An analemma.

Time (from Old English tima) is a measure of the motion of some material system relative to the motion of another system which changes at uniform speed (a "clock"). [1] For example, the orbit of a planet around its sun, the rotation of a planet relative to another astronomical object (e.g. its sun, one of its moons, or a distant star), the vibration of an atom (atomic clock), a `clock circuit`_, an oscillating chemical reaction (chemical clock, e.g. the Briggs-Rauscher reaction), the circadian clock of an animal, or any other feedback loop.

The standard for time is the mean solar day of the Earth and the standard unit is the second. The mean solar day is divided equally into 24 hours. Each hour is divided equally into sixty minutes, each of which is divided into 60 seconds. (A second is so called because it the second division of the hour by 60.)

Can also be relative to any timekeeping device, which is really any device that moves from one state to another in a fixed amount of time. So an hourglass, or the unfolding of a coil.

... a measure of the transition of a material system from one state to another which is known take a constant duration.

Can also refer to the process of transitioning? or the thing which "causes" transitions?

How can we know if transition time is fixed? Would need some other thing which is fixed to compare against first. Need a physical constant?

Same problem with length and mass. How do we know the length and mass of a thing doesn't change? Seems obvious, but it might be hard to perceive. (With mass in fact, things do since every time you touch something, it loses some weight. Or could imagine that a spec of dust might be affecting it. Or since mass is calculated from weight and is affected by gravity, gravity field might be different if standard is moved to new location or if the Earth itself loses mass.)


1   Measurement of a day


Over the course of a day, the Earth moves about one degree along its orbit, so it must rotate one additional degree for the Sun to reappear at the meridian. [3]

We can define the length of an Earth day in two ways.

  1. The time it takes for the Sun to reappear in the prime meridian (a solar day).
  2. The time it takes for a distant star to reappear in the prime meridian (a sidereal day or stellar day) or, equivalently, the time it for the Earth to complete one rotation around its axis.

The length of a solar day is different from the length of a sidereal day. This is because the Earth orbits around the Sun as it rotates around its axis. Since it takes approximately 360 stellar days for the Earth to orbit once around the Sun, the Earth moves approximately 1 degree around the Sun each stellar day. And because the direction of Earth's orbit around the Sun and its axis is the same (both are counter-clockwise), the Earth must rotate one additional degree for the Sun to appear on the same meridian. [2] Thus, the length of a solar day is longer than the length of a stellar day. The Earth rotates 15 (360/24) degrees in one hour, so to rotate one degree takes 4 (60/15) minutes. Thus the length of a solar day is approximately 4 minutes longer than the length of a sidereal day. [3]

The length of a solar day varies throughout the year due to the eccentricity of Earth's orbit around the sun. Earth moves faster on its orbit around the Sun when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion). The accumulated effect of these variations produces seasonal deviations of up to 16 minutes. [2] The average solar day is defined as 24 hours long but this average is not exactly 24 hours as measured by atomic clocks so adjustments - leap seconds - are made to UTC. [2]

The Earth does not rotate cleanly around its axis because of the water on its surface.

In the 20th century, three types of variation in the rotational period of the earth have been discovered: a steady increase, periodic changes, and random fluctuations. [7]

The steady increase in the length of the day is due to tidal friction. The phenomenon is caused by the moon's tide-raising force in the shallow seas. It is known that the length of the day increases at a rate of about 0.0016 second/day/century. This means that today is about 0.0016 seconds longer than a day one century ago. Although the amount seems minuscule, the effect is cumulative. The accumulation over a century is 29.22 seconds of time. The effect can be measured by comparing the prediction paths of ancient solar eclipses with those actually recorded. [7]

The measurement of Universal Time is also influenced by axial precession of the earth. The North Pole wanders in a circle of radius 8 m with a period of 14 months. [7]

In 1956 the International Astronomical Union resolved to adopt special time scales that remove the regular inequalities of practical importance. UTO is Universal Time at a local observatory. UTI is UTO corrected for migration of the earth's poles. It is the true astronomical measure of the earth's rotation and is used in navigation and surveying. UT2 is UT I corrected for seasonal variation and is nearly uniform. Time signals were based on this scale until 1972.

Because the variations in the rotation of the earth are complex and cannot be predicted precisely, the International Committee for Weights and Measures referred the study of a new definition of the second to the International Astronomical Union in 1948. At the suggestion of G. M. Clemence, the IAU decided that the new standard of time ought to be based on the period of revolution of the earth around the sun, as represented by the Tables of the Sun computed by the American astronomer Simon Newcomb in 1895. The measure of time defined in this way is called

Ephemeris Time (ET).

