He had soon developed entirely new systems of time. Two-and-a-half seconds going into fifteen-minutes going into three-quarters-of-an-hour into three-days into six-days into sixty-days (here, he stopped even trying to match the words of our customary demarcation) into six-hundred-days into twelve-hundred-days, and so forth.
He got up and grabbed a mechanical pencil and a spiral notebook, half of the pages of which were devoted to coordinate systems dressed with unenlightening, often squiggly, shapes, along with (starting in the margins, but creeping slowly onto entire pages) several doodles of demon-like pencil-gray eyes above tantalizing smiles and the occasional button or upside-down-seven nose. Upon returning to the bed, he opened the spiral to its inside back cover, pushed with extracted more lead from the pencil with a relished push to the eraser, and began a new system of time.
It started in the same way as before, but now named. A two-and-a-half-second was called a "secant."
There were eight secants to an "octant," and ten octants to a "suptant."
A whole dozen of the rather large suptants added up into an entirely new wording scheme; they filled a single "thirdian," three of which made an "wholian."
Here occurred another jump by factor of twelve, as twelve wholians were exactly enough to count as a single "dame."
... And, so forth...
The timing scheme entertained Orr throughout the morning. He, in all, had 9 units of measurement, the last of which (a "warp") made up a single non-leap year. Though he had a brief vision of establishing these as the new measures of time, it was short-lived. After all, the only advantage of this system (other than the fact that you didn't have to bother with variable-sized months) was the fact that it was different than the current one. If his became popular, a new genius could one day come forth and have as much right to topple it for a new one, or maybe in favor of the current system. Secant time, sadly, was destined to give pleasure and ease the life only of its inventor. But, to this fate it attached most readily, for it kept Orr preoccupied and happy until well after lunch. And, when his stomach finally forced him to abandon his bed, he had both completely filled the inside and outside covers of the front and back of his notebook (partly, of course, with block-letter logos) and completely forgotten about the cube-adorned beast in the corner of his room.
Secant time also proved to have another, far less obvious, repercussion, the result of which would eventually cause secant time itself to all but fade from Orr's memory.
On Sunday afternoon, after a day of relishing the freedom of weekends by watching television, playing Duke Nukem on his computer and doodling a few more secant-time logos (one of which was even accompanied by two drop-like eyes, thinking critically about the uselessness of the existing demarcation system for time, while sitting atop a flat-lining mouth), he opened his secant-time notebook one more time, but this time into the middle, heaved a mammoth textbook out of his backpack, and began working on his geometry homework.
The work was just beginning to be top-heavy with proofs, each of which would take Orr as many as three minutes to think through, and another ten to scrawl correctly, in as little space as possible, into the notebook. The result was so close to illegible that three of the five days of the previous week, Orr's teacher had asked him to remain after class and explain to her his solutions for the problems that she couldn't read, and the last time, he had found that he couldn't read them either.
Luckily, this weekend's homework was only half proofs, and half geometrical word problems. So, he found himself all but done after an hour. Only the last problem remained, a word problem, measuring a lamppost's height given its shadow and a person of a given hight a given distance away whose shadow ends with the lamppost's. Orr had seen several quite similar problems already, and would have solved it quite easily, but for a little snag: the units between the person's size and the shadow's length were different (the former in feet, the latter in meters). Aggravated, Orr flipped to the front of the textbook for its cheat-sheet on unit conversions. His eyes flew up and down the page, and registered "foot," and "meter," as they were supposed to, but also"secant," which appeared several times lower down the page. The connection sent his brain in two directions concurrently, both to: Oh, so that's where I'd seen that word before! and to: Wait, but feet and meters are just as arbitrary as seconds and minutes! For all its usefulness in self-understanding, the first realization quickly died out to the second. The world, with all of its units, came crashing down on Orr. Feet, meters, yards, liters, pounds, quarts, all collapsed from their heavenly stature of givens. Sure, Orr had known that there were two accepted scales for measuring anything, the American and the metric, but only now did he realize that the fact that there were two proved just how arbitrary the systems actually were. Length, weight, volume, temperature, one by one Orr realized that they were continuous, and that splitting them up in any particular way was arbitrary. He could invent secant length, secant weight, secant volume, and secant temperature.if he wanted to, each system just as able to measure as the ones currently accepted.
