Gonon: Building a Clock with No Numerals | Hacker News Reader

Gonon: Building a Clock with No Numerals

tonygaeta.com

50 pointsnullpath40 comments

Crowing over omitting Arabic numerals in the name of avoiding any kind of cultural influence or bias seems silly when everything is still going to be expressed in decimal.

I was also confused why the outer ring must only show zero or one, and then it struck me — twelve hour system.

The author wanted it to retain some practical value, hence the discussion of the four “layers” of time—departing from the 12-hour system completely, even if there is a better way to represent time outside of it, would make the clock difficult to use.

I struggle to see how this clock would be less practical to use with a 24 hour system

Or if we want to keep the numbers small to make them easier to read in this clock's numerals, why not a 6 hour system?

And in hours, minutes and seconds. Yes, those are near universal (I guess there may still be a few tribes in the Amazon or Indonesia that don’t use them), but still are cultural.

Also, having each hour have the same duration is cultural. The Romans, for example, at some time, used a clock where “the period of the natural day from sunrise to sunset was divided into twelve hours” (https://en.wikipedia.org/wiki/Roman_timekeeping). That means hours were shorter in winter than in summer.

<quote>The answer turned out to be geometry.</quote> The answer turned out to be creating a cool piece of digital art that's essentially unusable as a timepiece. Don't get me wrong, it's a cool art project, but it's not a practical timepiece.

If you want to see another cool artpiece clock, there's the one in the Berlin Europa Centre, https://www.youtube.com/watch?v=jTUiWYLXD9g.

Seems nice, but beyond 6 points the polygons are hard to distinguish easily. Certainly not something you can quickly glance at in a rush. I'd say sticking to 5 maximum would be best.

I don't think empty for 0 necessarily makes the best sense. You wouldn't easily be able to see where the gaps are at a distance.

Using base 60 and encoding digits doesn't necessarily make the most sense.

For instance hours, it might make sense to use 2x times base 5, probably with no 0 encoded so that there's always something in the hours column.

Or, of course you could do an encoding with a base 4 and a base 6, which is mentally easy to convert back to to a regular 24 hour clock. TBH I'd probably encode that as maybe a square where there's 1-4 sides enclosing a polygon of 0-5 points.

Maybe I'd encode half-minutes with 3 base 5 encodings and some encodings unused, or a base 3, base 4 and a base 5 encoding for minutes.

I would probably also then group them into functional groups that touch each other within the group, so you can easily see the groups, but tell them apart easily.

Actually, I was going to completely edit this comment with a different suggestion, but decided to leave that to show the thought process.

Thinking more about the hours, I like the circle progressing round, but also maybe you could do it as a box with 1-4 sides present enclosing a polygon of 0-5 points. It's easy to mentally convert that to both 12 and 24 hour clock format.

For the minutes, I'd be tempted to do something like the current hours, done as a fraction of the circle arc with an additional polygon of 0-5 points for the minute. It's relatively easy to eyeball the size of the 5 minute segment, and the polygon just refines that a bit. You could locate the polygon so it touches the arc at the 1/12 of the circle corresponding to the base, which would help with estimating the arc length too.

Either way, I wouldn't make the encoding rely on colours, especially colours that look very similar.

Go with vertices the 0 is a circle. 1 is a guitar pick. 2 is a 2 points joined by two curves.

Very interesting. Only thing that I see is that it's difficult to tell a difference between an 8 and a 9. Like I could see how it was different on the physical clock as it changes, but if I were to just look at it on its own, it would be hard to tell without literally trying to count the sides. I'd probably just make up some symbol for those. but otherwise very cool!

Grouping the dots would probably help.

Ignoring the orientation constraint, one easy way to tell is that one has a flat line on the bottom and the other doesn't.

Nice idea and interesting discussion in the article. However, I think the article might benefit from a few more editing iterations by a human author.

As others already mentioned: the article first sets out to strip away all culture-specific aspects of a clock but then retains the concept of seconds, minutes and hours. This makes some sense, of course, and is implicitly mentioned as "Calibration to a timescale". However, I would have liked a discussion of alternative ways how this could have been achieved and why the 12/24-hour system is used in the end.

Another nitpick:

> 4. A readable mapping. Humans don't read raw oscillations. We read "14:37:09" or "sunset in 42 minutes." Reading time is always a translation layer.

> That fourth point matters more than most people think. A sundial reads apparent solar time, which is local and visibly tied to the Sun. But apparent solar time is not uniform.

