Martin Luther King Jr. Day

I share the Reverend Dr. Martin Luther King Jr.'s dream.  Among other things, for people to be judged by the content of their character rather than the color of their skin.  It is an ideal.  Since that dream has still not been achieved more than 50 years after he gave the speech, it's apparently a challenging ideal.  Given events of the last few years, I'm not confident that we're closer to it than we were 20 years ago.  Maybe I was just that naive 20 years ago, maybe I just hear about more than I used to.  And maybe we as a nation have ceased the effort towards that ideal.  In many respects, though, it doesn't matter.  Something is only an ideal if you are approaching it ever more closely through time.  And that's not where we are.  It's only an ideal if, indeed, people actually agree that it is an ideal to strive for.

I also encourage all to read his letter from a Birmingham jail.  Not only is it a fine piece of writing, it mentions many specifics of our (USA) failure to live to our ideals as expressed in the Constitution and the Declaration of Independence.  The preamble to the constitution reads:

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

  It is not justice for the law to be applied differently based on the color of someone's skin, rather than the content of their character.  It does not ensure domestic Tranquility to make police forces comparable to occupying military forces.  Nor can the Blessings of Liberty be secured by treating part of your citizenry like 'other' -- not truly citizens, not really deserving of the Blessings of Liberty, or Justice.

I've seen some bizarre interpretations of the Constitution.  For some, since the constitution was written by slaveowners, slaves and their descendants are not included as part of 'We the People'.  Other absurdities on par with that abound.  But, if one wants to tread that route, be sure that all of your ancestors signed the Declaration.  None of mine did, so I incline to the interpretation that it is a) people and b) of the United States -- all citizens -- who should be (ideals again) included.  Even though for more than four score and seven years we treated part of our population as property.  The step forward in ideals is to include all our people.

About a century before letter from a Birmingham jail was Civil Disobedience, by Henry David Thoreau.  He was in jail, on grounds of his protest of his taxes going to support slavery.  For both men, there was this consistency, often lost by current people: They knew full well that in breaking unjust laws, they would likely go to jail for it.  That is part of engaging in civil disobedience.  When a friend visited Thoreau in jail, the friend asked "How can you be here?" (in jail).  Thoreau answered "How can you not be?"  A couple years ago, I testified in favor of giving civil protections to a class of people who were being discriminated against, not for reasons of their character.  I was astonished by one of the people testifying against the nondiscrimination law.  Not, sadly, because she was opposed, but because of her panic reaction to a later person noting that our names would be recorded and history would judge us.  If you argue that public law should be one way or the other, you should certainly be willing to be known for it!  Not even a threat of jail time.  Ideals mean little if you are not even willing to be known to hold them.

I don't have answers, but this year I'll be doing more towards achieving those, and below, ideals.

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Which way is up?

Simple questions sometimes have subtle answers.  Of course, some answers are also pretty simple.  Which way is up starts out simple and then gets pretty subtle. (Note on scientist-speak: subtle = complicated and/or difficult).  This winds up being related to What is a day? as we get a little more complex.  But, while we can, let's go with simple.  Up is the opposite of down.  Slightly less simple, down is the direction a ball falls.

Even less simple: hang a weight on a string.  Hold it still.  This is difficult, so maybe hang it from a nail or off a board.  There's probably still a little swinging back and forth.  So either wait (it'll come to a halt eventually, but who says scientists are always patient?!) or get a large (larger than your weight) cup or bucket of water and bring that up underneath the weight.  Make sure the weight is made of something that doesn't float if you use this approach!  Once the weight comes to a halt, the string gives you a line which points up and down.  The weight is the 'down' side of the line.

By the way -- not only do you not have to be good at math to be good at science, you also don't have to be good at drawing. For me, this is pretty good artwork. Some people are great at drawing, same as some are great at math. Some of us, well, you see my caliber of artwork.

 Now for getting subtle ... which also explains why the earth isn't exactly a sphere.

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Messy Science

The type of science I like is what I call 'messy science'.  'Neat science' is the sort where you are looking at only one or maybe a few (easily counted) objects, which can be described by one or only a few number, like mass and momentum.  Celestial mechanics is a 'neat science' in this way, at least for the solar system.  Also, I hope, obvious is that being neat does not mean that it's easy.

