Abstract
Two different clock systems –
24-Hour and 12-Hour – developed over centuries are in use. The 24-Hour system
is widely used across the globe while the 12-Hour system in some countries,
especially the English-speaking countries. In the later system, the 24-hour day
is divided in to two 12-hour periods. The two periods are differentiated by
referring to each one in relation to midday (meridiem from Latin). That is,
first half by “a.m.” (ante meridiem – after midday - AM) and the later by
“p.m.” (post meridiem – past midday - PM). The 12-hour system is epoch based
with midday being the epoch moment resulting in ambiguity, especially, in
referring to midnight (12:00 AM) and midday-noon (12:00 PM) moments. For, 12:00 PM, is neither
12 hours before nor 12 hours after midday and; 12:00 AM is 12 hours after
midday of previous day and 12 hours before midday of following day. This system
uses the numerals 1 to 12 to refer different moments at one hour interval from
start of the period. With this usage of time referencing, the first period ends
at 12, and; the second period starts at 12 ending at 12. This results in
referring different moments, that are at one minute interval in the first hour
of each period, by 12:mm (mm - minutes 0 to 59) with appropriate suffix of
“a.m.” and “p.m.” and; the one hour since start by 1:00 indicating 12 comes
before 1. So, a period of 12 hours is a closed system and the usage 12:mm is
more conventional and inappropriate. For, the start of the period, represented
by 0 (zero) is not considered in the current time referencing format of the
12-hour system.
Here, it is proposed that each
period of 12-hour duration to start at 0 (zero) and end at 12. This obviates
the need for referring the moments in the first hour by 12:mm and can be
referred by 0:mm an appropriate format. In this format, midday also gets two
identities, 12 (end of first period) and 0 (start of second period) as also
midnight, which has two identities, 24 (end of previous day) and 0 (start of
following day) in the 24-hour system. It is also proposed to drop the common
reference point (meridiem moment) and each period should be referred in
relation to their respective starting moments. This helps in exclusively
identifying different moments of the two periods using same suffixes (with
altered expansions) AM (After Midnight) for first period and PM (Past Midday)
for second period respectively. The propositions, use of 0 (zero) and dropping
of common reference of the two periods to meridiem removes the ambiguity stated
earlier and also simplifies the conversion from one system to the other.
Introduction
A day, divided
in to twenty-four hours, is defined to start at midnight and pass through
midday after twelve hours and; end at midnight after another twelve hours. The
hours comprise sixty minutes and which in turn comprise sixty seconds. The
notation commonly used in time referencing is hh:mm:ss (long format) or hh:mm
(short format) depending on the required accuracy. Clock one of the oldest
devices in use, measures and indicates the time, in desired units, shorter than
a day [1]. Two different clock systems – 24-hour
and 12-hour – developed over centuries are in use. The 24-hour system is widely
used across the globe while the 12-hour system in some countries, especially
the English-speaking countries [2-3].
24-Hour System
In the shorter
format of time notation, which is commonly used, a day is indicated to start at
00:00 and the last minute starts at 23:59 with the day ending at 24:00. The
moment at which a day ends, that is, 24:00 is the same moment at which the
following day starts, that is, 00:00. So, the same moment at midnight may be
indicated as the end of a previous day or start of the following day.
The notation
hh:mm indicates number of hours and minutes since midnight. That is, 6:00,
12:00 and 18:00 refer to six, twelve (Midday or Noon) and eighteen hours (and
zero minutes to be precise) since midnight respectively.
Typically, the
usage of time referencing of the midnight moment is 00:00 for start of an
activity and 24:00 for the end of an activity. That is, for example, in
transportation system, trains and buses departure time is indicated as 00:00
and arrival as 24:00. That is because, a vehicle departure signifies start of a
journey and arrival signifies end of a journey coinciding with start and end of
day respectively. There is no particular confusion in the usage of the 24-hour
system. The countries using 12-hour system also use the 24-hour system for
activities that require no ambiguity in time reference.
12-Hour System
In this system, the 24-hour day is divided in to two
12-hour periods. The first period or the first half of the day is between
midnight and midday and the second period or second half of the day is between
midday and midnight. The numbers 1 to 12 are used to refer different moments at
one-hour interval since the start of the period in each of the two periods.
That is, each period has a starting point 0 (zero) and an ending point
12.