It is now possible to measure time with atomic clocks. The precision of 1 part in 101 3 far exceeds the precision attainable by any other kind of physical measurement. The "balance wheel" of an atomic clock is a beam of cesium atoms. The clock is run by an rf oscillator whose frequency can be adjusted precisely against the natural frequency of the cesium hyperfine transition via a feedback mechanism (Fig. 14). In 1967 the Thirteenth General Conference defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom."

The Bureau International de l'Heure in Paris coordinates the timekeeping activities of the world. Using an adopted weighting procedure applied to the atomic time scales of various national laboratories, the BIH establishes the time scale known as International Atomic Time (T AI). In contrast, the time scale of civil clocks is Coordinated Universal Time (UTC), which is intended to approximate UT 1. UTC corresponds in rate with TAl but differs from TAl by an integral number of seconds. UTC is disseminated in the United States by the NBS radio stations WWV and WWVH on carrier frequencies of 2.5, 5 , 10, 15, and 20 MHz.

The second defined by the cesium hyper fine transition is essentially equal to the ephemeris second defined by Newcomb's Tables of the Sun. It is therefore roughly equal to the average value of the mean solar second during the 18th· and 19th centuries, the time span from which Newcomb's data was obtained.

Since 1972 the difference between TAl and UT 1 has been accounted for by inserting "leap second" adjustments into T AI about once a year to obtain UTC. In this way UTC is kept within 0.9 s of UTI at all times while still beating atomic seconds defined by TAl.

2   Standards

2.1   GMT && UTC

Greenwich Mean Time is the mean solar time at the Royal Observatory in Greenwich, London. Greenwich Mean Time was established shortly after the invention of rail travel to solve the problem of re-setting timepieces as train progressed through towns, each of which had had its own local time. This location was chosen because by 1884 two-thirds of all nautical charts and maps already used it as their prime meridian..

Originally, astronomers considered a GMT day to start at noon while for almost everyone else it started at midnight. To avoid confusion, the name Universal Time was introduced to denote GMT as counted from midnight. Astronomers preferred the old convention to simplify their observational data, so that each night was logged under a single calendar date. Today Universal Time usually refers to UTC or UT1.

3   Calendars

A calendar (from Latin calendarium "account book," from calendae/kalendae "the calends" the first day of the Roman month, when debts fell due and accounts were reckoned; from calare "to announce solemnly, call out" as the priests did in proclaiming the new moon that marked the calendars. n Rome, new moons were not calculated mathematically but rather observed by the priests from the Capitol; when they saw it, they would "declare" the number of days till the nones (five or seven, depending on the month). The word was taken by the early Church for its register list of saints and their feast days.) is the year as divided systematically into days and months.

datum forms the basis of the English word "date", from the Roman convention of closing every article of correspondence by writing "given" and the day and month -- meaning perhaps "given to messenger" -- led to data becoming a term for "the time (and place) stated."

3.1   Date formats

RFC 822

Published in 1982 to standardize email for use in the APRA Internet.

Fri, 26 Oct 2018 00:00:00 +0000.

ISO 8601

First published in 1988 to provide an unambiguous methods of representing dates and time so as to avoid misinterpretation when data is transferred between countries with different conventions for writing numeric dates and times.

The ISO 8601 standard, or most officially ISO 8601:2004 Data elements and interchange formats -- Information interchange -- Representation of dates and times, approved by ISO in 1988, updated in 2000, again in 2004, defines a large number of alternative representation of dates, times, and time intervals. Thus, rather than the date and time standard, it is just a general framework. To achieve uniformity, we must select one or a few formats from it and apply them consistently. [10]

The ISO 8601 standard does not specify whether a date or time (or date and time) designation refers to a singular point in time or a time period. In particular, a designation of a date can be used to refer to a full 24-hour day or a specific moment of time within it, probably by default the start of the day (00:00). [10] Similarly, a time notation like 9:00 could refer to nine o'clock absolutely sharp or the period from 09:00 to 09:01 or anything else. [10]

ISO 8601 describes a large number of date/time formats. For example it defines Basic Format, without punctuation, and Extended Format, with punctuation, and it allows elements to be omitted.

