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Re: [PrimeNumbers] Distributed as regularly as possible

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  • Shi Huang
    ... It is in fact a tautology to define primes by the way you find them. Whatever you find by the Sieve is prime. If the Sieve way is regular, then prime is
    Message 1 of 7 , Feb 7, 2007
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      --- "Werner D. Sand" <Theo.3.1415@...> wrote:

      > Demonstration of the statement "the prime numbers
      > are distributed as
      > regularly as possible":
      >
      > Regula 1: All numbers > 1 are prime.
      > Try: 2,3,4 oops, 4 is not prime. 4 is equal, hence
      >
      > Regula 2: All numbers >1 which are not multiple of 2
      > are prime.
      > Try: 2,3,5,7,9 oops, 9 is not prime. 9 is multiple
      > of 3, hence
      >
      > Regula 3: All numbers >1 which are not multiple of 2
      > or 3 are prime.
      > Try: 2,3,5,7,11,13,17,19,23,25 oops, 25 is not
      > prime. 25 is multiple
      > of 5, hence
      >
      > Regula 4: All numbers >1 which are not multiple of 2
      > or 3 or 5 are
      > prime.
      > Try: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49
      > oops
      >
      > and so on. The regulas become more and more exact.
      > The prime numbers
      > are distributed "as regularly as possible".
      > It's simply the Sieve of Eratosthenes.
      >
      > Werner
      >

      It is in fact a tautology to define primes by the way
      you find them. Whatever you find by the Sieve is
      prime. If the Sieve way is regular, then prime is of
      course regular. but it is a tautology. The fact that
      the Sieve is regular cannot prove itself to be
      regular. If regularity is already defined in to
      primes, that same regularity cannot be used to prove
      that prime is regular. the same kind of regularitys
      cannot prove the same regularity. If prime is defined
      by regularity or the regular way of finding primes,
      those way of finding primes cannot be used to prove
      that primes are regular. What needs to be done is to
      define primes by a kind of regularity that can then be
      used to prove another kind of prime regularity.
      Regularity A proves regularity B (B could be the sieve
      or the non-divisibility). But regularity B cannot
      prove itself. If prime is defined by regularity B,
      then B cannot be used to prove prime regularity. It
      is to use B to prove B, a tautology. You have to use
      A to prove B. To prove prime is regular is to prove
      that the essence of prime is regular. From that
      regular essence, we deduce other manifest regularities
      such as the Sieve or the non-divisibility. But the
      regularity manifestation of a prime does not
      necessarily mean or prove that the essence of prime is
      regular. The essence could be random but still
      produce a manifestation of regularity. The manifest
      regularity of nature does not prove that the essence
      of the universe, the quanta, are regular. In fact,
      many believe that the regularity nature is caused by a
      random essence. Thus, the regularity of primes (the
      sieve or non-divisibility) could be caused by a random
      essence and does not prove that prime has the true
      property of being as regular as possible.


      To prove or explain the hardness and rareness
      properties of diamonds, one must start from its
      essence carbon and its way of creation. To explain
      matter, one must start with its essence quantum
      particles and its way of creation. To prove or
      explain the regularity of a non-prime number, one must
      start from its essence which is the prime number and
      its way of creation.

      To prove or explain the regularity of primes, one also
      must or may have to start from its essence and its way
      of creation. What is the essence is unknown at
      present, which is most likely the reason why the RH
      cannot be proven. Non-divisibility is not the essence
      of primes, just like divisibility is not the essence
      of non-primes (the essence of non-prime is the prime).
      Essence here simply means the building block. If the
      essence of non-prime is the prime, it is only fair and
      logical to go down the hierarchy to ask what is the
      essence of prime. That essence logically cannot be a
      number since prime number is the lowest level a number
      can be.

