On the nature of time: Cycles

Well, so far I haven't been doing a very good job of making regular posts in this blog (or in my other blog on LiveJournal, for that matter). I intend to get back to writing regularly on the topic soon.

As part of that resolution ;-), I offer the following observations.

My wife, Shadowfoot, was reading a post to me yesterday about a circular calendar that someone was using to help in planning. Rather than using the block calendar so typical in Western cultures currently, with one row for each week and one page for each month, the poster was thinking of using a circular calendar, so that all of the dates were clearly visible, and he could get a better idea of how long it was going to take for something to be completed (such as planting to harvest) by seeing how much of an arc the event would take; for example, you could quickly see that 90 days would take approximately a quarter of a year, or that 120 days would take approximately one third of a year.

The examples above may seem fairly obvious, but you could also see quickly if your planting schedule would cause your harvest time to be staggered or all fall on about the same date.

You can do this with the block calendar, of course, but it may involve some complicated arithmetic, depending on the nature of the planning, but the visualization of thinking of a circle for the year can help you get a grasp on what that arithmetic means.

It occurred to me that I often visualize a year that way, like a giant clock with the Winter Solstice or New Year at the 12:00 position (depending on context). Further reflection revealed to me that I do not think of calendar months that way, although I do think of the phases of the moon that way.

Our Grove gathered for a little holiday socializing yesterday, and since we are a "teaching grove", we typically get into some interesting subjects of discussion even when we aren't having an "official" meeting. One of the topics that came up (I may have been the person who brought it up) was the Mayan calendar.

Anyone who has seen the Mayan calendar knows that it is a circular calendar.

Since I've been doing research on calendars used by various cultures, both past and present (and some speculative calendars for the future), I was past time for looking at this calendar. Without going into the significance of the Mayan calendar's end of the Long Count (Winter Solstice 2012), there were two particular points in the calendar that I was not expecting.

First of all, the Mayan calendar is not a lunar calendar. It does not follow the cycles of the lunar phases, although it might mark those phases.

Second, the Mayan calendar is not a true solar calendar, either, although one (!) of the definitions of "year" that is used is 365 days long (the other is 260 days long). There is no adjustment of that year over time, so the equivalent "new year" under that system falls behind the actual astronomical event by about a day every four years.

I was not expecting either of those points.

The Mayans were accomplished astronomers. They knew quite well that the fixed, 365 day year wasn't exact, that particular solar events would fall on different dates over the years. However, rather than make periodic adjustments to the length of the year (e.g. using leap days as in the Gregorian calendar), they accounted for it by knowing how many iterations of the calendar it would take before a particular solar event (such as the Winter Solstice) occurred on the same date in that calendar.

Timekeeping in general has to keep in mind two major components: cycles and forward progression. The cycles help us to know when something is likely to repeat, and the progression helps us know when discrete events have happened or when they will happen.

The hours of the day are cyclic in nature: there's a beginning, middle, and end, and then it starts over again for the next day. Daylight follows night time, and night time follows daylight, over and over. We record the progression of days by counting how many times this cycle occurs, usually picking some point as the beginning/ending of the day (typically midnight in modern Western cultures, sundown in several historical Western cultures as well as several Middle Eastern cultures).

The same can be said for lunations: new moon, first quarter, full moon, last quarter, and new moon again, to use the way that the phases of the moon are recorded on modern Western calendars. Again, we count the progression of lunations to record their progression, picking some point in the cycle (typically new moon or first quarter) as the zero point.

The solar year also follows that pattern: Vernal Equinox, Summer Solstice, Autumnal Equinox, Winter Solstice, and then back to Vernal Equinox again. We pick a [somewhat arbitrary] point in the cycle of the year as "New Year", and count how many times that event has passed (we also use our own birth date for marking the repeats of the solar year, or a date of marriage).

We use these cycles and their progressions, numbering or naming them, to record when things happened or predict/schedule when they will happen. We can predict when a crop is likely to be ready to be harvested by the date that we plant, and we can schedule that planting according to when they will likely need to be harvested.

We know when we need to get certain farm equipment out of storage and checked over, because we have an idea of when we are going to need it to be ready to work.

We know how old the chickens need to be before they will start producing eggs that we can use or sell, and how old they will be when they are likely to stop producing, so we can schedule when we need to get replacement chickens.