The formats are as follows: [8]

   YYYY (eg 1997)
Year and month:
   YYYY-MM (eg 1997-07)
Complete date:
   YYYY-MM-DD (eg 1997-07-16)
Complete date plus hours and minutes:
   YYYY-MM-DDThh:mmTZD (eg 1997-07-16T19:20+01:00)
Complete date plus hours, minutes and seconds:
   YYYY-MM-DDThh:mm:ssTZD (eg 1997-07-16T19:20:30+01:00)
Complete date plus hours, minutes, seconds and a decimal fraction of a second
   YYYY-MM-DDThh:mm:ss.sTZD (eg 1997-07-16T19:20:30.45+01:00)

The international standard notation for the time of day is:


where hh is the number of complete hours that have passed since midnight (00-24), mm is the number of complete minutes that have passed since the start of the hour (00-59), and ss is the number of complete seconds since the start of the minute (00-60). [9]

Without any further additions, a date and time as written above is assumed to be in some local time zone. In order to indicate that a time is measured in Universal Time (UTC), you can append a capital letter Z to a time as in 23:59:59Z or 2359Z. (The Z stands for the “zero meridian”, which goes through Greenwich in London, and it is also commonly used in radio communication where it is pronounced “Zulu” (the word for Z in the international radio alphabet.) [9]

The strings +hh:mm, +hhmm, or +hh can be added to the time to indicate that the used local time zone is hh hours and mm minutes ahead of UTC. For time zones west of the zero meridian, which are behind UTC, the notation -hh:mm, -hhmm, or -hh is used instead. For example, Central European Time (CET) is +0100 and U.S./Canadian Eastern Standard Time (EST) is -0500. [9]

There exists no international standard that specifies abbreviations for civil time zones like CET, EST, etc. and sometimes the same abbreviation is even used for two very different time zones. In addition, politicians enjoy modifying the rules for civil time zones, especially for daylight saving times, every few years, so the only really reliable way of describing a local time zone is to specify numerically the difference of local time to UTC. [9]

The full standard defines in addition a number of more exotic notations including some for periods of time. [9]

This method has several advantages: [9]

  • It's human readable and succinct
  • Easily readable and writeable by software (no 'JAN', 'FEB', ... table needed), and language independent
  • Easily comparable and sortable with a trivial string comparison
  • Consistency with the common 24 hour time notation system, where the larger units (hours) are written in front of the smaller ones (minutes and seconds)
  • Notation has constant length, which makes table layout easily
  • Identical to the Chinese date notation
  • A 4-digit year representation avoids overflow problems after 2099-12-31
  • It includes fractional seconds
  • ISO 8601 is endorsed by W3C
RFC 2822

Published 2001.

This standard specifies a syntax for text messages that are sent between computer users, within the framework of "electronic mail" messages. This standard supersedes the one specified in Request For Comments (RFC) 822, "Standard for the Format of ARPA Internet Text Messages", updating it to reflect current practice and incorporating incremental changes that were specified in other RFCs.

I'm not sure anything changed.

Fri, 26 Oct 2018 00:00:00 +0000.

RFC 3339

Published July 2002.

Date and time formats cause a lot of confusion and interoperability problems on the Internet. This document addresses many of the problems encountered and makes recommendations to improve consistency and interoperability when representing and using date and time in Internet protocols.

This document includes an Internet profile of the ISO 8601 [ISO8601] standard for representation of dates and times using the Gregorian calendar.

RFC 3339 is listed as a profile of ISO 8601. Most notably RFC 3339 requires a complete representation of date and time (only fractional seconds are optional).


JSON does not specify how dates should be represented, but usually uses ISO 8601.

The `Long Now Foundation`_ prefers to write years with five digits instead of four, to emphasize long-term thinking.

On the Internet, the notation of times and dates has always been problematic. In particular, the format of Internet E-mail messages, as defined in 1982-08-13 (with some later modifications) by RFC 822 remained valid (which is still valid as an Internet standard) for a very long time. specifies a relatively uniform notation for date and time. It allowed some variation, but the most common alternative was something like Fri, 8 May 1998 15:57:33 +0300 (EET DST) There was enough variation to make it difficult to write simple programs for processing such data, too little variation to please everyone. In 2001-04, RFC 2822 was published as a successor to RFC 822. It restricted the recommended date and time formats to the format exemplified above. Note that this format is hardly used outside the Internet. [10]

4   History

Keeping track of time is the cornerstone of agriculture, and therefore civilization, because it relies on the ability to predict the seasons and the climate.

