Time Does Not Run Clockwise. Here’s Proof!

The shadow from a vertical stick moves in a counter-clockwise direction. So then, why do clocks go clockwise? (Experiment conducted March 11, 2018.)
The setups: We marked the four compass points around a vertical stick and used bark chips to mark the location of the shadow each hour. A table-top version turned out to be easier to read.
A time-series of the hours of the day. The rotation of the stick-shadow is clearly counterclockwise.
Paolo Uccello’s clock-face. Photo from https://www.florenceinferno.com/paolo-uccello-clock-florence-cathedral/

What’s going on?

Photo adapted from https://commons.wikimedia.org/wiki/File:World_map_with_tropic_of_capricorn.svg#/media/File:World_map_with_tropic_of_capricorn.svg

Why do Clocks Go Clockwise?

Activity: Do you live in the northern hemisphere? If so, repeat the activity my father and I conducted and see the shadow of the vertical stick move from left (west), to forward (north), to right (east), and thus turn in the opposite direction we observed.

Let Aussies Rule the Day! (And let us solve an annoyance in mathematics for you.)

The preferred direction of rotation in mathematics is counterclockwise.
By insisting North be upwards, we are forced to set the motion of the Sun to be counterclockwise in our diagrams.

What got me thinking about sundials

a) Tomorrow I am flying from Hanoi, Vietnam to Adelaide, Australia. I depart 1025 hours Hanoi time and arrive 2145 hours Hanoi time. How many hours long is my flight?

b) I forgot to mention I depart 1025 March 7 and arrive 2145 March 8. (It’s a very slow flight.)

c) Did I forget to say March 7, 2018 and March 8, 2020? (It’s an exceptionally slow flight!)

Question: What might students in Darwin, north Australia, notice too?

Question: Folk living between the Tropic of Capricorn and the Tropic of Cancer, say, on the equator perhaps, observe the Sun passing directly overhead how many days of each year?

Some Mathematical Questions and Ponderables

a) Is it surprising that the spacing between the bark chips marking each hour is not uniform?

b) It seems unlikely that the Sun was at its highest point during the day at 12 noon. Is it possible to estimate from this photo the time of day the Sun was at its peak?

c) According to this photo the Sun rose just north of east and set just south of west. Is that possible? Is our data an illusion? Does the Sun not actually rise directly from the east each day of the year?

d) Sun dials don’t use vertical sticks at their centers but instead angled ones. (Set at what angle?) What is the reason for this?

e) The Earth’s axis of rotation is not perpendicular to the plane the Earth sits in when revolving around the Sun. Is it possible to determine its angle of tilt to this plane using shadows?

a) Suppose we marked the location of the tip of the shadow cast by a fixed vertical stick each day at noon for a year? Do we expect the location of the tip to change from day-to-day? If so, what path should the tip trace?

b) For those living less than 23 degrees from the equator, do conduct the sundial experiment each day for a year. When does the shadow cast by the stick change direction of rotation?

a) Have you ever noticed how the number four is presented in Roman numerals on clock faces? Although the subtraction principle is used to express nine as IX, clock-makers don’t use the principle with the number four. Why?

It is the clock-makers tradition to write four as III on clock faces.

b) Look at Paolo Uccello’s clock face. He didn’t use the subtraction principle at all in his Roman numerals. But what made him choose counter-clockwise for his ordering of the numerals? Florence, after all, is in the northern hemisphere!

c) What is the story of our 12-month calendar? There used to be only ten months in our calendar year with a “quiet time” over the winter period. What happened to make it a 12-month calendar, with February set as the “tag along” month whose count of days doesn’t match the others?

d) What is detailed history of cartography that led us all to agree to place north upwards on maps?

End Notes

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