TrimixToo
Contributor
Your physics/math is correct, and you agree with my point but not my phrasing of it, as I chose not to go into detail but to keep it brief.
When I explain to students, (with a little bit of rounding) I explain that pressure will change one-sixth on a 15 foot rise from 60 feet, but will change one-third from 15 foot to the surface.
For a new diver all the non-linear effects of shallower depth variance are what they need to have drilled into their consciousness until it is second nature - increased risk of lung expansion injury, increased difficulty of bouyancy control, and increased air time remaining.
So be careful about announcing “common mistakes” when you don’t like the shorthand description - while you are technically correct, you are emphasizing the wrong practical message - many casual readers will absorb the absolute wrong take away and continue to think in terms of the shallow depth as “only” 15 feet.
I'd agree if you said "volume" rather than "pressure." Volume changes nonlinearly with depth. Pressure does not.
I phrased my post carefully. I'm afraid that saying it's the pressure that behaves in a nonlinear way with depth and not the volume *is* a very common mistake among instructors and other divers alike. The hazards you describe are real. The behaviors you are trying to train are the right ones. I think it's worthwhile to tell people the actual basis for both, but what do I know?