Sometimes in life, you stumble across something that holds more meaning than first meets the eye. Meeting your future husband or wife for the first time and not realizing it is a good example. Mathematically, Dirac's equation is probably the most famous something. Dirac had the ability to visualize an equation in terms of geometry . Dirac came up with an equation that was more insightful than he first realized which you can look up in the Internet . Riemann's something was when it was realized that his zeta function said that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros of the zeta function . You and I can read the words but what is the meaning without repeating the sentence as an answer ????
Numbers basically break down into the following three areas:
- IrrationalRational Numbers have a beginning and an end. Examples of rational numbers are ( 1, 2, 3, 4 ) . Imaginary numbers are numbers such as the square root of ( - 1 ) ( √ -1 ) . Irrational numbers have a beginning but no end, and seem to go on forever. Examples of Irrational numbers are Pi, “e” or Euler's number . It suddenly occurred to me that when it was realized that Riemann's zeta function said that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros they were really talking about irrational numbers except that these irrational numbers were governed by zeros in the digits of the number . If you put all the prime numbers on a straight line and numbered them, you'd know their location on that straight line . Of course this is impossible . If Riemann's zeta function said that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros there is an implication that an irrational number controlled by the placement of zeros ( 0 ) in the digits when multiplied by the prime number would indicate the true position of the prime on that line and by extension all the primes that preceded it . If you multiply a number by an irrational number that has a beginning and no end you will soon see that you get different answers. Riemann also said that all his non-trivial zeros had a value of ( ½ ) which seems odd when you think about it . How can a zero have the value of ( ½ ) ???? Exercising our imagination, which seems to be as temporarily irrational as is our theme, it seems that every time a zero is on Riemann's line ( y = ½ ), it has the value of ½ . If you are also looking for a major brain freeze, you can also say that if all the primes are placed on the line ( y = ½ ) from 1 to infinity they also have the value of ( ½ ) . Weird as it may seem, we are busy finding non-trivial zeros on the line ( y = ½ ) that have a value of ( ½ ) because they are on the line ( y = ½ ) . Consequently, we now have primes and zeros on the line ( y = ½ ) which all have the value of ( y = ½ ) because they are on the line ( y = ½ ) . A prime is a number that can only be divided by itself and one ( 1 ). The position of the primes from ( 1 to 31 ) can be calculated by multiplying the primes ( 1 to 31 ) by ( .509999999 ^ 1). From ( 37 to 97 ) the primes can be multiplied by ( .509999999 ^ 2 ) to keep the calculated distance close to the actual distance. This is how it works in principle by manipulating zeros ( 0 ) and the addition or subtraction of two irrational numbers Pi and “e” .