      Assuming we know the essence of prime, we can imagine
      two ways to create a prime. A random way of
      manipulating the essence or a non-random and highly
      regular way. It is of course possible with near zero
      probability for the random way to create a population
      of primes that would show regular pattern. But it is
      far more likely that the random way will not produce
      any regular pattern of primes. On the other hand, the
      non-random and regular way of creating primes would
      exclude any irregularity as a viable outcome. It
      would demand or predict that primes are distributed as
      regular as possible. In this case, the RH would be a
      logical deduction of the prime essence and its lawful
      way of creation, just like hardness and rareness of a
      diamond is a logical deduction of the carbon essence
      and its way of creation. What canbe logically
      deducted from an essence or axiom must be true. To
      prove something is to deduce it from some basic truth,
      essence, or axioms. To prove that human is made by
      God using quantum particles is to deduce humans from
      the particles essence and God in a step by step and
      lawful way. Without knowing the law of God or the way
      of creation using particles, we can never prove or
      disprove the hypothesis that God created humans.
      Analagously, without knowing the way of creating
      primes from its essence, we can never prove or
      disprove the hypothesis that prime is created in a way
      that is as regular as possible, which automatically
      predicts the RH.

      The regularity of primes is what we observe. The
      regularity includes many forms, such as
      non-divisibility, prime number theorem, and the RH.
      But it leaves open the question of what causes the
      regularity, is it randomly caused or not. To prove
      the RH means we can exclude any randomness in primes
      including their causes. If the RH is true, the cause
      for the regularity of prime cannot be random. The
      phyical universe provides a good analagy. The
      regularity and lawfulness of matter above the quantum
      level is what scientists observe and is why scientists
      have a job. The regularity includes many forms, such
      as the various physics laws and the fact that life is
      built by DNA. But it leaves open the question of what
      causes the regularity, is it randomly caused or not.
      Scientists believe, without any proof, that it is
      randomly caused because of lucky accidents. Religions
      say it is caused by God. The position of science can
      never be proven since randomness can cause many
      outcomes, including randomness itself and the near
      zero probability event of regularity. Since both
      randomness and regularity can be logically deduced
      from a random cause, neither is a certainty and
      neither can be proven by invoking a random cause. But
      the God position has a chance to be proven true. If
      we give God a creation law and that law predicts only
      one outcome which is regularity, then we would have
      proven that the regularity of nature is caused in a
      non-random way which is a way of law that predicts
      only one specific outcome of regularity. To prove
      that an outcome is caused by the essence is to show
      that all other outcomes are non-viable. The random
      position cannot exclude randomness as a viable outcome
      and cannot therefore prove that the regularity outcome
      is caused by the random essence.

      So to prove the RH, we need a creation law for the
      primes that predicts only one outcome regularity.
      Irregularity is not allowed by that law and is not a
      viable outcome. By finding that law, we prove that
      the cause for the regularity of primes is not random.
      If the cause is not random, then there is no chance
      for the primes to display any aspects of randomness,
      which is the same as saying that primes are as regular
      as possible, which thus proves the RH.

      So it is my assertion that the only way to prove the
      RH is to find the essence of primes and the law of
      creation. It is comparable to prove the hypothessis
      that the regularity of nature is caused by God and his
      law rather than randomness. But the only way to prove
      God is to find his law of creation using particles.
      Until one finds a creation law that uses
      essence/particles to create primes/nature, one can
      always say that the regularity of primes/nature is
      caused by chance, no matter how small a chance. One
      can never say that primes/nature are as regular as
      possible or as non-random as possible. If a thing is
      caused randomly, it surely cannot qualify as the most
      regular possible or as regular as possible, because
      another equivalent thing that is caused non-randomly
      would have more regular properties and would better
      qualify as the most regular possible.

      To say primes are as regular as possible means
      everything about primes, including its way of
      creation, are non-random. The RH makes a big claim
      that is inherently or in principle unprovable by
      anything that deals only with behaviors of primes.
      The RH does not deal with how prime is created from
      its essence. Thus, even if proven true, it cannot
      support its claim that primes are as regular as
      possible. The RH is logically in capable of proving
      its own claim. This is perhaps the reason why it
      remains unprovable. Its claim is bigger than it can
      possbily deliever. It simply cannot deliver its
      claim. Proving the RH will not prove its big claim,
      which is the same as saying proving the RH will not
      prove the RH. The claim of RH is logically in capable
      of being proven by proving the RH. The RH is simply
      unprovable from its own perspective. Its claim has to
      be proven from another perspective.

