Some people think I am an alarmist. I have expressed deep concerns about the challenges presented by global warming, peak fossil fuel production, and over-population. I have asked myself often, why has my concern grown so much of late? It is true that the potential consequences of these phenomena are devastating for human civilization, if not the whole population. But why am I more worried than ever?While pondering that question I began thinking about things I learned while in the Navy onboard a ballistic missile submarine. I was an enlisted man; having gotten a warning that I would soon be drafted during the Viet Nam conflict, and having no desire to join that brouhaha, I enlisted in the Navy and dropped out of college (I had had an interrupted education and under the rules of the draft I was on the eligible list - can't tell you how I knew my number was up, but let's just say I was lucky in who I knew!). I ended up driving submarines, which was actually a great way to serve the country and learn quite a lot.
In college I had taken calculus courses and had an intellectual understanding of the meanings of derivatives and integrals, but that was just book-learning. In driving the sub I learned first-hand what the meanings of velocity and acceleration (first and second derivatives), and the accumulation of mass over time (integral) were. And those lessons, I realized, apply now to what is happening in our world.
Driving a sub involves three basic components that have to be coordinated. Subs operate in three dimensions, like an airplane, but have another aspect that airplanes don't, namely buoyancy (actually gravity and lift are sort of like this aspect but air speed is the key control for staying up). It is necessary to adjust buoyancy as well as distribute the weight of water taken into tanks to create a neutral buoyancy condition. So there are three operators controlling the submarine's depth, direction, and pitch. It would take a long time to fully describe the complete operations of a submarine, so I'll direct the reader to the excellent Wikipedia article for further reference. Instead I will focus on just one of the operations to make my points.
The 'sail planes' (some subs have bow planes) of a ballistic missile submarine are used to fine-tune the depth of the boat continuously. The planes operator has a stick that is pushed forward to trim downward and back to trim upward. At normal operating speeds these fins are effective in terms of reasonably fast response to stick movement and changing the depth. However, the objective is to maintain a steady depth with as small an excursion up or down as possible. And that is where the skill is tested.
Submarines are big, heavy bodies operating in a viscous fluid environment. They are slow to respond to any control motion due to their inherent inertia. And this is the critical factor. Once a control signal has been issued (changing the angle of the planes) it takes a little while before the boat starts to change its depth. If an operator puts too much angle on the planes the boat can overshoot its target depth and then the operator will have to position the stick in the opposite direction in an attempt to stop the overshoot. This, if you can imagine it, can and does often lead to an oscillation where the boat goes up too much then goes down too much relative to the desired depth. Newbie operators have this problem until they get used to using the instruments provided (this happens in sub school using a simulator for training).
The instruments include a depth gauge, obviously, which reads out the absolute depth. But there are two more gauges that are essential to controlling the sub. The next gauge is the rate of change of the depth, or the velocity up or down. This gauge tells you how fast the sub is raising or falling. So your depth might be five feet below the target depth and the rate of going downward could be 0.5 feet per second. This information is useful in knowing how much to pull the stick back to not only slow the rate of descent to zero, but also to anticipate that the boat will start back upward again. In order to gauge this anticipatory signal — the slightly greater position of the stick that will ease the descent rate to zero and then turn it to a gradual ascent, is the acceleration rate, or how fast is the rate of change, itself, changing.
A skilled operator can use the three gauges to just barely tweak the stick forward or backward to keep the sub at desired depth with a minimum of error. That is, under circumstances of no disturbing forces like currents or waves the sub can run steady. The problem is that when there are forces operating on the sub from without, it is much more difficult to keep it within reasonable bounds near the desired depth. It takes a great deal of skill to use the gauges correctly to keep the sub from oscillating up and down. Sometimes, in the worst-case conditions (heavy wave action for example) the operator looses control and the sub will oscillate wildly up and down. It is not generally a problem to go much below desired depth (unless you are operating in shallow water) but it is a big no-no to breach the surface during operations. In my day the 'Soviets' were always on the prowl looking for our subs and just letting the sail (conning tower) pop out of the water could give away our position. So that was a big problem. You could tell you had a problem when the accelerometer was pegged (at its maximum reading) and the velocity meter was, as a result, moving toward an extreme (in the same direction). You could watch, in despair, as the depth gauge just kept moving up. At that point, no matter how hard you pushed the stick forward you just simply weren't going to prevent a breach. The momentum was too great and you were screwed (at least potentially if any Russians were about).
