If you're having math problems, I feel bad for you, son...

[napoleon_in_rags]

34. You're awesome Tama.

I hope you know that. I've been really busy lately, but that and linked to document has been occupying my mind since I read it, like a week ago. I chose my set number as I did because it has the same amount of information as the entire set. I've been looking a lot at information theory, how it could possibly be a foundation for math. Really sort of rolling my own math, and having a lot of fun with it.

One thing about the math I'm making is every mathematical concept is tied to the amount information needed to express it. Infinite objects, like e and numbers that go on forever, exist as measurable potentials, with every measurement made on them as finite, though you make more and more accurate measurements involving more and more information: So the third measure of pi might be 3.14, the 4th 3.141, the 5th 3.1415, etc.

So I got to thinking, my system can't have an infinite number except as a potential field, so what would the measurements on an infinite prime be? Well, if you write the set numbers I described above in binary, for all the natural numbers up to n (with n increasing at each step) you get, and the naturals including zero you get:
11 =2 = {0,1}
111 = 7 = {0,1,2}
1111 = 15 = {0,1,2,3}
and so on.
So what might measurements on a certain infinite prime look like? Well, they'd be the best approximation of the number within the information constraints, and so that all the information enumerated at a point was part of the larger definition. (like with pi example above) They would have a quality of there being a prime, greater than all the finite numbers so far.

So anyway there are these primes called the Mersenne primes, which when written in binary are a long string of 1's, just like those set numbers. If you interpret these as set numbers, and calculate the sets, you get the set of all natural numbers up to but not including some prime, which plays the role of the "infinite prime" for that finite set of numbers. So if there are infinite Mersenne primes, each long set of binary one's that corresponds to the next Mersenne prime could be seen as a measurement on that infinite prime.

That thought crossed my head, and I liked it. Its like the "artists interpretation" in some old school book with painted pictures of what dinosaurs might have looked like:

You saw it when you were young, back in the days when Boards of Canada were beings streamed into our subconscious minds by an alien satellite: Its not what the author was talking about, but its the best approximation I can fit into my limited information space at this time, and with my next measure I will be closer still. We are always getting closer.

PEace