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It’s Earth Day, so time for a brief break from my laserlike, day-long focus on complexity theory, and for my long-promised post about climate change.

Let me lay my cards on the table. I think that we’re in the same position with climate change today that we were with Hitler in 1938. That position, in case you’re wondering, is on the brink of a shitstorm. And as with the lead-up to that earlier shitstorm, some people are sanely worried, some are in active denial, and the rest are in “passive denial” — accepting the obvious if pressed, but preferring to think about more pleasant things like NP intersect coNP. It’s frustrating even to have to defend the “worried” view explicitly, since it’s so clear which way the debate will have been settled 50 years from now.

At the same time, I can’t ignore that there are thoughtful, humane, intelligent people — just like there were in the 1930’s — who downplay, equivocate over, and rationalize away the shitstorm that (again from my perspective) is gathering over our heads.

After all, isn’t the climate change business more complicated than all that? Do we even know the Earth is getting warmer? Okay, so maybe we do know, but do we really know why? Couldn’t it just be a coincidence that we’re pumping out billions of tons of CO₂ and methane each year, and 19^th-century physics tells us that will make the temperature rise, and the temperature is in fact rising as predicted? What about feedbacks like cloud cover, ocean absorbtion, and ice caps? And sure, maybe the feedbacks could at most buy a few decades, and maybe some of them (like melting ice caps darkening the Earth’s surface) are rapidly making things worse rather than better, but even so, wouldn’t the loss of some low-lying countries be more than balanced out by warmer winters in Ontario? And granted, maybe if our goal was to run a massive, irreversible geophysics experiment on an entire planet, it might be smarter to start with (say) Venus or Mars instead of Earth, but still — wouldn’t it be easier to adapt to a climate unlike any the planet has experienced in the last 200 million years than to drive Priuses instead of Cherokees? Isn’t it just a question of how to allocate resources, of how to maximize expected utility? And aren’t there other risks we should be more worried about, like bird flu, or out-of-control nanorobots converting the planet into grey goo?

I’ll tackle some of these questions in future posts or comments — though for most of them, the professionals at RealClimate can do a better job than I can. Today I want to try a different tack: flying over most of this well-worn ground, and aiming immediately for the one place where the climate skeptics invariably end up anyway when all of their other arguments have been exhausted. That place is the Chicken Little Argument.

“Back in the 1970’s, all you academics were screaming about overpopulation, and the oil shortage, and global cooling. That’s right, cooling: the exact opposite of warming! And before that it was radiation poisoning, or an accidental nuclear launch, and before that probably something else. Yet time after time, the doomsayers were wrong. So why should this time be any different? Why should ours be the one time when the so-called crisis is real, when it’s not a figment of a few scientists’ overheated imaginations?”

The first response, of course, is that sometimes the alarmists were right. More than once, our civilization really did face an existential threat, only to escape it by a hair. I already mentioned Hitler, but there’s another example that’s closer to the subject at hand.

In the 1970’s, Mario Molina and F. Sherwood Rowland realized that chlorofluorocarbons, then a common refrigerant, propellant, and cleaning solvent, could be broken down by UV light into compounds that then attacked the ozone molecules in the upper atmosphere. Had the resulting loss of ozone continued for much longer, the increased UV light reaching the Earth’s surface would eventually have decimated populations of plankton and cyanobacteria, which in turn could have destabilized much of the world’s food chain.

As with global warming today, the initial response of the chemical companies was to attack the ivory-tower, tree-hugging, funding-crazed, Cassandra-like messenger. But in 1985, Joseph Farman, Brian Gardiner, and Jonathan Shanklin looked into a weird error in ozone measurements over Antarctica, which seemed to show more than half the ozone there disappearing from September to December. When it turned out not to be an error, even Du Pont decided that planetary suicide wasn’t in its best interest, and CFC’s were phased out in most of the world by 1996. We survived that one.

But there’s a deeper response to the Chicken Little Argument, one that goes straight to the meat of the issue (chicken, I suppose). This is that, when we’re dealing with “indexical” questions — questions of the form “why us? why were we born in this era rather than a different one?” — we can’t apply the same rules of induction that work elsewhere.

To illustrate, consider a hypothetical planet where the population doubles every generation, until it finally depletes the planet’s resources and goes extinct. (Like bacteria in a petri jar.) Now imagine that in every generation, there are doomsayers preaching that the end is nigh, who are laughed off by folks with more common sense. By assumption, eventually the doomsayers will be right — their having been wrong in the past is just a precondition for there being a debate in the first place. But there’s a further point. If you imagine yourself chosen uniformly at random among all people ever to live on the planet, then with about 99% probability, you’ll belong to one of the last seven generations. The assumption of exponential growth makes it not just possible, but probable, that you’re near the end.