      To use an analagy. The laws of physics above the
      quantum level says that nature is as regular as it can
      be, limited only by the random noise of atoms. But
      such a claim imply that the cause of nature is also
      regular, since a nature that is regularly caused would
      be more regular than a nature that is randomly caused.
      Proving the laws of nature that describe behaviors of
      nature cannot prove that nature is caused/created
      non-randomly. So they can never justify the claim
      that nature is as regular as possible. The claim can
      only be proven or justified from finding the
      non-random law that is used to create nature.

      So, if the RH really claims, in layman terms as the
      Wikepedia says, that primes are as regular as
      possible, proving RH will not justify the claim. This
      simply means that the RH is inherently unprovable from
      the same level of thinking that leads to the RH. It
      means that the RH cannot be proved by any number
      theory. It can only be proven by finding the essence
      of primes and by finding the non-random law of prime
      creation. To prove the RH is the same as to prove
      that the regularity of nature is caused by a
      non-random creation law and a law giver. In this
      sense, it is the same as to prove God. This is the
      reason for the RH to be regarded as the most
      fundamental problem of mankind. It is interesting
      that another equally fundamental problem with
      relevance to God, the Darwinian theory of evolution,
      came out the same year as the RH in 1859. Darwinists
      are people who look at the primes and say that they
      are caused randomly. The RH implies that everything
      about primes, including its essence and its way of
      creation, is not random. To prove the RH is to
      disprove Darwinism and is to prove God. The two
      opposite theories have the same birthday and most
      likely will have the same judgement day, which
      hopefully will be very soon.

      Shi



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    • Werner D. Sand
      Hello Shi, I do not define the primes by the E-Sieve, they are defined as they are. The Sieve is only a method to develop them. I don t prove a regularity of
      Message 2 of 7 , Feb 8, 2007
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        Hello Shi,

        I do not define the primes by the E-Sieve, they are defined as they
        are. The Sieve is only a method to develop them. I don't prove a
        regularity of the primes by a regularity of the Sieve, but I show
        that the Sieve IS a regularity and thus the primes follow this
        regularity. A regularity is not necessarily a formula like f(n) but
        may also be a calculation instruction like Euclid's algorithm or the
        Fibonacci numbers or the prime numbers. The prime numbers are a
        natural constant just as pi or e or sqrt(2). You cannot predict the
        678th digit of pi, but pi/4 = 1 - 1/3 + 1/5 - 1/7 +… Random or not?
        Do you call sqrt(2) random because you cannot predict the 101th
        digit? Probably you say "sqrt(2) is as it is". And such are the
        primes.

        Tell me something about the "essence" of mathematical constants: are
        they "God"? Are they "Tao"? Are they "Nothing"?

        Werner





        --- In primenumbers@yahoogroups.com, "Werner D. Sand"
        <Theo.3.1415@...> wrote:
        >
        > Demonstration of the statement "the prime numbers are distributed
        as
        > regularly as possible":
        >
        > Regula 1: All numbers > 1 are prime.
        > Try: 2,3,4 oops, 4 is not prime. 4 is equal, hence
        >
        > Regula 2: All numbers >1 which are not multiple of 2 are prime.
        > Try: 2,3,5,7,9 oops, 9 is not prime. 9 is multiple of 3, hence
        >
        > Regula 3: All numbers >1 which are not multiple of 2 or 3 are prime.
        > Try: 2,3,5,7,11,13,17,19,23,25 oops, 25 is not prime. 25 is
        multiple
        > of 5, hence
        >
        > Regula 4: All numbers >1 which are not multiple of 2 or 3 or 5 are
        > prime.
        > Try: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49 oops
        >
        > and so on. The regulas become more and more exact. The prime
        numbers
        > are distributed "as regularly as possible".
        > It's simply the Sieve of Eratosthenes.
        >
        > Werner
        >
      • Shi Huang
        ... Werner, You certainly have no jusitification or proof to call primes mathematical constants. If everyone agrees that the essence of numbers or non-prime
        Message 3 of 7 , Feb 8, 2007
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          --- "Werner D. Sand" <Theo.3.1415@...> wrote:

