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"On the Import of Numerical Precision"

Title: "On the Import of Numerical Precision"
Fandom(s): Doctor Who
Characters: Fifth Doctor era
Pairing(s): None
Rating: G
Genre: General
Word Count: 1151

Summary: Mathematics is a precise science. Errors will not be tolerated.



Mathematics is a powerful tool. It is not just sums and fractions, or even differentials and matrices. It is a self-consistent system of definitions, used to describe the universe, from the tiniest subatomic particle to the fabric of space-time itself. In the hands of a master, mathematics - just the abstract concepts of numbers and equations - can shape all of reality.

In the hands of a lesser individual, say a young genius who is brilliant but has not yet trained enough to master the intricacies of sublime maths and who is not yet mature enough to know that he has not, mathematics can produce unexpected results. Transform the group in the wrong way, and the spanner is created of the wrong size, or perhaps its handle is bent. Apply the integral over the wrong range, and the salinity of the lake is a tad too high to support life. Forget to carry the two, and the bird's feathers are a bright pink instead of a properly camouflaged brown. The more complicated the system, the more likely such a mistake might be made.

Thus, it was quite remarkable that the young boy, for all of his maths prowess, had managed to create an entire city with only one error in the entire system. He had constructed the buildings and the looping floorplan to be a trap that was easily entered but impossible to leave, then populated it with citizens who were blind to the impossibilities that defined their world and their lives. These were fashioned perfectly down to the last decimal point. However, buried far down in the arrays that stored the data for the amenities the city had to offer - food and clothing and luxuries to keep the city's denizens and the target it was meant to lure and imprison content and unsuspicious - was one tiny error, the transposition of two digits in a five-dimensional map. A tiny error, however, can produce momentous consequences.

There has been some debate as to whether the error had been an inadvertent mistake due to distraction by the boy’s tormentor, the one who had forced him to create the elaborate illusion, or if he had deliberately introduced it to provide some assistance to the fly for whom the web was spun, perhaps a warning to turn away or a tool to turn the trap on the trapper. An argument can be made that if it was the latter, the boy either possessed some elevated insight beyond his tender years or was simply very, very lucky that his gift had been identified and utilised wisely, for indeed, it was well-hidden so as not to alert his captor.

Thus it happened that in the kitchens of the impossible city, the request came to provide a traveller seeking respite in the Dwellings of Simplicity with refreshment. The inhabitants set to work assembling a meal designed to nourish the body whilst it soothed the soul. Inasmuch as such repasts often depend more upon presentation than on flavour and texture, the culinary artist undertook the task of arranging each comestible just so, to balance the perceived masses whilst mixing their colours and lines in a pleasing manner with just a dusting of chaos - for unsullied order dulls the mind and dampens the senses. The tableau was embellished by a vase of slender pale lilies, the only purely ornamental piece on the tray.

And there the error lay, hidden in plain view. Two digits in the wrong places meant that lilies did not exist in this fabricated realm. In their place, leafy greenery occupied the box of trimmings and garnishes, and the chef chose the freshest cuttings to complement the setting. He did not predict that it would foil his intent, for the traveller, upon appraising the display, interpreted the bouquet as part of the meal. It was, perhaps, risky for the boy to select celery as the sign of danger, for many persons have an intense dislike of the taste of the vegetable, calling it bitter or astringent, and if the traveller had been of such a mind, he might have overlooked that part of the display altogether. Detractors of the theory of premeditated design point to this as incontrovertible evidence that the error in the calculation was just that, an inadvertent and almost invisible mistake. However, whether it was an intended selection or the sloppy work of an exhausted, tortured soul, the occurrence was fortunate: the traveller was drawn immediately to the vegetable and, selecting a stalk, took a hearty bite whilst proclaiming that this tiny village was the very model of civilisation.

Thus the suspicion that all was not as it seemed in this perfect habitation was kindled in the traveller’s mind, for though he was pleased with the offer of the edible stalk, not only was the vegetable served with full leaves, but it was presented in a large cup, not on a plate, and soaking in water - all of these unusual choices at best, and especially puzzling in this domain of perfect repose. Perhaps he did not consciously note any of this, but the seeds of doubt were planted, and subsequent events and explorations of the town nurtured them until he could see what no one else could, that Castrovalva was a fiction designed to draw him in and trap him in its recursive paths, then destroy him as it folded in on itself and imploded. With the help of the boy, who, as the city’s creator, alone understood its topology, he escaped into the forest surrounding it, at last observing the real world with his recuperated faculties.

As it turns out, the traveller was so pleased with the celery that during his repast, he endeavoured to palm a piece of the stuff and secret it away in one of his deep pockets, absconding with it as he was wont to do. (Indeed, he originally embarked on his travels in the same manner, with the theft of the vehicle in which he journeys to this day.) As soon as he escaped the city with his travelling companions - a varied group, consisting of an attendant on an air travel service, a scientist of royal lineage, and the young mathematical genius - he affixed the stolen greenery to the lapel of his coat and wore it proudly. It has been speculated that this affectation was a thumbing of his nose at the expectations of society, a proclamation that he cared little for the dictates of fashion, and indeed, he wore it well, his demeanour silencing most expressions of shock before they were uttered. However, in truth, it was a symbol of his escape from the cunning trap, of his hard-won freedom, as well as, it turns out, a practical ornament, as it also served as a biochemical sensor. If he was aware of its prominent role in the first trial of his new, young life, he certainly never let on.