The two periods are differentiated by referring to
each one in relation to meridiem, midday in Latin. That is, first half by
“a.m.” (ante meridiem - Latin) and second half by “p.m.” (post meridiem -
Latin). The English usage of the abbreviations is “A.M.” and “P.M.”
respectively. The variations am/pm and AM/PM are also in use [3]. That is, each of the twenty-four moments of a
day at one-hour interval since the start of the day at midnight are labelled by
numbers between 1 and 12 suffixing them with AM or PM depending on the period
they occur in.
Thus, the times 06:00, 12:00 and 18:00 in the 24-hour
system are referred as 6:00 AM, 12:00 PM (or 12 noon) and 6:00 PM respectively
in the 12-hour system. The time 24:00, in 24-hour system, is referred as 12
midnight or 12:00 AM in 12-hour system. The notations 12:00 AM and 12:00 PM are
commonly not used and recommended for usage for both the start of an activity
or end of an activity as they lead to ambiguity [2-5].
The starting moment, of each of the two periods, is not referred by 0 (zero) but
are referred to by using 12.
AM/PM Usage and Ambiguity
The 12-hour system is epoch based [6] with midday being the epoch moment resulting in
ambiguity, especially, in referring to midnight and midday moments. For
example, 12:00 PM (noon) is neither before nor after midday, the reference moment,
on any particular day. And, 12:00 AM (midnight) is twelve hours after midday of
previous day and twelve hours before midday of following day [5]. These suggest the inappropriateness of AM and PM suffix
to midnight and midday hour numeral. So, the recommendation is, midnight be referred
by days between which it occurs (i.e. midnight day1-day2 or 12:00 day1-day2) [6], the day identified by a date or weekday, or
alternatively, use 11:59 PM or 12:01 AM, and; midday as 12:00 noon or 12 m (m
meridiem) to avoid the ambiguity [3-5]. The
ambiguity in referring to these two moments is stated by many institutions with
one switching from one reference (12:00 AM midnight) to the other (12:00 PM
midnight) and the other moment in the opposite. [3].
A diagram in [7] shows
the relation between the start times of days (at dawn, noon, dusk or midnight) in
different calendars that are adopted over the years. It showed 12:00 AM
corresponding to noon and 12:00 PM corresponding to midnight.
The usage or 6:00 AM reference of a moment six hours
since midnight in the day refers to the same moment six hours before midday.
So, no ambiguity in referring to this moment (06:00). This is because (06:00)
is halfway between midnight and midday in the first 12-hour period of the two-period
system.
For example, 5:00 AM is conventionally considered as 5
hours since start of the first 12-hour period [the period before midday (AM)]. It
means, 5:00 AM is interpreted as 5 hours since midnight, that is, 05:00. But,
5:00 AM translates to 5 hours before midday, to suggest it is indicating 07:00.
Similarly, 7:00 AM is interpreted as 7 hours since midnight, that is, 07:00.
But, 7:00 AM translates to 7 hours before midday, to suggest it is indicating
05:00.
The 12:00 AM reference to midnight translates to 12
hours before midday, which is true. However, the midnight moment (start of the
first half of the day), 12:00 AM, occurs before 1:00 AM and not after 11:00 AM
although 12 is numerically greater than 11. And; the moment one hour since
11:00 AM is referred as 12:00 PM.
PM (post meridiem) means past midday. So, the
reference to noon (midday), 12:00 PM, translates to the moment 12 hours past
midday, which is not true. As, it is not referring to the moment it
should. Again, 12:00 PM occurs before 1:00PM and not after 11:00 PM.
This is due to dual reference points (midnight and
midday) for each of the moments at one-hour interval since start in the first
period. That is, the hour numbers (1-12) reference is from the start of the
period (midnight) for each of the moments at one-hour interval since start and
are labelled in relation to the end of the period (midday).
That is, the meridiem (midday) moment which is used for
differentiating the two 12-hour periods, in the usage of AM and PM, is
functioning as an epoch moment, a moment, at which change occurs. And, an epoch
is a point at which, the points to its left (or before it) are negative and to
those on the right (or after it) are positive.
So, it is convention that assists in correctly
interpreting “H:00” (1 <= H <= 12) AM and not by it itself. As also,
12:00 PM. The rest of the moments at one-hour interval since midday referred by
“H:00” (1 <= H <= 11) PM are unambiguous. This is due to single reference
point (midday) for each of these hour moments in the second half of the two periods
of a day in the 12-hour system.