This argument - which is used to introduce the next section - makes no sense. A sundial has a readable mapping. (And I would argue that it might be the most non-culturally-defined, useful type of clock for humans).

Next, the author introduces "layers of time" that do not actually seem to be layers but different views (though partially layered).

Then we are given a number of requirements for the implementation - e.g., "no daylight savings time". The clock at the top is adjusted for local daylight savings time, however.

Finally, large parts read as if an LLM has written them (many cases of "Not X, Y", a full screen page explaining that n*2+1 is more than twice as large as n, a discussion of the irrelevant test suite, ...). [^1]

[^1] the few references to other sources have apparently been copied without changing the source markdown to hyperlinks. I think a human author would notice this when checking the rendered article, no?

As others have already noted, using decimal notation as a base here is problematic in many ways. I'd suggest seximal (base 6) instead. I'd also shift the digits by one, so have 1-6 instead of 0-5, because having empty ring for 0 is not good. The rings also need to be rotated by 30° relative to each other so that "2"s do not overlap like they do now.

60 in base 6 is 140, so in theory you'd need three rings for both minutes and seconds. But because that highest digit can only be 0 or 1 I think there would be other ways to represent it, so you'd manage with two rings. One option is to reverse the colors (/fill the ring).

I wonder if this article got inspired by the recent movie Project Hail Mary?

Another thing related to this subject is the frequency in watch making. I own a manual winding watch that I wear everyday. It is certainly an engineering marvel. These watches are ticking by the hair spring and its frequencies are targeted to 2.5Hz to 4Hz (5 times per second, or 8 times per second). I don't know the rationale behind these numbers. I guess that they must have been a combination of engineering constraints and finding a good balance to keep every second accurate.

Esthetism also counts, a high frequency means a smoother second hand movement. It is one metric watchmakers are fighting on. I found this article that sum it up quite well : https://www.ethoswatches.com/the-watch-guide/mechanical-watc...

2.5 Hz was the standard in big pocket watches, with a big balance wheel. 4 Hz is the standard for wristwatches, with a smaller balance wheel.

You are right that it is an engineering compromise. Higher frequencies mean a greater acceleration of the balance wheel. The inertia of the balance wheel is itself a compromise with the strength of the main spring. You want to have a large oscillation amplitude, but also that the watch can self-start, and not too much pressure on the escapement's contact points.

5 Hz is, surprisingly, a big engineering gap especially with regards to lubrication: only dry lubricants work, and it was figured out (at scale) only in 1969 by Zenith with their "El Primero" movement (which is still in production and is a major milestone in watchmaking for many reasons, on top of having a crazy history).

But when Rolex decided to use El Primero movements in their second version of the Cosmograph Daytona, they reverted it back to 4 Hz to avoid having to retrain all the watchmakers in their vast service network.

When you remove every cultural assumption you end up with a sundial, not "geometry".

But those are numerals. Made-up numerals, but still.

A friend of mine once prototyped a clock that would make a full walk along a loop in the RGB color space every 24 hours. That's closer to what I would call a "clock with no numerals".

That's what I was thinking too. A clock without any culture-specific aspects could just rely on astronomy. The most objective form of that would just be a progress bar, from zenith to zenith. Perhaps with a marker half-way, and so on.

The question that started this wasn't about clocks. It was about what happens when you remove every cultural assumption from timekeeping and ask: what's left?

This still measures the time of day in seconds since midnight. It still encodes the number of seconds into the common base 60 system of hours, minutes, and seconds. It still encodes the base 60 digits as base 10 numerals. The only differences are the choice of digits - regular polygons instead of an established set of digits like the Arabic digits - and the writing direction - increasing in scale, radially outwards instead of horizontally or vertically - defining the positional value of each digit.

Simply a dot moving around a circle once per day would have abandoned way more cultural assumption than this. Of course at the cost of making it harder to read precisely and looking less fancy.

This combination of base 60 and base 10 can also be understood as a multi-base numeral system. 12:34:56 can be understood as 123456 with non-uniform positional values 1, 10, 60, 600, 3,600, 36,000 from right to left directly yielding the number of seconds since midnight as 1 x 36,000 + 2 x 3,600 + 3 x 600 + 4 x 60 + 5 x 10 + 6 x 1 = 45,296.

