encoded notions

While studying for my optics midterm I find that I do not feel comfortable with the material. I do understand it all and I could do all of the problems given enough time and access to my textbook, but I still don’t feel secure in my ability to do the problems with only an equation sheet to assist.

I’ve felt similarly about the following classes:

• history
• psychology
• political science
• discrete math
• physics classes such as:
  • lab techniques
  • modern physics 2
  • thermal physics

The one thing that these classes all seem to have in common is that there is no clear overarching organizational structure linking all of the material together. In some cases, the structural maps may be weakly connected or fuzzy with approximate relationships, but nothing concrete and fixed.

I like to learn by grasping quantitative relationships. It’s like an initial value problem in classical mechanics. If you know the state of the system at one time, and how that system evolves in time, you can know the state of the system at all future and past points in time. By having a fundamental understanding of the most basic constituents of a system and the processes by which this system of information evolves, the whole field of information becomes easy to grasp.

For example, the programming aspect of computer science becomes nearly trivial once you realize that it is all about representing and manipulating data. The programming languages are completely arbitrary and are inconsequential—they’re simply different ways of solving the same problem.

In most of my other physics courses, the quantities we derive are interrelated by things like energy, forces, fields, and time. The structural map is clustered around these more basic physical concepts with a web of connections surrounding them. Leaves of this tree are often connected via a substitution involving the basic quantities.

The problem I run into in optics is that the entire course is about light, what it can do, and the rest of the book is spent deriving relationships and approximations between the many optical quantities in several different experimental setups. The quantities are all completely calculatable, but derivationally they are dead-ends. It feels as if the information hierarchy for optics is a star pattern with light in the middle all of the other concepts and quantities are directly connected to it, but not to each other.

My preferred method of learning and condensing information fails horribly on an organizational structure like that.