How to interpret PCA loadings? While reading about PCA, I came across the following explanation:

Suppose we have a data set where each data point represents a single student's scores on a math test, a physics test, a reading comprehension test, and a vocabulary test.   
We find the first two principal components, which capture 90% of the variability in the data, and interpret their loadings. We conclude
  that the first principal component represents overall academic
  ability, and the second represents a contrast between quantitative
  ability and verbal ability.

The text states that PC1 and PC2 loadings are $(0.5, 0.5, 0.5, 0.5)$ for PC1 and $(0.5, 0.5, -0.5, -0.5)$ for PC2, and offers the following explanation:

[T]he first component is proportional to average score, and the second component measures the difference between the first pair of scores and the second pair of scores.

I am not able to understand what this explanation means.
 A: Although years are passed since last comments, I think the answer to the original question should be toward a more qualitative interpretation on how to read a "loadings matrix" (regardless of the assumptions we used to build it). If the vertical 'weights' are all the same (as in the original case for PC1 with all 0.5) it means that for PC1 all variables have same weight (0.5). If all variables have same weight it means that the 'scores' (in the PC matrix which is the matrix of the original data matrix projected along the eigenvectors) are proportional to th average of scores in the original data matrix. So PC1 tells me to evaluate a generic student based on its PC scores average (which is different in this case from the original average by a factor of 2x)
In relation to the second question, it's true that mathematically it's the difference between the scores of the two pairs, but the analysis of the PC2 tell us something about where the student is good or bad (as defined by PC1): so we can say that x1 and x2 move together and as much as x1 (and x2) is far from the average of its scores, x3 (and x4) is far from the average of its scores by the same amount in the opposite direction => as much more a student is good in math and phisics its scores in read/vocabulary decreas by the same amount.
So in conclusion by reading the Loadings Matrix we can formulate hypothesis that can be verified by looking in the 'PC matrix' and the 'scores': if you average the row for a generic student you can say how much he is good or bad by just looking at the value (don't forget that we decide that high/low means good/bad), if you then pick x1 (or x2) you can expect they are similar (both high or both low) and you can say from that if that student is good or bad in that subject, and by consequence you can expect he's bad or good  in x3 (or x4).
