Actually whether a diver is using tables, computers, digital or analog pressure and/or depth gauges, all of these tools, if used properly in the water, should only confirm what a diver already knows based on their situational knowledge of their dive and dive conditions at any point in time. (Some numbers are harder than others.)
For example, I always think how many bar I have in my tank before I look at my SPG, based on the dive profile. The SPG should confirm what I already know based on my knowledge of where I am in my dive profile and how much air has been consumed (based on depth, conditions, etc). I was taught this as a solo diver (and when solo diving, I like to have two dive computers, my pony and pony regs, and often a spare mask, not to mention a minimum of two torches in my pockets, SMB and reel just in case... etc.)
This has evolved to something similar with my dive computer, and I try to know my depth and NDL time (NDLs) before looking at the computer. Quite often I'm wrong, but it is great practice in keeping your mind on your dive and dive profile. I also do this when fun diving with a buddy or leading a dive with a less experienced diver, if the situation permits (sometimes leading a dive I tend to pay more attention to the gas consumption and limits of the less experienced diver), using the dive computer to verify, or cross-check, what my mind thinks it should be.
Tables? I have them in my dive bag, standard and the Nitrox ones, but tend to never use them; as I always use my dive computer and if I need to plan, I use the PDC planning mode. But, I also do the same mental check for planning, and try to estimate what the limits are based on my prior dive profiles (in my head), before looking at the planner in my computer.
I agree with NetDoc who, in an earlier post, mentioned that the tables will someday be a footnote in diver history; but they are still useful to teach the concepts of nitrogen loading as others has mentioned, including outgassing and decompression theory. But, in daily practice, and on dive boats all over the world, everyone I see has as a dive computer on their wrist. Only students are playing with tables and after the complete the training, they are diving with a computer. I think this is very good, especially in the world of multilevel (or continuous mode) diving.
On the other hand, no dive computer, table or timer can compensate for a lack of situational knowledge of what is going on in the body when diving. Yes, guessing NDLs in our heads can be difficult, and so is tracking depth at times. I'm not very good at NDL tracking in my head, but I'm pretty good at knowing how much air is left in the tank and my depth and approx dive time, before looking at the little friend on my wrist or gauge hanging here and there.
I do find dive tables useful for providing a hard and smooth surface for writing on paper when there is no suitable smooth service
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