Messy science is things like organismal biology or, for my own professional work, climate.  In climate, you can take something simple, like the rotation of the earth, and wind up with a lengthy list of things which affect it.  Conversely, you have a long list of things affected by it -- including the climate.  In What is a Day?, I mentioned a few things which affect the earth's rotation.

Another thing that is involved is the fact that the earth's inner core -- sitting about 5000 km below us -- rotates at a different rate than the crust.  In between the two is the liquid outer core, which has its own angular momentum, and whose top is about 3000 km below us.  More recent work (that paper was published in 2000) is now suggesting that one can learn about climate by studying the earth's core's rotation -- here for the press release, or here for the Dickey, Marcus, and deViron, 2011 paper: Air Temperature and Anthropogenic Forcing: Insights from the Solid Earth.

What a lovely, messy, situation!  We can look to the earth's core for signs about what is happening in climate!

I'll come back to this later for a discussion of the research paper itself.  Maybe, like many new ideas, it won't hold up.  If not, somebody else will get to write the paper which shows why not.  In the mean time, here's another candidate for the messiness of climate.  There's also another datum for how small the scientific community is.  I've met the lead author; it was she who explained to me how it was possible to measure length of day variations to such very high precision.

What is a day?

Some friends have been puzzled about how an earthquake or a tsunami could change the length of a day.  This question comes, of course, from the tremendous earthquake in Japan.  I trust you're all aware of it, the severity, and are doing what you can.  Given how late I am to comment at all, I'll take up my friends' puzzlement.

As is common in science, once you get detailed about just what you are talking about, you also understand much about the thing.  So: What is a day?  There are really at least 4 different definitions of 'day' that we can fairly easily point to.  Only two of them are still in serious scientific use.  One is commonly used, kind of.  And the one with the longest history is no longer in use.

What we need, in order to define a day, is something that takes 1 day to happen.  The longest history for a meaning of 'day' is: "The time between maximum elevations of the sun."  Almost equivalent would be time between sunsets or sunrises.  Maximum elevation of the sun is a much easier and accurate measurement to make.  Don't look at the sun!  You also don't need to.  Get yourself a stick and put it straight in to the ground (on a desk, sheet of paper, ...).  Be sure that the ground is flat and the stick is vertical.  Every so often through the day, mark where the shadow ends.  At some point, the shadow will reach its greatest shortest length.  That's solar noon.  The direction of the shadow (if you're in the northern hemisphere mid or high latitudes) is north.  (There's more fun to be had by repeating this exercise many days through the year.)

This notion of 'day' is affected by earthquakes, since it depends on how fast the earth is rotating.  (This also makes it one of the more obscure ways of showing that the earth does rotate.)

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How to make sanity checks

In late September, I wrote a note on whether Lake Superior still remembers the last ice age.  The answer was no (read that post for why).  But along the way I illustrated a simple sanity check that would have given the author I was responding to a heads up that he was seriously wrong.

The check I used was to compare volumes.  If something the volume of Lake Superior remembered conditions for 10,000 years, then something with 100,000 times the volume would (could/should/...) take 100,000 times as long to adjust.  The ocean is that much bigger, so would take that much longer.  Yet we know (sanity) that the ocean's circulation time is only a few hundred to a few thousand years. 

This doesn't prove that the original 10,000 year estimate was wrong.  That's not the purpose of a sanity check.  Rather, the sanity check alerts us to examine the system more carefully.  Maybe there's something fundamentally wrong about using volume for comparison, maybe there's something fundamentally wrong about what lead that author to saying 10,000 year memory for Lake Superior.  As we found out, it is the original claim of 10,000 years that was severely wrong.  (Turned out to be about 6 months.)

In the comments, though, there were some noting that my approach to sanity check wasn't right.  Or at least that I could have made a better estimate than I did.  Since I take sanity checking to be a heads up process rather than a proof, I'm not very concerned with whether I chose the most accurate (I did choose one of the simplest) method.  But it is worth its own discussion how you might make better estimates.

