Maximum Parsimony – In Diving and the Cosmos

Image credit: Niko Lang and Booyabazooka

I admit it, my early training in physics has made me irritatingly sensitive to the principle of parsimony.

Parsimony, pronounced similarly to “alimony”, can be summed up by the following: the simplest approach to understanding nature should be considered before contemplating a more complicated line of reasoning. In a famous example, it is more probable that planets, including the Earth, orbit around the sun than the visible planets and the sun orbit around the Earth. Of course, in a different time that probability was not obvious to the common man. But then they hadn’t been thinking about parsimony.

Thank-goodness someone (Nicolaus Copernicus) did.

In the search for habitable exoplanets (planets outside of our solar system), the following statement was recently made by astronomer Steve Vogt in response to a storm of skepticism about a potentially habitable planet. “I do believe that the all-circular-orbits solution is the most defensible and credible,” he said. “For all the reasons I explain in detail … it wins on account of dynamic stability, goodness-of-fit, and the principle of parsimony (Occam’s Razor; in Latin, lex parsimoniae).”

William of Occam (also Ockham) was an English theologian of the 14th century. He did not invent the premise behind his razor, but he famously used it to slice through the complicated philosophies of the day and rebut them by an unfaltering demand for simplicity over complexity.

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Medical students are taught essentially the same principle, albeit using different words: “When you hear hoof-beats, don’t think of zebras.” Wise physicians know that occasionally zebras do show themselves, but they should not be the first thought when a patient presents with unusual symptoms.

If simplicity is to be generally preferred over complexity, then an example in the diving literature comes to mind. This example annoys me to no end, but I’m slowly coming to terms with it. It is the growing popularity of referring to the respiratory effort required to breathe through a scuba regulator or a closed-circuit underwater breathing apparatus (a rebreather) as work (in joules, J) per tidal volume in liters, L.

When work in joules (J) is divided by volume (L), dimensionally the result is pressure (kiloPascals, kPa). To be exact, what is often called work of breathing in diving is actually the average pressure exerted by a person over the entire volume of a breath. The principal of parsimony says that if it is a pressure, if it has units of pressure, then we should call it a pressure (kPa)  and not something more complicated, such as Work of Breathing specified with units of J/L.

The light grey ellipsoidal area within this pressure-volume loop is equal to the work (J) of breathing for that breath.

(Examples in the regulatory diving literature correctly using Work of Breathing with units of joules can be found in early editions of NATO STANAG 1410. EN250:2000 is an example using the units of J/L for work.)

I find in my dealings with non-respiratory physiologists, that the concept of work of breathing is difficult to grasp since mathematically it involves a definite integral of pressure over a change in volume. I have made various attempts to simplify the concept, but I still find knowledgeable medical professionals misunderstanding it. In fact, mathematical integrals seem to be as frightening to most physicians as poorly dissected cadavers would be to laymen. Even engineers who certainly should grasp the intricacies of work and power end up confused.

I’m sure it adds to the confusion when some diving physiologists speak in quotients. For example, since a cubit is a length of 48 cm, and a hectare is 2.47105 acres, you could describe a person’s height as 165,400 cubic cubits/hectare. Dimensionally, that would be correct for a six foot (1.8 m) tall individual. However, most people would prefer the units of feet or meters rather than cubic cubits per hectare. Certainly, the simpler description is far more parsimonious than the former.

The shaded area within this triangle is equal to the “Work” inside the previous P-V loop. By dividing by tidal volume, you obtain the average mouth pressure on the vertical axis.

For the same reason, it makes more sense to speak of a descriptor with units of pressure as simply pressure (kPa) rather than a quotient of work per liter (Joules/L).

If describing a simple parameter like pressure as a quotient is not defensible scientifically, is it defensible psychologically?

Maybe. The U.S. Navy has used terms like “resistive effort” to convey the impression that a volume-averaged pressure is something that can be sensed by a diver. To breathe, divers have to generate a pressure in their chest, and that pressure generation requires effort.

