Base 3 Time

localroger

Ever since Bits' thread on base 3 computing...

http://forums.parallax.com/showthread.php?141509-base-3-computer-issues

I've been nagged by a project I started and never finished, to build a true Base 3 clock. My white paper and latest version of the emulator was wiped out when a virus hosed my computer last year, but I did salvage an early version of the emulator from work. I'd had the idea of using a Propeller and time/date module to make a real standalone clock in this form factor, with an alternate mode that maps a little more closely to hours and minutes, but time (whether decimal or ternary) kind of got away from me. So I figured I'd share my ideas and my little emulator here in case anybody is interested.

An excerpts from the PDF to whet your appetite:

So it seems reasonable to assume that Ramans have a day and need to divide it up into intervals. A single trit conveniently divides the day into three intervals that conveniently match our own clocks, morning from 0 to 1, midday from 1 to 2, and evening from 2 through midnight.

A second trit gives us decimal 9 divisions, each being exactly 2 hours 40 minutes long. This is actually close to the system used by monasteries, which divided the day into decimal 8 intervals, and which led directly to modern time notation.

A third trit gives decimal 27 divisions which is conveniently close to the 24 hour divisions we use, with each interval being 53 minutes 20 seconds long. If the Ramans use base 27 tribbles this would be a single digit. We can represent it nicely as a row of three trits, which has a nice three-ness about it.

What do we call this one-tribble division of the day? The etymology of hour is fairly ancient and in a lot of cases has little to do with the way we divide the day today. For the rest of this essay I am going to assume the Ramans have a 27-house astrological system, flip to another language, and call it a casa. Feel free to pick your own random word when you write your followup essay.

As the medieval Ramans improved their clocks they would surely proceed to add a second tribble to subdivide the casa. Unlike the casa tribble where each trit has some significance at this point we're just counting off smaller intervals; a second tribble gives us an interval of 1 minute 58 seconds, allowing the Ramans to get a precision with two elegant tribbles (or two rows of three trits) that our notation needs four to achieve. Since the Spanish word for “room” isn't as punchy as the word for “house” I'll flip to French and call this ternary minute a salle. The Ramans would probably use the salle about as we use the minute for scheduling activities that don't fall neatly on the casa but don't really involve mechanical precision.

And adding a third tribble, which is a pleasantly three-ish thing to do, gives us a division of 4.389 seconds, for which I will flip back to Spanish and snag the false cognate estante. Behold the standard Raman clock, all full of delicious threes:

msrobots

@localroger,

It's totally obvious that this is 12:36 PM, right?

I really like the way you are writing. It is allways fun to read. First time I found out was as you where writing about gambling. Very nice to read. Did you ever wrote a Book? Or maybe delicious three ?

Back to the three-ness of your clock. There is some harmonic balance in those 3 rows of 3 LEDs.

But it forms a square. So it is harmonic for you and me. But for the Ramans? I guess they do neither like squares nor cubes but tetraeder?

I will dowload and try on Windows 7... works without problem.

Enjoy!

Mike

skylight

I like it but am totally confused as to how to read it, if I understand it right the top row in your pdf example reads:
yellow, yellow,red if green =0 and yellow =1 and red=2 then that equates to ternary 112 or decimal 14

second row reads green, yellow,yellow or ternary 011 or decimal 4


third row reads red,green,yellow or ternary 201 or decimal 19


the example says the time is 12:36 PM

please could you show me where i'm going wrong and how to actually read the clock I presume it's by row not column

Or is this one of those "You must think in Raman" moments?

localroger

Sorry for the delayed reply, we had an 80 hour power outage thanks to Isaac and this slipped.

The pure Raman time display is, well, Raman. Other than the 8:00 4:00 12:00 thing it doesn't correspond very well with our time at all. (You can kind of squint and get an idea of the hour by applying an increasingly large fudge factor to the the second and third trits of the top line, bearing in mind that the Ramans have 9 casas per third-day while we have 8 hours.)

I had come up with a possible alternate scheme for easier conversion to human time, starting with eliminating a casa from each third-day to make casas correspond exactly to hours. The situation with the other two lines is a bit more problematic; line 2 has 27 states but needs 60, or at least 30, which I was thinking of doing by turning one of the trits OFF to create a fourth state. (With today's LED's one could also use blue for this superternary state.)

The third line just doesn't have anything to do with human time no matter what you do with it. I think I had a pattern where the bottom trit blinks four times per transition instead of three, so you could tell what mode the clock was in, but all that got lost with the computer crash and I didn't bother to reconstruct it. Might make the project more useful if I went ahead and added that though...

skylight

Thanks for replying, I won't exchange it for my binary watch just yet then