Cook's New Electrogravity Theory

The NET 01

Note: you do not need to understand anything on this page in order to understand the NET. Breath easy! You do not even need to know how to add 2+2 to understand what will follow. The math on this page is for mathematical minds only who pretty much despise reading dialog, preferring only to see the numbers. 'Kay? Got it? Let's go!

When looking to name a constant with some significance mathematicians often like to asign them Greek symbols--'cause Greek symbols simply look cool. But there is one number so intriguing in the history of art, science and mathematics that it was given the nickname, "the golden number," representative of the precious metal gold of course. The number itself is: 1.61803 39887 49894..., and it can be calculated with precision using the following equation:

Ah, beauty!

But what about ugly numbers with significance? What about those numbers? Can a material be assigned to such a number that still pays it respect?

Mr. Cook chose the metal tin for just such a number. Tin is not a particularly strong metal, inexpensive and not revered by jewelers in the least. Yet, when alloyed with others metals, copper for one, the alloy (bronze) gains strength greater than the sum of its constituents. Such is the nature of tin that Cook compared this property to a value of perceived significance, as this number, while indeed not entirely pretty in the traditional sense of number-beauty, has a peculiar way of "bonding" with other more precious numbers. Indeed, it may very well be that this lone ugly number bonds all numbers in ways that no other may be able to do.

Would that be a stretch? Can one even say this about a number, to "bond" other numbers? Mathematicians wouldn't choose such wording, would they?

Let's see. Here is the value being discussed:

Where phi is the "golden number," pi is the value 3.141592... and e is the base of natural logarithms equal to 2.718281....

Well, it's ugly alright, but so what? Cook just threw a few fancy constants into an equation and called it, "tin?" And that's significant how?

But it's not like that at all. This value actually began popping up all over the place in Mr. Cook's New Electrogravity Theory, particularly in his work with X-Waves and singularities and it took some quality time to finally find the elementary means above to calculate it.

For starters, observe the following:

Where the variable p are all the prime numbers > 3 to infinity raised to the negative power of 10.

The resulting value of this function can be referred to simply as chi, which is not only irrational and not only transcendental, but also a Liouville number; the nth digit after the decimal point is 1 where all the primes are factorials, the factorials of non-negative Integers n, denoted n! and are the products of all positive Integers < or = n.

This can be proven by the following:

And the above is at least true for n = 5, the first of our primes > 3, p = q < 2n > 1. Which means, if p = 2 and q = 2 and n = 5, the absolute value of (iv) < 1 / q^n. And it is also at least true when p and q are equals greater than 1 and less than 2n.

So is the Tin Number irrational, transcendental or a Liouville number, as it is not shown above how either of the two are connected, "bonded?"

It is currently unknown. Mr. Cook's best guess is that the Tin Number is likely irrational, possibly transcendental, but not likely a Liouville number.

What is more important for the NET is the following:

Where n in the chi function is a prime of a given magnitude x that takes chi (p) through all the primes up to n, providing a value for q (x), which is a mixed rational fraction when x is a positive Integer. Thus, given the prime number 31, x = 9, as 31 is the 9th prime > 3, where n = 31. And the value of q (x) when n = 31 and x = 9 is 1000 + ( 1010 / 10000 ).

And this next function will also need to be brought forward before anything else can properly follow:

Which, when taking all of the negative Integers beginning with -1 to negative infinity (the NET and Mr. Cook are only particularly interested at this time with negative Integer values of x), the function looks like this when you multiply all results by -1:

Graph of the F Function * -1

Where the first value of F (x) * -1 = pi.

And now we can begin to tie this initial discussion up with this:

Where q (x) is from (v), theta is the Tin Number, chi is Cook's Liouville number from (iii) and di is any Imaginary number one so chooses to apply to the function.

Please note the raised 5 above and then refer back to the Sqrt {5} in the Golden Number, as this will be your only slight hint that something mathematically significant will be presented in the NET that has never before been recognized before with incredibly beautiful implications--which can be proven up and down and every which way west. In fact, as you read through the following pages, you will know something wonderful is just over the horizon when you see another raised 5 in Quantum equations. At that point you will be able to say to yourself, "I see it coming."

In the meantime, for at least all positive values of x, the following is true.

Please note also that the above (viii) provides a Real result for all Real values of x even though it is a Complex function, which simply means that the Imaginary part of the solution always = 0 for a Real x.

So what, again Mr. Cook is simply throwing a handful of seemingly significant (significant at least to him) functions together to make something look "bonded."

It's not like that. Here's Cook's conjecture regarding this.

The following:

Where chi is Cook's Liouville number from (iii), G (Re) is the Real part of G (x) and pi is the value equal to 3.141592...,

1. Is only true for Imaginary values di when x = -1

Or,

2. When di = Imaginary alpha (the Fine Structure Constant times i ) where x does not equal -1 and di equals the Imaginary part of theta * 10^x / G (x).

And that's that.

What the heck is that supposed to mean?

Here, if x = -1, then d in di can be any value and the result of F (x) will always = -pi, in the similar manner that anything divided by one equals itself. It's related to the notion of the primes that a prime is only divisible by 1 or itself--at least as far as Integers are concerned.

What's significant in this is that those two functions F (x) & G (x) only join up, at least in accordance with the conjecture, in two seemingly separate circumstances: 1) when x = -1, where d can be any value under the sun and 2), when d = alpha (AKA, the Fine Structure Constant), where x need not equal -1.

In other words, there is another value of x that makes (ix) true when d = alpha than -1, and this only occurs when d = alpha. Additionally, this value of x is a constant that Mr. Cook calls, for lack of a better Greek letter, kappa.

kappa = -0.04531444644...

Which can be indeed be calculated by the fact that (ix) is true when d = alpha, which I will not show right here and now, as it's...well, it's hard. Actually, such a proof is not necessary at all for the NET and therefore not a real priority.

Furthermore, using x = -1 and x = kappa gives different results entirely, as could be assumed, for the value of F (x). F (kappa, alpha) does not equal -pi, as it does with F (-1). While yes, (ix) is true (and only true in accordance with the conjecture) when x = kappa and d = alpha, F (x) instead results in the following:

F (kappa-alpha) = -4.14154949...

Can this conjecture be summed up at all?

Easy.

Cook's conjecture: di equals the Imaginary part of theta * 10^x / G (x) only when d = +/- alpha.

And even if this conjecture turns out to be wrong, particularly the word "only" above, the fact still remains that it is indeed true when d = alpha, only or not.

What is much more important to recognize in this is that for the above to be true, n in chi (n), and thus q (x) must equal the infinite prime number. This means that alpha takes all prime numbers from 5 to infinity through chi (p), where no other number does.

What is absolutely certain, and straightforwardly solved for, whether the conjecture is true or not is that the following is true:

Where the Imaginary part of the result equals an Imaginary Fine Structure Constant.

This is significant for Cook's New Electrogravity Theory, but not until some 100 or so equations are presented. Then all this will tie in well enough to not only proven laws of Physics, but also some basic elementary geometric principles, as well as Fibonacci sequences.