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Verifying forecasts 2

As I said last week, verifying predictions is difficult, and was prompted in to looking again at the matter by someone doing it wrong.  Of course the standard of 'wrongness' involved is mine.  Forecast verification is something of an art as well as mathematics and science.  But some points I think I'll get little argument from Allan Murphy* and his intellectual colleagues and descendants for are:

• You have to be clear what you're forecasting
• what variable
• at what time (or time span)
• for what place or area
• You have to be clear how the forecast is going to be evaluated
• You should evaluate all forecasts
• Forecast must be public
• Forecasts must be verifiable

That last might seem a little strange.  I hope not.  Suppose I said next July 20th at 3:34 PM at Washington National Airport the official temperature would be hot.  Very specific about what I'm forecasting and what it will be evaluated against.  But what is 'hot'?  To me, anything over 80 F (27 C).  As such, it's a near certainty that my forecast will be correct.  It's also awfully easy for me, on July 21st, to say, regardless of the temperature, that it was 'hot'.  This is one reason that we prefer numbers in science.  You can, and we do, work with qualitative predictions.  But it takes more work, as you have to find some way of making 'hot' objective, so that we can all agree that such a forecast was correct or not.

In general, if not as universal, we add a couple more items, at least desirable if not mandatory:

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Verifying forecasts 1

I already discussed my earlier sea ice estimates and how they came out, but a few things have happened since then to occasion a two part look at forecast verification.  As usual, it's prompted by seeing someone do it wrong.

One of the errors, which I have to remedy on my own part, is that you should verify (compare to reality) all your forecasts.  I think that the end of May ice estimates are the most interesting and important, rather than later in the year.  Partly this is because of how I think the sea ice pack behaves.  Partly it is because the practical uses of sea ice information I know of require that kind of lead time.  It takes a long time to get a tanker up to Barrow from Seattle, for instance.

Xingren and I did submit a later estimate, for the August Sea ice outlook.  That estimated 4.60 million km^2 for the September average sea ice cover.  An excellent approximation to the NSIDC's reported minimum (4.60) but not as good compared to the observed average extent of 4.90.  Actually a touch worse than our May (30th, even though not reported by SEARCH until June) estimate of 5.13 from the model.  Both estimates were well within 1 standard deviation of the natural variability (errors of +0.23 and -0.30 for May and August's predictions, respectively, versus about 0.5 for the natural variability).  So, on the whole, pretty reasonable.  Just that we'd have expected better from the later estimate.   But ... there's more to that story ...

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A heuristic for stratospheric cooling

I mentioned in the climate fingerprinting post that if you have more greenhouse gases in the atmosphere, we expect the stratosphere -- the upper atmosphere -- to get colder.  That, naturally, brought on the question 'why'.

I'm far from the first person to make the comment, or to attempt to write up a description of how it works on a blog.  Recently the Stoat took a swipe, or rather referenced a prior attempt and one by Realclimate, and the Rabett has also had a go.  Plus, I'm sure, there are a raft of other efforts in existence.  Yet the questioner is still asking.  That being the case, and having seen prior efforts make the attempt to describe the full situation that you have, I'll aim for a simpler version.

This will be a heuristic description.  It will be capable of being made rigorous, in the sense that you can take the heuristic and put solid math behind it.  But it will be incorrect in many of its details.  The merit of such heuristics is that even though they are incorrect in details, they lead your intuition in the right directions, such that you can then work with and understand the version of the argument that is completely correct in its details.

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Models and Modelling

"All models are wrong. Some models are useful." George Box

Box was a modeller, and the sentiment is widely spread among modellers of all kinds. This might be a surprise to many, who imagine that modellers think they're producing gospel. The reality is, we modellers all acknowledge the first statement. We are more interested in the second -- Some models are useful.

But let's back up a bit. What is a model? In figuring out some of this, we'll see how it is that models can be imperfect, but still useful.

There are several sorts of model, is one thing to remember. On fashion runways or covers of magazines, we'll see fashion models. In hobby shops, we can get a model spacecraft or car. We could head more towards science, and find a laboratory model, or a biological model animal, statistical model, a process model, numerical model, and so on.

Common to the models is that they have some limited purpose. A fashion model is to display some fashion to advantage -- making the dress/skirt/make up/... look good. She's not to be considered an attempt to represent all women accurately. The model spacecraft is not intended to reach the moon. But you can learn something about how a spacecraft is constructed by assembling one, and the result will look like the real thing.

