Look at the graph and imagine that the sine wave is one process in time (e.g. Temperature) and the cosine wave is another process (e.g. CO2 concentration).
Then, depending on what time you choose to start looking you can say that cos leads sin by Pi/2 radians (90 degrees) (starting at time t = 0) or that sin leads cos by 3Pi/2 radians (starting at time t = Pi/2).
Now, if you make the mistake of assuming that one curve causes the other it's easy to show either that global warming affects CO2 or that CO2 causes global warming. Worse, if you examine specific time segments you can come up with any conclusion you like; let's assume the sine wave represents process s and the cosine represents process c, then:
From time 0 to Pi/2: c decreases as s increases.
From time Pi/2to Pi: c decreases as s decreases.
From time Pi to 3Pi/2: c increases as s decreases.
From time 3Pi/2to 2Pi: c increases as s increases.
So if we confound the issue by seeing causality we can induce anything we like including CO2 decreases global warming. Does this make sense?
Stu
4 comments:
Hi Stu,
You bring up a very interesting and practical question in analyzing statistics or time-series. What you say about the impossibility of determining lag or lead in a pair of sine waves is exactly true.
However, in the case of ice core data concerning temperature and CO2 content, we are not looking at a pair of sine waves. I'm sorry I can't post the graph for you, because of my blogging ignorance, but the graph is available if you google "global warming, ice cores. carbon dioxide, inconvenient truth." The graphs of temperature and carbon dioxide are highly complex (containing many sine waves of different frequencies if you like Fourier analysis), so that there is little doubt that temperature leads carbon-dioxide, not the other way around. In other words there is only one lag-lead time which will match up all frequencies.
The fact that temperature rise precedes carbon-dioxide rise apparently is the reason that the UN dropped the graph from its latest report on global warming. It was an "inconvenient truth" for those who have total confidence in the existing computer models of the Earth's energy balance.
Stu (and Joel):
Each of you deserves thanks for bringing up (and bringing down) a great philosophical issue related to the direction of causation.
If you were to look at the graph Stu posted (assuming you didn't know about sine and cosine) you would definitely notice the close correlation between the blue and red curves and, based on the smaller time-lag, you would probably say whatever is represented by the blue curve "caused" whatever is represented by the red curve.
As Stu points out, the blue curve leads the red curve by 90 degrees, while the red curve leads the blue one by 270 degrees. Absent any other knowledge, we normally assume the shorter the time lag the more likely that is the direction of causation.
[In actuality, there is no "causation" in either direction between sine and cosine. Both are mathematical abstractions, caused by mathematicians!]
An example of assuming the shorter time lag represents likely causality inthe accident scenario I presented in an earlier Topic thread. Say there were two accidents at a given intersection on a certain day, one in the AM and one in the PM. Say you were presented with a graph of the traffic delay and the police for the whole day. You would notice there was only a ten minute time between the delay increasing and the police increasing, both in the AM and the PM and, therefore, say the traffic delay caused the police to be dispatched.
A cynic might claim the PM delay was actually caused by the Police departing the intersection after the AM accident was cleared away. "NO!" you would argue, "the PM delay happened six hours after the Police departed the AM incident. The real cause of both the AM and PM incidents was two separate accidents. The accidents caused the delay and the delay caused the police."
"You are wrong," the cynic would reply, "And I can prove it! Had the police not cleared the AM accident, the wrecked cars would still have been blocking the traffic lanes in the PM, and the delay would still have been high, so traffic would be moving too slowly to cause the PM accident. Based on the data, accidents happen when delay is low and cars are moving fast. Who is responsible for the low traffic delay just before the PM accident? Obviously the police!"
Switching our discussion back to Global Warming, we notice a relatively short delay (~800 years) between the rise of surface temperature and the rise of CO2, so we conclude that warming causes CO2 to rise.
The cynic might say "No! The ice core data shows that Global Warming cycles start around every 100,000 years, and they always start when CO2 levels are at a low point. Therefore, it is the reduction of CO2 at the end of a 5000-year Global Warming cycle that *causes* a new cycle to start, 95,000-years later!"
Research is underway to develop ways to "sequester" carbon and remove it from the atmosphere (for example by developing fast-growing plants that rapidly absorb carbon). [NOTE: This sentence is true.]
Imagine, 50 years from now when those fast-growing plants become endemic and CO2 levels in the atmosphere begin to fall precipitously, a new generation of environmental activists will become alarmed. "The ice core data," they will cry, "Shows that Global Warming cycles always start when the CO2 levels are at a low point. CO2 is dropping rapidly because of those damned carbon-sequestering plants. Let's burn those plants to release the carbon into the atmosphere, raising CO2 levels to stop the next Global Warming cycle! :^)
Ira Glickstein
Thanks Joel and Ira for the excellent feedback on my posting.
While I think we all realize that the most prudent course at present is to attempt to reduce the amount of human-caused CO2 into the atmosphere, we also realize that science is not a perfect (or the only) tool for uncovering truth but that, much like democracy, it's the best system we've discovered so far.
I think that that the human mind with its propensity to make order from chaos is a marvelous mystery but we have to keep an eye on it.
Stu
"Philosophy is a battle against the bewitchment of our intelligence by means of language."
Ludwig Wittgenstein
from Quotes of the Day
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