But then, he wondered, why do we use the systems we use? How did we come to decide on sixty-second minutes, and on twelve-inch feet? Why do some people use the metric system, but we don't?
These are difficult questions, especially for a thirteen-year-old, genius or not. And, they set Orr pacing around his room, barely able to avoid the neglected textbook that sat on the floor, still open to the front inside cover. When pacing proved ineffectual, he tried sitting on his bed, nibbling absent-mindedly on his lower lip. Then, he tried lying down and staring at the ceiling. The tiny bubbles of dried paint looked like a vast Universe of stars, making arbitrary constellations: a giant man, a goat, the letters "CM." But, no amount of staring at the Universe can help to explain why people make the decisions they do. Indeed, the vast network of stars in the Universe, much less the bits of dried paint on Orr's ceiling, are not nearly as complex as the social systems that brought the units of measurement to their current state. In fact, they can barely be compared to the the neural system that once resided in the cranium of Anders Celsius. So, it should be of little surprise that the paint, for all its complexity, did not help Orr a single bit, and he soon got up, disgruntled, still full of questions, and disappointed that his own massive heap of neurons hadn't come through for him, and finished his homework problem.
Orr's lentil soup dinner helped to spur his brain slightly, and on his way upstairs, he came upon a realization. It was by no means an answer, but it was a step in a more fruitful direction than his previous steps around his room. His thought was about the metric system, something about which most high school nerds occasionally joke, that is: mathematically, it is extremely simple because it follows a set pattern. "Kilo" means "one thousand," no matter what single unit it precedes. "Centi" means "one hundredth," no matter which single unit it precedes. And, so forth. Furthermore, each prefix is a factor of ten away from its neighboring prefixes. In other words, much about the metric system, even if it is arbitrary, makes sense. It helps to quantify numbers of bigger and bigger size easily.
Orr reached his room, and looked at the monster in the corner. Last morning, though, time had failed him. Not seconds nor minutes nor hours had been the proper unit for measuring the time it had taken him to build that beast. The problem was in the system's inability to appropriately signify the largeness of something that seemed really big to him. And, the other systems of units would have to fall into similar problems. The problem, in other words, was that the units didn't take context into account. The time that he had spent on his monster could be measured in small hours or big seconds, but the seconds didn't seem big enough individually, and the number of hours was too small. The time that he had actually spent on it was two "mini-adventure" days or, perhaps less romantically, fifteen "small project" hours. Those days, those hours, they weren't normal hours, they were hours in a context.
In this way, Orr came upon his final child prodigy invention, and the one that he would be most proud of in later years, beyond the monster in the corner and beyond secant time. He called the idea (and the products of it) "units that feel right" or UTFRs.
UTFRs are two-part units. The first is a context that gives an idea of how the person on whose experience the value is based experienced it, whether it felt big or small, scalding, lukewarm, freezing, and so forth. It is usually given in the form of a category of experience most people can appreciate, so the hottest day Orr had ever experienced (on a vacation to Israel when he was 10) could have as its first part, 'burn-your-hand-on-a-stove.' The second part is the quantitative unit, just as regular units have, like "centimeter," or "kilowatt." Put together, we have, for example, "10 trying-to-fall-asleep-before-a-test minutes."
Orr, after pacing around his room, thinking through what a UTFR would be, grabbed the same old geometry notebook that was still lying splayed on the floor, flipped to the last page, scrawled "UTFR" on the top, in big, hurried letters, and proceeded to his bed, where he sat and began coming up with useful contexts.
