Copyright © Karl Dahlke, 2022

Why do the hands of a clock turn clockwise? Is it arbitrary? Did someone flip a coin? As it turns out, there is a reason. Pause for a moment and see if you can guess what it is.

Before there were clocks there were sundials, so take a step back in time and consider a sundial in Europe or Asia. The central post that casts the shadow is called a gnomon. The shadow points to numbers ranging from 8 to 6, indicating 8:00 AM to 6:00 PM. If the shadow lands between 10 and 11, perhaps it is 10:30.

So where is the sun, and where is the shadow? The sun floats above the equator more or less. It may be a bit north of the equator, or a bit south, depending on the season, but if you live in Europe or Asia, i.e. in the northern hemisphere, then the sun is always to the south. It rises in the east, slightly southeast, and it sets in the west, slightly southwest. Throughout the day it travels from east to west, but always south of your position, always south of the sundial. When the sun rises in the east, the gnomon's shadow falls west, but a bit northwest. By noon the sun is directly south, and the shadow points north. Late in the day the sun is in the west by southwest, whence the gnomon's shadow points east by northeast. The shadow sweeps across the sundial from west to northwest to north to northeast to east, in other words, clockwise. Numbers are painted on the sundial in accordance with the moving shadow, with 8 9 10 11 12 from left around to top, and 1 2 3 4 5 6 from top around to right. Thus the numbers march around clockwise. It was natural for clockmakers to put numbers on their clocks consistent with sundials, consistent with what the public recognized as common and correct. 12:00 was at the top, with 10:00 AM to the left and 2:00 PM to the right. 🕑 Of course the clock was a complete circle instead of a semicircle, but the numbers were placed in clockwise order, and the hands traveled in a clockwise direction, just like a sundial's shadow.

If clocks had been invented in Australia, south of the equator, the numbers and the hands would run the other way around. We would still call it clockwise, like a clock, like a sundial, but the hands would spin left instead of right.

If you live on the equator, a sundial would be rather confusing. Half the year, when the sun is just a bit below the equator, the shadow runs clockwise across the top of the sundial, just as it does in Europe. For the other half of the year, when the sun is just above the equator, the shadow runs counter clockwise across the bottom of the sundial, just as it does in Australia.

Deasil is another word for clockwise, and widdershins is another word for counterclockwise.

Time Zones

In the 1800's, each town had its local time, putting the sun overhead at noon. Since folks rarely traveled, this was not a problem. If you hopped on your horse and went 23 miles to the county seat to buy some equipment for your farm, you probably ignored the time change, because it was just a day trip - but if you looked at the clock on the courthouse, you might notice it was 3 minutes off from your watch. Watches weren't very accurate, so you might dismiss this out of hand, but if you checked into the matter, you might find that your town, and the big city to the east, have local times that differ by 3 minutes.

Railroads made this system untenable. A passenger could hardly be expected to change his watch every ten minutes as the train traveled from town to town, and it was nearly impossible to post departure and arrival times in any meaningful way. The trains might be running on time, and nobody could tell. The solution was a coordinated system of time zones, one per hour. This began in England in 1847, putting all of Great Britain under one time zone. It was known as railway time, and some towns, unable to leave conventions behind, had separate clocks for railway time and local time. Some clocks even had two minute hands, one marking local time and one marking Greenwich mean time. By 1880, railway time became the legal time for all of England.

America was more chaotic, since it could not be embraced in a single time zone. 🌎 Furthermore, each railroad company decided to institute its own time zones. One city, served by a particular railroad, might observe a different railway time than another city, 300 miles due north, which was served by a different railroad. This was confusing, to say the least. In 1883 a national standard was established, defining 5 time zones: Intercolonial, Eastern, Central, Mountain, and Pacific. The Standard Time Act of 1918 redefined the times zones as they are known today: Eastern, Central, Mountain, and Pacific. These roughly reflect four bands of longitude on the earth, each band 15 degrees around. A railroad passenger could travel from New York to Chicago and change his watch only once, and that change was precisely one hour. You can read more about time zones here.

Some regions, like the island of Newfoundland, an eastern province of Canada, observe a time zone that is a half hour off from the others. When I visited Ontario I heard tv and radio announcements like this one: “Tune in to All Things Considered, at 6:00, 6:30 Newfoundland.” Even stranger, Nepal has a time zone that is ahead of universal time by 5 hours and 45 minutes.

