Being and Change is a U-tube. But what is a U-tube when it’s at home?
(For Winston and Theodore)
That which is above is like to that which is below, and that which is below is like to that which is above.
Hermes Trismegistus, The Emerald Tablet
Next to our kitchen sink is a tall, nickel-plated, double-barreled water purifier resting on stilts that looks from a distance like the holding towers atop older high-rise buildings in cities like Manhattan. Into its top tank, Kari and I regularly pour unfiltered tap water. Powered only by gravity, the raw input slowly makes its way through a series of filters—their glossy specs assure us that in a pinch, the filters could purify water from our pond—before dripping into the purified holding tank below. From the attached spigot at the base of the lower tank, we channel purified and excellent-tasting water into drinking glasses and cooking pans several times each day. Because of its shiny nickel plating, whenever they visit, our North Carolina grandsons call the contraption’s output “Silver Water.”
Until recently, the merits of drinking silver water were not as convincing as they might have been. The water tasted better and, by all accounts, was healthier for us. But because its stacked canisters were fashioned from germ-repelling stainless steel, their opacity prevented our seeing where, and how much, water was at any moment tied up in its top-to-bottom journey. Unable to calculate at a glance how much volume had made its way from the raw input tank, through the various filters, and into the purified tank, Kari and I could not readily know when the upper tank needed to be topped off. We could sometimes guesstimate that if we hadn’t refilled the upper tank in a while or if the strong, steady flow from the spigot ever weakened, both tanks were probably low. But, like Schrödinger before us, we could not know for sure without standing on tiptoe to remove the lid and peer inside the top canister or clumsily lifting the sometimes heavy top canister from atop the purified water tank on the bottom. Why was the sure knowledge of the combined water levels inside our silver, black box important? Because aside from running out of purified drinking water at inopportune times, if we got the levels wrong—if, say, Kari filled the upper chamber at 9 am, and I, not knowing of her prudence, filled it up myself at 10 am—we could cause, and for years periodically did cause, a kitchen flood, not just from water breaching the top of the bottom canister to drip onto the counter, but when that same water made its way to the countertop falls that spilled to the hardwood kitchen floor below.
***
If you pick up one end of the stick you also pick up the other.
African Proverb
Several years ago, after an arduous bike trip in the hills of southern France, the soreness in my left thigh and calve muscles did not repair itself as rapidly as it usually did. On a visit to the local medicin, I was warned that the varicose veins on the back of my thigh and calve might have already led to a deep vein thrombosis, or DVT, that could put my lungs at risk for a pulmonary embolism. I needed surgery. When I asked what he planned to do about it, the elderly country doctor merely shrug-puffed his lips as if to say, “Alors, ca?” before replying.
“Mais, non, monsieur, this lovely but tiny corner of Provence is not the place you will wish to have such a risky procedure performed.”
On consulting vascular specialists in Geneva, Switzerland, a city I lived before moving to France, I was told that surgery should be avoided if it could be known or predicted that its aftermath would show little or no reduction in the probability wave that, deep inside my leg, a blood clot had already formed, or might soon do so.
“Heureusement pour vous, monsieur, we have just the device to help us solve ce mystère. Do you know the ‘U-tube’?”
I did.
(We have all by now heard of YouTube, whose trademarked name is a clever portmanteau for “Your Own Boob Tube.” My time in Europe predated that kind of YouTube but not its homonymous connection to the less obscure but not entirely unknown word “U-tube.” A U-tube is a U-shaped tube or pipe used to measure the pressure of a liquid or gas. (See Perpetual Moment to learn of my failed but fun college try to employ a U-tube to pit the forces of gravity and buoyancy against one another and thus power the entire world forever with free, renewable energy! Hehe) One of the principles of a U-tube is that absent a semipermeable membrane at the nadir of the “U,” the pressure of a gas or liquid will always be the same on either leg or side of it. Picture pouring colored water into a clear glass-shaped U-tube. The water level on the left will always equal the water level on the right.)
“Here you see the visible side of the U-tube,” continued the Swiss physician after his assistant had wheeled in and somehow connected me to a new machine. (I must have, all these years later, repressed the gory details.) On the top of the contraption, I could see what looked a little like an oversized but curvy mercury thermometer, but without the mercury. Its vertical limits were measured by some other means that I couldn’t figure out at first.
“And here,” he said, touching my bad leg, “is the invisible side of the same tube.”
“If we can connect together both sides of the U-tube—your leg and this ‘contraption,’ as you call it—we can simulate the effect of performing the ligation (stripping away your bad veins) by regarding the visible pressure of your blood when we manipulate the invisible pressure inside your leg. Since what we see on the meter will always be equal to the pressure we cannot see in your veins, we know they are the same number. We can predict with approximate certainty the impact of the ligation before taking such a risk.”