So what does this lesson in the physics of inertia and the calculus have to do with our current challenges and why I am so worried? It turns out there are direct correspondences between the dynamics of these challenges and the submarine's control problems. Take global warming as an example. The burning of fossil fuels puts CO2 into the atmosphere and ocean. This is like the control signal and the sail planes angle. The angle corresponds to the rate of emissions. But these bodies are huge and have a slow response in terms of greenhouse heating and acidification, respectively. There is considerable 'inertia' to overcome in both of these cases. That means that once the input signal starts to have an effect (e.g. temperature rise) it will take a carefully tuned counter signal to slow the rate of change. Temperature is like the depth of the sub. Once it starts to rise you need to know the rate of rise and the acceleration in order to correct the signal and keep the temperature at the right level (sub at depth). Our problem is that we are just looking at the depth gauge (average surface temperature) and guessing about the velocity or acceleration. Thus our original estimates of when we might expect to see real problems were based on insufficient information. And it looks like we were really wrong!
Our first derivative information on heating is now coming from the study of ice melting at the poles and in glaciers. And guess what? The information tells us that the velocity of increase in temperature is higher than we thought. Moreover, we are now getting acceleration information from the year-to-year melting rate, which is much higher than originally estimated. The glaciers are melting at a faster rate than we can explain by the temperature alone. So the accelerometer is showing a positive result, the velocity meter is in very positive territory and we know for a fact that the temperature is higher. As an experienced submarine driver who learned to watch all three gauges to estimate the corrective signal it looks to me like we are headed for a breach of the surface — a point of no return, so to speak.
The peak oil phenomenon shows a similar pattern. If we look at the rates of change in oil production (extraction and delivery) globally, we see not only the level of oil production but also the decrease in velocity of production. Furthermore, some sophisticated analysis by oil engineers and geophysicists provide evidence that the rate of change in production itself is changing. It is decelerating such that we should expect the velocity of oil production to go down more rapidly and soon. At the same time the world has seen a dramatic increase in demand for oil with the economic growth of China and India leading the way. In this case you have two interacting rates of change that are headed for collision.
Finally, look at the population rate. This one is interesting in that there are indications that the acceleration of growth has already diminished toward zero. That is a good thing given that the absolute level is already above the carrying capacity of the planet without the energy subsidization of fossil fuels (e.g. in growing food). But the velocity is still fairly high and even though it is about to go down due to deceleration of the births-minus-deaths numbers it is still going to drive those absolute numbers toward an excess of 9 billion people by 2050.
So what makes me worried? I look at these first and second derivative signals as a clue about what to expect from the absolute values we will be contending with in the future. At the rough indications we have for these clues it seems to me that the rates are going to take us into breach territory much sooner than anyone may have expected. About ten years ago when I started a concerted effort to study the science behind global warming and peak oil, I believed the then estimates of when calamity would strike as being reasonable. It wouldn't be in my children's lifetimes; we were talking about hundreds of years before the climate would drastically change. But now the evidence from velocity and acceleration information strongly suggests otherwise.
It's hard to grasp the significance of velocity and acceleration until you've sat at a sub control panel and watched helplessly as the depth gauge swirls toward zero (breach) even while you push the stick forward frantically. People have a hard time imagining the implications of exponential growth and how quickly things can get out of control when you don't pay attention to the derivative signals. But I fear that is where we are now.
I wish our so-called leaders had driven submarines. Unfortunately, I don't think they are even aware of our depth, let alone how fast we are rising.