Sunday, August 9, 2009

God Said - Importance of Mathematics


Faraday's disc generatorImage via Wikipedia


God Said:

 \nabla \cdot \mathbf{D} = 4\pi\rho_f
 \nabla \cdot \mathbf{B} = 0
 \nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t}
 \nabla \times \mathbf{H} = \frac{1}{c} \frac{\partial \mathbf{D}} {\partial t} + \frac{4\pi}{c} \mathbf{J}_f


And then there was Light.

Above is what I once saw on a tee shirt when I was a student at University of California, Berkeley. I was immediately struck. As I looked at the equations I immediately grasped the significance of the message. These four equation sum up exactly what we know about light. These are the equations we use to describe almost everything about light. They are known as Maxwell's Equations. Maxwell was not the first one to come up with all of them, but he did realize that they summarize nearly everything about light. When I first learned about them, I learned them in their integral forms in my lower division physics courses. In upper division and in many text books you will see them in their vector calculus forms. Here is a chart I found on a great website.


Maxwell's Equations

Integral form in the absence of magnetic or polarizable media:

I. Gauss' law for electricity
II. Gauss' law for magnetism
III. Faraday's law of induction
IV. Ampere's law
Differential formDiscussion
Index
Maxwell's equations concepts
HyperPhysics***** Electricity and Magnetism R Nave
Go Back




I'm not going to get into what these equations are and what they mean in great detail but to point out how connected electricity and magnetism are. For example, a moving electric field (such as an electric charge down a wire) generates and magnetic field. And a changing magnetic field can be used to generate an electric current (i.e. a motor). These equations represent the base principles for all of our electric/magnetic theories and devices. They can be applied in every field of science I can think of. For example in geology, piezoelectric rocks can generate electric fields and current. In addition magnetic rocks are also dug out of the ground.

I found out in my studies that mathematics is the language of science. Without mathematics there is no point to doing science. We would not be able to communicate, quantify, qualify, or analyze anything. Some have even said that it is through mathematics that we truly get a glimpse into the mind of God. We get to understand through it's logic and order how God put the universe together. Think of the Fine-Tuning argument for the existence of God. Without mathematics we could not measure or even grasp the concepts of cosmological constant and how much on a "knife-edge" on which they sit. We would not be able to see the tight tolerances these quantities must be in order to see that these qualities of the universe are not coincidental. However, it's more than all that. Mathematics is beautiful. It's almost too difficult to put it into words the way it makes me feel thinking about how so much fits together. It's like looking into the infinite, grabbing a small, minuscule piece and understanding it. I love it.

No one can deny that math is the product of reasonable, logical, ordered minds. It's principles and qualities transcend us. We don't invent math as much as we discover it. Like morality, there is no basis to assume that humanity came up with it. It appears more and more obvious the higher you go in mathematics and sciences. It's so in-your-face in the theoretical edge, I don't understand why some mathematicians don't accept God. I mean it's like closing your eyes and hoping despite overwhelming evidence. I simply don't have enough faith to ignore the Fine-Tuning evidence nor the mathematics.

Another source.

No comments:

Post a Comment