Queen Manasa huddled naked in her bathtub, gazing moodily at the clear water lapping her ankles. A sun beam through the high window sent shiny reflections rippling on the far wall. The water was warm enough to suit her. Lydia had stoked the cistern fire with commendable precision, and even in the not-yet-chill of late summer Manasa was thankful to be in one of the few castles with heated plumbing in all of Ordossia.
“Is anything amiss, my lady?” queried Lydia standing in attendance by the tub, holding a wooden tray in readiness and stocked with paraphernalia fit to groom a queen.
“Um… no,” Manasa looked up at her handmaid with a slight smile, “Just preoccupied. Affairs of state, you know. Trying to see the future… with this tub.”
“The tub?” Lydia looked bemused, “I did not know that my lady could scry…”
“Not with magic,” chuckled Manasa, “I am not a Wizard anymore than you are. But there is more than one way to peer into the future, even if that vision is murkier than a morning fog. That much I have learnt by watching a Wizard at work.” She tapped the finely crafted cedar, “This tub is a tool… a prosthetic for my mind, if you will.”
“If you say so, my lady,” nodded Lydia doubtfully.
“You think I am barmy,” Manasa smiled fondly at Lydia, “But once you abstract out the clutter, what’s left can be entirely understood in terms of stocks and flows. You follow?”
“No, my lady,” the girl was young, diligent and unlike the courtiers wasn’t afraid to make a fool of herself, “unless you mean our stock of wine in the cellar.”
“Take my city for instance,” Manasa continued, “which is bursting at the seams. More people crowd in from the villages each year adding to the squalor. How am I to plan for their future without acquiring a feel for quantities that have not yet come to pass?”
Manasa swept her fingers through the water, “Imagine for a moment that the water in this tub represents my kingdom’s population. Babies are born all the time,” Water streamed in as she twisted the faucet and the tub slowly began to fill, “but there are people dying all the time too, ” Manasa dislodged the drain plug, wedging it with her toe without completely pulling it out. The water level continued to rise but more slowly until it stabilized to fill a quarter of the tub.
“Lydia, note that the population increased at first even as people died,” Manasa looked at her handmaid, “and then stopped rising. Can you tell me why?”
Lydia frowned at the tub, her thoughts forced into unaccustomed grooves, “The water… there was less at first. But as the level rises, so does the force of water through the drain… until it balances out?”
“True,” Manasa nodded encouragement, “but can you explain why that might be true for populations as well?”
Lydia sighed, knowing that her mistress would be unrelenting until her silly riddles were given due consideration. After a longer pause, the handmaid ventured, “It stands to reason that a big town would have more people dying in a given year than a tiny village, simply because the town has a lot more people to begin with. And so it is with any number of people. More births mean more deaths eventually until it all balances out.”
“Good girl,” Manasa grinned in approval and then her smile faded, “I know you aren’t old enough to remember, but for most of our history the biggest share of fatalities came from illnesses in newborns. Then a meddling Wizard came along and put an end to that. And presto… no more infant deaths from illness.” Manasa pushed down her toe, plugging the drain nearly closed except for a crack. The water level resumed its rise.
“The Ayulnaut,” Lydia whispered in reverence, “My mother spoke of him.”
Master of Life they called him, thought Manasa scowling. Master of Death was more like it. Her old teacher turned Dark Wizard, now a special prisoner in the north-east tower. But the changes he had introduced to Ordossian society were irrevocable. Even the queen could hardly ask expectant mothers to keep losing three out of five children to illness. There was no putting that genie back in the bottle.
“But more people also means more births,” Manasa continued, “So for every inch of water added I will twist open the faucet a notch more.”
“The population…” Lydia watched the rising water line as if mesmerized, “It rises ever more quickly.”
“It’s called exponential growth,” nodded Manasa grimly, her voice tinged with frustration, “Tell me, Lydia, why do farm wives keep bearing so many children even when most survive to adulthood?”
“Oh,” Lydia looked surprised, “that’s easy my lady. There wasn’t much food for each kid on the farm when I was growing up, and things are worse now I expect. While most kids pull through, some don’t. I lost a sibling to… I think you would call it malnutrition. So farm wives end up having more kids than they need, just in case they lose some, you see.”
“Secondary self perpetuating loop,” murmured the queen, twisting the faucet open further, “triggered by resource depletion.”
Lydia stared at the water now gushing from the faucet, “The water approaches the rim, my lady.”
“What happens when there’s no more food for anyone?” Manasa raised an eyebrow.
“Everyone starves,” whispered Lydia, for once forgetting to suffix her utterences with the usual honorific. Manasa yanked out the drain plug, causing the tub to slowly empty with a gurgling noise. When the water level droped low enough, Manasa plugged the drain again.
“And so the cycle repeats,” concluded the queen, “luckily we have a couple of generations of breathing time before we reach that point. The Actuarial Guild has estimated the carrying capacity of extant farmland, and forests are being cleared as we speak. Well… this concludes your lesson. I’m ready for my bath now, Lydia.”
Apart from the humanitarian disaster there was another reason why Manasa was keen to avoid a mass die off among her subjects, though Lydia didn’t know anything about that. Each such death would strengthen the potentially immortal Dark Wizard that had set this system dynamic in motion, making him too powerful to be safely contained. And the Dark Wizard knew the full measure of human folly. Humans are like lemmings, Manasa my dear, too driven by instinct… too little awareness of their own best interest, the Dark Wizard’s chuckle echoed in her mind.
Lydia fussed around preparing the bath, though her eyes retained a faraway look, “I would expect mass starvation to be the least of my lady’s problems…”
“Why do you say that?” Manasa demanded staring in surprise at her handmaid.
Lydia froze, “Beg pardon, my lady. I… I didn’t intend to say that aloud.”
“Spit it out, girl,” the queen gestured testily.
“Well, ma’am…” Lydia replied hesitantly, “I was thinking that most people live in the city and the city is crowded enough as you mentioned. And it’s only getting worse…”
“Yes, what of it?” Manasa frowned.
“When we herded cattle into the barns to hole up for winter,” mused Lydia, “we had to be really careful not to overcrowd them. Or we could lose the whole herd to disease.”
“What ?” screeched Manasa.
“Is… is my lady feeling well?” Lydia asked in concern.
The queen’s face had paled. A plague epidemic from overcrowding? In the capital? That was unheard of. Sure, the capital had outbreaks of disease from time to time, but those usually petered out without afflicting too many. Wait… didn’t military campaigns lose more troops to disease than in combat? Shit, I’ve been a bloody fool, Manasa cursed. She had focused on population size. But what if population density reached a threshold? Would disease spread quicker if there were too many people too close together? What caused disease anyway? Manasa didn’t know, but she could bet that the Dark Wizard imprisoned in the tower could model disease mechanics far better than she could. And she had accepted his explanation at face value, without wondering if there might be more than one limiting factor to exponential growth. If Lydia’s guess was correct there would be no breathing time… no warm sunset before the coming of the night.