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Narrative

Of Linear and Geometric Growth

Even after all this time up here on the Moon, Spruance Del Curtin still found it difficult to get used to the idea that most of his instructors were not teachers in the way the ones back in Houston had been. Instead, they were people who happened to have sufficient background in a subject to teach it at the relevant level, whether or not they had any formal training in teaching.

Which was how he had a radio astronomer teaching his statistics class. Not that Dr. Doorne was a bad teacher — she certainly knew her stats, and was introducing the to professional-grade stats packages and real data — but it was sure clear that astronomy was the woman’s real interest. All it took to get the class off on a tangent was to have someone bring up one of her particular interests, especially the ones that had to do with signal processing.

He’d done it himself, a couple of times when the station was having weird difficulties that neither Engineering nor IT could hash out. As soon as he’d laid out the problem, that woman just ran with it, and damn if she wasn’t cute when she had a problem that captivated her. People talked about someone’s eyes lighting up when they got an idea, but her whole face took on this glow of excitement.

Today wasn’t going to be one of those days. She’d brought in a bunch of data sets from the rodent labs, passed out the USB sticks and told everyone to copy the data onto their laptops and proceeded to talk about exponential growth curves.

Sprue knew the theory — start with a single pair of mice and watch the population explode in a a few generations. Of course in the wild you never got anything like that except on isolated islands where they had no natural predators. But in the artificial environment of a laboratory, with complete safety and effectively limitless food, they could just keep breeding, and breeding, and breeding. And the data in front of him was bearing that out.

“However, it’s also important to remember that it is very difficult to distinguish between an exponential growth curve and the early parts of an S-curve without further data. Eventually, some forms of growth will reach a limit and level off.” Dr. Doorne looked around the room. “A population of rapidly reproducing animals will eventually reach the limits of even the most generous habitat, even if it is only because the researchers operating the laboratory take measures to limit their growth. What other forms of growth will start by looking like an exponential curve, and then level off into an S-curve?”

Trust a Chaffee to always be the first one with his hand up. Sprue still remembered taking intro to geology with one. The kid was practically the teacher’s pet within the first week of class.

“How about pyramid schemes and Ponzi schemes. Eventually they run out of suckers, for the simple reason that the human population was finite.”

Sprue was a bit taken aback. Usually that geneset was such a bunch of goody-two-shoes that you’d think they didn’t even know the concept of confidence games.

However, Dr. Doorne seemed to find it utterly unremarkable. “Who else can provide an example?”

This time Sprue made sure he got her nod. “The expansion of a virgin-field epidemic.”

Dr. Doorne’s eyes went wide. “Where did you hear about that?”

Sprue held his ground in the face of the implication that he had overstepped a boundary. “I do work at the radio station. A lot of stuff goes past the news desk.”

“That’s enough.” Dr. Doorne’s voice went hard, a tone Sprue had never heard her use. “Now, let’s turn our attention to the data sets in folder two.”

Make it definite, she knew something that wasn’t for general circulation, and did not like discovering that he was aware of it. Now the big question was whether she’d go complaining to Captain Waite too. Sprue didn’t think the big boss would be so easy-going a second time.

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