Wow.... I am surprised that this topic caused so much conversation. I understood how to use the tables, I just wanted a clarification on the math behind them.
Welcome to the internet ;-)
But back to your original question. Quite honestly, I think the "User Interface" for the standard tables is terrible in a way, because although it is simple to use them as instructed to get a result, they do not build a coherent "mental model" of the process.
As noted before, the residual nitrogen TIME is adjusted for depth. So if the table shows a No Deco Limit (NDL) of 30 minutes at a certain depth, it is saying that if you have no residual nitrogen in your body, if you remain for up to 30 minutes at that depth and surface using the proper protocol, you have an acceptably small likelihood of suffering from decompression sickness.
Given a dive to a certain depth and a surface interval of a certain amount, you may discover that you have 22 minutes of Residual Nitrogen Time at that depth. This is a complicated way of saying that the residual nitrogen remaining in your body is equivalent to spending 22 minutes at that depth.
Since that depth had an NDL of 30 minutes, you now dive to that depth for no more than eight minutes while still maintaining an acceptably small likelihood of suffering from decompression sickness.
The reason why the RNT is
greater for a shallower dives is that you would need to spend more time at a shallow depth to accumulate that much nitrogen. So really, all those different RNTs are a way of expressing the quantity of nitrogen in your tissues. The different numbers for different depths serve to simplify the calculation for someone who just wants to follow the table by rote, but complicate things if you want to try to infer the underlying process from the mechanics of the tables.
On the other hand, our existing models for the underlying process are actually quite complicated. If we discuss tissue compartments and gas gradients and so forth, we could work out a dive plan by hand from first principles, but the math would be heinous.
The models we have do not have a direct and obvious correlation to the tables, either. For example, if you know that you have a NDL of 30 minutes at a certain depth, you might assume that you accumulate nitrogen at a rate of 1/30th of your maximum residual nitrogen per minute. But this may not be so, the accumulation may follow a curve.
Likewise you may mistakenly assume that the tables follow depth in a straightforward way, but upon closer examination you will discover that they are closer to following pressure in atmospheres, such that 60 feet of depth does not have twice the pressure of 30 feet of depth but rather only 50% more pressure.
So swerving back to our digression, teaching a table does not directly teach an understanding of the underlying process, nor is it a direct simplification of the process. But it serves a certain limited useful purpose, as does the computer.
My personal observation is that I learned almost nothing about the process in my OW class, I quickly realized that the instructor was just trying to rush us through the course and into his dive shop. I did my OW checkout while on vacation, and the instructor there sold me on taking the "Nitrox Diver" program, and I felt like it was the "missing manual" for the tables.
I am not qualified to compare and contrast agencies or curriculae, but I can tell you that I felt that the Nitrox course did a lot to answer questions the OW course raised. There were and still are a lot of questions in my mind, but it was a start.