half a link
Posted: Wed Apr 06, 2005 9:33 am
In a universe of motion, motion is both continuous (a progression) and discrete. Because the discrete units are units of progression, the progression continues within the units of motion. Aside from the surface contradiction that motion is both continuous and discrete, I've always had a hard time with this notion. I'm hoping someone can shed some light.
Larson likens the situation with a chain.
Quote:
We do this with everyday vectorial motion all the time. We say the trajectory of some object is at a specific point at a specific time, but that is an impossibility -- no matter how finely we slice up the instant to get at the object's position. If motion is a continuous whole, then it can never be measured at a precise location. The most we can say about its position at a given instant is that that is the location if would occupy if it came to a halt, or where it would be passing through at some instant. I feel like we have an analogous situation with regards to identifying a portion of a link: we are spatializing the motion and confusing it with some sort of abstract space we overlay it onto.
Larson likens the situation with a chain.
Quote:
The situation with the chain is clear enough. We can identify a half a link because we can measure it. A fractional position is always relative to the length of the link. My question is, can we really do the same with a unit of motion? It seems to me that if we do, we are only once again in the position of merely spatializing motion. When we identify the progression as "being" at the midpoint of a unit, we are freezing the motion, halting it at some "spatial position", to make our identification, and violating the continuity of the progression.The absence of fractional links in the chain does not prevent us from identifying different parts of a link, or from utilizing fractions of a link for purposes such as measurement. For example, we can identify the midpoint of a link, and measure a distance of 10½ links, even though there are no half links in the chain. The same principles apply to the discrete units of scalar motion.
We do this with everyday vectorial motion all the time. We say the trajectory of some object is at a specific point at a specific time, but that is an impossibility -- no matter how finely we slice up the instant to get at the object's position. If motion is a continuous whole, then it can never be measured at a precise location. The most we can say about its position at a given instant is that that is the location if would occupy if it came to a halt, or where it would be passing through at some instant. I feel like we have an analogous situation with regards to identifying a portion of a link: we are spatializing the motion and confusing it with some sort of abstract space we overlay it onto.