“Effort” is admittedly not a hard-science term: it doesn’t even pretend to be. However, the use of “Work of Breathing” connotes hard science; the concept of work is pure physics. But as I have shown, the way it is increasingly used in diving is not pure physics at all. So its use is misleading in the eyes of a purist, and undoubtedly confusing to a young engineer or physicist.

But to a diver, does it matter? Does it somehow make sense? Do divers care about parsimony?

Well, I have yet to find anyone who does not intuitively understand the notion of the work involved in breathing. If they have asthma, or have tried breathing through a too long snorkel, they sense the work of breathing. So I imagine that the inexactitude of J/L is of no import to divers.

However, I also believe that the over-complication of an arguably simple concept should be just as unappealing to designers of underwater breathing apparatus as it was to William of Occam or, for that matter, the designer of the Cosmos.






Cold Water Scuba Regulator Testing — U.S. Navy vs. EN 250

Under thick ice in the Ross Sea, near McMurdo, Antarctica.

When scuba diving under 3-m thick polar ice with no easy access to the surface, the last thing you want to worry about is a failure of your scuba regulator, the system that provides air on demand from the aluminum or steel bottle on your back.

However, cold water regulators do fail occasionally by free-flowing, uncontrollably releasing massive amounts of the diver’s precious air supply. When they fail, the second stage regulators, the part held in a scuba diver’s mouth, is often found to be full of ice.

The U.S. Navy uses scuba in polar regions where water temperature is typically -2° C (28° F).  That water temperature is beyond cold; it is frigid. Accordingly, the Navy Experimental Diving Unit developed in 1995 a machine-based regulator testing protocol that most would consider extreme. However, that protocol has reliably reflected field diving experience in both Arctic and Antarctic diving regions, for example, in Ny-Ålesund, Svalbard, or under the Ross Sea ice near McMurdo Station.

There are currently both philosophical and quantitative differences between European standards and the U.S. Navy standard for cold water regulator testing. Regulators submitted for a European CE mark for cold water diving must pass the testing requirements specified in European Normative Standard EN 250 January 2000 and EN 250 Annex A1 of May 2006. In EN 250 the water temperature requirement for cold water testing ranges from 2° C to 4° C. Oftentimes, regulators that pass the EN 250 standard do not even come close to passing U.S. Navy testing.

An iced up, highly modified Sherwood SRB3600 Maximus second stage regulator

The Navy’s primary interest is in avoiding regulator free-flow under polar ice. The breathing effort, which is a focal point of the EN 250 standard, is of lesser importance. For instance, the 1991 Sherwood SRB3600 Maximus regulators long used by the U.S. Antarctic program have been highly modified and “detuned” to prevent free-flows. You cannot buy them off-the-shelf. Detuning means they are not as easy to breathe as stock regulators, but they also don’t lose control of air flow to the diver; at least not very often. Here is a photo of one that did lose control.

NEDU performs a survival test on regulators, and any that pass the harshest test are then tested for ease of breathing. The so-called “freeze-up” evaluation breathes the regulator on a breathing machine with warmed  (74 ±10°F; 23.3 ±5.6°C) and humidified air (simulating a diver’s exhaled breath) at 198 feet sea water (~6 bar) in 29 ± 1°F (-1.7 ± 0.6°C) water. Testing is at a moderately high ventilation rate of 62.5 L/min maintained for 30 minutes. (In my experience a typical dive duration for a dry-suit equipped diver in Antarctica is 30-40 min.)

To represent polar sea water, the test water is salted to a salinity of 35-40 parts per thousand.  The possible development of a “freeze up” of the regulator 2nd stage, indicated by a sustained flow of bubbles from the exhaust port, is determined visually.

In contrast, the European standards call for slightly, but critically, warmer temperatures, and do not specify a duration for testing at an elevated respiratory flow rate. I have watched regulators performing normally under EN 250 test conditions (4° C), but free-flowing in water temperatures approaching 0° C. Those tests were run entirely by a non-U.S. Navy test facility, by non-U.S. personnel, using a U.K. produced breathing machine, with all testing being conducted in a European country. The differences in testing temperatures made a remarkable difference.