According to scientists from Harvard University, the earliest record of any sort of time keeping method dates back to 30,000 years ago. Alexander Markshank claimed that carvings in a ancient animal bone were a lunar calendar.

Stonehenge, built 5,000 years ago, seems to be a calendar as well. On the longest day of the year, June 21, the sunrise solstice can be seen from between Stonehenge's two most eastern pillar. On the shortest day of the year, December 21st, the sunset solstice can be seen from between the opposite stones.

4.1   Ancient Greece


In the time of the ancient Greeks and Romans, the earth was considered the center of the universe, which was itself a sphere containing all the stars. This celestial sphere rotated from east to west, carrying not only the stars but also the sun and the planets. Therefore, the sun revolved around the earth. This is what caused day and night. The earth did not rotate. The sun did not travel around the earth in a circle at right angles to the earth's axis (which was also the axis of the celestial sphere) as the stars did. Rather, the sun traced a circle along the celestial sphere, centred on the earth, known as the ecliptic. [4]

The ecliptic plane meets the equatorial plane at approximately 23.5°. This is known as the obliquity of the ecliptic. The circle of the ecliptic more or less intersects the twelve constellations of the zodiac, and the time of year (corresponding to modern months) was reckoned by what sign of the zodiac the sun was traversing. (Regardless of the exact location of the zodiac constellations, the ecliptic was divided into 12 equal arcs of 30° each, leaving most of the constellations off-centred and often not entirely in their designated 30° region.) The sun's motion along the ecliptic circle takes a (solar) year. The dual motion of the sun (on the celestial sphere and along the ecliptic) means that the sun follows a different path in the sky each day. From the perspective of the northern hemisphere, during the summer, the sun is higher in the sky and remains visible for a longer period of time. Since the ancients always divided the daylight into twelve equal hours, these summertime hours were longer. In the winter months, the sun is lower in the sky and visible for a shorter period of time. Consequently, the winter hours were also shorter. [4]

Time in the ancient world was first measured by naturally occurring events, such as sunrise, sunset, and meal times. [4]

The first and simplest water clocks were small bowls. In the centre of the bowl was a small opening through which water could flow. The empty bowl was placed in a basin of water and allowed to sink as water leaked into the bowl through the opening. The clock's attendant would announce that the interval of time had passed and reset the bowl to sink again.[10] This process was easily inverted so that water flowed out of small tanks rather than into them. The openings could be plugged to stop the water from flowing out. The immediate use of this kind of clock was the timing of speeches in law courts, most notably in Athens. Several Athenian sources indicate that this kind of judicial water clock was in common usage around 430 B.C. including Aristotle, Aristophanes the playwright, and Demosthenes the orator.[11] This water clock was used as a timer to prevent trials and speeches from going too long. The type of speech or trial determined how much water with which the clock was filled. [4]

Dionysius Exiguus came up with the modern world's most-used system for numbering years (Anno Domini, sometimes rebranded Common Era) in the early sixth century. For hundreds of years, however, the few Europeans dating documents preferred to continue the traditional system of dating by regnal year. By the high Middle Ages, chroniclers like Herman of Reichanau are numbering their entries by A.D. year, but we're still not quite at the point where they're common usage in charters or in people's minds. (Court testimony from even the late Middle Ages sometimes has people figure dates from either kings' regnal year or with reference to more local events). Just to make things even more interesting, Hebrew calendar years are also a creation of the High Middle Ages.

And yet, in these 4-5 centuries of only scattershot use of the A.D. system, there are isolated instances of writers who do pick it up and run with it. Bede in 7th-8th century England is perhaps the most famous. How did they do it? Easter!

The Christian liturgical calendar(s) involves some feasts that are fixed to a date and others that are more fluid. Most importantly and controversially, Easter, the history (and present, see: Catholic versus Orthodox) of whose dating is a giant mess. The early Church decided on a date for Easter that relates to the vernal equinox.

As you know, and as ancient people knew, years are not actually 365 days. Hence the introduction of leap years. And the presence of leap years (in the Julian calendar, which has too many leap years and so would be a problem by the sixteenth century) combined with the decision that Easter must always be a Sunday meant that the date of Easter had to be calculated. Indeed, this computus was a crucial duty of the early medieval clergy. They made table after table that calculated and listed the dates of Easter for centuries to come. So even across centuries of sporadic functional use of AD/CE, the medieval Church placed an absolutely premium on keeping track of the advancement of years in terms fixed to the date once presumed to be either the conception or birth of Christ.

