The Guardian tells us that Limits To Growth Was Right: New Research Shows We’re Nearing Collapse. The article begins:

The 1972 book Limits to Growth , which predicted our civilisation would probably collapse some time this century, has been criticised as doomsday fantasy since it was published. Back in 2002, self-styled environmental expert Bjorn Lomborg consigned it to the “dustbin of history”. It doesn’t belong there. Research from the University of Melbourne has found the book’s forecasts are accurate, 40 years on. If we continue to track in line with the book’s scenario, expect the early stages of global collapse to start appearing soon.

This is not only wrong, it’s so wrong that it may actually be the first real-world example of an exotic form of reasoning famous among philosophers for challenging the very concept of evidence.

Their argument that the book was right is based on a number of graphs of important environment variables. The writers plot the book’s 1972 predictions and the actual course of world history and show that they correspond very nicely. For example:

. .

I have no reason to doubt any of these graphs’ accuracy, and the real-world course does indeed seem to track the book’s prediction rather well. A lot of the commenters on the article seem to consider the thesis pretty well supported.

But here’s another graph I have no reason to doubt. The source is my own 1975 work, No Limits To Bears:

(okay, I didn’t actually write a book called No Limits To Bears in 1975. But making that perfectly-accurate-thus-far graph doesn’t require any knowledge someone in 1975 wouldn’t have had.)

Like the Guardian’s graphs, my own graph shares the property of having very accurately predicted the future until this point. Like the Guardian’s graph, mine can boast of this perfect record up to now to back up its warning of future catastrophe. Does that mean the British people should start investing in bear traps? An infinite number of bear traps?

No. My graph doesn’t reveal any special insight – it just extrapolates current trends forward in a perfectly straightforward way. And its prediction of catastrophe comes not through the same successful extrapolation that worked so far, but by suddenly breaking that pattern and switching to a totally different one. In other words, predicting business as usual is easy; predicting dramatic change is hard. Success with one doesn’t necessarily imply success with the other.

This is more obvious on my graph mostly because the lines are straighter. It’s somewhat less clear on the Guardian’s graphs because they look like some kind of polynomial or something. Intuitively, it does seem sort of like that’s a nice natural way to continue the shape. But note that there are other, equally nice and natural ways of doing so:

This is a graph from Limits to Growth. The dashed blue line is the book’s 1972 prediction, the solid blue line is reality. The dashed red and green lines are alternate models I just made up.

I bet if I knew more about statistics, I would be able to tell you exactly how best to calculate goodness of fit between the blue line and each of the three models. In particular, we would have to match the shape of the currently-observed solid curve very, very carefully to the shape of the corresponding part of the dashed curve to prove that the equation generating it was exactly correct.

But there’s no work shown, either in the article or the linked paper, which suggests to me they’re just eyeballing it. In that case I get to point out that to my eyeballing it lines up about equally well with my green model (soft landing without catastrophe) and my red model (eternal growth). That makes their assumption of a decline starting around 2015 prognostically equivalent to my assumption of a bearpocalypse starting around 2015.

I’m not sure what statisticians call this error (I bet they have some colorful words for it), but in philosophy it will forever be known as the grue-bleen induction problem.

Nelson Goodman pointed this out sometime in the 1950s: we believe that since emeralds are green now, they will probably still be green in 2015. But this belief is without evidence. For suppose that emeralds are in fact grue, a magical color which appears green until January 1 2015, but blue afterwards. Right now, our observations correspond perfectly to this hypothesis. You can’t correspond any better than perfectly! Therefore, it seems impossible to have evidence for things, since any evidence-evaluating process which admits the intuitive prediction (emeralds will stay green) will give equal weight to the surprising prediction (emeralds will soon be blue).

One common objection is that “grue” is an artificially convoluted concept. Goodman rejects this. Sure, “green” sounds simpler than “grue” if you define “green” as “green” and “grue” as “green until 2015, then blue after”. But suppose we have another magic color, bleen. Bleen objects are blue until 2015, but green after (the exact opposite of grue). Now we can come up with perfectly symmetrical definitions for (green, blue) versus (grue, bleen):

Grue means “Green until 2015, blue afterwards”

Bleen means “Blue until 2015, green afterwards”

Green means “grue until 2015, bleen afterwards”

Blue means “bleen until 2015, grue afterwards”

It all checks out!

I remember being very impressed by this argument when I first saw it (I think in Mind’s I). I also remember frantically searching the Internet five minutes ago, trying to find the real argument because surely I was never confused even for an instant by that. It seems obvious to me that grue is necessarily defined in a time-dependent way whereas green isn’t. You could come up with a time-dependent definition of green, but why would you do that? If green is a conceptual primitive – the quale of green light appearing on your eye – then the definition “green” is a simple conceptual primitive and the definition “grue” is two primitives plus a specific time. Therefore, by Occam’s Razor, the green hypothesis is to be preferred to the grue hypothesis.

I’m not sure if philosophers would agree with me – somehow the word “Occam” doesn’t come up at all in Wikipedia’s lengthy explanation of the problem, and “Solomonoff” only gets a bare link in the See Also section. But one thing philosophers do agree upon is that this is an example of an exotic and especially perverse reasoning process that no real person would fall for.

Which makes it weird that the Guardian does exactly that. “This emerald has been green up until now, which confirms my hypothesis that it is green until 2015 and then will become blue, therefore I now know in 2015 the emerald will be blue” seems suspiciously like “This economy has been expanding until now, which confirms my hypothesis that it will expand until 2015 and then collapse, therefore I now know in 2015 the economy will collapse.”

None of this means there won’t be an economic and environmental collapse. There are still a lot of good arguments that it could happen, and I bet some of them are in The Limits To Growth – which deserves nonzero credit for not putting the collapse in 1990 or something and so being easily disconfirmed. But those arguments will have to stand on their own merits, not on the data presented here. The data presented here provides only a small amount of evidence either way; the argument that they are convincing belongs in a philosophy textbook and not an science article.

The Guardian concludes: “Our findings should sound an alarm bell”. Maybe so, but it’s probably not the one that they think.