Re: About random, primes and statistics
- From: "john707070@xxxxxxxxx" <john707070@xxxxxxxxx>
- Date: Tue, 21 Aug 2007 15:33:34 EDT
Knowing that statistics is an area of mathematics
that physics
students get rather familiar with I thought it'd be
of interest to
explain a simple area where mathematicians routinely
lie--I think in
order to keep research grants.
First you need to learn a bit of number theory, as 7
mod 3 = 1, where
1 is the residue modulo 3, so the bit of math is that
shown x mod y,
you take x-ky where k is the largest positive integer
that will fit,
and use what's left over, which is the residue.
I picked 3 because there is a fascinatingly boring
thing about numbers
modulo 3--perfect regularity:
Starting at 1 and counting up you have
1, 2, 3 followed by 4, 5, 6 followed by 7, 8, 9 on
out to infinity
which modulo 3 gives
1, 2, 0 followed by 1, 2, 0 followed by 1, 2, 0
repeated on out to
infinity.
(It's like a perfect waltz to infinity!!!)
That is an absolute and I'd say a trivial one at that
but it will
challenge everything you think you know about
mathematicians as decent
researchers as you have primes and you have
composites and composites
are products of primes--kind of like their
children!--so if primes
tended to pick a particular residue modulo 3, then
composites would
follow along!
But they don't. They split evenly between 0, 1 and
2.
Therefore, I strongly suggest to you, primes split
evenly between
having a residue of 1 and 2 modulo 3.
If that is true then the residue of a prime other
than 3 modulo 3 will
be random.
Here is what you get with the first 23 primes greater
than 3:
5 mod 3 = 2, 7 mod 3 = 1, 11 mod 3 = 2, 13 mod 3 = 1,
17 mod 3 = 2,
19 mod 3 = 1, 23 mod 3 = 2, 29 mod 3 = 2, 31 mod 3 =
1, 37 mod 3 = 1,
41 mod 3 = 2, 43 mod 3 = 1, 47 mod 3 = 2, 53 mod 3 =
2, 59 mod 3 = 2,
61 mod 3 = 1, 67 mod 3 = 1, 71 mod 3 = 2, 73 mod 3 =
1, 79 mod 3 = 1,
83 mod 3 = 2, 89 mod 3 = 2, 97 mod 3 = 1
So the sequence is
2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2,
1, 1, 2, 2, 1
and I suggest to you it is random, like flipping a
coin, but better as
it is absolutely random.
Now then what if it were NOT random so that there was
some pattern in
there?
Well, composites are products of primes, so where
primes go, so do the
composites, so if primes tended to have say, a
residue of 1 modulo 3,
then so would composites, like 7*13 = 91 and 91 mod 3
= 1.
If there were some more hidden pattern, for instance,
when I've
brought this subject up before sci.math'ers would
claim that if 1
tends to be followed by 2 and 2 by 1 and they
produced statistical
tests claiming those proved that, then the sequence
is not random!
But if 1 tends to be followed by 2 and 2 by 1, how
would they push the
composites? Into what pattern?
Now then, let's leap forward and say you accept that
the rigidity of
the ordering of counting numbers, where you have
1, 2, 3 followed by 4, 5, 6 followed by 7, 8, 9 on
out to infinity
which modulo 3 gives
1, 2, 0 followed by 1, 2, 0 followed by 1, 2, 0
repeated on out to
infinity
convinces you that primes other than 3 modulo 3 give
a random
distribution, why should anyone care?
Well, random is useful in physics but more
intriguingly, if you accept
that then you end a lot of research paths in modern
mathematics!!!
Because if you push the argument to p_1 mod p_2,
where the p's are
differing primes, then it turns out some supposedly
big questions in
modern math, like the Twin Primes Conjecture are
easily answered!
But there are mathematicians getting federal funds
for research in
those areas, if random is the call then those funds
cease.
BUT if no one notices, those mathematicians can work
endlessly in an
area where they can never get an answer, at least not
a correct one.
That is a highlight of how you can find controversy
in the math field
in a simple area where you can run your own
statistical analysis to
see.
Oh yeah, and remember a while back the math awards
where one guy
famously refused to accept his, while the others did
accept?
Well, if primes are random then one of those people
won a prize for
supposedly innovative research into an area where no
pattern actually
lies.
Maybe you believe I'm wrong and there is some hidden
pattern in primes
modulo 3, or more technically
p mod 3
with p not equal to 3, as you go out to positive
infinity.
I've given the beginning of the sequence:
2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2,
1, 1, 2, 2, 1
where the start was the number 2 which has itself as
a residue modulo
3.
In answering my bringing this issue up before posters
on sci.math
claimed that this area has been checked and that
statistical analysis
proved non-randomness but there is no why here given.
Why would primes care? Especially when their
products, the composites
can't swing one way with the primes swinging another?
I suggest to you that math people lie in this area,
where you can do
the statistical analysis yourself to see that they
lie, or I'm wrong.
I've been wrong before, but I don't think I'm wrong
here.
I know people lie. And I know some of you in the
physics field who
like to play with statistics can crank up some
machinery and play with
primes to see for yourself.
Remember, BIG research grants are wrapped up in this
where some
mathematicians have worked in this area for decades,
so their entire
livelihoods are about it NOT being true that p mod 3
is random.
Their entire LIVES are about that not being true, so
they are totally
invested.
James Harris
There is a controversial person on this forum who has factored both primes and composites mod primes.
What you have said is already known to him.
If i say "not popular" "cantor critic" and "factoring tricks" you should know who i mean.
He is "the One".
No offense but he is way ahead of you.
He already pointed this out months ago.
Even told you to look at his factoring tricks.
And he also has pointed out lies of the math community.
Not based on ignorance but economics (fundings) and media (hyping cantor e.g.).
I dont want to compare you both to much.
But this post clearly makes that indication.
However he accepts the "order" of Riemann into the primes.
Im not sure if you accept Riemann as a great mathematician or accept RH.
He does.
Consider him.
Consider "The One"
john
.
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