The real point of the endeavour was to reconcile various things with the natural world (leap days and such) and to be able to calculate Easters effectively, which it did.


The Egyptians were the first to split the full cycle of day and night up into 24 hours, a system that was later improved upon by Greek astronomers Ptolemy and Hipparchus who further split it up in a sexagesimal (60 as a base) system, and that's where the second comes into play. First you divide an hour into 60 parts, creating the minute, and then you divide that a second time, hence the name, creating 1/60th of a minute. Further splitting up a second in sixthieths is called a third, but that's not really used nowadays.

At the time it wasn't possible to keep time that accurate, but towards the end of the 16th century mechanical clocks were able to measure seconds accurately, which is also when the English word for them came into use.

So historically, lots of things have been divided into 12 parts. There were originally 12 ounces in a pound (the word "ounce" comes from the Latin word for "twelfth"). And the day (sunrise to sunset, that is) was divided up into 12 parts, which we English-speakers now call "hours".

Precise time measurement is a relatively recent invention; hours, usually as determined by a sundial (meaning they weren't all the same length), were good enough for thousands of years. But when we started to need units smaller than hours, we again wanted to divide them up into a convenient-for-grouping number. You might expect that we would just pick 12 again and have 12ths of 12ths, but that's not what happened. Don't get me wrong; 12 is great - like I said, you can distribute evenly around a group of 2,3,4, or 6 - but you'll notice that list skips a number: 5. If you want to be able to handle 5 groups with a whole number of pieces each, you need to bump the total number of pieces all the way up to 12 times 5, which is 60. (Presumably for this same reason, those Sumerian/Babylonians I mentioned actually counted in base 60, which is related to how we got 360° in a circle.)

So the hour was divided into 60 parts, called the "small part of the hour". Eventually, of course, we needed even smaller pieces, so they renamed those as the "first small part of the hour", and divided them into 60 again, making the new smaller unit the "second small part of the hour". (And yes, there was also a "third small part of the hour", and at least some documented uses of even smaller subdivisions; but these days those have been replaced by decimal fractions of the second.)

Those "whateverth small part of the hour" names are kind of unwieldy, however, so naturally they got abbreviated. Back when there was only one small part, it got abbreviated to just "small". When the second one came along, it was naturally abbreviated "second". Except all of the scientific writing where these units were first needed was done in Latin, so the names were likewise Latin. From Latin for "small" we get "minute", and from Latin for "second" we get "second".

But the Earth is a lousy clock by modern standards - it wobbles due to all sorts of influences: gravity from the Moon, the asymmetrical effect of wind and tides on its uneven surface; basically, it's actual rotational speed is not consistent. So while its rotation is the ultimate source of the unit we call the "second", it's no longer part of that unit's definition. Instead, we have a much more precise definition based on counting cesium radiation emissions. Those emissions are impossible to predict individually, but happen very quickly - so fast that there are almost 10 BILLION with a B of them in a single second. Thanks to the law of large numbers, the amount of time required to collect such a huge number of emissions is amazingly consistent. Based on the number of emissions counted during the second as previously defined, we now define the second as the amount of time it takes to rack up 9,192,631,770 radiation cycles of cesium-133.

Greek astronomers were the first to establish the modern hour, by dividing the day into six parts and then dividing those parts into four more. They also had an early version of the minute, which was how long it took for the sun to travel one degree along the sky, or about four minutes.

The Babylonians went a little nuts, also dividing the day into six parts, but then divided each part by sixty for their sub-units, up to at least six subdivisions, the smallest individual units being as accurate as two microseconds. However, instead of using a 1/24th of a day hour like the Greeks, they had a 1/12th day hour (120 min), but did use the 1/360th day minute, and something resembling a second called the barelycorn, about 3.5 modern seconds and still used in the hebrew calendar today as the helek. In 1000, a Persian scholar named al-Biruni first termed the word second when he defined the period of time between two new moons as a figure of days, hours, minutes, seconds, thirds, and fourths. The minute was the first subdivision of the hour by 60, then the second, and so on. Roger Bacon did this again in the 1200's, but started with hours, giving a more accurate figure. The term third still exists in some languages, such as Polish, but fourths were apparently too small for any practical use and fell out of style with the general population. The late 1500s what the first time a true standard second came to being with the advent of mechanical clocks, so that the time could be measured objectively from mean-time instead of deriving it from the apparent-time. The first clock with a second hand was built between 1560-70and 1579 saw the first clock with actual markings denoting the seconds. However, they weren't very accurate, and the second remained arbitrary from machine to machine and unable to be reliably measured.

