Prev: six counterexamples to the Goldbach Conjecture and one for FLT #212; 2nd ed; Correcting Math
Next:  Roman Abramovich's M/Y Eclipse; John Fredriksen, the ship·builder.
From: Archimedes Plutonium on 14 Oct 2009 02:32
One parting comment about the Goldbach Conjecture, since I am on it at
this
moment and not terribly advancing on the Indirect NonExistence
research.

But in mathematics, it so often happens that we run a few examples
through
our minds and come to a statement such as "hard to imagine Goldbach
Conjecture
not being true". Or we run through some examples of FLT and similarly
saying hard to imagine it being false. But this is the problem of
mathematics
that has only a BackView of the numbers it wants to talk about or in
the case
of the Reals where it has only the FrontView of each Real and never
the BackView.

In the case of Goldbach Conjecture, no honest and sincere
mathematician ever
raised these doubts. That if the primes become thinner and thinner and
rare and more
rare the higher you go in the numbers. Here I am not talking about
10^10^10^10 or
such staircases of exponents for that is a tiny number compared to say
the number
2000....000000 or 4444....444444, not to mention numbers like
99999....99999.

So in the history of mathematics where all those minds focused on
Goldbach Conjecture,
that none seemed to have had these thoughts:

1) if the Counting Numbers go from 0 to 1 to 2 to all the way up to
999...9999
2) if the Primes thin out as the Prime Number Theorem x/Ln(x)

Then given those two facts that we can accept, then it is very hard
and extremely
difficult to see how every even number is the sum of two primes.

If the Prime Number Theorem is true and the Counting Numbers go from 0
to
9999....99999 then there maybe a infinite-substring of all composites
say from
about 97......97 to 9999....99999 there were no more primes. Under
such a
rarefied thinning out where there is an infinite sequence of nothing
but composites
it is extremely difficult to see how a Goldbach Conjecture could ever
hold up under
that sort of stress and strain.

To be sure, there are an infinitude of primes but given an interval
that is infinitely
long of composites, and since the primes thin out, then the Goldbach
Conjecture,
on an honest appraisal should be seen as false.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
 | 
Pages: 1
Prev: six counterexamples to the Goldbach Conjecture and one for FLT #212; 2nd ed; Correcting Math
Next:  Roman Abramovich's M/Y Eclipse; John Fredriksen, the ship·builder.