The following is the preliminary result of about 15 years attempting to solve i. Lines 2-4 of the text should be read in vector notation (i.e. n, -n, 1, -1, N, the square root of 1, i, and, of course, =). It should be noted that this is only a prelim. result, and that advice is being sought in regards to the tremendous leap of logic in lines 5-6 of the text body:

The Stars Won’t Rust
© Denis Fitzpatrick, B.A., 1999-2004

Upon first observing Newton’s Third Law of Motion, one further notes:
n[A on B]N = -n[B on A]N
1[A on B]N = -1[B on A]N
Therefore, the square root of 1[A on B]N = the square root of -1[B on A]N
i.e. i[B on A]N = 1[A on B]N or -1[A on B]N
i.e. i = 1 or -1, O.T.E.
Therefore, i = -1 when 1 is taken as the square root of 1, and
i = 1 when -1 is taken as the square root of 1.
Thus, with Newton’s incidental help, the number plane has now been fundamentally balanced. This basic solution can also be expected to replace the fundamental core provided by the fine structure constant (alpha), which is now a variable. With basic, fundamental, and hardcore Universal balance established mathematically (the number plane is, after all, the essential core of the Universe) one can expect a Big Crunch to complement the Big Bang, etc., in an essentially benign, harmonious balance.
This solution not only basically balances the Universe, but allows for ‘Reality’ to continue emerging, in line with Complexity Theory, at a stable, constant and assured rate. After all, Its Core is in place (the balanced number plane), so now the System can relax, and continue to emerge while making stable quantum interconnections.
Finally, this novel solution implies that if every number is now within reach, then obviously every star is within reach, with persistence. Coupled with a variable alpha, this solution to i makes serious interstellar travel mathematically possible as well, and creates a new direction for Electrical Engineering.

> Finally, this novel solution implies that if every number is now within
> reach, then obviously every star is within reach, with persistence. Coupled
> with a variable alpha, this solution to i makes serious interstellar travel
> mathematically possible as well,


I am simply incapable of answering your post properly, however, I would like to comment on the snipped section:


I prefer Douglas Adams' math...

[snip]
It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not everyone is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the universe is said to be zero. From this it follows that the population of the whole Universe is also zero, and any people you meet from time to time are merely the products of a deranged imagination. ("The Restaurant at the End of the Universe" pg. 148)
[/snip]

Which leads me to believe that, mathematically speaking, I should just stick with my walk to the Deli. I'm forever amazed I can make it that far, with all them thar possibilities afloat, you can never be sure when the universe will decide that the probability of your existence (already below 100 or 1) will also = 0 and then find yourself going "poof" into some quantum haze just as you are about to pay the clerk for your coffee.

(yeah, I know there's a boo-boo in the Adams', but then it wouldn't "feel" so true!)

:)

The ratio of inhabited worlds to 'worlds' is probably like the ratio of number of real numbers compared to number of Integers.