Binary clock concept

 kw: ai experiments, binary time, binary clocks, art generation, simulated intelligence

Near the end of 2024 I was thinking about what clock faces would look like if a culture had a binary concept of time. That is, an 8- or 16- or 32-"hour" day, based on, for example, 32 divisions per "hour" and 32 further subdivisions. Everything based on powers of two. I decided to have several art generating programs attempt to draw a clock dial ("face") with sixteen symbols on it…with no success! Every program stuck to 12- or 24-hour format, with one exception.

This image generated by ImageFX (IFX hereafter) shows a dial with 13 items that look like jewels. Their spacing is rather uneven. Other scales around the dial have as many as 21 symbols, also not evenly spaced. If nothing else, IFX is good at producing unique symbols.

I had in mind a culture, perhaps on another planet, that had no contact with our Babylonian 24-60-60 scheme. They developed a number system based on binary digits. Perhaps their "hands" have four or eight "fingers".

I learned to think in sixteens when I had to write a lot of computer code for two different operating systems. One was based on Octal digits (0-7), and another on the much more common Hexadecimal digits (0,1,2…8,9,A,B,C,D,E,F). My colleagues and I were adept at thinking in 8's and 16's. 

Let's consider a 16-hour daytime and 16-hour nighttime. And let's use words from another language to get away from the English terms:

• The planet rotates in one nichi composed of 32 jikan.
• One jikan contains 32 bu.
• One bu contains 32 byoh.

This language has no inflections for pluralization. 32x32x32 means that one nichi is divided into 32,768 byoh. If the inhabitants are of similar size to humans, perhaps their heart beats at about the same rate. This implies a nichi that is about 40% as long as an Earth day. If this is intended to pertain to a culture on Earth, the byoh would be about 2.64 seconds.

This is another of the images IFX offered up. The outer ring has 32 symbols, spaced evenly, so perhaps this symbol set could serve for a full-nichi dial. However, the next ring in has 19 symbols. Perhaps we can posit that the planet's orbit is divided into month-like periods, let's call them tsuki, of 19 nichi each. That's unlikely in a binary-based culture. Ditto for the outer ring of 28 "petals". And I am not sure what to do with the weird spiral. Clearly, I am not going to get far using SI, at least not yet.

By the way, look carefully at the two gears below the spiral. The teeth don't mesh. IFX "knows" what gears are, and that they have something to do with clocks, but it doesn't "know" how they work.

I created a set of symbols based on numbers used in Sumerian cuneiform:

The basic set is four. Two fours stacked is 8, 4+8 = 12, and two eights are 16. However, it might be better to devise a symbol for zero (a filled circle will do; it's what the Sumerians used), so the "16" would look a lot like our "10". On the other hand, perhaps such a culture would not be ready for a 2-symbol number until after 31 (the bottom two symbols set next to each other, effectively 24+7). Then the single tall wedge followed by the circle would represent 32.

I wanted a way these could be arranged around a circular dial. When we have numeric digits on a clock, they are usually upright, but we place Roman numerals all pointing outward from the center, like the pseudo-Roman symbols in the image above. The next image is a concept of these wedge-digits arranged that way.

Making this dial with PowerPoint was easier than I thought. Right away I noticed that when you turn a shape by its handle, the angle is shown in a status line on the Format menu. 360°/16 = 22.5°, so that was easy. The lines in the diagram help line up the symbols correctly.

I let all this percolate for a month or so. Then I went back to the art generator programs and tried a different tack. After much experimentation I settled on this prompt:

A colorful circular dial with sixteen ordered symbols evenly spaced around it

A few hours of playing around yielded lots of interesting images. I'll present 27 of them, from five programs, with a bit of discussion after each set of nine.

These are three each from three programs: Gemini, Dall-E3, and DreamStudio. The prompt for the first Gemini image left out the words "colorful" and "ordered", and "colorful" was added for the other two. Out of a large number of offerings, only the first two had sixteen items, although they are numbers and have repetition. The third is admirably wonky, but nothing like a clock dial, though the outer ring does have twelve items. All other images were produced using the full prompt.

Dall-E3 produced one dial with 20 symbols in the outer ring, and 12 in the inner rings; a dial with 24 symbols plus four knifelike items intervening and an inner ring of 24; and the third image goes off the rails in a big way. If DE3 were to produce a 16-member ring, it would be purely by chance!

DreamStudio went farther off the rails than that, and stayed there. Some of the rings in these images can be counted, and some, not so much. None is 16, and some have an odd number of symbols. Another set:

These were all produced by Leonardo AI, in various Styles. In the top row we have a dial with several sets of 12 items, primarily Roman numerals, secondly a dial with a main ring of 24 symbols, a mixture of Romanesque and "various", and lastly a dial that indeed has 16 symbols of alternating sizes (I like that!), while its inner ring has eight divisions.

In the middle row we first have a ring of 12 larger symbols, then a ring of 16 (Yay!); then a dial with two rings of 14; and the third dial also has 16, with the whole business offset by a half step, or 11.25°.

The bottom row starts with a dial that looks like needlework, and has 16 items. The second dial has an outer ring of 19 symbols, a narrow ring of 18 digits and digit-like symbols, then a compass-rose-like dial with 12 divisions. The last dial has 16 rather complicated symbols, and all the rings within it are also sets of 16. Now we're getting somewhere! Now the final set:

These were all produced by ImageFX. Most of these are easier to count, and several achieved at least one 16-symbol dial. At upper left, the counts are 16 and 10; next to it, they are 15, 9, and 6; and the "rainbow dial" has 16 and 16 only. Another great result.

In the second row we first have a dial with 14 symbols, a narrow ring of such variety I can't determine how to count it, and an inner ring of 8 symbols; secondly an oblique view of a dial with 15 symbols and an inner ring of 7 or 8, unevenly spaced; and thirdly a dial with 16 symbols, a narrow ring of 16 small symbols (maybe pronunciations?), and a narrower uncountable ring of many symbols.

The bottom row starts with an oblique view of a dial with 19 symbols and an inner ring of 12 divisions with barely visible symbols; then a dial with 16 symbols, a narrow ring of 16 numbers (in no particular order but all have 2 digits), a ring with numerous "words", then a very small ring of alternating colors totaling 16 symbols; and finally a dial with 16 symbols, and several rings with eight members each. This one could also prove useful.

Experiments like this show how the training sets of the SI programs affect the images they produce. Getting away from the notion of "clock" made it possible for a couple of the programs to generate images that could be useful to illustrate a clock for binary timekeeping. We get the most interesting results when we explore the edges of such software's capabilities.