Misguided

I'm sorry for the confusion. My post was truly a response to the the original post by zebov. I just included the extra information to let them know how I ended up across the thread, and how I came up with my response. I really do appreciate your responses though because they made me take another look, and I feel that I better understand zebov's remark about longevity.

On 2/10/2006 at 10:54 AM, zebov said:

Ever since learning to integrate in high school Calculus, I've been curious as the the physical meaning of the integral of position w/ respect to time. Over the years, the topic has come up again and again in my mind, and have finally decided to put an end to my pondering; or at least let others ponder with me.

 

Is there any firm grasp of the concept of the meter-second already in existence? Is there a good use for this?

 

I have come to call the integral of position wrt time "longevity" as that seems to be the best term in my mind to describe it. From what I have been able to determine with some simple thinking is that longevity can be related to amount of energy or force placed on object in a gravitational field (ie. if you put a high amount of kinetic energy on an object, it will have a larger longevity than if you put a small amount of kinetic energy on an object).

 

Any thoughts on this?

I realize this is an old post, but I'm currently studying nutrition, and in my studies I just came across a measurement called glycemic response. I have doubts about the textbook's reliability, and that's another issue, but basically the units for glycemic response according to this book should be in mM*min. In attempting to understand the unit, I decided to google meter-second to see if it would help me in any way because I also remember coming across the idea in calculus.

The post by Casey Wood, because of its roots in math, made me think of some of the situations that I've come across when trying to interpret the meaning of certain functions.

On 8/23/2015 at 4:45 AM, Casey Wood said:

This is a fascinating question that I'm sure has puzzled many calculus and physics students. The best explanation comes from understanding what happens geometrically when we integrate. For example, the integral of a volume is an area, the integral of an area is a displacement, thus the integral of a displacement is a point. The ideas associated with considering the unit of the meter second as a unit of spacetime are valid.

 

The integration of the displacement equation gives an infinitessimally small point in spacetime that can be thought of as a coordinate. Some might consider such a point to be a "singularity". Nevertheless, the idea is useful for allowing us to place a clock at each one of those points, so that we can analyze concepts such as time dilation due to the constancy of the speed of light, and the so called "cosmic speed limit". So think of it this way, the integral of a displacement yields a point in spacetime.

Anyway, one facet to the elegance of math, in my opinion, comes from the simplification of expressions. Unfortunately, it hides information that is helpful for me in understanding it -- think about the zeros that are randomly added to certain problems to arrive at a solution. Well, the point is that functions or even a plain number will have equivalent expressions. What I mean is, for example, 4 can be expressed as 2x2 or as 1+3 or 28/7 and whatever else. So, I thought, why not do the same for meter-second? Meter-second can also be expressed as meter per inverse second, i.e., m/(1/s) or m/Hz. Don't get me wrong, I still don't know what it means, but it somehow seems more understandable.