Find China on a map or on a globe, and note its east-west spread, more than 2,000 miles. 🌏 If you consider the curvature of the earth, China covers 5 time zones, even more than the contiguous U.S., which only has 4. And yet, all of China runs on one time zone. Everybody in China sees the same time on their watch. Why? My speculation: it simplifies the interactions between a billion people. Companies, cities, etc, all observe the same time. But it's a little quirky. If your watch says noon, and you're standing in the middle of the country, then the sun is indeed overhead. (They don't mess with daylight savings time so that's never a factor.) If you're on one side of the country the sun is still rising and it looks like 10 AM. If you're on the other side of the country the sun has passed its zenith and it looks like 2 PM. Waking up, going through your day, and getting ready for bed; the position of the sun will depend on where you live. They just take it all in stride.

Let's look at some corner cases, places where the time zone isn't obvious at all. For example, which time zone is observed in Antarctica? There's no geographic time zone at the south pole. The research stations use the time of the country they are owned by or the time zone of their supply base (e.g. McMurdo Station and Amundsen–Scott South Pole Station use New Zealand time due to their main supply base being Christchurch, New Zealand). Nearby stations can have different time zones, if they belong to different countries. That would be strange - drive 75 miles to visit another station and change your watch by 9 hours.

The International Space Station runs in UCT 0, i.e. the original time zone of Greenwich England. That doesn't correspond to any participating country or supplier. I guess its a compromise between The States and Russia, or maybe somebody just likes the number 0.

Resonance Orbit

I would like to jump from time zones to the calendar, and ask why every fourth year is a leap year, and that means we have to talk about orbits.

When I was a kid, my introductory book on the solar system said Mercury was in a locked orbit, presenting one face to the sun at all times. That seems plausible; after all, the moon presents one face to the earth at all times. The moon rotates exactly once on its axis for each revolution around the earth. Each rotation, and each revolution, is 29.5 days long. It's a perfect lock. This can happen when a moon orbits close to its planet, as our moon did several billion years ago, or when a planet orbits close to its parent star. Mercury is close to the sun, and as best we could tell in 1970, one side faced the sun at all times. One side was perpetually day, and the other side was perpetually night. There really was a dark side of Mercury, or so we thought.

That was wrong; Mercury is not close enough to the sun to become tidally locked. However, it is close enough to acquire a resonance orbit. Isaac Newton explained this phenomenon in his masterpiece on universal gravity. Extremely close orbits lock, and somewhat close orbits fall into resonance. It's complicated, so I'll save the explanation for another day. For now, let's describe a resonance orbit, with Mercury as an example. As seen from the fixed stars, Mercury rotates exactly 3 times on its axis for every 2 revolutions around the sun. It's a perfect whole number ratio of rotations to revolutions. It isn't a fraction like 4.6317. This is what we mean by resonance. If people lived on Mercury, the days and the years would line up, and there would be no need for a leap year.

All the other planets are too far away from the sun to establish a resonance orbit. Rotation and revolution have nothing to do with each other. There is no reason the earth should spin exactly and precisely 365 times for every trip around the sun, and it doesn't. There is no reason there should be exactly and precisely 365 days in a year, and there aren't.

Ever since we started counting days, people realized there were a little more than 365 days in a year. In fact the ratio seems to be 365 and a quarter. In four years, the earth spins 365 and 365 and 365 and 365 and 4 quarters, thus an extra day. Every four years we need another day to balance the books. This is called a leap day, and the year containing the leap day is a leap year.

Early Roman Calendar

The first Roman calendar tracked ten lunar months, March to December, leaving a vague non-month winter period that lasted 64 days, more or less. Eventually this period would be filled in with January and February, but for a time, March was the first designated month of the year. The first 4 months were named after Roman gods, but the last 6 months were given rather unimaginative names, reflecting their numerical order: Quintilis (July), Sextilis (August), September, October, November, and December. You may recognize quint sext sept oct non and dec as the Latin prefixes for 5 through 10. Quintuplets are 5, an octagon has 8 sides, the decimal system is base 10, etc. That is why September through December have names indicating 7 through 10, even though they have become months 9 through 12 on our calendar.

The non-month winter period could be short or long, for reasons that were sometimes political, and a year could be anywhere from 355 days to 378 days. The romans tried to average things out over the decades, so that July was always summer and December was always winter, but you could hardly predict what any given year was going to look like. As a result of this precedent, the Julian calendar, and all calendars to follow, put leap day at the end of the winter period, i.e. at the end of February. If we were starting over we might put it at the end of December, at the end of our year, but leap day has been February 29 for 2000 years and we're not going to change it now.

