Thursday, November 12, 2009

Unpacking Equations

Equations are poetry. In the abstract they signify shapes, in science we add the significance with units and measurements. It is the cross-over between shape and meaning that creates the poetry of equations. Looking at a common example:

The poetic meter of equations comes from the standard method of algebra. It helps in unpacking the meaning. This reads: The gravitation force between two objects is the mass of object one multiplied by the mass of object two multiplied by a constant, divided by the square of the distance between those objects. This is really just a first step in understanding, as that it a lot of information to process. Actually, I think the reason we use equations is because they help us to process massive amounts of information with less effort. Plus they're all objective 'n shit, which Scientists happen to think is a good way to stay hip with the kids.

The first reading is akin to substitution. You have mathematical symbols that can be translated into words, and stating those relationships using words helps in understanding what an equation is saying in the grand scheme of things. In this case I understand that the mass of both objects can differ, so if the mass of either object changes, so will my force. In this case, it has a positive correlation between the force, whereas an increase in distance has a negative one -- or, in more accessible language, the heavier the objects involved are the greater the gravitational force between them, and the further apart they are the lesser the gravitational force is between them. Something else to note is the fact that the decrease happens at a squared rate, where mass is only linear (unless, of course, you increase the mass of both objects under consideration by the same amount). All that's left is big "G" which never changes. It's actually just something that's determined by measuring, and it's a factor that makes this equation work.

So, the equation states a relationship between things we observe. But if they're an actual relationship, we can also determine other parts from the Force, such as the mass of an object in space, without actually measuring that mass on a scale. Or, for this same equation, we can determine the Potential Energy of an object.

The definition of energy is a Force applied across a distance, or for the above:

dF = G((m*M)/r^2) dy

where "m" is the mass of any object on the earth, and M is the mass of the earth. I put it in y so that it will appear more familiar in the end. In this, we simply integrate from point zero (the ground) to whatever point above the ground we're interested in, and thus obtain:

PE = (m*M) [(-1/r)] from 0 to y = -GmM/y

And so we have a statement about the universe from the above equation that required a little digging to see. Big M and G do not change, and the potential energy is the negative of an inverse relationship between the mass of the object on earth and the distance that object is moved away from the surface of the earth. Not only did this require a little digging, if you haven't had a background in Calculus then it probably didn't make as much sense. While it is preferable to be lucid, I'm trying to make a point: That math is a language. The meter of a poem and the conventions of language bring out the meaning in lines. The operators in math is this meter that creates the poem describing what we see, and thereby, letting us as humans understand  at a deeper level than once we did. While what I use and look for in poetry might differ, the experience is largely the same. You read an equation over and over again, looking for the implicit relationship and meaning, and make connections over time that reveals a deeper truth -- in the case of poetry, about the emotion, and in the case of equations, about the universe.

No comments:

Post a Comment