Haakon Hop of the Norwegian Polar Institute in Ny-Ålesund, Svalbard.

The NEDU testing results have been validated during field testing by scientific diving professionals under Arctic and Antarctic ice. The same regulators that excel in the NEDU protocol, also excel in the field. Conversely, those that fail NEDU testing fare poorly under the polar ice. For instance, a Norwegian biologist and his team exclusively use Poseidon regulators for their studies of sea life inhabiting the bottom of Arctic ice.  (The hard hat in the photo is to protect cold skulls from jagged ice under the ice-pack.) Poseidon produces some of the few U.S. Navy approved cold-water regulators.

As is usual for a science diver in the U.S. Antarctic Program, a friend of mine had fully redundant regulators for his dive deep under Antarctic ice. He was fully prepared for one to fail. As he experienced both those regulator systems failing within seconds of each other, with massive free-flow, he might have been thinking of the words of Roberto “Bob” Palozzi spoken during an Arctic Diving Workshop run by the Smithsonian Scientific Diving program. Those words were: “It’s better to finish your dive before you finish your gas…”

In both NEDU’s and the Smithsonian’s experience, any regulator can fail under polar ice. However, those which have successfully passed U.S. Navy testing are very unlikely to do so.


A previous blog posting on the subject of Antarctic diving may also be of interest.


Diving Under Antarctic Ice

You are 100 feet down using scuba, with your dive light spotlighting the most exotic looking Sea Hare you’ve ever seen.

It’s noon at McMurdo Station, Antarctica but it’s dark at your depth because between you and the surface of the Ross Sea lies19 feet of snow-covered ice.  Your dive buddy has drifted about 100 feet away, but you can see him without hindrance in the gin clear water of the early Antarctic springtime.

The 800 foot water visibility also means you can easily see the strobe light hanging on the down line 200 feet away, the line leading to the three and a half foot diameter hole bored through the ice.

Under these conditions, you should not have to worry about your regulator, but you do, because you know that any scuba regulator can fail in 28° F water, given enough opportunity. You also know that some regulators tolerate these polar conditions better than others, and you are using untested regulators, so yours might free-flow massively at any moment.

Should that happen, you have a back-up plan; you will shut off the free flow of air from your failed regulator with an isolation valve, remove the failed second stage from your numb and stiff lips and switch to a separate first and second stage regulator on your bottle’s Y-shaped slingshot manifold, after first reaching back and opening the manifold valve. Of course, that backup regulator could also free-flow as soon as you start breathing on it – as has already happened to one of your fellow test divers.

In that situation you would have no choice except to continue breathing from what feels like a torrent of liquid nitrogen, teeth aching from the frigid air chilled to almost intolerable temperatures by unbridled adiabatic expansion, until you reach your dive buddy and convince him that you need to borrow his backup regulator. Once he understands the gravity of the situation, that two of your regulators have failed, then the two of you would buddy-breathe from his single 95 cu ft bottle as you head slowly towards the strobe marking the ascent line. And of course he will be praying that his own primary regulator doesn’t fail during that transit.

Once you reach the ascent line you are still not out of difficulty. The two of you cannot surface together through the narrow 19-foot long borehole. So you would remove your regulator once again and start breathing off a pony bottle secured to the down line. Once it is released from the line, you can then make your ascent to the surface; but only if a 1300-pound Weddell seal has not appropriated the hole. In a contest for air, the seal is far more desperate following an 80 minute breath-hold dive, and certainly much more massive than you. Weddells are like icebergs – their cute small face sits atop a massive body that is a daunting obstacle for any diver. 

But you even have a plan for that — you’ve heard that Weddell seals don’t like bubbles, and they get skittish about having their fins tugged on, and will thus relinquish the hole to you. … At least, that’s what you’ve been told. You certainly hope he would leave before you consume the meager amount of air in your pony bottle.

The text above was taken from a U.S. Navy Faceplate article I wrote concerning  a 2009 Smithsonian Institution sponsored diving expedition to Antarctica in which I participated. On and under-the-ice photos were taken by expedition members Drs. Martin Sayer and Sergio Angelini.