How Long is a Mayan Minute?

[davilla]

Brain Thumper #3

The apocryphal Mayan clock has two faces. The left face is divided into 13 equal sections partitioned by marks that include one pointing straight down. Each section is labeled with a number 1 to 13, starting with a dot at the very top and proceeding clockwise with three dots, a bar, a bar and two dots, and so forth, ending with two bars and two dots. There are two hands on this face, a day hand and what can roughly be called an hour hand. At midnight, both hands point directly at the new day number, halfway between marks. The day hand moves counter-clockwise, making less than half a revolution in one day, thus incrementing the day number by one. Every time the day hand is halfway between marks, it coincides with the hour hand, which moves clockwise. Just as we have a.m./p.m., the Mayans had several periods in their day identified by the crossing of these hands.

The right face has 20 equally spaced marks offset by 9 degrees. Each section between marks is labeled with a day name glyph. The day names start with the first, Imix, at the very top and increment clockwise, ending with the last name, Ahaw. This face has two hands, a minute hand and another day hand, both of which turn clockwise. The day hand points to the day name, or what roughly corresponds to the day of the week, making a full revolution in 20 days. At noon, the day hand is halfway between marks. The minute hand makes a full revolution of 20 in the time it takes the hour hand to move between day numbers. When the hour hand points at a mark on the left face, the minute hand is pointing straight down.

How long is a Mayan minute?

 

[gnome]

You seem intent on reinforcing our appreciation of digital clocks.

The hour hand makes 25/26 of a revolution in the time that the left-face day hand travels 1/26 revolution. That day hand travels 6/13 or 12/26 of a revolution per day, so the hour hand travels (25 x 12)/26 = 300/26 revolutions per day. It coincides with a day-number 13 times per revolution, therefore 13 x 300/26 = 150 times per day, and therefore the minute hand makes 150 complete revolutions per day.

The rest is not exactly clear. If you are saying that one complete revolution of the minute hand represents one "M-minute", and if the Mayan day is equal in length to our day: there are 24 x 60 = 1440 minutes in our day. Assuming one revolution of the minute hand represents one M-minute, there are 150 M-minutes in a day, and one M-minute is 1440/150 = 9.6 of our minutes.

Alternatively, if you are saying that one complete revolution of the minute hand represents 20 M-minutes, then there are 150 x 20 = 3000 M-minutes in a day, and one M-minute is 1440/3000 = .48 of one of our minutes, or 28.8 seconds.

Is is safe to assume that you collect clocks?

 

[davilla]

The hour hand makes 25/26 of a revolution in the time that the left-face day hand travels 1/26 revolution.

This would require that the hands meet on the mark. The day hand coincides with the hour hand every time it is halfway between marks, and not at any other time.

one complete revolution of the minute hand represents 20 M-minutes

Yes, this is what I meant by "a full revolution of 20." I'm sorry it wasn't clearer.

Is is safe to assume that you collect clocks?

I would guess you're being sarcastic, but you do know what apocryphal means?

 

[gnome]

This would require that the hands meet on the mark. The day hand coincides with the hour hand every time it is halfway between marks, and not at any other time.

My fault -- I drew the picture incorrectly.

So now:

The hour hand makes 12/13 of a revolution in the time that the left-face day hand travels 1/13 revolution. That day hand travels 6/13 of a revolution per day, so the hour hand travels 6 x (12/13) = 72/13 revolutions per day. It coincides with a day-number 13 times per revolution, or 13 x 72/13 = 72 times per day, and therefore the minute hand makes 72 complete revolutions per day.

One complete revolution of the Mayan minute hand represents 20 "M-minutes", so there are 72 x 20 = 1440 M-minutes in a day, and an M-minute is exactly the same as one of our minutes.

 

[davilla]

an M-minute is exactly the same as one of our minutes

gnome with the point!