Re: Quantum Gravity 291.97: The Numbers 3, 4, 5 of the Probable Causation/Influence (PI) Set Turn Out to Be Key in Tree Number Theory



OsherD skrev:
From Osher Doctorow

H, Lee Price, who has 2 or 3 papers in arXiv (I can't find his
affiliations), in his new paper "The Pythagorean tree: a new species,"
arXiv: 0809.4324 v1 [math.NT] 25 Sep 2008, 14 pages, shows that the
numbers 2, 3, 5 are key in the Number Theory of Pythagorean Trees and
Fibonacci Boxes.

Since most physicists will probably not go that deeply into
mathematical Number Theory on any particular day, I will just say that
the proof of Price's main Proposition 1 is somewhat in the direction
of difficulty of Fermat's Last Theorem (though much simpler than the
latter), which even to most mathematicians is very, very difficult.

The interesting thing (arguably at least) to me is that the PI
(Probable Causation/Influence) Set:

1) {0, 1, 2, 3, 4, 5, 7, 10, 11, 13, 26}


How do you derive this set from Probable Influence/Causation:

P(A---->B) = 1+P(AB)-P(A)

??

has 2, 3, 5 as the first primes and they are a substantial part of the
PI Set.

There is some history associated with Price's paper which is rather
remarkable. The Pythagorean Triple [a, b, c] are any triple of
positive integers that satisfy:

2) a^2 + b^2 = c^2

The Primitive Pythagorean Triple (PPT) is a Pythagorean Triple in
which all numbers a, b, c, are divided by their greatest common
divisor.

It turns out that an extensive list of PPTs was found on a cuneiform
table or tablet around 1800 B.C. They were rediscovered in 1963 by
B.C.E. Barning and then in 1970 by A. Hall, independently! These and
Fibonacci numbers play a key role in the paper.

Osher Doctorow
.