Adios, Cingular.

So far as I can tell, AT&T just repurchased itself from itself for a lot of money. I’m sure that can’t really be the case, though.

I just can’t handle the math.

Math can be useful. It can help us understand when circumstances we don’t like are built into the fabric of the space-time continuum. That’s particularly handy for companies that have a blame-oriented culture and are wondering whose fault it is.

For example:

Combinatorials: I’ve mentioned the formula n(n-1)/2 before. You can use it to calculate the number of pairs of objects in any collection. It explains why an entrepreneurial startup venture can operate as a “band of brothers.” Until, that is, it succeeds.

Imagine the startup consists of five old friends who know and trust each other. n(n-1)/2 means it contains 10 pairs of people. With only ten pairs, everyone can maintain trust; everyone knows what everyone else is good at, and the company operates smoothly.

So the company succeeds. Pretty soon it has 100 employees — 4,950 pairs. There’s simply no way every pair will exhibit mutual trust. Some pairs are total strangers; others consist of people who just plain don’t like each other; who see each other as rivals; or otherwise can’t work together effectively.

Surface area to volume ratio: Blow up a balloon — for simplicity, imagine it’s spherical. When it’s an inch in radius, its rubber surface covers 12.566 square inches (4*pi*radius^2) and encloses a volume of 4.189 cubic inches (4/3*pi*radius^3). Surface Area/Volume = 3.

Blow up the balloon to a five inch radius. It now has a surface area of 314.159 square inches, and encloses 523.598 cubic inches. Surface Area/Volume = 0.6.

Small balloons have a lot of surface area for each unit of volume. Big ones have very little. It’s why we’re made out of many itty bitty cells instead of being big globs of protoplasm. The quantities of oxygen and nutrients cells need (and wastes they must dispose of) depends on how much stuff they contain — their volume. Their surface area limits how fast they can exchange it all with the outside world.

If this still doesn’t make sense, compare the five-inch balloon to 125 one-inch balloons. Both enclose about 524 cubic inches. The five-inch balloon contains it in 314 square inches of rubber. The 125 one-inch balloons need about 1,570 square inches — five times the surface area.

It is because small objects have a much higher surface-area-to-volume ratio that iron dust is highly flammable while iron bars are not (nor do a prison make, not that it’s relevant).

It also explains why it is that in small entrepreneurships, every employee has a clear view of real paying customers and what they need, while in large enterprises almost nobody does. The surface area has become far too small relative to the company’s volume.

AND logic: Back when I was studying electric fish I learned to wire together simple electronic circuits. Many included AND gates. Feed nothing but 1s to an AND gate and it outputs a 1. Make any input a 0 and it outputs a 0.

AND logic extends to any number of operands. (A AND B AND C AND D) is only true if A, B, C and D are all true. If any are false, the entire proposition is false.

The executive suite is one big AND gate. In order to proceed on an idea suggested by an employee, the employee’s manager, the employee’s manager’s manager, and the CEO, CFO, COO, and CAO all have to say yes. If any say no, the entire corporation has said no.

Big companies become risk-averse, not because their individual executives are excessively timid, but because of AND logic.

Sympathetic vibrations: Pluck a string on a guitar. It vibrates. Place the guitar near another identically tuned guitar and the same string on the other guitar will vibrate, too.

It’s called a sympathetic vibration.

In business, sympathetic vibrations are why bad ideas can take on lives of their own. It works like this:

A superficially attractive idea (move our factories to China, perhaps) creates good vibes. An executive with vision but no attention to detail picks up on it and repeats it, making it louder — and therefore better-able to induce sympathetic vibrations in yet more executives. Soon, everyone repeats the idea, and it sounds just like an informed consensus.

But really, it’s just one boneheaded idea that, through the physics of sympathetic vibration, ends up filling the company.

Don’t agree? How else do you explain it?

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?

* * *
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.