          > Hello Shi,
          >
          > I do not define the primes by the E-Sieve, they are
          > defined as they
          > are. The Sieve is only a method to develop them. I
          > don't prove a
          > regularity of the primes by a regularity of the
          > Sieve, but I show
          > that the Sieve IS a regularity and thus the primes
          > follow this
          > regularity. A regularity is not necessarily a
          > formula like f(n) but
          > may also be a calculation instruction like Euclid's
          > algorithm or the
          > Fibonacci numbers or the prime numbers. The prime
          > numbers are a
          > natural constant just as pi or e or sqrt(2). You
          > cannot predict the
          > 678th digit of pi, but pi/4 = 1 - 1/3 + 1/5 - 1/7 +…
          > Random or not?
          > Do you call sqrt(2) random because you cannot
          > predict the 101th
          > digit? Probably you say "sqrt(2) is as it is". And
          > such are the
          > primes.
          >
          > Tell me something about the "essence" of
          > mathematical constants: are
          > they "God"? Are they "Tao"? Are they "Nothing"?
          >
          > Werner
          >

          Werner,
          You certainly have no jusitification or proof to call
          primes mathematical constants. If everyone agrees
          that the essence of numbers or non-prime numbers is
          the prime, then tell me what is the essence of prime?
          Dont tell me that prime has no essence. That simply
          shows that you dont know the answer.

          Just like from the essence of non-primes, we can prove
          or deduce that non-primes are always regular and
          predictable, we should be able to deduce or prove from
          the essence of primes whether primes are always
          regular but unpredictable. Whthout knowing the
          essence of primes, certain things can never be proven,
          such as the predictability or the RH. Without knowing
          the essence of diamond to be carbon, how can you be
          sure or prove that diamond cannot be rock made of
          silicon?

          Primes are touted as the building blocks or atoms of
          numbers. Well, you should ask what is the building
          block of primes, is it quantum particles? Isnt is odd
          that no one has a clue about such fundamental
          questions?

          Shi



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        • Werner D. Sand
          Shi, first of all: what do you mean by essence ? I love doing philosophy instead of mathematics, but I must know about what we are speaking. Maybe I tell you
          Message 4 of 7 , Feb 8, 2007
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            Shi,

            first of all: what do you mean by "essence"? I love doing philosophy
            instead of mathematics, but I must know about what we are speaking.
            Maybe I tell you that the "essence" of the primes are the primes. You
            didn't answer my question about pi or e or sqrt(2). What do you
            consider to be the essence of sqrt(2)? Sqrt(2) has a definition, but
            no essence. What difference is there between the prime numbers and
            pi or e? pi=3.1415926…, e=2.718281828…, p=2.35711131719… That's my
            justification to call the primes a natural or mathematical
            constant.You may as well call the set of the prime numbers
            P={2,3,5,7…} or each single prime number a constant.

            In a sense you can say the primes are the atoms of the numbers. Then
            you mean multiplication. In another sense you can call One the atom
            of the numbers. Then you mean addition. What do you think about
            the "essence" of One? Perhaps the "essence" of the prime numbers is
            the combination of addition and multiplication. If there is only
            either addition or multiplication, there are no prime numbers. If you
            have the number 2 and only multiplication, you get only numbers 2^k.
            If you have the number 1 and only addition, you don't know what
            division is. It is somewhat like Yin and Yang: each of them alone is
            nothing, both of them together are the reality. Is that a bit nearer
            to what you call "essence"?

