The Clock

(If you fancy a puzzle, go look at The Clock first, try to figure out how it works, then come back here for the explanation.)

Inspired by Gonon: building a clock with no Numeral (HN discussion), I decided to build my own as a sort of practical art project.

One of Gonon's goals is to build a timekeeping device that carries no cultural baggage or assumptions. Considering it still uses decimal (base-10) numbers and sexagesimal (base-60) time units, it hasn't fulfilled that particular goal – but it's still nice to look at and analyze.

So it got me started thinking, what could the time-keeping device look if we're free from any cultural baggage – and yet be practically useful once you understand how it works. Ideally, if the aliens visit us on Earth and see one of these in operation, it shouldn't be hard for them to understand it without knowing anything about our civilization, writing, or language.

Starting from scratch

Let's start easy, by throwing out everything we can't use: * numbers of any kind (requires number base systems and numerals) * directionality (what is more, what is less, what's the “correct orientation”) * any symbols or markings that have some cultural meaning (like am/pm or “:“) * assumptions about time zones, weeks, calendar months

On the other hand, if you just start from nothing, say, by defining natural numbers, the user manual for the clock will be rather large. I'd like to make it a practical device, so I'm willing to use something – as long as that something is a physical fact that everyone can agree on. Here are a few:

  1. Earth rotates around its axis – one rotation is called a day
  2. “Noon” is defined as when the sun is exactly above a spot on earth (longitudinally speaking)
  3. Earth orbits around the Sun – one rotation is called a year; we'll ignore that it's not a circle, as it's an irrelevant detail for the calendar
  4. Earth's spin and orbit are in the same direction

The time piece is keeping local time for a specific spot on Earth (in my case, Zagreb, Croatia).

Earth is a (pretty good approximation of a) sphere, rotating any place on it makes a circle and the orbit is an ellipse (that we'll stylize here as circle – we're not doing orbital mechanics here). So looks like sun as the “anchor point” and circles should play a role in our design.

Day One

Let's start by having a dot representing sun, and earth as a circle (looked at from above) that rotates. Zagreb is marked by a small tick on the circle. Here's the sped-up version (1440x, one minute represents one day):

While we have an impression of Sun going from East to West, it's actually Earth rotating from West to East. When the tick comes directly under the sun, that's (solar) noon, and one whole rotation is one day. If you squint a bit, it's already some kind of time-keeping device.

Let's see what else this point of view gives us. Well, given that half of the planet is in darkness, maybe we can indicate that as well:

Note the day/night line is a bit tilted – it's not exactly perpendicular to the sun. This is because, as I write this, Croatia uses DST (Daylight Saving Time) clock shift so we intentionally have more daylight in the evening. While this shortens the daylight in the morning, most people are asleep at that time so won't mind it.

Carve Diem

The “clock” we have so far is somewhat practical – we know roughly where in the day we are, compared to dawn, noon and dusk. But in everyday life we need more granular time precision instead of eyeballing the angles between our location on the Earth's surface, the center of the Earth, and Sun. Beyond the night/day line (which changes throughout the year, remember), there's very little natural phenomena that we could use.

One option would be constellations, but these suffer from not being visible at day. Another option is to arbitrarily divide the day into, let's use a random number – 24 hours! ....okay, I admit, I cheated, I had a reason to use that one – so that the clock is more people-friendly. But since any division is arbitrary, the aliens visiting from another planet won't be surprised to find some division.

Now that we've carved the day into fixed-size chunks of time we'll call “hours”, why not “zoom into” and make it easier to show progression within each hour? This slippery slope leads us to minutes: a new, smaller (“minute” – see?) circle within the Earth/day circle. The minute arc sweeps until it completes a full circle, which coincides with our Zagreb marking touching an hour tick.

While this looks like I'm caving under “cultural assumptions” pressure, notice we never define how many minutes is in the hour – this is a continuous variable. This is just a concession to the fact that humans need to be able to tell time on a smaller timescale than half a day or so, and the daily circle is not good enough for that (or it needs to be large).

I'll second that!

I'll slip on that slippery slope even more by adding a second circle inside the minutes to mark – no surprise here – seconds. The seconds are also sweeping until they complete a full circle, at which point we (the people living on Earth) know one minute has passed. The aliens, having no clue about our minute-to-second conversion ratio, don't know that, but if they have space flight, they'll quickly figure it out from rotation speeds.

