The Infinite Complexity of Nature

So we want to measure something, let's say, a desk. We take a ruler or measuring tape and determine that the desk is 2 feet wide...give or take an inch. Give or take? No, let's be precise. We determine the desk to be 2 feet and 1 inch wide...give or take one half of an inch. No, no, let's try again - we determine the desk to be two feet and one and a half inch wide...give or take an eighth of an inch...
This excersize could go on until we run out of little lines on our ruler...and then when we bring in a more precise scientific measure it continue on even longer...and then, when we bring in a microscope...how long could we continue this?
How precisely do we measure things? As precisely as possible or as precisely as we need to? Scientists are finding ways to be more and more precise, but how precise is the most precise possible? The distance from one end of an inch to another can be split an infinite number of times, making impossible to ever measure a truly exact inch, but we measure things not as precisely as is theoretically possible, but rather as precisely as is needed. When Scientists need to measure something more precisely than is possible given the instruments they have, they develope new more presice instruments equal to the task.
Mathematics, the language of science, is used in a simlar way. For example, consider the number "pi" (π - 3.14159265358979323846…). It is one of the most important mathmatical constants and yet it is not an exact number. While the value of pi has been computed to more than a trillion (1012) digits, still no one knows the exact number and it is said to have an infinite decimal expansion.
If our most precise tools and measures are approximate at best, then where are we? We have grown so comfortable speaking of scientific "facts" and "laws" but these were all developed over time by fallible human beings using aproxmate tools. And besides, scientific laws have been proven false in the past as well.
Take Newton vs. Einstein. Newtons work is useful for approximate applications, but Eisteins much more complex theory disproves Newtons work.
But this is how we reason and understand things. We use generalities, catagories and labels, to develope, share, and catalogue our observations about the world around us, and when "words fail" we make up new ones and thus language evolves as does our understanding of the universe.
There are other ways to communicate things to complex for labels, catagories, and words. Art and music help here.
...[thought still in progress to be revised / edited / continued]...