The document discusses various standards and concepts related to timekeeping, including solar time, mean solar days, Coordinated Universal Time (UTC), time zones, leap seconds, Unix time, and Network Time Protocol (NTP). It explains how UTC approximates solar time, how time zones define offsets from UTC, and how leap seconds are inserted to keep UTC synchronized with solar time.

1. Dates and Times
2015-07-01T12:40:00-07:00

2. Solar time

3. Solar time
● We’ve always equated the passage of time
with the sun’s position in the sky.
● This is called solar time.
● Time for the sun to return to its previous
position in the sky is called a solar day.

4. Mean solar day

5. Mean solar day
● Length of a solar day varies throughout the
year.
● A clock that ticks a constant number of times
per day cannot keep solar time.
● So we compute the mean solar day.

6. GMT

7. GMT
● Long ago, Britain had a kick-ass navy.
● Many nautical maps referred to Greenwich,
London as their Prime Meridian.
● All clocks synchronized against its mean
solar time.

8. Tidal effects

9. Tidal effects
● Tides redistribute a big chunk of the Earth’s
mass.
● Decreases its rotational speed.
● Length of the mean solar day is increasing.
● But the second was defined as 1/86,400 of a
mean solar day...

10. UT1

11. UT1
● Universal Time 1, succeeds GMT.
● Measured from stable celestial points of
reference.

12. SI seconds

13. SI seconds
● SI 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 caesium 133
atom.”
● Atomic clocks won’t gain or lose such a
second over millions of years.

14. TAI
● International Atomic Time.
● Averages over 400 atomic clocks worldwide.
● Defines the rate at which all clocks should
tick.
● Was 10 seconds ahead of UT1 in 1958.
● 86,400 SI seconds is consistently less than
mean solar day, so now 36 seconds ahead.

15. TAI
TAI
UT1

16. UTC and leap seconds
● We want clocks to reflect solar time, or UT1.
● We want clocks to tick SI seconds, like TAI.
● UTC is an integer offset from TAI that
approximates UT1.
○ English: coordinated universal time (CUT)
○ French: temps universel coordonné (TUC)
● Leap seconds pump the brakes on TAI.

17. UTC and leap seconds
UTC
UT1
inserted leap second

18. UTC and leap seconds

19. Local time
● UTC is great, but it approximates the mean
solar time in Greenwich, London.
● Region defines all of its clocks as running
ahead or behind UTC by an offset.
● Clocks adopt a local time within a region,
and the region itself defines a time zone.

20. Local time

21. Daylight saving time
● Some regions have more daylight in the
summer than in the winter.
● Shifts the majority of the extra sunlight to
later in the day.
● Region switches away from standard time.
○ e.g. PST (UTC-8) to PDT (UTC-7)
○ In U.S., happens at 2 a.m. in each time zone.

22. Daylight saving time

23. Daylight saving time
"I have seen reports that show changing the
time twice a year has an adverse effect on
people's health. When the time changes,
people experience more mishaps, accidents
and even more heart attacks. Sometimes, no
change is good."
- Senator Cliff Pirtle R-Roswell

24. tz database
● Defines regions where all clocks have
shared the same time since Jan 1, 1970.
● Has history of time zones with UTC offsets
and daylight saving rules for each region.

25. tz database

26. tz database
$ ls -l /etc/localtime
... /etc/localtime -> /usr/share/zoneinfo/America/Los_Angeles

27. tz database
los_angeles_tz = timezone('America/Los_Angeles')
tz_fmt = '%H:%M %Z%z on %B %d, %Y'
utc_dt = datetime(2015, 1, 10, 16, 30, tzinfo=pytz.utc)
los_angeles_dt = utc_dt.astimezone(los_angeles_tz)
print los_angeles_dt.strftime(tz_fmt)
# 08:30 PST-0800 on January 10, 2015
utc_dt = datetime(2015, 6, 10, 16, 30, tzinfo=pytz.utc)
los_angeles_dt = utc_dt.astimezone(los_angeles_tz)
print los_angeles_dt.strftime(tz_fmt)
# 09:30 PDT-0700 on June 10, 2015

28. tz database

29. ISO 8601
los_angeles_tz = timezone('America/Los_Angeles')
kathmandu_tz = timezone('Asia/Kathmandu')
tokyo_tz = timezone('Asia/Tokyo')
now = datetime.now(los_angeles_tz)
print 'America/Los_Angeles: %s' % now.isoformat()
# America/Los_Angeles: 2015-06-30T23:33:11.498959-07:00
print 'UTC: %s' % now.astimezone(pytz.utc).isoformat()
# UTC: 2015-07-01T06:33:11.498959+00:00
print 'Asia/Kathmandu: %s' % now.astimezone(kathmandu_tz).isoformat()
# Asia/Kathmandu: 2015-07-01T12:18:11.498959+05:45
print 'Asia/Tokyo: %s' % now.astimezone(tokyo_tz).isoformat()
# Asia/Tokyo: 2015-07-01T15:33:11.498959+09:00

30. Unix time
● Number of seconds since January 1, 1970 at
00:00:00 UTC.
● This is called the Unix epoch.

31. Unix time
$ date +%s
1435733200

32. Unix time
Language Method name Units Data type
C time seconds integer
C gettimeofday microseconds struct
Java currentTimeMillis milliseconds 64-bit long
Python time seconds floating point
Objective-C timeIntervalSince1970 seconds floating point

33. Unix time
● Unlike UTC, Unix time does not include leap
seconds.
● Midnight between days is always 86,400
seconds.
● Unix time is discontinuous around leap
seconds.
● It is a lossy encoding of UTC.

34. Obsered unix time
UTC Unix time (internal) Unix time (observed)
2012-06-30T23:59:59.75 1341100799.75 1341100799.75
2012-06-30T23:59:60.00 1341100800.00 1341100800.00
2012-06-30T23:59:60.25 1341100799.25 1341100800.01
2012-06-30T23:59:60.50 1341100799.50 1341100800.02
2012-06-30T23:59:60.75 1341100799.75 1341100800.03
2012-07-01T00:00:00.00 1341100800.00 1341100800.04
2012-07-01T00:00:00.25 1341100800.25 1341100800.25

35. Observed unix time
● Not POSIX compliant.
● Same POSIX standard that wrongfully
considered the year 2100 a leap year…
● Google modified NTP to perform a “leap
smear” which is over the preceding day.

36. NTP
t0
t3
t1
t2
● Time to propagate the request and
response is (t3
– t0
) – (t2
– t1
)
● Assuming latency in both directions
is equal, correct time at t3
is
t2
+ [(t3
– t0
) – (t2
– t1
)] / 2
● So t3
+ δ = t2
+ [(t3
– t0
) – (t2
– t1
)] /
2
● δ = [(t1
– t0
) + (t2
– t3
)] / 2
client server