At first, many of his contexts were, unsurprisingly, based on his personal experiences. The longest ten minutes of which he could dream were "10 being-pinched-in-the-cheek-by-your-aunt minutes." The longest one-hundred feet were "100 carry-your-bike-home-after-a-bad-crash feet." And, the biggest two-thousand liters were "2000 curdled-milk-mixed-with-salt-and-sugar liters." This last, as he scribbled it onto the page, brought a giggle, wriggling through his throat. Once, at the age of five, his parents had both been working late, so when they arrived home, were too exhausted to keep an eye on Orr. At some point in the night, he became thirsty, and wanted a glass of milk, and, not wanting to bother his collapsed parents, he trampled down the stairs himself, pulled the fridge open, balanced the milk (unaware of the newly-purchased milk higher up in the fridge), found a cup in one of the cupboards, and poured himself some milk. It smelled awful (much, one might say, like curdled milk), and looked lumpy. Not remembering how his mother had made it look so perfect, he tried mixing it thoroughly with his finger and then thought, It doesn't smell sweet enough. Obviously, the solution was to add sugar, so he grabbed the salt shaker and proceeded to pour about half of its contents into the milk. He then mixed it some more with his finger, and smelled it again. Unsatisfied, and confused, his attention landed on the shaker, and he decided that such a large supply of sugar should not be wasted all into the milk. So, he poured himself a small handful and took a big lick. It was, needless to say, a rather disappointing to shock, and caused the rest of the salt in his hand, to fall to the floor. Disappointed, he looked back into the cupboards, found a bag of sugar, and hoped for the best as he opened it, and poured as much as would fit into the cup. A few finger-mixing seconds later, and the young Orr decided that he would have to ask his mother how she managed to get his milk so tasty, so that he could do it by himself next time, for this mixture still did not look or smell right. But, again, not wanting to be a bother, he decided to live with what he had made, drink it, and be done with milk for the night. This decision, the failed attempt to chug the putrid shake he had invented, and the final expurgation of it and dinner, left such a lasting impression on Orr that he still associated the curdled-milk-with-salt-and-sugar mixture as such a concentration of horror that not even scientists could condense anything further.
At this point, however, Orr hit a snag: there had not been two-thousand liters of curdled milk with salt and sugar. There had only been a single cup. So, he couldn't really know what two-thousand liters of curdled milk with salt and sugar really looked like, and without that piece of knowledge, 2000 curdled-milk-mixed-with-salt-and-sugar liters lacked some of the expressive power of a different contextual unit. With this realization in mind, Orr began trying to find contextual units that matched the measure that they tried to describe. So, "100 walking-home-from-school hours" would not be allowed, as nobody would ever walk home from school for 100 hours. On the other hand, "100 being-in-school-for-two-weeks hours" would be allowed, since two weeks of school added up to about one-hundred hours.
But, Orr had not really experienced so many kinds of movements that could fill up the entire spectrum, nor so many kinds of volume or temperature. So, he started to abstract. He imagined how big a football stadium was, and thought "x football-stadium-filled-with-water quarts" would be a good way to describe how big "x quarts" was... assuming he could figure out how big "x quarts" was to begin with. Similarly, the circumference of the Earth could describe length; the temperature of the sun could describe a really high temperature, and so forth.
After developing these two methods for creating contexts (based on personal experience without regard to the value, and based on common experience with regard to the value), Orr's brain turned itself off and refused to continue. After having invented a new way to measure time, and then a new way to measure everything, in the space of two days, it was exhausted, and demanded fit compensation in sleep. This request was accompanied by a helpful knock on the door by his father reminding him that it was now 9:30pm and time for bed.And, after a few minutes preparation, it took Orr little time to fall asleep. And, his dreams were filled with speeches of congratulations given by strange units of measurement (represented somehow by big squares with mustaches and sashes), in front of cheering crowds of the same.