Memory GaphicLearning something hard

by Matthew Leitch, 25 October 2001

Some things are really tough to understand at all. Normally this is partly the subject itself and mostly the way it is explained. Often it is hard because the source assumes more knowledge than you actually have. What makes something hard is that ideas you need to learn are explained using terms/ideas you don't already know. You have to be aware of this and backtrack where possible. You also have to learn what you can, notice the gaps, and keep searching until you fill them in.

Using your memory effectively is the key to reaching understanding. You must learn things as you go through or you will never understand.

Example: A mathematical definition. For example, a dictionary of mathematics says that a diagonally dominant matrix is "a SYMMETRIC MATRIX in which every element in the MAIN DIAGONAL is larger than the sum of the absolute values of the remaining elements of its row." I already know what a matrix is, but observe that:

The dictionary says that a symmetric matrix is "a square matrix whose entries are symmetric around its main diagonal" and it gives an example. I already know about square matrices and about diagonals. From the example I can notice that:

Now back to that original definition.

The deductions are important as they use and so reinforce my new memories, create useful redundancy, and give me a headstart in reasoning about diagnonally dominant matrices. Now if I have to learn something more about them I have more chunks and facts to build with and my inferences will be quicker and more numerous.

This example had a happy ending as I was able to go back and find all the explanations I needed. Often this is not possible and learning is, unavoidably, damaged. Well written explanations give you the elements you need in the right order so there is no need to go back. School text books often achieve this. I hope this web page also does.

© 2001 Matthew Leitch