Moments between 12:00 and 1:00
This is concerning the current practice of referring to
the moments that are between 12:00 and 1:00 (that is, excluding the later referred
moment) in each of the two 12-hour periods in to which a day of 24 hours is
bifurcated in to. For example,
1. The moments 00:01, 00:30 and 00:59 in 24-hour system
are referred by 12:01 AM, 12:30 AM and 12:59 AM respectively; and
2. The moments 12:01, 12:30 and 12:59 in 24-hour system
are referred by 12:01 PM, 12:30 PM and 12:59 PM respectively.
This usage or referencing the moments between 12:00
and 1:00 is not inappropriate considering the current convention of
interpreting “H:00” (1 <= H <= 12) AM/PM. The conventional reference of
these moments is based on the use of circular display for convenience in which
the starting and ending point are same and the point is labelled 12, the length
of a period, rather than 0 (zero) the start of a period. However, if
consideration is given to the definition of a 12-hour period, such a reference
to the moments under consideration will be inappropriate.
The two periods of a 24-hour day are of 12 hours
duration with a start and an end. The start of any system is at a 0 (zero)
point. And, the end is at the most extreme point of the system. So, in the case
of a 12-hour system, the end is at 12. That essentially suggests the number
system which identifies the moments at one-hour interval, since start, forms a
closed (both included) interval between 0 (zero) and 12. That is, at the end of
a period another starts. So, the succeeding period must start at 0 (zero) and
not at 12 as is the current practice in the 12-hour clock system.
Thus, a reference to a moment at the start of a
period, or more precisely, different moments at one-minute interval since start
during the first hour in each period, such as 12:mm (00<= mm <= 59) is
inappropriate. Referring to these moments by 0:mm (00<= mm <= 59) would
be appropriate.
Unambiguous AM/PM Usage
The first 12-hour period of the two-period system has
the same starting point (moment) as the start of the day at midnight (i.e. 00:00
in 24-hour system). Therefore, the moments “hh:mm” (00<= hh <=11 and
00<= mm <=59) and 12:00 in the 24-hour system may be referred by “H:mm” (0<=
H <=11 and 00<= mm <= 59) AM and 12:00 AM, in the first period of the
two in 12-hour system, with AM being After Midnight. Thus, the
moments between midnight and midday are identified as hours and minutes since
midnight in 24-hour system or hours and minutes after midnight (AM) in 12-hour
system. That is, in this usage, the moments between midnight and midday are
referred with a single reference to midnight, avoiding dual reference and
ambiguity, in the 12-hour system. Thus, the start and end of the first half of
12-hour system are identified by 0:00 AM and 12:00 AM respectively.
The second 12-hour period of the two-period system
starts at midday and ends at midnight. The moments during this period may be
referred by “H:mm” (0<= H <=11 and 00<= mm <= 59) PM and 12:00 PM
with PM being Past Midday. These correspond to the moments “hh:mm”
(12<= hh <=23 and 00<= mm <= 59) and 24:00 in the 24-hour system. Thus,
the moments between midday and midnight are identified as hours and minutes
since midnight in 24-hour system or hours and minutes past midday (PM) in
12-hour system. Thus, the start and end of the second half of 12-hour system
are identified by 0:00 PM and 12:00 PM respectively.
Thus, the midnight moment is, 24:00, end of the
previous day or 00:00, start of the following day in 24-hour system. It
corresponds to 12:00 PM, end of the previous day or 0:00 AM, start of the
following day in 12-hour system respectively. The midday, in 24-hour system is
12:00 and it is either 12:00 AM (end of the first period of two in 12-hour
system) or 0:00 PM (start of the second period of two in 12-hour system).
12/0 AM/PM Advantage
The use of 12/0 AM/PM with suggested alternative
expansion for AM/PM (After Midnight / Past Midday) will
remove the ambiguity, in 12-hour system, in referring the moments of midnight
and midday. And, it also, addresses the inappropriateness in referring to the
different moments during the respective first hours following these two
moments.
1.
… at 12:00 AM on 22nd
February means at “noon” (midday) on 22nd February (i.e. 12 hours After Midnight or start of 22nd
February at 0:00 AM). Times 0:00 AM and 12:00 AM here refer to the start and
end moments of the first period on 22nd February. It corresponds to
12:00 on 22nd February in 24-hour system.
