The Essence of Time

1 INTRODUCTION

2 THE TIME LINE

The best metaphor for time is a single straight line, analogous to the real number line but with no assumption as to where zero is.

Let's assume that we all live in the same "reality space" which has exactly one absolute objective time line. There may be other time lines in fiction, or in people's subjective perceptions, but we assume one time line.

An event is something that occurs at a point on the time line. Relativistic considerations are ignored. We assume that it makes sense to speak of synchronicity, i.e., two events occurring at the same time. Determining that to great precision may be quite difficult, but that's another matter. We also assume that time passes at the same rate for all observers.

The time line is directed, so there is a sense of before and after for any two distinct time points.

The time line is measurable, so that it is known whether one interval is shorter than another.

The time line is continuous and unquantized; there is no minimum time interval, and there are infinitiely many time points between any distinct time points.

Date and day-time are simply measurements of different granularity along the time line, much like miles and feet.

We take the basic unit of measurement to be the day, defined to be an interval on the time time line during which the planet Earth makes one complete revolution around its axis. Our model takes this to be a universal constant.

This interval is subdivided in the familiar ways into hours, minutes, seconds, and fractions of seconds, identified by numbers.

The boundaries of hours are synchronized on the time line (hence so are the boundaries of minutes and seconds), but the boundaries of days are not. There are twenty-four different zones in which the day begins at twenty-four different hour boundaries on the time line. (We ignore time zones which don't differ by an hour.) Hours are numbered from 0 to 23 within each day in each time zone. The concept of what day it is, or what time it is, is not defined on the time line, but only in each time zone. A given event on the time line might occur on different days and at different times in different time zones.

Time zones have geographic boundaries on Earth. The time zone in which the Greenwhich observatory is located is, by convention, used as a standard reference, denoted GMT (Greenwhich Mean Time).

Time zones are not fixed with respect to the time line. Twice a year they shift back and forth by one hour. On these occasions a day can have 23 or 25 hours.

Days are arbitrarily partitioned into groups of seven called a week, with each day in a week being given a different name. That's analogous to giving the twelve inches in a foot twelve names instead of numbers.

A "spot" is a fuzzy interval corresponding to the granularity (precision) of a time measurement. (A small spot might be called a "moment".) Dates, for example, identify spots whose duration is one day.

One of the main reasons for having a concept of time is to be able refer to specific spots on the time line. The only natural way is to refer to unique identifiable events, such as a memorable eruption of a certain volcano, or a memorable earthquake, or the birth or death of a particular person. This is not a very effective way to identify many time points to many people.

This is the reason for calendar systems, whose main purpose is to measure the distance on the time line between a given spot and some event chosen to serve as an arbitrary origin (zero) on the time line. Different calendar systems use different origins and different units of measurement, and they give different measurements in different time zones.

We customarily give precise measurements of large quantities in some convenient mixture of large and small units. Instead of expressing a certain distance in millions of inches, we express it in some convenient combination of miles, feet and inches. Would we tolerate a system in which different miles had different lengths, and so did different feet? Well, that's the way we measure large intervals.

A date is a measure of the distance between a day-long spot and some fixed origin spot. We measure it in years, months and days, analogous to miles, feet, and inches. Except that these units are not fixed, and we give some of them names instead of numbers.

The point in time identified as midnight of December 31, 1999 represents a very precise interval from the calendar origin, which can be counted as some definite number of days plus no hours, minutes, seconds, or fractions thereof. Since this point actually corresponds to twenty four different points on the time line, one for each time zone, it follows that each time zone has its own calendar origin, although they are all within 24 hours of each other on the time line.

3 NOTES

How do we measure large intervals? If we do it in days or hours or subdivisions of these, the meaning is well defined. But exactly how long is ten years?

We often think of date and time as being essentially different things, but they are really just different units for measuring the same thing in large or small granularity, analogous to miles and inches.

(Of course, we've been saying "date" in the sense of an absolute date of July 4, 1776, rather than a cyclic date such as July 4.)

The fact that a date is represented by three data elements, i.e., three fields, has no great significance. It does not signify a relationship among three distinc entities, any more than a length whose measurement is recorded in miles, feet, and inches. The three data elements are an accidental byproduct of the choice of representation. It could just as easily be two elements (year and day within year) or one element (a large number of days).

Much of the difficulty with temporal data has to do with the wildly varying sizes of spots, and trying to make sense of ovelapping intervals bounded by such diverse spots.