In talking about a laboratory model, read that as being a laboratory experiment. You hope that the set up you arrange in the lab is an accurate representation of what you're trying to study. The lab is never exactly the real thing, but if you're trying to study, say, how much a beam flexes when a weight is put in the middle, you might be able to get pretty close. If you want to know the stability of a full-size bridge with full size beams and welds and rivets assembled by real people, it'll be more a challenge -- represent the 1000 meter bridge inside your lab that's only 10 meters long. It won't be exact, but it can be good enough. Historical note for the younger set: Major bridges like the Golden Gate Bridge, Brooklyn Bridge, Tower Bridge, and such, were designed and built based on scale models like this. The Roman Aqueducts designed over 2000 years ago, still stand, and never came near a computer. They were all derived from models, not a single one of which was entirely correct.

In studying diseases, biologists use model animals. They're real animals of course. They're being used a models to study the human disease. Lab rats and such aren't humans. But, after extensive testing was done, it was discovered that the rats for some diseases, and other animals for other diseases, reacted closely enough to how humans did. Not exactly the same. But closely enough that the early experiments and tests of early ideas could be done on the rats rather than on people. The model is wrong, but useful.

Statistical models seem to be the sort that the most people are most familiar with. My note Does CO2 correlate with temperature arrives at a statistical model, for instance -- that for each 100 ppm CO2 rises, temperature rises by 1 K. It's an only marginally useful model, but useful enough to show a connection between the two variables, and an approximate order of magnitude of the size. As I mentioned then, this is not how the climate really is modelled. A good statistical model is the relationship between exercise and heart disease. A statistical model, derived from a long term study of people over decades, showed that the probability of heart disease declined as people did more aerobic exercise. Being statistical, it can't guarantee that if you walk 5 miles a week instead of 0 you'll decrease your heart disease chances by exactly X%. But it does provide strong support that you're better off if you cover 5 miles instead of 0. Digressing a second: Same study was (and is still part of) the support of the 20-25 miles per week running or walking or equivalent (30-40 km/week) suggestion for health. The good news being that while 20 is better than 10, 10 is better than 5, and 5 is way better than 0. (As always, before starting check with your doctor about your particular situation, especially if you're older, have a history of heart problems already, or are seriously overweight). This model is wrong -- it won't tell you how much better, and in some cases your own results might be a worsening. But it's useful -- most people will be better off, many by a large amount, if they exercise.

Process models started as lab experiments, but also are done in numerical models. Either way, the method is to strip out everything in the universe except for exactly and only the thing you want to study. Galileo, in studying the motion of bodies under gravity stripped the system, and slowed it down, by going to the process model of balls rolling down sloping planes. He did not fire arrows, cannon balls, use birds, or bricks, etc.. Simplified to just the ball rolling down the plane. The model was wrong -- it excluded many forces that act on birds, bricks, and all. But it was useful -- it told him something about how gravity worked. Especially, it told him that gravity didn't care about how big the ball was, it accelerated by the same rules. In climate, we might use a process model that included only how radiation travelled up and down through the atmosphere. It would specify everything else -- the winds, clouds, where the sun was, what the temperature of the surface was, and so on. Such process models are used to try to understand, for instance, what is important about clouds -- is it the number of cloud droplets, their size, some combination, ...? As a climate model, it would be wrong. But it's useful to help us design our cloud observing systems.

Numerical models, actually we need to expand this to 'general computational models' as the statistical, process, and even some disease models now, are done as computational models. These general models attempt to model relatively thoroughly (not as a process model) much of what goes on in the system of interest. An important feature being that electronic computers are not essential. The first numerical weather prediction was done by pencil, paper, and sometimes an adding machine -- more than 25 years before the first electronic computer. Bridges, cars, and planes are now also modelled in this way, in addition or instead of scale models. Again, all of them are wrong -- they all leave out things that the real system has, or treat them in ways simpler (easier to compute) than the real thing. But all can be useful -- they let us try 'what if' experiments much faster and cheaper than building scale models. Or, in the case of climate, they make it possible to try out the 'what if' at all. We just don't have any spare planets to run experiments on.

Several sorts of models, but one underlying theme -- all wrong, but they can be useful. In coming weeks, I'll be turning to some highly simplified models for the climate. The first round will be the four 1-dimensional models. Two are not very useful at all, and two will be extremely educational. These are 4 of the 16 climate models.

Statiscal significance of 150 years of data over 4.5 billion years

The subject line is close to a recent search query that lead someone here, and echoes a comment that's not unusual in blog comment sections. The thing about it is, it's not a very strong question.