We know when we're supposed to be at work, so we have a decent idea of when we should get up in the morning in order to be able to get ready and travel to the work site (if you're a farmer, the farm is the general work site, but you may need to travel to different parts of the farm -- I need to go up onto one of the hillsides today or tomorrow to clear some fallen tree branches before the next snows). We also have a good idea of what time we should be getting to sleep the previous evening, so that we can be sufficiently rested when we wake in the morning.

And the next day, we get up and do it all over again.

Each day is unique for what happens during that day, but the cyclic nature of the day gives us an idea of what to expect for certain things.

Happy New Year! May the progressive nature of the year cycles make it better for you than last year.

On the nature of time: Daylight, Sunrise/Sunset, Twilight, and Dawn/Dusk

Note: The writer is in North America, and is writing primarily about conventions in North America using American English for this post. If and when I get more information on this particular topic in other cultures, I will add that to the series.

Why does it matter what we name a unit of time (second, minute, hour), or call a particular point in time (daybreak, sunset, Noon)? Frankly, it's to facilitate communication. If I want to meet someone at a particular point in time, I might tell them that I want to meet them at 1300 hours, or 1:00 PM, or an hour after Noon, and I would have a reasonable expectation that we would be talking about the same thing if we had the same convention for referring to a particular time. When we don't have the same convention for referring to a particular time, we need to know that so that we can agree on when to meet.

In my last post on time (On the nature of time: hours), I noted that some systems of measuring time start the day at nightfall/sunset, daybreak/sunrise, or at midnight mean solar time. I also mentioned that saying nightfall or sunset may not be saying the same thing.

Since the hours of daylight are usually defined according to sunrise and sunset, the unequal hours time systems have to have an agreement on just what that means.

Let’s start this at the easiest point to deal with: Sunset (also called sundown in some areas). This is, from the term, the time of day when the sun, well, sets. As a point in time, sunset is usually defined as that time of the day when the sun's trailing edge disappears below the horizon at the end of the daylight period.

Sunrise, likewise, is that point of time when the sun's leading edge first appears above the horizon at the beginning of the daylight period.

Because these conventions refer to the position of the trailing and leading edge of the sun in relation to daytime, not the center of the sun's disk, that means that at the Vernal and Autumnal Equinox, when the path of the Sun crosses the equatorial plane of the Earth, the defined period of daylight, using the definitions of sunset and sunrise above, is actually slightly longer than the defined period of darkness.

Even if you do measure the daylight period as the period when the center of the sun's disk is at or above the horizon, we can still see the sun when it is actually physically below the horizon due to refraction of light in the atmosphere, and again, the day when observed daylight and nighttime are the same length does not fall on the equinox.

This can lead to some very interesting conversations as some folk who understand the sunrise/sunset convention of defining the daylight period, or the effect of refraction, try to explain to others that the days that daytime and nighttime are the same length don't actually occur on the day of the equinox.

We call that period when the sun is not visible but there is still light in the sky twilight. In the morning, twilight begins at dawn, and in the evening, twilight ends at dusk.

So, what are dawn and dusk? There are three common definitions in use.

EDIT NOTE: In the following definitions, it is important to note that the sun's disk appears to be ½° wide, and that during all periods of twilight, the sun's disk is completely below the horizon.

Civil or civilian twilight: That period of time between when the center of the sun's disk is less than 6° below the horizon and the upper limb of the sun's disk is visible above the horizon (sunrise/sunset). The beginning of the morning twilight is called civil dawn and ends at sunrise, and the end of the evening twilight period is called civil dusk and begins at sunset. It is also sometimes referred to as the elapsed half hour before sunrise and the elapsed half hour after sunset, for simplicity's sake.

Nautical twilight: That period of time between when the center of the sun's disk is less than 12° below the horizon but greater than or equal to 6° below the horizon. The beginning of the morning twilight period is called nautical dawn and the end of the evening twilight period is called nautical dusk.

Astronomical twilight: That period of time between when the center of the sun's disk is less than 18° below the horizon but greater than or equal to 12° below the horizon. The beginning of the morning twilight period is called astronomical dawn and the end of the evening twilight period is called astronomical dusk.

Each type of twilight is often thought of by what kind of activity you can undertake during that period. During civil twilight, you can still perform regular outdoor activities without artificial light (one convention is that if you can no longer read, it is no longer twilight). During nautical twilight, you can still distinguish large objects at a distance, and there is sufficient darkness to take sightings of brighter, known stars and compare their positions to the horizon for navigation purposes (there are some additional practical definitions of nautical twilight regarding whether or not you can still see the rings of a target at a fixed distance). During astronomical twilight, you can observe most stars, but some of the dimmer objects, such as nebulae, are not distinguishable.

