Northern Hemisphere, Southern Hemisphere, Magic Number Seven, and Sixteen LEDs

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On the photo above you can see digital clock. While it has only sixteen LEDs it is twenty four hours clock, which shows time with fifteen seconds precision. Appearance of this timepiece  is non-traditional and most people  may say that using it to read time would be not easy. In this post I'll try to disprove this claim.

Let us start with this episode of StarTalk Youtube channel. Here Neil deGrasse Tyson explains  the reason why all mechanical clocks (almost) have hands moving in the same  (clockwise) direction.

This episode only fifteen minutes long, but in case you are too busy to watch it  I'll provide short brief.

1. Precursor of mechanical clock was sundial. During the day  shadow of sundial gnomon moves  following the sun.  Inventors of first mechanical clock  built it in such a way that hands of clock   moved  similarly to shadow of gnomon. This is how  clockwise direction appears in our life.

2. Shadow of sundial moves clockwise only in Northern Hemisphere. In Southern Hemisphere shadow of sundial moves counter-clockwise. If mechanical clock would be invented in some place  to the south of the equator  clock scale and clock hand movement  would be different. Probably this  picture of a backward clock shows us how southern invented timepiece may look. You can buy such clocks on Amazon and after some time even get used to it. 

3.  Apart of  clockwise and counter-clockwise movement Neil in this episode discusses how invention of digital clock  changed human perception of the time.  Mechanical clock makes human think about time from geometrical perspective.  Angle between axis  and clock hand corresponds to the time which already passed or left. Recent invention of digital clock creates illusion of precision but deprives us from geometric association.

LED clock presented here is a hybrid. It works partially as a regular (like invented in Northern Hemisphere) clock and  partially as backward (invented in Southern Hemisphere) clock. And I want to think that it is a hybrid in other aspect: while be digital it still  gives some geometry perspective. To understand this timepiece  interface I invite you to play with the web model:  Half-Dial-Clock-Model Link

In case you don't want to click unknown link you can play with model locally. Here is my GitHub repository https://github.com/jumbleview/Clock16  You need to copy content of directory p5model

to your computer and open file index.html  with browser of your choice.

Model has four clocks,  which all synchronized and show the same time.

1. First clock at the left is the regular analogous clock. Nothing to comment here.

2. Second clock works similarly to the first, apart of the fact that in place  of clock hands there are circular arcs. Normally clock shows time by  angles between vertical axis and hands . This arc clock shows time by angles occupied by arcs (outer arc for minutes, inner arc for hours ). Arcs start at twelve mark and grows clockwise. 

3. Third model is a half-dial version of ark clock. For hours less than six and minutes less than thirty  reading the time is not different of the previous clock. Arcs start at twelve mark and grows clockwise. But when hours are in the range 6..12 or minutes are in the range 30..60 there is the change. Hands of the regular clock under these conditions  are positioned at the left side of dial. But for this arc clock there is no left side. Arcs here occupy the same right side but there are change of starting points   and direction  where arcs grow. Under these conditions arcs start not at the twelve mark but at the six  mark and they grow counter-clockwise. That way clock show hours from 6 till 12 and minutes from 30 till 60. In other words this clock works closer to normal clock for hours from 12 till 6 and minutes from 0 till 30. Otherwise this clock works closer to backward (Southern Hemisphere) clock. 

4. Fourth  clock is similar to the previous model but arcs are dotted not solid. This clock does not need dial marks: dots itself are marks. White dots of inner half-dial shows hours, green dots of outer   half-dial show time with five minutes precision. Additional  one minute precision achieved by a color of the last dot of minute arc. Just add color reading to the time provided by green dots (for cyan add +1, for purple add +2, for red add +3, and for blue add +4 ).  This last clock model is very close to the real LED based clock  (just substitute dots with LEDs). 

Model allows to play with clocks dynamically. Three time modes exist:

1. Manual mode. Top slider allows to change clock time.

2. Real time mode. Clock shows current local time on the machine where browser is running.

3. Simulated mode. Time change is simulated (bottom slider allows to increase or decrease simulation speed).

Real LED clock is different of dot half-dial model  by having two more lighting elements. 

1. Central LEDs changes color each fifteen seconds (cyan, purple, red, and blue). When clock is in set mode this LED is dark.  

2. LED on the left part of the clock is AM/PM flag. This LED is OFF during AM half of the day and ON during PM half. 

Clock is built around Atmega328p microchip. Circuit diagram, C program and Microchip Studio project you can find in the Git repository:  https://github.com/jumbleview/Clock16

And one last thing to say about the project. The clock has seven LEDs on the hours scale and seven LEDs on the minute scale. There is known psychology phenomenon:  "Magic Number Seven, Plus or Minus Two".  Invented by psychologist George A. Miller, it argues that  seven is  number of items human can keep in short-term memory to operate. Anything significantly more is out of cognitive capabilities of average person.  In  this regard clock presented here looks just right. I believe it is easy enough to get used to its interface.