by jdumars » Sat 19 Apr 2008, 15:54:25
$this->bbcode_second_pass_quote('emailking', '
')I think I sort of see what you're getting at, but this is just shifting the pile under the rug. For one 0.9999... is equal to 1. That's just true. Also, setting pi = 1 doesn't change it's weirdness. It still can't be written as a ratio of integers and is thus irrational (transcendental even). I don't know how quantum mechanics is supposed to come into this, but any attempt to make sense of that bizarreness is going to have to come from a new understanding of the physical world or a shift in what "makes sense" to us.
I think you missed my point altogether. My frame of reference is not an arbitrary system, but a representation of the physical world. Math and numerology make some very bold assumptions, like there can be 2 objects/quantities, etc. that are
exactly identical. That's what a quantity is. 2 apples, 2 electrons, etc. While this is convenient for approximation purposes, it is not factual at all. There are no 2 identical anythings, because every assemblage of matter is wholly unique. Once you delve into the lowest states of energy/matter, it becomes clear that everything is in a unique state of immeasurable flux, with the only certainty being past-tense observation. You can describe objects in terms of observable probabilities, but this must be done in reference to a specific assemblage of matter at a specific reference point. Math/numerology creates a pseudo-universe that overlays on our existing one to provide useful but inaccurate approximations. In a sense, math is the science of "close enough."
My model simple accepts this blasphemous fact -- that humans are incapable of creating a system that
exactly describes the natural world. So to achieve this, yet still have the ability to relate conceptual notions of measurement, I have done away with the idea of accuracy altogether, other than 2 states: yes/no, happened/didn't, can't happen/will absolutely happen. Anything between can be measured in terms of its likelihood of happening. And, if you think of all matter surrounded by a field of proximal probability, the entire concept becomes crystal clear.
Imagine walking down a street. You see a tree ahead. What is the probability that it will start jumping around singing Radiohead's Pyramid Song? What about the probability of its leaves rustling in the wind? What about the probability of it respiring, or having sap flow inside of it? There is a whole situation-dependent array of probabilities that can only be described in the direct interaction of multiple fields. The field boundary is determined by an edge of zero probability -- meaning you can only interact with other fields where a probability greater than zero exists. You may interact with forces you have no knowledge of such as interstellar objects, various energy fields, etc. Or, it can be much more immediate like the tree.
So back to pi. Pi is a way of mathematically extrapolating an object that can only best be described as an infinitely-sided polygon. Basically it is "squaring the circle" -- which is impossible because a circle is not an infinitely-sided polygon, it is a circle. The reason pi does not resolve is because you can add an infinite amount of sides to a polygon, and it will always be a polygon. A circle, however, has no such angular relationships. It is an infinite array of points equally distanced from a center point. Thus, were pi to resolve, it would have "become" a circle, which is impossible. The two states are mutually exclusive.