Pease read my response to Economagic.
As a matter of fact, I do understand that relationship very well. I did learn it in high school, but most people don’t, so we are both ahead of that game.
It is true that since the temperature rises in proportion to the rise in the square root of CO2 concentration, it increases less rapidly than it would if it were a linear function of CO2 concentration. It is also true in a sense that it rises “slower” than does CO2, but the two are not really commensurate (comparable) as they have different units.
But that is irrelevant to the way we perceive the rate of temperature rise.
Exponentials are tricky. They are in a sense self-similar at all scales, like fractals, meaning that they all have exactly the same shape, depending only on the “zero point” (not quite a rigorous description, to avoid a long digression) and the relative scales on the axes. That is the reason it is helpful to think of them in terms of doubling time (the lily pad riddle–try it using linear axes and a calculator).
With linear scales on both axes, all exponentials have a “hockey stick” bend at a very specific point. With the independent variable (“time”) on the horizontal axis, To the left of the vertical axis the dependent variable declines slowly, never quite reaching zero. But to the right of that point they soar off to infinity quite rapidly.
Since temperature empirically rises exponentially (as long as CO2 concentration does–both are only approximately exponential), regardless of the particular relation between it and CO2 concentration, there will always be a short period of time in which its rate of increase goes from negligible to very rapid – the hockey stick. The fact that temperature rise is proportional only to the square root of CO2 concentration actually “flattens out” the curve compared to what it would have been if the relation were direct, delaying the point in time at which the hockey stick occurs (so at a higher level of technology to address it), and also increasing the time between the point at which we see the hockey stick and any given percentage level of temperature rise.
This is not “dif-eq,” but it is still tricky. If it is still not clear, I may be able to find a more comprehensive but still concise article online. It is the exponential growth itself, not the square root relation to another exponential, that creates the hockey stick, the surprise when we awaken and find the pond suddenly completely covered with lily pads.
You got the gist of it ok.
Over short time horizons, the square root causes the stick part of the temperature hockey stick to be half as steep as the stick of the CO2 concentration hockey stick. To see why this is true, you just need to expand the two exponentials for small arguments.
It is unfortunate that the temperature hockey stick is half as steep as the CO2 hockey stick, because that lowers the sense of urgency.
“Whew” again. Yes, as is almost always the case it is the human factor that is absolutely critical and absolutely unpredictable. So far we have botched it very badly.
And yes, extraction WILL come to an end, either as a fairly abrupt planned decline or as a screeching halt. This is not exactly Malthus’s population outstripping the food supply, but to the best of my knowledge he was the first to elucidate the principle that unlimited growth in a finite system is impossible; pretty insightful for 1798.
By “surplus” I take it that you mean what is commonly called “waste.” The principle applies equally to organic and inorganic resources. Some Permaculturists are now saying, "REFUSE, reduce, reuse, repair, re-purpose, (and when all “utility” has been “extracted,” then) recycle. I was saying 40 years ago that there is no such thing as “disposable” because there is no more “away” left in which to throw stuff. But inorganic resources such as minerals face a hard constraint at the source as well, being “perfectly non-renewable.”
In order for humans to survive, we have to close the circle, starting as soon as we realize fully that it is not an infinite straight line.
I really appreciate your approach, acknowledging the enormity of the challenge we face while still recognizing that la guerre n’est pas fini. The aspect of CD that I like the least is the prevalence and certitude of naysayers and nihilists.
Yes, that is correct, although the “steepness” (slope; derivative) is always increasing (monotonic) from left to right in the usual graph. But what you call “lower sense of urgency” I call “more time to deal with the problem,” the glass half full rather than half empty (although which is which is never clear). When I first learned of the problem (1972) it was believed that we had about 150 years to deal with it. For an absolute end point, and given how primitive the science of climate was then, a pretty good estimate.
No, it’s not over 'til it’s over. And it is almost unprecedented to see much past even a single bend in the river, though we have a lot more data than we did.
Malthus got a lot right. But so much of human behavior is culturally imposed and malleable that there’s no practical and straightforward ratio of persons per habitat. That does not mean that population can increase forever, of course. It just means that a reasonable count of how many humans can thrive on the surface of the planet has to be relative to how we behave.
Yes! Surplus is waste and waste surplus. But comparing waste money to a treasure in manure or insects probably begs the question. But yes, that’s it; we have to close the circle. The products of one process have to be the materials for the next.
Here’s to that realization!
Money – HUH! It certainly is an a category of its own, not comparable to anything necessary to carbon-based life forms, and perhaps now increasingly unsuited for its historic roles.
Appropriately, your comment brings us full circle, back to the subject of the article.
I spent a long time battling and trying to understand money until it dawned on me that it is a fiction–not unreal nor nonexistent nor less than influential among us benighted H sapiens types, but a semiotic thing, more like a language or iconography or symbol set or mythology than like a resource in what we loosely call a material sense.
And it still leaves me puzzling sometimes. But you know, so does Gilgamesh.
Good description. I told my classes that I had studied classical monetary theory with a master and was pretty sure that no one really understands what money is or how it works, including myself and certainly all mainstream economists. Less than ten percent of the two graduate courses had anything to do with the real world, and “Modern Monetary Theory” merely corrects some of the grossest errors from the 18th century. I think anthropologist David Graeber’s great tome, Debt: The first 5,000 years, is pretty good, and there are a number of other non-economists making useful contributions. Again, I am saving this thread out for reference. I have yet to tackle Gilgamesh, although I heard a fascinating interview by Terry Gross with the author of a new translation in about 2006.