`Zeno of Elea`_ came up with a paradox that time never passed using the paradox of the arrow.

4.2   Rome

In 46 BC, Gaius `Julius Caesar`_ reformed the Roman calendar to form the Julian calendar. ("July" takes its name from him.) It took effect on January 1, 45 BC, by edict.

The Roman calendar had a regular year of 365 days divided into 12 months. In addition, every two years an additional month (called mercednius, Latin for "work month") was inserted between February and March, to align the conventional 355-day year with the solar year. (Unclear to me why this makes sense.) However, the decision to insert the additional month was made by the `pontifex maximumus`_, who would often manipulate the decision to allow friends to stay in office longer of force enemies out earlier. Such unpredictable intercalation meant that dates following February could not be known in advance, and Roman citizens living outside of Rome would often not know the current date.

The Julian calendar has a regular year of 365 days divided into 12 months. A leap day is added to February every four years. Although Greek astronomers had known that the year was slightly shorter than 365.25 days, the calendar did not compensate for the difference. As a result, the calendar year gains about three days every four centuries. Pope Gregory XIII corrected this discrepancy by the Gregorian reform of 1582.

4.3   Medieval

A Moment was a medieval unit of time. 1 day was divided into 24 hours and 1 hour was equal to 12 lengths of the period from sunrise to sunset. The hour was divided into 4 puncta, 10 minuta, or 40 momenta. Considering an average 12 solar hours: 1 moment = 90 seconds.

4.4   Mechanical time

Before mechanical time, human activity was temporally regulated by nature: the crow of the rooster in the morning, the slow descent into darkness at night. As the economic historian Douglas W. Allen argues, the problem was variability: “there was simply too much variance in the measurement of time … to have a useful meaning in many daily activities”.

“The effect of the reduction in the variance of time measurement was felt everywhere”, Allen writes. Mechanical time opened up entirely new categories of economic organisation that had until then been not just impossible, but unimaginable. Mechanical time allowed trade and exchange to be synchronised across great distances. It allowed for production and transport to be coordinated. It allowed for the day to be structured, for work to be compensated according to the amount of time worked — and for workers to know that they were being compensated fairly. Both employers and employees could look at a standard, independent instrument to verify that a contract had been performed.

4.5   The mechanical clock & the hourglass

See clock.


Perhaps the most underrated invention in history is the humble hourglass. Invented in Europe during the late 13th or early 14th century, the sand glass complemented a nearly simultaneous invention, the mechanical clock. The mechanical clock with its bell was a centralized way of broadcasting the hours day and night; the sand glass was a portable way of measuring shorter periods of time. These clocks were made using very different and independent techniques, but their complementarity function led to their emergence at the same time and place in history, late medieval Europe.

The sandglass was more portable than a water clock. Since its rate of flow is independent of the depth of the upper reservoir, it was also more accurate. And, important in northern Europe, it didn't freeze in winter.

An advancing technology in 13th century western Europe very different from mechanics was glass-blowing. The origin of the sandglass is quite obscure, but its accuracy relies on a precise ratio between the neck width and the grain diameter. It thus required extensive trial and error for glass-blowers to arrive at hour glasses for sand, ground marble, eggshell, and other sized grains, and techniques for mass producing these precisely sized works of glass, besides a ready of market of users, which Europe turned out to be.

There are no demonstrated cases of sandglasses before the 14th century. Manufacture and use of the sand-glass was widespread in western Europe by the middle of the 14th century.

The sandglass, not the mechanical clock, became between the 13th and 16th centuries the main European timekeeper in activities as diverse as public meetings, sermons, and academic lectures. It was also the main navigational and scientific clock during that period.

From the point of view of later engineers, the mechanical clock was the more important invention -- they were on the cutting edge of technology from the time of their invention until the industrial revolution. However,

For contemporaries....the sandglass was equally or more important. Until the widespread use of small table-top mechanical clocks, the sandglass was the primary means of fair timekeeping. The sand glass was visible to all in a room, and it could only be dramatically and obviously “reset”, it couldn’t be fudged like a mechanical clock.