A moment's reflection should be sufficient to realize that sunrise and sunset, dawn and dusk, and the periods of twilight are all dependent on time of year and geography (including but not limited to the observer's latitude and longitude). They are local conventions.

Here's to local conventions.

On the nature of time: Hours

Time passes.

Well, that seems to be a simple enough statement on the face of it. Most of us have a sense of past, present, and future, and the language to refer to the differences.

I've been doing a little research recently on how time is marked in different cultures, both currently and in the past: Seconds, minutes, hours, days, weeks, months, years, decades, centuries, millenia, etc. I've posted previously on how the seasons are marked, and the differences in determining when a particular season begins.

Recently, our AODA study group discussed the calendar of Coligny, a lunisolar calendar that may or may not have been Gaulish in origin (it's an interesting exercise to look up everyone's opinion on the origins and details of that calendar). That re-sparked my interest in the nature of recording time, and sent me down all sorts of different paths in short order. This is part of one of those paths.

I know from earlier studies that there is more than one way to track time during the day, and more than one meaning to the word hour in western culture.

The obvious meaning refers to the mean solar hour, which is 1/24^th of the length of the mean solar day (solar days actually vary in length during the year). We understand that the hour has 60 minutes, and that each minute has 60 seconds in it. We're taught this in school (at least the part about 60 minutes and 60 seconds, and 24 hours in the day), and might learn later that there are atomic clocks out there that measure and report a fixed, precise time that at least the U.S. government agrees on (my computer has a program that synchronizes the computer's clock to one of those atomic clocks). The day begins at midnight, and the hours run from 1 to 12 to reach noon, and then from 1 to 12 again to reach midnight (unless you're using a 24 hour clock as the military and some computer centers do. Oh, and Hong Kong as well).

Astronomy and astrology both use this definition of hour, historically and currently, for taking measurements and recording events.

But that's not the only way to measure the hours, or to determine when the day begins.

There's a concept of unequal hours that goes back a long time. Under this concept, the periods of daylight and darkness are each divided up into a predetermined number of units (called hours in western culture for convenience), and because the period of daylight and period of darkness may be of different lengths, the hours of daylight may be different lengths from the hours of darkness.

This use of hour was applied to the Canonical Hours, the marking of when to perform particular sets of prayers in the various Christian churches, such as Prime (first hour of daylight), Terce/Tierce (third hour of daylight), Sext (sixth hour of daylight/midday), None[s] (ninth hour of daylight). We still keep one of those words in common use, None[s] (noon), although it's been moved up to midday from its later position). The hours of nighttime were divided into a set number of Watches, Vigils, or Nocturnes, depending on the convention in use.

This use of hour is also applied to the Planetary Hours, which is used to determine which of the seven planets (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon) govern a particular time of day, so that you can know what hour a particular activity is best performed during. As with many mathematical concepts these days, there are websites, spreadsheets, and computer programs available that can help you determine exactly when these planetary hours fall on a given date.

The planet that governs the first planetary hour of daylight also governs that particular day: The Sun governs the first planetary hour of daylight on Sunday, the moon governs the first planetary hour of daylight on Monday, Mars on Tuesday, Mercury on Wednesday, Jupiter on Thursday, Venus on Friday, and Saturn on Saturday. This is [supposedly] based on the ancient Chaldean order of the planets for astrology.

The day might be considered to begin at different times as well. The so-called Italian system starts the day at either nightfall or sunset (not necessarily considered the same time), the Babylonian considers the day to start at daybreak or sunrise, and the so-called Local system considers the day to start at local midnight (the modern system), all either for equal or unequal hours.

Going east to Asia, China and Japan also have both concepts of hour, as either an equal division of the mean solar day, or an unequal division of daylight versus nighttime. The major difference is that, traditionally, the total number of divisions in a day is 12, rather than 24. The Japanese hour system, further, counts backwards from 9 to 4 for the first half of the day, and again from 9 to 4 for the second half of the day (1 to 3 are reserved for religious reasons, the number of bell strokes to call Buddhists to prayer). I have seen a picture of a Japanese 12-hour clock, but it is a full day clock, not a half day clock like most western clocks.

Time to go — it's Noon/Sext/Midday/the 9^th hour of the day/the 3^rd hour of daylight/time to make and eat lunch.