One part of the question's failure is that it isn't really a proper statistical question. Given limits of search strings, that's no surprise. But it does show up in comments (usually in the vein of assertion "150 years is too small a statistical sample of 4.5 billion years of climate.") where such limits don't apply.

The basis of any good question is to try to understand something. If what you are trying to understand is not statistical, then pursuing statistics is not going to help you. "What is your height?" is marginally statistical. If you measure the length of a short metal bar many times, which I did in freshman physics lab, you'll get slightly differing answers. So you may well answer statistically with your mean and a sample standard deviation. This is only marginally statistical, in that it is purely descriptive statistics and no hypothesis testing is involved.

Your question, however, could be non-statistical: Did it rain in my back yard last night? How much rain did my rain gauge capture? If so, you will be wasting your time if you chase after statistical tables. More at hand, someone raising statistics in a blog debate about a non-statistical question is wasting your time.

But suppose that what you're trying to understand truly does require statistical considerations beyond minor description. What would such a question look like? One could be "Given the population of voters in the USA, how many randomly selected voters would I need to ask a yes/no question in order to have a standard error in my sample of 3% or less as compared to asking the everybody?" or, for more climate-related flavor "How many satellite observations with a (known) standard error of measurement would I need to find an average sea surface temperature whose standard error would be less than 0.1 K?"

Required is a description of the 'population' -- all possible observations (the population of voters in the USA, satellite observations) -- of your 'sample' (ask some number, which we want to determine, of voters, or satellite observations -- and what statistic you are trying to estimate (% of voters who like your candidate, mean sea surface temperature).

So, back to the original question. Does it describe the population? No. 'data' certainly doesn't limit us to anything in particular. I'll guess that it is global mean temperature, of the earth (maybe it's Mars -- I've read interesting papers about Martian climatology), that is the point of interest. But we shouldn't have to guess, a good question is clear on what it is asking about. Does it describe a sampling method? Not really. 150 years, well, I'll guess that this means 'take the most recent 150 years'. Most importantly, however, does it describe what statistic one is trying to estimate? No. Again, I'll guess: that it is "Global mean temperature over the entire history of the earth."

Putting it all together, the statistical question more reasonably posed is something like "Does the last 150 years of global mean air temperatures provide a good estimate of the global mean air temperature through the history of the earth?" (better would be to define 'good', say 'standard error within 0.2 K')

That's the statistical side. But since we're not interested solely in statistical questions regarding climate, at least not most of us, we also have to ask, "Is this a physically meaningful question?" The person who did the search, I don't know what they have in mind. They could indeed have in mind a question for which the mean temperature of the planet throughout its history is exactly the right number to answer.

Usually, though, comments about the 150 years vs. 4.5 billion surface in debates about modern climate and modern climate change. I'll have to invite contributions on what relevance the planetary mean temperature from 4.5 billion years ago to ... oh, let's say 30 million years ago ... has to questions of current climate and climate change. Certainly one wants to know how climate has changed through all of time, and why. I'm one such person. But at hand is those who argue that the global mean over that entire period matters.

What's important regarding human responses to climate change is the climate on human time scales. The last 150 years handily covers me back through my great-grandparents. The next 150 years will cover my children, grandchildren, and possibly great-grandchildren. Even a 'mere' million years ago, much less 4.5 billion, there weren't any humans around to think about climate change at all. So the 4.5 billion years is, for 'what do we do now' questions, a spectacularly large red herring.

Human society infrastructure also dictates a much shorter term (than 4.5 billion years) concern. Almost every mile of paved road in the world is less than 150 years old. Almost every mile of railroad. Almost all port structures. Absolutely all air transport terminals are less than 150 years old. Absolutely all electrical distribution structure, all phone lines, and even more so all cell phone towers are less than 150 years old. Coal, oil, natural gas distribution networks, again, are almost entirely or entirely less than 150 years old. Many of the world's major cities are less than 150 years old (I'll count Chicago here, as the great fire in 1871 erased so much of the city).

The climate-related concern here is that all these things were constructed based on what climate was like around the time of their construction. That climate drove what the standards would be for, say, tolerance to flooding, tolerance to drought, high winds, high rain rates, high and low temperatures, and so on. If climate changes outside the range that the infrastructure was built for -- almost all of it globally being much less than 150 years old -- then there is a serious risk that the structure will fail when it encounters brand new climate conditions.