During the voyage of Ferdinand Magellan around the globe, his vessels kept 18 hourglasses per ship. It was the job of a ship's page to turn the hourglasses and thus provide the times for the ship's log. Noon was the reference time for navigation, which did not depend on the glass, as the sun would be at its zenith.[8] More than one hourglass was sometimes fixed in a frame, each with a different running time, for example 1 hour, 45 minutes, 30 minutes, and 15 minutes.

Arab and Chinese navigators lacked this crucial piece, and thus by the time of the exploration explosion had not developed navigation techniques that could rival those of Western Europe.

Clocks run from "left to right" because in the Northern hemisphere that's how sundials cast shadows. Before clocks it was referred to as "sunwise" and not "clockwise". (It remains so in Swedish.)

4.6   Pendulum clocks

In 1644 it was realized that a pendulum of a specific length would have an oscillation period of exactly two seconds, and by 1670 William Clement had tinkered with the physics enough to build a clock precise enough that the second was now an established unit of time. By 1862 it was established that the second would be the base unit of time for all scientific research, along with the millimeter and milligram, by The British Association for the Advancement of Science (BAAS), defining the second as 1/86,400th of a solar day by the 1940s. [5]

4.7   Marine chronometer

A marine chronometer is a timekeeping piece that works on the harsh conditions aboard a ship.

The first marine chronometer was invented in 1761.

Why couldn't sailors use watches instead of a marine chronometer?

4.8   Atomic clocks

Since 1967, the definition of a second is based on an extremely predictable measurement made of electromagnetic transitions in atoms of cesium. These "atomic clocks" based on cesium are accurate to one second in 1,400,000 years. [1]

According to NIST the time unit second is defined as follows:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

4.9   Time zones

There are more than 24 time zones, as might commonly be guessed. For instance, Bangalore is on (UTC +5:30). The state of Indiana alone has eleven documented time zones

5   Daylight savings

PDT = Pacific Daylight Time, PST Pacific Standard Time

6   Perception

Research by David Eagleman suggests that the perception of time is related to number of distinct memories. Eageleman performed an experiment to test whether time slowed down for people in life threatening situations or if the duration seemed longer because new memories were being formed. He ruled out the former.

This suggests to me that if we want to feel like we've spent a lot of time with someone, we need to do new things with them.

7   Resources

8   Further reading

9   References

[1](1, 2) Technocracy Inc. 1945. Technocracy Study Course. Lesson 2. https://ia600204.us.archive.org/10/items/TechnocracyStudyCourseUnabridged/TechnocracyStudyCourse-NewOpened.pdf
[2](1, 2, 3) Suresh Embre. April 26, 2014. Difference between sidereal day and solar day on Earth. https://sureshemre.wordpress.com/2014/04/26/difference-between-sidereal-day-and-solar-day-on-earth/
[3](1, 2) Solar Days and Sidereal Days https://community.dur.ac.uk/john.lucey/users/e2_solsid.html
[4](1, 2, 3, 4) John J O'Connor and Edmund F Robertson. Timekeeping in the Ancient World: Sundials. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Sundials.html
[5](1, 2) John J O'Connor and Edmund F Robertson. Timekeeping in the Ancient World: Water-clocks. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Water_clocks.html
[6]Nick Szabo. A very underrated invention. July 20, 2013. http://unenumerated.blogspot.com/2013/07/a-very-underrated-invention.html
[7](1, 2, 3) Robert Nelson. Dec 1981. Foundations of the international system of units. http://www.physics.umd.edu/deptinfo/facilities/lecdem/services/refs/refsa/Nelson-FoundationsSI.pdf
[8]Misha Wolf, Charles Wicksteed. Sep 15, 1997. Date and Time Formats. https://www.w3.org/TR/NOTE-datetime
[9](1, 2, 3, 4, 5, 6) Markus Kuhn. 2004-12-19. A summary of the international standard date and time notation. https://www.cl.cam.ac.uk/~mgk25/iso-time.html
[10](1, 2, 3, 4) Jukka Korpela. Info on ISO 8601, the date and time representation standard. http://jkorpela.fi/iso8601.html

An epoch is some point from which time is measured.

A similar impulse in a more secular form led Benjamin Franklin a century later to invent the idea of daylight saving time. While American minister to France, Franklin was shocked that the people of Paris lost many hours of light by sleeping until midday, and then burned candles far into the night. He tried to enlighten his French friends in an essay called An Economical Project which proposed what we call daylight saving time.