“In other words, we’ll be looking at the blood flow in my leg through this surrogate here.”
“Exactement! ‘Surrogate’ is le mot juste”
The doctor and his assistant began to manipulate my leg by pinching and pressing on various places on the visible varicose veins to simulate removing them. With the amplification of an auxiliary microphone, we were also able to hear the difference each time the pressure changed. Still unable, decades later, to picture how the docs connected the liquid in my veins to the visible half of the U-tube, I only remember seeing (and hearing) that when they simulated removing the veins, the “needle” did not budge.
“As you can see, monsieur, a ligation will have no impact on the surface circulation nor the underlying veins at risk for DVT. Performing the operation might even compromise the vasculature of the leg. We highly recommend you do not undertake this risk.”
And so I didn’t. Not then and there, anyway. Persuaded by the physics experiment, I accepted from the Swiss that I was not at risk but decided not to return to France. I stayed in Switzerland four months and then returned to the States.
On examining my leg, my parents’ go-to surgeon, who had not heard of what he termed the experimental U-tube test, took one look at the visible tip of my vasculature iceberg and recommended he be allowed immediately to put my leg under the knife.
“We really need to reduce all possible risk of DVT.”
Just as the Swiss predicted, within months of the surgery, all the veins grew back, look just as bad today as before they were stripped, and whose ligation, I am now told, may have contributed to conditions leading to my saddle pulmonary embolism earlier this year.
***
This year, after the hardwood floor in our kitchen began to show signs of being periodically bathed overnight in a puddle of silver water—the occasional miscalculation of the height of the probability wave that predicted that in this universe, at least, the combined chambers of our water tower were just too much for it—we now have a U-tube in our kitchen. The makers of our water tower had experimented with a black plastic beta version of a spigot connected to a glass tube. (What would Winston and Theodore have made of plastic parts dispensing silver water?) But when the stainless steel version finally came out, I just had to buy one.
The tube attaches to the top of the spigot and runs to the full height of the bottom purified water canister. Like Schrödinger’s vile of cyanide—silver water sounds exotic but is not lethal—is made of clear glass. Its transparency allows us to “see” into the lower tank without removing the top canister. We need only look at its surrogate. And because the U-tube sits outside the tank—that’s the point, right: to echo the same information about the water level inside the tank?—the transparency of the glass tube and of the water inside it allows light to pass through both substances to reveal behind them the nickel plating on the lower tank. Depending on the light in the kitchen, Kari and I must sometimes squint to differentiate the slight refraction that signals the top of the water in the glass tube. Winston and Theodore were correct. It really does look like silver water.
***
Just as the visible portion of the Swiss U-tube that allowed my doctors to “see inside” the vasculature of my leg without breaking its skin, so to speak—as I said, I don’t recall how the Swiss doctors connected my vein to their contraption—the U-tube on our water tank allows Kari and me to peer inside at the actual water level without lifting Schrödinger’s lid. These two half-circle U-tubes bring this indirection full circle to Rudy Rucker’s interpretation of Abbott’s Flatland. In that classic 1884 novel, a surgeon living in a higher dimension is able to perform heart surgery on a patient in a lower dimension without breaking her skin1.
What is the message here, besides there being more in heaven and earth, Horatio, than is dreamt of in our philosophy?
As above, so below, we are surrounded by the sometimes invisible, visible ends of a thousand U-tubes we can put to use—if we squint—to predict/guess/estimate/know with precision a thousand hidden things about their opposite number concealed beyond our reach. With much, much more to come about this rich and ubiquitous phenomenon, I’ll close here with just one more strange loop.
The blood is full of visible markers for invisible conditions. I once helped AstraZeneca create a biomarker data mining system whose object was to bait signs of disease in order to catch their cures. In hospital earlier this year, I underwent five days of tests attempting to recreate what might have caused the “shower” of blood clots that gummed up both my lungs. Home these past two months, I can no longer see inside me as the ER radiologists must have done, and am told that for a host of reasons, I will not need additional scans as my recovery presses onward. Like walking back the Big Bang in hopes of determining not the moment but the driving force of creation, my blood has now been mined for dozens of biomarkers, none of which directly revealed to my medical team the precise condition of my lungs before or after their unwanted shower. But like the visible end of the U-tube in my leg or in my kitchen, the visible markers in my blood told my team—indirectly—the condition of the invisible furniture inside the temple of my body without even (other than a dozen annoying pinpricks) breaking my skin. What other ends of the stick might I practice picking up in order to peer under my lid?
***
NOTES:
- In Then, Now & Yet, I expand on Rudy Rucker’s thought experiment where a “heightful” being from a three-dimensional world such as our own passes through Edward Abbott’s Flatland, a two-dimensional, “heightless” existence whose objects possess only length and width. In Rucker’s version, such a supreme bring could empty a Flatland home of all its furniture by passing through neither window nor door.