Now Compiz, Beryl is all over the place and there are massive discussions about it. But I have a few doubts about it.
First of all, how do we benchmark an interface, especially its efficiency. I would like to propose a few speculations that could hopefully evolve into some sort of quantifying standards of a desktop interface.
In an interface, I think there are two important elements. The capacity of active working area and the convenience to approach something else useful.
More specifically. First, we could have a factor a = number of normal size characters contained times area per character (font size) / the area of the whole screen. In my opinion, the larger the working area, the better because ideally, the whole screen is usable and should be utilized for current purpose. So the larger the better. Suppose this percentage is a (active window percentage or AWP).
Suppose you are in your favorite house and you want to cook your favorite food. You have a microwave and an oven. What's a good expectation of how long it will take you to cook. Well, the proportion of times you cook with a microwave times the time it takes to cook with a microwave plus the proportion of times you cook with an oven times the time it takes to cook with an oven.
So what's your efficiency of cooking?
The longer it takes you to cook, the lower your efficiency of cooking is. It is, the weighted average of 1 over the time it takes for you to cook, ie. the proportion of times you cook with a microwave times 1/ the time it takes to cook with an oven. plus the proportion of times you cook with an oven times 1/ the time it takes to cook with an oven.
What if you have two microwaves.
If you have two microwaves, your efficiency of cooking go up. Now, I assume your efficiency goes up "twice". In the microwave cooking case. Within a reasonable range, it is valid.(If you have 100 microwaves, it's not likely you're 100 times efficient because it simply blocks your way.) So your efficiency index is weighted average of the first term, 1 over 1st microwave's cooking time plus 2nd microwaves cooking time and the second term 1 over the oven's cooking time.
Now, you're all ready to go for the math. The analogy is only here because some people find weighted average confusing.
Read ahead if you've mastered the math: