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Useful Info
This page contains snippets that have been or might be useful for documents about Time.
The conceptual model proposed several regimes:
- Event Regime - No clocks, logic only
- Clock Regime - Clocks, ticks, integer arithmetic only, no –ve times
- Coordinate Regime - CRSs, number line to interpolate between ticks, real arithmetic, extrapolate before zero/datum/epoch
- Calendar Regime - Calendars, abnormal arithmetic, earth sun and moon rotations, months, weeks
Set of EVENTS ordered in time (ta, tb, tc, … tn), that may be: Finite or Countably infinite (like the integers)
No clocks
USually there is no Epoch, until an event can be related to another Temporal Reference System
Simple Logic Operators defined to determine if 2 times are: The same, or one earlier, the other later (maybe an earliest and latest times?)
2 times define Relation(ta,tb), ta<tb, but NOT duration (tb-ta)
Any 3 or 4 events could allow logic (Allen 1983) such as:
tb is in (ta,tc), ta<tb<tc
(ta,tc) overlaps (tb,td), ta<tb<tc<td,
(ta,td) contains (tb,tc ), ta<tb<tc<td,
(ta,tb) disjoint from (tc,td), ta<tb<tc<td,
No other times exist or can be interpolated
Similar to RCC8 spatial operators, and the logic is a formal mathematical algebra.
Not sure about continuum. Probably OK. Operations are the distinguishing features.
Examples: Geology, Archaeology, Ice and sediment cores, King Lists and Genealogies
Could be multiple sets, each with own ordering, may or may not be relations between events across sets
ISO8601 notation 2014-10-07T10:00 is a BAD notation for this regime. Notation should just be labels E.g. “Jurassic”, “65My ago”, “Reign of Tiglathpileser III”, "1.562m from top of core" (?? not sure about ice cores? Tree rings are definitely Regime 2, clocks)
“Clock” defined as any regularly repeating physical event that can be counted (or perhaps measured?)
Countably infinite set of ordered time INSTANTS.
Fixed precision, determined by interval between instants
No intermediate times can be calculated between ticks
Similar set of operations: Same, Earlier/later, Operations for Instants and Intervals
tb is in (ta,tc), ta<tb<tc
(ta,tc) overlaps (tb,td), ta<tb<tc<td,
(ta,td) contains (tb,tc), ta<tb<tc<td,
(ta,tb) disjoint from (tc,td), ta<tb<tc<td,
Can now calculate duration (tb-ta) as metric defined
Could be an earliest or latest, or an epoch (datum time)
Examples:
- TAI International Atomic Time, which cannot be used to time events to femtosecond precision, or cannot be used to time events prior to Epoch!
- Pendulum swings
- Heart-beat
- Vibration of a piezo-electric crystal
- Rotation of earth around sun
Notation implying higher accuracy than ticks not appropriate. E.g. Julian days labelled 2014-10-07T10:00:00.0+01:00
Precision defined with countably infinite set of ‘ticks’
Assume normal mathematical interpolation between ticks
Epoch defined, perhaps with practical earliest/latest times
Assume mathematical extrapolation before epoch or into the future: +/-
Logical Operations and calculations well defined
Other ‘UoM’ can be defined but must be totally ‘regular’ E.g: 1 hour = 60 mins, 1 day=24 hours, 1 year = 360 days E.g: milliseconds, kiloseconds
Examples: Unix milliseconds, Julian Days, Julian Years, etc
Epoch may be ill-defined (start of reign of Ashburnipal III) so CRS is relative, not absolute – see Regime 0.
Epoch should be defined in terms of TAI, UTC, etc
Regimes 1 & 2 blend
Think carefully about timestamp notation, such as ISO8601:
2014-10-07T11:00:00.0 actually implies LOCAL time, which could be solar!
2014-10-07T10:00:00.0Z implies UTC, and therefore leap seconds
Astronomers epoch is usually at midday, everyone else prefers midnight, of specified day
Anything requiring an algorithm beyond normal arithmetic
E.g: Years CE and BCE (AD & BC). There is no year 0BCE or 0CE, so ‘normal arithmetic’ gives unexpected results E.g. UTC Gregorian, Mayan, Jewish, etc
Should have an Epoch
May have earliest and latest defined times, or times when algorithm invalid
Usually approximates a CRS to astronomical events
Algorithmic rather than observed calendar
A CRS is not a Calendar, a Calendar is not a CRS!
A Timescale is regular/homogenous and monotonic, with usually only one UoM, but may be continuous or discrete.
A Timeline may hav gaps, or even duplicated times, so not necessarily monotonic, and may have several incompatible UoMs.
ISO 8601:2004: 2014-10-07T10:20:00.0
Is 0000-01-01T00:00:00.0 valid?
2013-07-01T00:00:00 minus 2013-06-30T23:59:00 = ?
59 or 60 or 61 seconds?
2012-07-01T00:00:00Z minus 2012-06-30T23:59:00Z = ?
59 or 60 or 61 seconds?
Do not assume notation implies arithmetic, CRS or calendar!
What notation applicable for each regime?
Answers: 2012-07-01T00:00:00 minus 2012-06-30T23:59:00 = 60 possibly, if local time is UTC
2012-07-01T00:00:00Z minus 2012-06-30T23:59:00Z = 61 precisely because ‘Z’ implies UTC, and leap seconds only introduced at "midnight" UTC
Astronomical times, local solar time, sidereal time, relativistic, helio-spatial, accountancy, etc Requires observation of moon, sun or stars
Could be several regimes:
Observation based calendars
Sidereal time
Local Solar time, Mean Tropical Year
Space weather time on Sun
Relativistic
Etc
Plenty of realistic detailed use cases
Accountancy? Weeks and months!
Plenty of calendars in this regime