of variance should be approximately equal when comparing several DIFFERENT proteins across species.

    Finally, we would expect the ORDER of "emergence" to remain the same when comparing different proteins.


    The above experiment is a reasonable test to determine if evolution has taken place in the past.

  2. #2
    Join Date
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    Quote Originally Posted by Harmonic View Post
    If you get a moment, you may like to have a look at some research I have been working on. I would be pleased if you would share it with other intelligent people in your network, as you see fit.
    http://archive.org/details/IntroductionToNoCoincidence
    http://archive.org/details/PrimeNumbers_986
    http://archive.org/details/Music-Mod9
    http://archive.org/details/Fibonacci-Mod9
    Other papers also available by clicking on my name on any one of these document titles.
    All the best
    Anthony
    Hey there Anthony,

    Welcome to our forum!



    I looked at your analysis of prime numbers modulo 9 (the second link). You said:
    The first thing I did was to simply apply Mod 9 to the first 65000 Prime numbers, only to discover that the results exclusively returned 1 2 4 5 7 or 8 for numbers greater than or equal to 5. I could find this information nowhere else on the Internet.

    Please note that the 72 number sequence that I discovered in Music, being 6 octaves of 12, led me to arrange the numbers 1 to 72 and place them into 6 columns as laid out above. This layout quickly shows why prime numbers will exclusively return these remainder values infinitely because the Prime numbers only occur in Column 1 and Column 5 which simply repeat 7 4 1 and 5 2 8 respectively.
    That patterns you found are common knowledge and really quite trivial. There was no need to apply mod 9 to all those numbers because the result can be demonstrated quite easily for all numbers. The reason the primes mod 9 yield a residue in the set (1,2,4,5,7,8) is because no prime can be a multiple of 3 and 9 = 3 x 3. That's why 3, 6, and 9 are missing from the set of residues - the are not relatively prime to 9 whereas the other numbers are. Likewise, the reason the primes appear only in columns 1 and 5 when you list all natural numbers in six columns is because all primes greater than 3 are of the forum 6n +/- 1. This is because 6n + k is composite for k = (0,2,3,4) as should be obvious. Thus, they must be either in the first or the fifth column.

    Likewise, the reason you get a residue of (1,4,7) in the first column and (2,5,8) in the second is because the primes must also be of the form 3n +/- 1 since otherwise they'd be be multiples of three. Specifically: 1 = 0 + 1, 4 = 3 + 1, 7 = 6 + 1, and 2 = 3 - 1, 5 = 6 - 1, and 8 = 9 - 1. It's all elementary number theory.

    Mathematics can be a lot of fun, but the results can be quite misleading if you are not trained in the fundamental theory.

    All the best,

    Richard
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

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