That’s one formulation (though not the best one) of the infamous Doomsday Argument, which says (roughly speaking) that the probability of human history continuing for millions of years longer is less than one would naïvely expect, since if it did so continue, then we would occupy an improbable position near the very beginning of that history. Obviously cavemen could have made the same argument, and they would have been wrong. The point is that, if everyone in history makes the Doomsday Argument, then most people who make it (or a suitable version of it) will by definition be right.

On hearing the Doomsday Argument for the first time, almost everyone thinks there must be a fallacy somewhere. But once you accept one key assumption, the Argument is a trivial consequence of Bayes’ Rule. So what is that key assumption? It’s what Nick Bostrom, in one of the only metaphysical page-turners ever written, calls the Self-Sampling Assumption (SSA). The SSA states that, if you consider a possible history of the world to have a prior probability p, and if that history contains N>0 people who you imagine you “could have been,” then you should judge the probability of your being a specific one of those people within that history to be p/N. Sound obvious? Well, you might imagine instead that you need to weight the probability of each history by the number of people in it — so that, if a history has ten times as many people who you “could have been,” then you would be ten times as likely to exist in that history in the first place. Bostrom calls this alternative the Self-Indication Assumption (SIA).

It’s not hard to show that switching from SSA to SIA exactly cancels out the effect of the Doomsday Argument — bringing you back to your “naïve” prior probabilities for each possible history. In short, if you accept SSA then the Doomsday Argument goes through, while if you accept SIA then it doesn’t.

But before you buy that “SIA not SSA” bumper-sticker for your SUV, let me point out the downsides. Firstly, SIA forces you to treat your own existence as a random variable — not as something you can just condition on! Indeed, the image that springs to mind is that of a warehouse full of souls, not all of which will get “picked” to inhabit a body. And secondly, assuming it’s logically possible for there to be a universe with an infinite number of people, SIA implies that we must live in such a universe. Usually, if you reach a definite empirical conclusion starting from pure thought, your best bet is to look around you. You might find yourself in a medieval monastery or an Amsterdam coffeeshop.

On the other hand, as Bostrom observed, the SSA carries some heavy baggage of its own. For example, it suggests the following “algorithm” by which the first people ever to live, call them (I dunno) “Adam” and “Eve,” could solve NP-complete problems in polynomial time. They simply guess a random solution, having formed the firm intention to

1. have children (leading eventually to an exponential number of descendants) if the solution is wrong, or
2. have no children if the solution is right.

(For this algorithm, it really does have to be “Adam and Eve, not Adam and Steve.”) Here’s the punchline: the prior probability of Adam and Eve’s choosing a wrong solution is close to 1, but under SSA, the posterior probability is close to 0. For if Adam and Eve guess a wrong solution, then with overwhelming probability they wouldn’t be Adam and Eve to begin with — they would be one of the numerous descendants thereof.

Indeed, there’s a loony, crackpot paper showing that if Adam and Eve had a quantum computer, then they could even solve PP-complete problems in polynomial time. Every day I’m dreading the Exxon ad: “If the assumptions underlying the Doomsday Argument were valid, it’s not just that Adam and Eve could solve NP-complete problems in polynomial time. Modulo a plausible derandomization assumption, a theorem of S. Aaronson implies they could decide the entire polynomial hierarchy! So go ahead, buy that monster SUV.”

If this discussion seems hopelessly speculative, well, that’s exactly the point. The Doomsday Argument is hopelessly speculative, but not more so than the Chicken Little Argument. Ultimately, both arguments rest on metaphysical assumptions about “why we’re us and not someone else” — about the probability of having been born into one historical epoch rather than another. This is not the sort of question that science gives us the tools to answer.

For me, then, the Doomsday Argument is like an ethereal missile that neutralizes the opposing missile of the Chicken Little Argument — leaving the ground troops below to slog it out based on, you know, actual facts and evidence. So I think the environmentalists’ message to the climate contrarians should be as follows: if you stick to the science, then we will too. But if you fall back on your favorite lazy meta-argument — “why should the task of saving the world have fallen to this generation, and not to some other one?” — then don’t be surprised to find that metareasoning cuts both ways.

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What am I mad about? Oh, God.

I’m mad about Bush receiving Michael Crichton in the White House, to be reassured that climate change is a hoax even as the Northwest Passage opens up for the first time in a few million years. I’m mad about the Democrats’ failure to capitalize on the Enron scandal, and particularly the infamous “Grandma Millie” tapes (having just watched the film Enron: The Smartest Guys in the Room). I’m mad about Pius XII, the man who arm-twisted Germany’s 23 million Catholics into cooperating with the Nazis despite their initial opposition, being considered for sainthood (I’m in the middle of a book about it, Hitler’s Pope by John Cornwell). I’m mad about my own procrastination in writing a popular article for Scientific American about the limits of quantum computing. I’m mad about a public school system that condemns any math or science tracking as “elitist,” while the football and basketball programs aren’t similarly condemned. I’m mad about people who declare that “a proof of P!=NP would be worthless, since what if there were an algorithm for SAT that took 1.0000001ⁿ steps?,” as if no one had ever had such a perceptive insight in the 50-year history of complexity theory.