In this vein, then, comments about the 'we did fine in the medieval warm period' are a different flavor of red herring. Chicago, Sao Paulo, Melbourne, Johannesburg, ... didn't exist back then. They did not 'do fine' in the medieval warm period, they never encountered it. Even cities that did, such as London, Rome, Xi'an, did so with far smaller populations than today's. London, ca. 1100, had a population around 18,000, and is about 1000 times larger today (taking the metro area). Rome was about 20,000 around 1100 AD, vs. 200 times as large now. Xi'an was among the largest of cities in the world then, and may have been about 500,000 around 1100 AD. But almost 20 times that today. (mostly Wikipedia figures). While a Rome or London of 10-20,000 survived a medieval warm period ok, Rome and London of many millions have never see it before.

As usual, we can get far by asking two questions: "Is this question statistically meaningful?" "Is the question physically meaningful?" After looking at the former, regarding the original search string, and not infrequent comment, we see that it isn't a meaningful statistical question. After rephrasing it to something that is statistically good, we check to see whether it makes physical sense. Turns out, for the sort of thing I'm concerned about and others use it, that even the rephrased question isn't physically meaningful. Knowing that global mean temperature for the last 4.5 billion years was 20 C (I make up a number) as opposed to 15 C still doesn't tell us whether major modern cities, and their millions of residents, will be able to manage likely climate changes. Nor does it tell us what adaptations to take, much less how expensive it would be to make those adaptations. And it doesn't tell us what the costs, both dollars and lives, would be if there were no adaptation.

Feedback

I'm actually referring to an important mathematical and physical concept, rather than the comments you give (which I also value).

Feedback is an extremely common process. Perhaps the most common case that people know is feedback involved public address systems. You have a microphone to pick up sound, which goes to an amplifier, and then out a speaker. If you put the microphone too near the speaker, then the microphone picks up some minor sound (say the sound of someone putting papers on the stand near the microphone), it goes through the amplifier and the louder sound comes out the speaker. The microphone now picks up that sound, it gets amplified even more and comes out the speaker again. Repeat through a number of cycles and the speaker is now as loud as it can be. This is a runaway feedback. Not all feedback is runaway.

A feedback can also be limited. Consider the atmosphere in this case. It has a temperature, carbon dioxide level, and water vapor level. Both carbon dioxide and water vapor are greenhouse gases, so if there is more of them, the temperature goes up. Suppose we put enough carbon dioxide into the atmosphere that its greenhouse effect (alone) raised temperature by 1 degree. If the atmosphere is warmer, we expect it to have more water vapor. That extra water vapor, let's say, produces another 0.5 degrees of warming. But, since temperature has gone up again, there's still more warming -- another half of this, for 0.25 degrees. This feeds back through increasing the water vapor to make another 0.125 degrees warming. Keep cycling through this feedback and it turns out to add another 1 degree of warming (1 = 0.5 + 0.25 + 0.125 + ...) after you've gone through an infinite number of steps. It's pretty close after a limited number of steps (99.9% of the way there after 10 cycles). We can look at these feedbacks in terms of how much of a response (multiplier) there is to a 1 degree kick to the system. I made up the number 0.5 here (every step is 0.5 times the previous). That's actually about the right size, in addition to being simple to work with. If the response multiplier is, say, 0.75 instead, then instead of getting back a total warming of 2 degrees, we would get back 4 degrees. The formula is
total = 1 / (1 - x)
where x is this multiplier, and the multiplier has to be less than 1.

Feedbacks can also produce cycles. A common illustration of this is predators and prey -- sharks and fish, or foxes and hares. Suppose one year, there are more fish than usual. The sharks, then, have a lot to eat and give birth and raise more sharks than usual. But, now that there are more sharks, they eat up even more fish than usual. That decreases the number of fish below the usual level. With fewer than normal fish, the sharks start dying off. That eventually gives us fewer than normal sharks, so the fish population recovers. And so on. The two populations could keep cycling (if the balances are right), or one could crash (depends on whether the extra sharks eat up too many fish, or whether the time of few fish lasts too long for any sharks to survive).

In the climate system, there are definitely some amplifying feedbacks and some cycling feedbacks. There don't appear to be any runaway feedbacks. That's not terribly reassuring, however, because life can get quite unpleasant even if temperatures don't run off to boiling the oceans.