Apparently hovering is physically impossible

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From my perspective, it is possible that one can be too analytical in learning buoyancy. I think I know what you mean, but after working on my buoyancy in the pool and practicing fin pivots, the light went on, and I soon understood buoyancy (vertical and horizontal) without even thinking about it. It was much like I didn't read a book on gyroscopic theory to understand how to ride a bike. I just crashed a few times, and figured it out quickly after that!
 
Me thinks you're putting way to much thought into what is a simple principle.

My thesis in college was on "fuzzy logic". You know, like when you set your thermostat in your house to 70* ~ but the temperature in your house is NEVER 70* ~ Maybe it's 69.342656876856346234213547657 degrees or 70.57601293872346523491320498320 degrees. :)

Or like how your speedometer in your car says you're going 55 MpH, yet it is mathematically impossible statistically to drive exactly 55 MpH.

Buoyancy is a "generalization", not an exact pin-point measurement. No matter if you do hold your breath, and even hang on to the anchor line, you'll never achieve exact true buoyancy. Even our 1.8 billion dollar nuclear ballistic subs can't achieve exact buoyancy, and they are some of the most accurate launch platforms ever designed. An iron tube does not change in displacement (enough to matter) and water isn't compressible, so in theory, an iron submarine with just the right amount of water in it's buoyancy tanks should travel perfectly horizontal. But it doesn't. The dive planes are still needed to make small vertical adjustments.

If you can get it within 6", then you are "neutrally buoyant" for the purpose of diving. Once you get your weight right, your trim right, and your movement underwater right, you'll be able to stay vertically in that tolerance while breathing. I can't inhale/exhale normally and violate that tolerance. I'd have to exhale/inhale and intentionally hold it for minutes to ever rise/fall enough to move 6" up/down. This is assuming there aren't swells that are moving you up/down.
 
This was not explained in the PADI OWD course at all. Apparently the first course is just to provide basic familiarization. and to help keep you from accidentally killing yourself or your buddy in an emergency situation?

It appears that if I want to actually know how to be a proficient diver, I need to sign up for an untold number of additional courses, for a fee of course, whereupon the mysteries shall be revealed.

I feel like I've signed up to join a secret society, PADItology. Whoops, can't tell you those nuanced details of the craft until you have a 6th degree in the mystic arts, and know the special 3rd initiate handshake. Also, please have your credit card ready...

Thank you to everyone replying here for breaking the paywall and discussing this openly.

It appears that you had one of the poorer instructors. My OW instructor did indeed explain and demonstrate, and then require us to demonstrate, the ability to control depth with just breathing. We were actually vertical (the Buddha position), but were in mid-water, not sitting on the bottom or doing fin pivots, and had to hold depth for (I think) 30 sec.
 
It appears that you had one of the poorer instructors. My OW instructor did indeed explain and demonstrate, and then require us to demonstrate, the ability to control depth with just breathing. We were actually vertical (the Buddha position), but were in mid-water, not sitting on the bottom or doing fin pivots, and had to hold depth for (I think) 30 sec.
Some instructors try to get by with the very minimum whereas others actually try to produce divers that are safe in the water.

My instructor was one of the better ones I think in that all the divers he has produced that I have dived with have all got pretty good buoyancy and control. We did a similar exercise except it was holding position in the water in trim as opposed to "Buddha" position. I did struggle a bit initially but got there in the end (after being told to get out of the water, have lunch and clear my head - I think I was overthinking it).
 
Some instructors try to get by with the very minimum whereas others actually try to produce divers that are safe in the water.

My instructor was one of the better ones I think in that all the divers he has produced that I have dived with have all got pretty good buoyancy and control. We did a similar exercise except it was holding position in the water in trim as opposed to "Buddha" position. I did struggle a bit initially but got there in the end (after being told to get out of the water, have lunch and clear my head - I think I was overthinking it).

Mine was pretty good at teaching buoyancy and control in the water, and liked to show off by doing things like motionless headstands, etc, so we could see what can be done with practice. Other skills, not so much: his CESA drills were rather useless, IMO.
 
A side gig for me is teaching sailing, which of course involves in part, how to steer.

*no one* can steer a sailboat (or any boat) bolt-straight, nor can an autopilot--there are always subtle (or not so subtle) corrections, both to initiate a swing, to check a swing, to reverse a swing. But if you do it right, they'll all average out at your desired compass course. And you want to catch a swing early, or it will "run away" with you. So the tiller is almost always in motion, or at least off-midships. More experience, means less back and forth corrections, but you'll never eliminate them altogether, any more than you could driving a car. And you'll get better at anticipating when to start that subtle counter-steer to get, or stay, on course

Breathing is the fine-tune correction in the same way, except that we "have" to move our lungs in and out enough to get oxygen and exhale Co2. easier and more serene than overworking your inflate and deflate buttons, and more fun. So we will always wobble a little. And it's fun to "breathe your way over, or under" some obstacle.

We may struggle to understand this intellectually, but fortunately we have an easier time just getting used to it physically, it becomes second-nature and frees you to think consciously about something else.
 
Graveyard Diver points out the impossibility of being perfectly neutral. Add to his info. the fact that unless you hold your breath you are constantly breathing down your tank, as it gets lighter. Even if there is some sort of theoretical "exact point" you are neutral, again you'd have to hold your breath at that exact point. Skyflyer points out that you just "get it" with practice (and not a ton of practice--maybe a few dives). Ei. it ain't rocket science.
Jeesh--Sorry, I wrote about the same thing on Sept. 12......
 
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