The polygon numerals are actually similar to Babylonian cuneiform numerals [1]. They use a positional system just like Hindu-Arabic numerals with the positional value increasing by a factor of the base - 10 for Hindu-Arabic numerals, 60 for Babylonian cuneiform numerals - from right to left but there are not different digits 0 to 9 - or actually 0 to 59 because of base 60 - but they just repeat a symbol for one (I) [2] n times like the Roman numerals do. This IIII II is 42 but in base 60, so 4 x 60^1 + 2 x 60^0 = 242. Ignoring the edges, the polygon numerals express the digit value by repeating a vertex 0 to 9 times and each scale increase of the polygon adds a factor according to the 60 and 10 multi-base representation described above.

[1] https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals

[2] Because repeating the symbol for one (I) up to 59 times is inconvenient, they have a symbol for ten (<) as a shortcut, just as the Roman numerals have V for IIIII. <II <<<IIII is (1 x 10 + 2 x 1) x 60^1 + (3 x 10 + 4 x 1) x 60^0 = 754.

I get that this is an art project that is supposed to look cool and not necessarily be practical, but...

For practical purposes just having 3 "arcs" (hours, minutes, seconds) would be much more readable.

The "arc" idea already solves problems of relying on orientation and knowing that it is supposed to go "clockwise" (it is pretty funny, that the only word that we have to describe rotational direction is related to clocks).

Before clocks 'clockwise' was called 'sunwise', because that's the direction the Sun moves across the sky in the Northern Hemisphere. Anticlockwise was called 'widdershins'.

Something like this (if you leave off the numbers) captures it pretty well IMO. One clock hand which symbolically points at the position of the sun.

https://www.botta-design.de/en/products/uno-single-hand-24-h...

Humans are really bad at counting groups larger than five (might be related to the amount of things you can point on at once). So the choice of using ten polygons seems suboptimal to me, especially given the 12 hour system used. I think using only six shapes might work better for an actual clock.

Cool idea nevertheless.

I was about to say that if it's still using a 12-hour system, it should use duodecimal numeric system instead of decimal. But then the polygons became much harder to differentiate the larger the number is so I'm not sure. Perhaps make the polygons spiky?

Interesting, but some of the information is conflicting: the design was about "No assumed orientation. Something that works in a mirror" but then the 24-hour arc talks about "(top, 12 o'clock position) clockwise".

Placing midnight on top forces an orientation, while specifying clockwise makes mirroring impossible.

But this is only on the text description, the actual clock would work anyway.

What about a continuous scale ? Choosing a base 60/24 for counting time is cultural and even if it is now the world’s norm, I would argue that an alien would not get this choice

> remove every cultural assumption

And then have the data entry with am and pm.

:-)

> The answer turned out to be geometry.

But that’s how Arabic numerals are made, it’s the count of the angles in each one.

Still, I like the concept of this watch.

That's just a myth, by the way:

http://www.goodmath.org/blog/2015/07/21/arabic-numerals-have...

For that matter, they aren't really Arabic numbers, Europe got them from the Arabs though. Hindu-Arabic would be little more correct.

Liber Abaci by Leonardo of Pisa (Fibonacci) is an important interesting book to read. There he is trying to convince the readers to shift to this Hindu-Arabic system he had picked up from the Arabs.

The Fibonacci series is also introduced to the Europeans for the first time through this book. I don't recall whether he calls the series the Hindu series in this book or somewhere else. The series was known to Indian mathematicians (Pingala, Euclid's contemporary, roughly) as an enumeration sequence of short and long beats that an interval of time could be broken into.

This is akin to a clock that has a pile of apples, oranges and cherries that you have to count to know the time

It would be great if this could be a clockface for Pebble

You just need your normal watch without numerals?

That's what I thought, but in the 2nd para:

> No Roman numerals. No Arabic numerals. No left-to-right reading direction. No assumed orientation. Something that works in a mirror, in zero gravity, in any language spoken on Earth or beyond it.

As other comments have pointed out, base 10 is a pretty big assumption though.

Normal watch + "arc" remove the assumptions about orientation and direction.

Building a clock that uses shapes as numerals

I'm getting redirected do example.com.

Funnily enough it had always been geometry of motion for me.

Over the decades this effect has diluted somewhat, but for me time was always some landmark shapes of the hands of the clock and how far the current arrangement of the hands are from the chosen landmark. No names. No numbers.

This caused lots of problems when someone would ask me for the time. I really had to slow down and deliberately translate, with some conscious effort, what I saw into numbers and words. So for some tens of seconds I would be transfixed, frozen, time-sniped.

When I looked up time for myself I would skip the numbers and words entirely.

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