Here's the clock for around 10:30 Zagreb time, with seconds sweeping in real time (1x).

Note that time keeps going backwards! Or at least, the clock is using a non-standard – literally called anti-clockwise movement. The reason, of course, is that we want to mimic the earth rotation, going from west to east, not the perceived Sun rotation.

But here again is a subtle cultural bias – this is only true in north hemisphere, or when looking at Earth from above the North Pole. If you live in a southern hemisphere, the sun still goes from East to West, except that East is right and West is left (like, ahem, on most maps – talk about consistency). So, from a vantage point of a Kiwi or a Penguin, earth actually rotates left-to-right, ie. “clockwise”.

Which of these is correct? Both! The choice is arbitrary – so I'll take the southerner's point of view. Not because I'm from Argentina or Australia (I'd love to visit one day), but because the sweeps can then go clockwise, making it more familiar to the casual user. The choice between two equally valid approaches decided by user experience (UX).

Now we have a fully functional clock which mostly corresponds to the standard 24-hour analog clocks (not many people have those, but they do exist), with the added effect of showing the day/night cycle and DST, if in effect. Can we do better?

World clock

Since our tick on the day ring represents a place, there's nothing stopping us to add more. Here's the same clock with Zagreb, San Francisco and Tokyo, still showing around 10:30 Zagreb time. Note how natural it is to see the time zone differences when shown this way!

Perihelion or not?

Can we extrapolate this approach further and get a usable calendar?

With the calendar, there's no one obvious “anchor” point, as noon was for time of the day. There are several candidates: solstices, equinoxes, aphelion, perihelion, but all of them are changing slightly because of the slight perturbations in Earth's orbit and rotation axis.

Earth doesn't orbit the Sun in a perfect circle, but in an ellipse (nothing strange here, all orbits are ellipses, due to Newton's law of gravity), but not a very elongated one – if you squint, you can make it a circle. But, being an ellipse, this means there's a point where Earth is closest to the Sun (Perihelion) and furthest from it (Aphelion).

Since we already used “my point closest to the sun” for a daily anchor, using Perihelion is an exact analogue. Luckily, it falls very near the New Year – usually between 2nd and 5th of January. (Orbit wobbles a bit so the figures are not stable). We could use the Perihelion (which happens to be Jan 3 in the year I write this), but it's just so slightly off the expected “January 1st” that it looks like a mistake. So, we're going to go with a standard start of the year, with the additional excuse that it's almost when the Earth is closest to the sun, as it will be in our clock.

Let's draw another circle to represent a highly-stylized Earth's orbit and add a small dot on it to represent the current location of Earth.

Like with parts of the day, a full year is too large to be a useful indicator at a glance. At the very least we need to know roughly where we are in it, and we're going to use the same trick – have ticks for every month, taking into account how many days it actually has (so, they're not regularly spaced)

The Complete clock

There's still one thing missing: it's very hard to figure out the exact day in the month based on this alone. I've long debated with myself whether to add another ring for days, making it more useable at the expense of consistency and elegance. In the end I added it, which brings us to the complete clock:

You can see the final complete clock here.

The ET and us

Let's revisit our clock from the aliens' point of view.

If they found an operative clock like this on Earth, could they understand it? From tracking it for a day or so, they could quickly see that the rotation of one of the rings exactly matches the rotation of the earth, and could map a rough location of the place it refers to. The day/light length would help them narrow down approximately which latitude the place is at. The inner two rings would obviously show time passage, just at different scales, and if they looked closely enough, the larger of the two's full circle would exactly match one of the ticks on the day circle.

What about the longer periods? The ring encircling the sun would naturally imply orbit, even if drawn as a circle rather than an ellipse, and if they lingered long enough, they could confirm the movement of the Earth through it roughly matches what's on the clock. Once they figured that out, the second ring would obviously be a “higher frequency” counter, mapping the month ticks from the year and the day rotations. The aliens would no doubt be puzzled by the length of the 2nd month of the year.

One big caveat: all of this logic would break apart on any other heavenly body than Earth. The clock assumes that the Sun will be the obvious anchor point, and that Earth rotates. Other planets, other star systems, would need their own version of this clock.

Did we manage to get from our cultural influences? Turns out, not very far. We still have a circular time-piece and think in terms of seconds, minutes or months – purely human constructs. We *could have constructed a clock even without these, but it wouldn't be a very useful one.