"If they were truly random, primes ending in 1 would be followed by a prime ending in one 25% of this time, instead the mathematicians foundthis order occurred in only 18.5 per cent of cases.
"The chance of a prime ending in 1 being followed by a prime ending in 3 or 7 was about 30 per cent, and about 22 per cent for 9. "
This is all because of the false belief that numbers are somehow real objects. It is a basic issue in Philosophy. The "basic theorum of numbers" argues that every number must be either a prime or a unique product of factors. But this is a truism if you don't assume numbers somehow exist out there to be examined, but are mental constructs with no other ontology. Then we make up larger numbers by multiplying smaller numbers together, and the gaps where this does not produce a number to be slotted into the number line, are the Primes. They are the empty spaces between our constructed numbers, but become the substance of later numbers as they are inscluded as a factor.
It stems from a principle (I forget the name) perhaps attributable to Popper, that if there is a good Scientific Theory, then everything within it must be equally true and correct, and everything outside it is excluded as non-existent. The usual false conclusion from this is for Science to deny the existence of everything that is currently not covered by verifiable scientific theory. Another consequence is the conclusion that because all Science is couched in Mathematical terms, then as part of the valid theory, the mathematics must be valid, including the consequent ontologically "real" existence of numbers.
There are not an infinite quatity of numbers "out there" somewhere whether we know about them or not, like undiscoverd planets in distant galaxies, but this is not so. They come into existence when "observed" like Shroedinger's Cat, where the quantum probablity "breaks down" and an actual result is manifest when it is seen. The same happens with numbers. Science is still Platonic.
"Looking at prime numbers written in base
3 — in which roughly half the primes end in 1 and half end in 2 — he
found that among primes smaller than 1,000, a prime ending in 1 is more
than twice as likely to be followed by a prime ending in 2 than by
another prime ending in 1. Likewise, a prime ending in 2 prefers to be
followed a prime ending in 1."
Mathematicians Discover Prime Conspiracy | Quanta Magazine
Aparently discounted by mathematical theorists, the obvious reason is not because it is a property of the prime numbers themselves, but a consequnce of our cyclic numbering system, which in any base, repeats with the rhythm of the base-number. Numbers are like ripples into the distance, with a ripple for each prime number as it becomes a possible factor in future numbers. These ripples build on each other with bigger and bigger composite numbers, but occasionally there is a gap between the crests of the ripples where there is no ripple and there, in the gap is a prime. When we look at this sea of numbers, we use the torchlight of our numbering system, in base three or base ten, and this has an inbuilt pattern that causes an interference pattern with the ripples of numbers so that the primes show up in a pattern of distribution, as here idscovered. It is a kind of moire pattern.
No comments:
Post a Comment