The Julian Calendar

In 46 B.C., Julius Caesar developed a calendar that established the number of days in each month, and the years that would be leap years. Every fourth year is a leap year, thus July is always summer, and January is always winter, and there is no drift. Actually there is still a very slight drift, which the Greek astronomer Hipparchus had described a century earlier. It would be an amazing coincidence if there were exactly 365 days in a year, 365 spins every time the earth revolved around the sun, and there aren't, but it would be equally amazing if there were exactly 365.25 days in a year. Why should it be exactly 365 and ¼? Well it's not. There are 365.24217 days in a year. Adding a leap day every four years almost solves the problem, but not quite. After a thousand years you might be a few days off, but that hardly mattered to Julius, who declared his calendar the law of the land, and so it was. The calendar spread beyond the Roman empire, and was observed by most of the world. Although the Julian calendar wasn't perfect, it was a huge step forward. In fact the misaligned dates and months and years leading up to 46 B.C. were called the years of confusion. Years could be anywhere from 355 days to 378 days long, and if you didn't live in Rome proper, you probably didn't know the current date. You can read more about the Julian reforms here.

The Julian calendar sets the lengths of the months as they are today: 30 days hath September, April June and November, all the rest have 31 excepting February alone, which has 28 days clear and 29 in each Leap Year. Julius followed the earlier convention of adding a leap day to the winter period, thus leap day is February 29.

In 44 B.C., the year Julius was assassinated, the Romans renamed the month of Quintilis in his honor, calling it Iulius, now July. In 8 B.C. they renamed Sextilis to Augustus, in honor of Augustus Caesar. This month is now known as August. The other months retain their original names.

The Gregorian Calendar

After 1500 years of Julian drift, the calendar was 10 days out of sync with the sun. The winter and summer solstices came ten days early - even an ordinary farmer might notice. Pope Gregory XIII and is astronomical advisors found this situation intolerable. By a papal decree, October 4, 1582, would be followed by October 15, 1582, thus compensating for the 10 days of drift. It would be interesting to receive an official memorandum from your government, whatever country you lived in, that you should X out the dates from October 5 through October 14, and jump from 4 to 15. I imagine they just nodded and went about their business, dates playing only a very small part in most people's lives at that time. If you are in to genealogy, and one of your distant ancestors has a baptismal record dated October 9, 1582, somebody missed the memo.

Next, he tweaked the Julian calendar, (now the Gregorian calendar), so that it was accurate to one day in 3,030 years. Every fourth year was still a leap year, as Julius declared, but centuries were not. Thus 1700, 1800, and 1900 are not leap years. However, every fourth century is once again a leap year, thus 2000 was a leap year. This change was hardly noticed by the general public, but it balances the books. I won't live to 2100, and my children won't either, but perhaps my grandchildren will ask, with mild curiosity, why 2100 is not a leap year, and perhaps this chapter will explain it.

By the year 3200, we might decide that every year divisible by 3200 is not a leap year after all, thus compensating for the Gregorian drift. That would keep the calendar in sync for at least 100,000 years.


As I write this chapter, wendy and I are celebrating our 28th anniversary. We were married on a Saturday, and this year our anniversary falls on a Saturday, and it's 28 years married, which is a multiple of 7. Does that follow, or is it a coincidence? [Pause for thought.]

Each year the weekday advances by 1. If Sept 17 is Wednesday this year it's Thursday next year and so on. This because 365 is 1 plus a multiple of 7. That's pretty clear, but every leap year you push ahead 2 days, not 1. That means our anniversary could be on a Friday one year, then next year on a Sunday. Your seventh anniversary is not going to be on the same day you got married. It pushes 1 or 2 days ahead, for either 1 or 2 leap years in that 7 year span. Let's step back and rethink.

After 28 vanilla years of 365 days each, the weekday advances by 28, which is back around to start. But it also advances an extra day for every leap year, and how many leap years in 28 years? Aha - 7. So push forward another 7 days and it's back to start. 28 is a special year, a year that your anniversary will fall on the same day you got married, and that isn't guaranteed to happen again until 56.

If you're reading this book far in the future, and your 28 year marriage spans the year 2100, then the relation ship is off by a day. You can thank Pope Gregory XIII for that one, as he decided 2100 would not be a leap year.


We've all seen the word o'clock since we were in elementary school - but what does it really mean?

First, a dip into apostrophes. As far as I know, English is the only language that uses apostrophes in its words. Other languages have contractions. German, for example, combines in das to ins, and zu dem to zum, etc; but they don't have the compulsive need to stick in apostrophes to remind you that letters were removed. I took a little French and Spanish, no apostrophes there. I asked friends who speak other languages, no apostrophes there either. To further confound, we also use apostrophes for possessive. She's throwing away John's stuff. Therefore, English orthography is remarkably atypical.

Now let's return to o'clock. That weird apostrophe gives us a clue. Letters were removed.

Aha! The original phrase was of clock. 800 years ago, in merry old England, someone might say, “It's 4 of clock. Time for tea.” We then compressed it into o'clock, and there you have it, another word we can't use in Scrabble because of the apostrophe.