2.
… at 0:00 PM on 22nd
February means at “noon” (midday) on 22nd February (i.e. 0 (zero) hours Past Midday or 0 (zero) hours after start of second period
on 22nd February at noon). It refers to the same moment as 12:00 AM
on 22nd February. It also corresponds to 12:00 on 22nd
February in 24-hour system.
3.
… at 12:00 PM on 22nd
February means at “midnight” on 22nd February (i.e. 12 hours Past Midday (noon), the end of
first period on 22nd February at 12:00 AM or 12 hours after the
start of second period at 0:00 PM). Times 0:00 PM and 12:00 PM here refer to
the start and end moments of the second period on 22nd February. It
corresponds to 24:00 on 22nd February in 24-hour system.
4.
… at 0:00 AM on 23rd
February means at “midnight” on 23rd February (i.e. 0 (zero) hours After Midnight or 0 (zero) hours
after start of first period on 23rd February at midnight). It refers
to the same moment as 12:00 PM on 22nd February. It corresponds to
00:00 on 23rd February in 24-hour system.
5.
… at 0:30 AM on 23rd
February means the moment that is 0 (zero)
hours and 30 minutes After Midnight on 23rd February or 0 (zero)
hours and 30 minutes after start of first period at 0:00 AM on 23rd
February. It corresponds to 00:30 on 23rd February in 24-hour
system.
6.
… at 0:30 PM on 23rd
February means the moment that is 0 (zero)
hours and 30 minutes Past Midday on 23rd February or 0 (zero)
hours and 30 minutes after start of second period at 0:00 PM on 23rd
February. It corresponds to 12:30 on 23rd February in 24-hour
system.
Departures and arrival times
of various transport services can be stated using 12-hour system with no
ambiguity just as in 24-hour system with 12/0 AM/PM usage. The use of 12-hour
system for such operations or for any other activity, requiring no ambiguity,
would be useful for common people who are more used to 12-hour system as
compared to 24-hour system in the regions which use the 12-hour system.
The start of the day Midnight
and Midday are both abbreviated by the letter ‘M’, After by ‘A’ and Past by
‘P’. The expansion for ‘AM’ could be ‘After Midnight’ or ‘After Midday’.
Similarly, expansion for ‘PM’ could be ‘Past Midnight’ or ‘Past Midday’. In the
English language alphabets, the letter ‘A’ is before letter ‘P’. And, in the
definition of day Midnight is before Midday. So, ‘After’ is associated with
‘Midnight’ and; ‘Past’ is associated with ‘Midday’. That is, the word starting
with the first letter or earlier occurring letter in the alphabets is
associated with first moment, Midnight, of the day and; the word starting with the
later occurring letter in the alphabets is associated with later moment,
Midday, of the day. Thus, ‘AM’ expands to ‘After Midnight’ and ‘PM’ expands to
‘Past Midday’. This, facilitates the continued use of the abbreviations ‘AM’
and ‘PM’. Any alternate abbreviations may cause inconvenience to the user.
12-24-12 Hour Conversion
The 12/0 AM/PM format of referring different moments
of the day in 12-hour system will simplify time conversion from one system to
another between the two, 12/24-hour, clock systems, in use. The conversion from
one to the other only changes the hour numerals and minute numerals remain
same. That is, the notation H:mm [(1<= H <= 12 in 12 AM/PM format) or (0<=
H <=12 in 12/0 AM/PM format)] in 12-hour system changes to hh:mm (00<= hh
<=24) in 24-hour system.
References:
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01 https://en.wikipedia.org/wiki/Clock
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02 https://en.wikipedia.org/wiki/24-hour_clock
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03 https://en.wikipedia.org/wiki/12-hour_clock
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04 https://en.wikipedia.org/wiki/Noon
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05 NIST Times of Day FAQs Access Date: February 22, 2018
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06 Arnold Joseph Toynbee, John Jamieson Carswell Smart and Others. Time. Encyclopædia Britannica. Encyclopædia Britannica, inc. May 22, 2017.
https://www.britannica.com/science/time. Access Date: January 09, 2018
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07 Mapping Time - The Calendar and its History by E. G. Richards, 1998, Oxford University Press. (Kindle Version: Location 3525 of 5268)
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