# Measuring things

1. Feb 17, 2006

### kungfool

This morning I tried to draw a line four inches long on a piece of paper. After about three hours I gave in to frustration and ultimately gave up. Every time I thought the line was four inches long I looked more closely and saw it was either too long or too short. The pencil tip being too fat was becoming an issue, so I sharpened it, eventually replacing it with a safety pin in which the tip was covered in a fine coat of graphite dust. But then the markings on the plastic ruler were too wide, so I switched to a better made steel ruler. Using a magnifying glass, and eventually a tabletop microscope I was forced to finally be satisfied with a line which started within the the bounds of the first tick on my ruler and ended somewhere in the bounds of the 4" tick. I was forced to bring my efforts to a conclusion, as the individual grains of graphite dust and fibers of the paper, as well as the surface texture of my ruler were becoming so pronounced that they were undermining my ability to resolve the vital distinctions between line, paper and ruler needed in order to draw and measure the line. In short, all I was seeing were a bunch of uneven and crooked three dimensional surfaces instead of the flat black line on its nice white background.

When someone takes a measurement what is really going on? When someone seeks to increase the accuracy with which something is seen, what is it that happens?

If I measure (quantify?) something am I doing anything more than comparing what is being measured to a scale? As the precision of the measurement goes up does the need to isolate the entity being measured from its "surroundings" increase as well? As a measurement becomes more precise does this automatically narrow, or otherwise alter the perspective from which the measurement is being made? Is this what uncertainty is all about?

Are there any scales that can be infinately divided or infinately reduced while at the same time remain infinately relevant or comparable to the entity I am wishing to precisely measure?

Is it impossible to determine a line to be exactly four inches long without changing the identity of the line?