This time of year always feels a bit like this time last year. As the year comes full circle, last December now seems as close to us - in a way - as the summer just past.
In The Metronomic Society, Michael Young considers this cyclical nature of time as another dimension, over and above the dimension of linear time. The cyclical impression is caused by the daily spin of the Earth on its axis, the phases of the moon, and our annual sweep round the sun. These cycles not only frame societies, but are hardwired into the biorhythms of the bodies of Earthlings. Physicists of different species - even if they disagree on everything else - at least share the same basic units of time.
Now somewhere deep in space, an alien civilization inhabits a really boring neighbourhood where there are no heavenly bodies of note, no great cycles in the sky or celestial chronometers. The natives have no natural rhythm. Life is rather uneventful, with no particular pattern. Like an interminably long phone call, you lose track of where you have been, and where you are going. The local philosophers consider time to be just an endless train journey over a featureless plain (without the view out the side).
In our solar system, however, the celestial mechanics conjure up the impression of more dimensions of time. Our calendar can be arranged not only as a line, but in tables of days and months, time of day against day of week, or months against years: with every cycle we effectively add another dimension. Yet while the temporal landscape may be multi-dimensional, the passage of time is still linear. It is like text in a book - it forms a single trail from start to end, but winds over the two-dimensional plane of the page, and stacks up to form a three-dimensional volume. All dimensions are present simultaneously, but we follow a single track.
Now, in one of those duller corners of the universe, from a species with a temporally-deprived evolutionary childhood, there comes an ambitious alien engineer, who aims to recreate the cyclical nature of time, building it into the architecture of a single space construction. (It is difficult to get funding for creating multiple extra-planetary bodies just for their time effects). In search of inspiration, the alien wins itself an intergalactic fellowship to Science City, Earth.
Finding Tsukuba just a bit too, well, homely, the alien is drawn to Tokyo, with its bright lights and buzz - and best of all, trains, train lines, and timetables. The newcomer especially enjoys circling round the Yamanote line. Once, while paused in Tokyo station, idly staring out the carriage, the alien realizes it can see clearly into the next train, on the adjoining track. Though the next carriage is only a few feet away, it is not directly accessible. Yet it feels - in a way - as close as the other end of the alien's own carriage. The alien realizes that passage along the aisle of its own carriage is like a direct trajectory in linear time, whereas the carriage of the adjoining train is like 'this time last year'. The alien imagines seeing the glow of glittery Christmases past, echoing through several ranks of train carriages, as far as the eye can discern.
But then the carriage alongside is not a different train, but part of the same train, only wound round the whole Yamanote Line, come back to the next track. And the carriage two tracks distant is also the same train, wound round again. (While each track represents a different year, the adjoining carriage is always 'last year', whichever year-track it happens to be on.) From this train of thought, the globetrotting alien gets its idea for fabricating cycles of time in its space-city construction.
The engineer first imagines a grand new Yamanote Line going round not a paltry uptown loop, but girdling a whole planet the size of a city. Let's call the planet-city Edo, the time-warped alter-ego of terrestrial Tokyo. So Shin-Shinjuku becomes the antipodes of Edo-Eki. This planetary Yamanote is calibrated so that each circuit takes a 'day'. (The engineer takes a bit of creative licence, and puts part of the far side in a tunnel, to simulate the passage of night.)
So it takes 24 hours to go round the planetary Yamanote, arriving back at the same place, more or less, a day on.
But you don't arrive back at exactly the same place: you arrive at the track next to the last one. The Yamanote 'line' is a spiral. The carriage you see into on the next track is, this time, calibrated to be 'the same time yesterday'. Like a Tokyo station as wide as a planet, the parallel tracks extend side by side as far as you can see (in the direction of the past, at least).
Except, what this describes is not a planetary globe, but more like a planetary spiral-wound cylinder. And more: it is not a cylinder with a straight axis going off into space. Rather, it curves round on itself, like a giant doughnut. And it takes a year to go round this one. Imagine a translucent space-station-tube of a doughnut, wound round with 365 and 1/4 spiral coils of train track.
But when you go round this 'doughnut', you don't return to the same point, but to a point one space-station-tube-diameter away from where you started. Then, you can gaze back though the translucent glass of the space-station-tube to get a view of 'this time last year'. (At this point, being winter, you are on the flank of the doughnut furthest from the nearest star.)
So the alien engineer has successfully created a time-cycle-simulating space architecture: not a closed loop, but a giant spiral that winds onwards indefinitely (and is, accordingly, forever under construction). Around the turn of the year, the rhythm-instilled inhabitants of Edo toast their founding Engineer, and look backward, and forward, to another winding of the great space-station-spiral, and wish each other a Happy New-Planetary-Yamanote-Year.
(c) Stephen Marshall, stephen[at]cyberspace.co.jp
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