But, as for the “not gonna take it anymore” part, one does have to restrict one’s focus a bit. So recently I decided to concentrate my anger on overpriced journal subscriptions — and in particular, on the gouging of university libraries by companies like Kluwer and Elsevier. I’ve just written a three-page polemic about this issue (technically a book review), which is going to appear in SIGACT News, possibly with a rebuttal and counter-rebuttal. I’d be grateful for comments. Note that what I write about scientists’ “peculiar anger deficiency” applies to many other issues, global warming being one obvious example. There comes a time when it’s no longer enough to be correct: you also have to be angry!

Thanks to Bill Gasarch, both for commissioning the review and for suggesting the title of this post.

Note: My diatribe is also available in HTML and postscript.

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As winner of the Best Umeshism Contest (remember that?), Peter Brooke earned the right to ask me any question and have me answer it on this blog. Without further ado, here is Peter’s question:

If it is assumed that God exists, what further, reasonable, conclusions can be made, or is that where logical inquiry must end? Reasonable means in the light and inclusive of present scientific understanding. Defend any assumptions and conclusions you make.

At least Peter was kind enough not to spring “Is there a God?” on me. Instead, like a true complexity theorist, he asks what consequences follow if God’s existence is assumed.

Alas, Peter didn’t say which God he has in mind. If it were Allah, or Adonai, or Zeus, or the Flying Spaghetti Monster, then I’d simply refer Peter to the requisite book (or in the case of the Spaghetti Monster, website) and be done. As it is, though, I can’t assume anything about God, except that

1. He exists,
2. He created the universe (if He didn’t, then it’s not He we’re talking about), and
3. He’s a He.

(Note for Miss HT Psych: the third assumption is a joke.)

So the only way I see to proceed is to start from known facts, and then ask what sort of God would be compatible with those facts. Though others might make different choices, the following facts seem particularly relevant to me.

• About 700,000 children each year die of malaria, which can easily be prevented by such means as mosquito nets and the spraying of DDT. That number will almost certainly grow as global warming increases the mosquitoes’ range. As with most diseases, praying to God doesn’t seem to lower one’s susceptibility or improve one’s prognosis.

• According to our best theories of the physical world, it’s not enough to talk about the probability of some future event happening. Instead you have to talk about the amplitude, which could be positive, negative, or even complex. To find the probability of a system ending up in some state, first you add the amplitudes for all the ways the system “could” reach that state. Then you take the absolute value of the sum, and lastly you take the square of the absolute value. For example, if a photon could reach a detector one way with amplitude i/2, and another way with amplitude -i/2, then the probability of it reaching the detector is |i/2 + (-i/2)|² = 0. In other words, it never reaches the detector, since the two ways it could have reached it “interfere destructively” and cancel each other out. If we required the amplitudes to be positive or negative reals rather than complex numbers, there would be some subtle differences — for example, we could just square to get probabilities, instead of taking the absolute value first. But in most respects the story would be the same.

• From 1942 to 1945, over a million men, women, and children died in one of four extermination complexes at Birkenau, or “Auschwitz II” (Auschwitz I was the smaller labor camp). Each complex could process about 2,500 prisoners at a time. The prisoners were ordered to strip and leave their belongings in a place where they could find them later. They were then led to an adjacent “shower room,” containing shower heads that were never connected to any water supply. Once they were locked inside, guards dropped pellets from small openings in the ceiling or walls. The pellets contained Zyklon B, a cyanide-based nerve agent invented in the 1920’s by the German Jewish chemist Fritz Haber. The guards then waited for the screams to stop, which took 3-15 minutes, depending on humidity and other factors. Finally, Sonderkommandos (prisoners who were sent to the gas chambers themselves at regular intervals) disposed of the bodies in the adjacent crematoria. With the arrival of 438,000 Hungarian Jews in 1944, the crematoria could no longer keep up, so the bodies were burned in open pits instead. Besides those killed at Auschwitz, another 1.6 million were killed at the four other death camps (Sobibor, Belzec, Treblinka, and Chelmno). In the USSR and Poland, another 1.4 million were shot in front of outdoor pits by the Einsatzgruppen; still others died through forced starvation and other means. Judged on its own terms, the extermination program was a spectacular success: it wiped out at least 2/3 of Russian and European Jewry and changed the demography of Europe. The Americans and British declined numerous opportunities to take in refugees, or to bomb the camps or the train tracks leading to them. Most of the perpetrators, except for a few top ones, returned to civilian life afterward and never faced trial. Millions of people today remain committed to the goal of a Judenrein planet; some, like my friend Mahmoud, are working to acquire nuclear weapons.

