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?

Some days you get to be a grand visionary. This being October, you’re more likely to be busy preparing your budget.

Budgeting is a problem. It’s a time-consuming, annoying, expensive process, almost always implemented as stupid game-playing (the game is Pin the Tail on the Donkey), and the only thing worse is not doing it.

One difference between budgeting and other games, like bridge or Scrabble, is that you can choose to not play bridge and Scrabble. If you want to be in management, you have to learn how to play the budget game to win, or failing that to play it to not lose. It isn’t easy, since the other side holds most of the good cards.

(Sidebar: A group called the “Beyond Budgeting Roundtable” is trying hard to replace the budgeting game with a more rational approach, built on two major pillars — continuous, adaptive planning and decentralized decision-making. I wish them well. If your company hasn’t adopted Beyond Budgeting, though, I don’t recommend that you be the first to say, to the CEO and CFO, “You know that our budgeting process is a stupid game that promotes unethical behavior. Why don’t we adopt this promising alternative?” Unless, that is, you’re seriously interested in committing career suicide.)

There is no single, magic formula for preparing and successfully defending next year’s IT budget. Here are some techniques that should help you survive the experience, and even to have intelligent conversations on the subject:

  • Separate spending for value maintenance from spending that enables new business value. Value maintenance is “non-discretionary” — curtailing it isn’t a realistic choice. So long as the company is in business you will run day-to-day operations, modify the accounting software to accommodate changes in the tax code, and implement new labor contracts in the payroll system.Value enablement, in contrast, is “discretionary”: The business has a choice about each proposed software enhancement and major project, and about business expansion that drives the need to invest in additional infrastructure — for example, opening new branch offices.
  • Base spending for value maintenance on ratios. The cost of maintaining already-delivered value is the result of some basic drivers, such as the number of servers each sysadmin can support and the cost per seat for software licenses. Build your budget on these ratios, so you can defend the need to increase non-discretionary spending if the business situation calls for it.If you can, add another layer of sophistication by going beyond ratios, to break down costs into fixed and variable components.
  • Build continuous improvement into spending ratios. When you can, of course: You can’t build continuous improvement into per-seat software license costs. You can, in contrast, take steps to increase the server/sysadmin ratio, and you should, if for no other reason than to prevent complacency from seeping into your organization. Improving these ratios is how you shift spending from value maintenance to value enablement without reducing the value you maintain in the process.
  • Decide whether value-enabling spending is driven by capacity or demand. If you’re capacity driven, it means governance decisions are purely about allocating the staff you have available to work on software enhancements, major projects, and business expansion. The budget decision is about how much staff you have available to allocate.If your spending is driven by demand, it means the company decides what it will take on and you provide the right mix of employees and outside resources to take care of it. That, in turn, means you can’t budget without the company’s plan. It also means you have to be very good at the discipline of project cost estimation.
  • Apply the “walkaway rule” to your budget negotiations. For better or for worse, in most companies budgeting is a negotiation, not a collaboration (okay, I lied; it’s almost always for worse). One of the most basic rules of negotiation is that whoever is in a better position to walk away from the deal wins.In practical terms, this means agreeing to whatever cuts in your budget are proposed by the other side, making two points clear in the process: (1) the business will have to do without something as a result of the cut; and (2) you won’t be the one in the headlights — the standard governance process will be the mechanism through which the company decides exactly what the business will have to do without. That’s what it’s for.

The only thing worse than having to play stupid games is losing stupid games you’re forced to play. You might as well play to win.