I thought I'd try a bit of math and philosophy, for a change. Right off the bat, I should tell you I'm no authority in neither... as you should have guessed by now, if you've been reading from a few days to this point.
What's the deal with Pi and Phi? For those who don't know Pi, it's the ratio between the perimeter and the diameter of a circumference and it's aproximately 3,14. Phi, if you haven't read the da Vinci code (such as myself), it's the ratio of growth of the golden spiral. It can be calculated as follows: Let A be the length of a given line. If B and C are lengths of lines as well and if B + C = A, Phi is the only number, say x, to which A / B = B / C = x. It's approximately 1,618. Now, the thing is, these are the archetypal examples of irrational numbers, i. e., numbers that cannot be expressed as the ratio of two integer numbers. Yes, I know, I just defined both as a ratio. You can make these ratios of integer numbers if you multply both the top and the bottom by a large enough power of 10 without changing the actual value of the ratio. I'm not too sure on the defenition of Phi, but Pi, the quintessetial irrational number, is, to the best of my knowledge, by defenition, a ratio. As I said, I'm no mathematician. Please shed some light on this matter, will you?
Fot the philosophy half of our post, I'll question the relevance of the first half with a single question. Do numbers exist or are they merely a convention stipulated and agreed on by an overwhelming majority of individuals? Aye or Nay, everyone. And now, to refute your answer with another question:
Aye (numbers do exist): Would you kindly define any given number? Take your pick. 1, 5, 2, 1000000, a 10^100, 6.23 x 10^23... Answers expected in comment form, if you please.
Nay (numbers don not exist): Then how is it that the vast majority of individuals from around the world came to count in the same fashion? How is it that we all share the comfortable same decimal basis? (I know, we have 10 fingers. We should have 16, though. First, it'd do wonders for my typing. Second, I hear a hexadecimal basis is much more stable and robust, mathematically speaking, whatever that means. Apparentely, having more factors in it is good.) Why is it that, in any given basis, all individuals agree in a given succession of symbols and values?
And for the third half, I bid you all goodbye. But first, I'd like to hear your thoughts on the cognescibility, which is hardly a word, yet should mean "posibility of becoming known", of infinity. Is it possible to grasp the concepts of an infinite ammount, and infinite length, or, the big bad boy, an infinite time (remember, this should be infinite both ways, as much into the past as into the future)?
It's not over yet! Four halves... Doble Post! Rejoice! Last, but not least, I'd like to introduce Gödel's paradox: Every sistem is either incomplete or inconsistent." To explain, if a system has a given premisse, say F, it would be incomplete if it lacked
not F (meaning the opposite of F), yet it would be inconsistent if it had not F, for they are mutually exclusive. If you'd like to accept self reference, i. e., the possibility of one refering to him/her/itself in the equation, "This sentence is false" is a good starting point. The trick is, people can figure that the sentence is false when it's true and its true when it's false, call it a paradox and move on. Computers, however, would likely, but certainly not always, either dwell on this until they crashed or try to track the sentece back to the very defenition of all terms and find... nought... and likely crash. So the question is, are people inconsistent or incomplete? I'd really like your answers, but please, no "women don't know what they want, thus they're inconsistent" tirades or such variations. It's been done, people.
ArabianShark has many questions... but no aswers. I'll go seek them now.
(whew, that's a big one)