• According to our best description of space and time, the faster an object is moving relative to you, the shorter that object will look in its direction of motion, and the slower time will pass for it as observed by you. In particular, if the object is moving at a fraction f of the speed of light, then it will contract, and time will slow down for it, by a factor of 1/(1-f²)^1/2. This does not mean, as some people think, that concepts like “distance” have no observer-independent meaning — only that we were using the wrong definition of distance. In particular, suppose an observer judges two events to happen r light-years apart in space and t years apart in time. Then the interval between the events, defined as r²-t², is something that all other observers will agree on, even they disagree about r and t themselves. The interval can also be defined as r²+(it)²: in other words, as the squared Euclidean distance in spacetime between the events, provided we reinterpret time as an imaginary coordinate. (This is known as “Wick rotation.”)

• When I was younger, my brother and I went to an orthodontist named Jon Kraut. Dr. Kraut was a jovial guy, who often saw me on weekends when I was home from college even though his office was officially closed. He was also an aviation enthusiast and licensed pilot. About a week ago, Kraut was flying a twin-engine plane to South Carolina with his wife, Robin, their three kids (ages 2, 6, and 8), and the kids’ babysitter. Kraut reported to the control tower that he was having problems with his left engine. The plane made one approach to the airport and was coming back to try to land again when it crashed short of the runway, killing the whole family along with the babysitter. On the scale of history, this wasn’t a remarkable event; I only mention it because I knew and liked some of the victims.

Now, based on the facts above, plus many others I didn’t mention, and “in the light … of present scientific understanding,” what can we say about God, assuming He exists? I think we can say the following.

First, that He’s created Himself a vale of tears, a theater of misery beyond the imagination of any horror writer. That He’s either unaware of all the undeserved suffering He’s wrought, or else unable or unwilling to prevent it. That in times of greatest need, He’s nowhere to be found. That He doesn’t answer the prayers of the afflicted, or punish evildoers in any discernible way. That He most likely doesn’t intervene in human affairs at all — though I wouldn’t want to argue with those who say He does intervene, but only for the worse.

Second, that He apparently prefers complex numbers to real numbers, and the L₂ norm to the L₁ norm.

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Genocide. Global warming. Nuclear proliferation. Sex trafficking in Cambodia. Famine in sub-Saharan Africa.

If history has taught us anything, it’s that problems like these tend to sort themselves out if we just ignore them for long enough. So I get annoyed when guys like Nicholas Kristof keep reminding people about them, thereby diverting attention from real issues like steroid abuse in the NFL.

In his latest piece of “offbeat” journalism, Kristof pulls out the stops, explicitly comparing humankind’s current failure to prevent the Darfur genocide with its failure to prevent earlier genocides:

During the Holocaust, the world looked the other way. Allied leaders turned down repeated pleas to bomb the Nazi extermination camps or the rail lines leading to them, and the slaughter attracted little attention. My newspaper, The New York Times, provided meticulous coverage of World War II, but of 24,000 front-page stories published in that period only six referred on page one directly to the Nazi assault on the Jewish population of Europe. Only afterward did many people mourn the death of Anne Frank, construct Holocaust museums, and vow: Never Again.

The same paralysis occurred as Rwandans were being slaughtered in 1994. Officials from Europe to the US to the UN headquarters all responded by temporizing and then, at most, by holding meetings. The only thing President Clinton did for Rwandan genocide victims was issue a magnificent apology after they were dead.

Much the same has been true of the Western response to the Armenian genocide of 1915, the Cambodian genocide of the 1970s, and the Bosnian massacres of the 1990s. In each case, we have wrung our hands afterward and offered the lame excuse that it all happened too fast, or that we didn’t fully comprehend the carnage when it was still under way.

And now — let me guess — the same is happening in Darfur. Arab Janjaweed militias, supported by the Sudanese government, are systemically massacring, raping, and mutilating non-Arab civilians, while the world watches on in horror but does nothing. Dude, what a shocker. I never could have predicted that one.

Think about it. Sixty years after Auschwitz, obviously the world must have solved this genocide thing. The US, or EU, or UN, or someone must have set up some sort of special army that, you know, goes in and stops it before it happens. I mean, anything else would be criminally insane! It would be like 911 putting people on hold for an hour, or a hospital telling a guy spewing arterial blood to sit in the waiting room and read a magazine. Right?

Even if not, I’ve just spent over 20 minutes of valuable procrastination time writing this post and sending some money. So regardless of what happens in Darfur, you can’t accuse me of having sat in my chair and done nothing. No, I sat in my chair and did something.

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