The art of approximation

Okay, I admit it. It was deliberate.

In last week’s column, in addition to misspelling bric-a-brac and messing up the barrels-to-pints conversation factor (it should have been 336 pints per barrel (somehow, Googling, I found the only site on the entire Internet that had it wrong) I quite intentionally ignored quite a few factors that have an impact on total CO2 emissions:

• The specific gravity of oil. A pint of oil weighs closer to 0.9 pounds.

• Hydrogen. It’s about 15% of your average hydrocarbon.

• Lubricants and plastics: Not all petroleum is burned.

• Natural gas and logs: We burn more than coal and oil.

• Bovine flatulence: It adds methane, a more potent greenhouse gas than CO2.

Why did I ignore all these factors? The answer is the subject of this week’s column: My goal was a first-order approximation.

First-order approximations answer two critical questions for managers who have too much to deal with and too little time with which to deal: Whether a subject is worth pursuing further, and what to consider as the default assumption.

They aren’t intended to drive final decision-making. That requires more thorough analysis, should the first-order approximation suggest it’s worth performing.

Here are a few guidelines, useful whether your goal is to understand CO2 emissions, to invest in improving a particular business process, or to spend more corporate time and energy improving customer relationships:

• Use approximations. 3 instead of pi is fine, for example. If you used 3.14159, you might fall victim to the false-precision syndrome — the impression you’ve produced a comprehensive analysis and not a first-order approximation.

• Exclude everything that looks a lot smaller than what you include. The more small factors you exclude, the more likely they’ll cancel each other out. Look at the list above. Three of the factors would reduce the estimate, two would increase it.

• Exclude feedback loops. This one is complicated. Bear with me.Some feedback loops are “in-band” (my term). In-band feedback loops are proportional, self-limiting, and smaller than the phenomenon itself. The more CO2 we emit, for example, the more the oceans dissolve, but never all of the excess emissions.Other feedback is out-of-band — triggered rather than proportional. The failure of the Gulf Stream, used to explain the new ice age in The Day After Tomorrow, would be an example if it weren’t so far-fetched. Out-of-band feedback is far too complex to include in a first-order approximation.

  Then there are false feedback loops. Increased absorption of CO2 by trees is a popular example. Some basic biology: When animals exhale CO2 it’s the result of metabolism — the equivalent of an operating budget. When plants absorb it, though, it’s to add biomass — a balance sheet effect.

  Trees could only absorb more CO2 than we emit if the net tree biomass on Earth was increasing. The opposite is true, so this is a false feedback factor.

• Don’t nitpick and don’t allow nitpicking. This isn’t the place for it. The question to ask is, “If you’re right, would it change our decision in any way?” If the answer is no then it’s nitpicking and should stop.

And finally, for those who wonder why I bring up non-IT issues like global warming, a simple answer: When I read the newspaper and encounter something interesting, I always ask how I can apply it to my daily work.

Don’t you?

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By the way:

Among the more persistent global warming half-truths is that in the 1970s, scientists were predicting an ice age. It’s proponents always cite “Variations in the Earth’s Orbit: Pacemaker of the Ice Ages,” (J.D. Hays, John Imbrie, N.J. Shackleton, Science, December 10, 1976).

It says, “A model of future climate based on the observed orbital-climate relationships, but ignoring anthropogenic effects, predicts that the long-term trend over the next several thousand years is toward extensive Northern Hemisphere glaciation.”

It also says, “Such forecasts must be qualified in two ways. First, they apply only to the natural component of future climatic trends — and not to such anthropogenic effects as those due to the burning of fossil fuels. Second, they describe only the long-term trends, because they are linked to orbital variations with periods of 20,000 years and longer.”

Legally, the half-truth isn’t perjury — three authors makes it “scientists” and sometime in the next 20,000 years is a prediction of an ice age.

But did I say half-truth? My first-order approximation is that it’s a 0.145% truth at best.