            Werner
          • Adam
            snip ... I have heard and read that the primes are the building blocks of numbers and I don t appreciate that at all. I was going to say get that but that
            Message 5 of 7 , Feb 9, 2007
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              snip>

              > Primes are touted as the building blocks or atoms of
              > numbers. Well, you should ask what is the building
              > block of primes, is it quantum particles? Isnt is odd
              > that no one has a clue about such fundamental
              > questions?
              >
              > Shi

              I have heard and read that the primes are the building blocks of
              numbers and I don't appreciate that at all. I was going to say "get
              that" but that isn't true, I do get it, I just don't appreciate it
              well. "1" is the building block of numbers. If you build numbers
              from 1, you get a finitely generated abelian group with group
              operation addition. If you build the numbers multiliplicatively,
              then you get an infinitely generated monoid with no zero divisors
              ("cancellative monoid"?). I vote for the abelain group over the
              monoid. It is a stretch to even understand the monoid without
              addition-I have got this big multiplication table and I "happen" to
              observe certain entries that are minimums in the POSet ordered by
              divisibility. That is really stretching the layman's understanding
              of "number". I think it is even stretching the mathematician usual
              view of "number".

              Adam
            • Phil Carmody
              ... Has this thread not suffocated from the morass of ill- or un-defined terms yet? It certainly looks moribund. ... What do you mean by tautology here? ...
              Message 6 of 7 , Feb 10, 2007
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                --- Shi Huang <shuangtheman@...> wrote:
                > --- "Werner D. Sand" <Theo.3.1415@...> wrote:
                > > Demonstration of the statement "the prime numbers
                > > are distributed as
                > > regularly as possible":
                > >
                > > Regula 1: All numbers > 1 are prime.
                > > Try: 2,3,4 oops, 4 is not prime. 4 is equal, hence
                > >
                > > Regula 2: All numbers >1 which are not multiple of 2
                > > are prime.
                > > Try: 2,3,5,7,9 oops, 9 is not prime. 9 is multiple
                > > of 3, hence
                > >
                > > Regula 3: All numbers >1 which are not multiple of 2
                > > or 3 are prime.
                > > Try: 2,3,5,7,11,13,17,19,23,25 oops, 25 is not
                > > prime. 25 is multiple
                > > of 5, hence
                > >
                > > Regula 4: All numbers >1 which are not multiple of 2
                > > or 3 or 5 are
                > > prime.
                > > Try: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49
                > > oops
                > >
                > > and so on. The regulas become more and more exact.
                > > The prime numbers
                > > are distributed "as regularly as possible".
                > > It's simply the Sieve of Eratosthenes.
                > >
                > > Werner

                Has this thread not suffocated from the morass of ill- or un-defined terms yet?
                It certainly looks moribund.

                > It is in fact a tautology to define primes by the way
                > you find them.

                What do you mean by 'tautology' here?

                > Whatever you find by the Sieve is
                > prime. If the Sieve way is regular,

                What do you mean by 'regular' here?

                > then prime is of
                > course regular.

                What do you mean by 'regular' here?

                > but it is a tautology.

                grrrr.

                > The fact that
                > the Sieve is regular

                grrrr.

                > cannot prove itself to be
                > regular.

                What do you mean by a sieve 'proving itself to be [something]'?

                > If regularity is already defined in to
                > primes,

                grrrr.

                > that same regularity

                grrrr.

                > cannot be used to prove

                grrrr.

                > that prime is regular.

                grrrr.

                > the same kind of regularitys

                grrrr.

                > cannot prove

                grrrr.

                > the same regularity.

                grrrr.

                > If prime is defined
                > by regularity

                grrrr.

                > or the regular

                grrrr.

                > way of finding primes,
                > those way of finding primes cannot be used to prove
                > that primes are regular.

                grrrr.

                > What needs to be done is to
                > define primes by a kind of regularity

                grrrr.

                > that can then be
                > used to prove another kind of prime regularity.

                grrrr.

                > Regularity A proves regularity B (B could be the sieve
                > or the non-divisibility). But regularity B cannot
                > prove itself. [...]

                I give up.

                Make it stop, please!

                Phil


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