MersenneForum solves the word time keeping problem.

[retina]

Originally Posted by xilman

No, I do not have an answer because the question is based on an unwarranted assumption.

Your question presupposes that units other than SI multiples of seconds are required and/or desirable. I thought my post had already established in a sane world only units of ..., ms, s, ks, Ms, Gs, ... would be used. Perhaps I wasn't explicit enough.

I see you misunderstood my question. The length of the second is arbitrary. We could recalibrate it to be 1e-5 of a current 86400 second 'day', thus 100ks per day. This would make stating days and subdays easier IMO. For example 1.5 days would simply be 150000 seconds.

[xilman]

Originally Posted by retina

I see you misunderstood my question. The length of the second is arbitrary. We could recalibrate it to be 1e-5 of a current 86400 second 'day', thus 100ks per day. This would make stating days and subdays easier IMO. For example 1.5 days would simply be 150000 seconds.

TL;DR: I see no need for units such as "minute", "hour", "day", "week", "fortnight", "month" and "year". In their absence the concept of making them easier to use does not arise.

The length of the second is arbitrary only in the sense that an international standard chose one particular number rather than another. Given that the second as presently defined is the SI standard unit and that that standard is universally recognised, it should be that which is used. IMO, of course, If you would like to use the millifortnight, go ahead.

What's so magic about the day anyway? Days vary in length when measured against the SI second. The variation is on many timescales, long and short. Tidal friction is leading to a secular lengthening of the day. An annual oscillation is caused by deciduous trees in the northern hemisphere --- during their summer many tonnes of water are raised by several metres as the trees come into leaf. The earth's moment of inertia is increased as a result and, by conservation of angular momentum, the day becomes longer. There are very much fewer deciduous trees in the southern hemisphere, not enough to counterbalance those in the north.

Come to that, there are at least two days of observational significance. The sidereal day and the (mean) solar day. Both are subject to the secular lengthening mentioned.

Of course, you could arbitrarily fix the length of the day but then either time of local noon drifts with respect to the end points of the day (which it does anyway under either systems under consideration) or, if that is kept fixed, either the speed of light varies with time or the length of the metre varies, or both.

[a1call]

I think it's time to divide this thread.
Way OT to OP: Additionally:

It is usually assumed (wrongly) that (Solar) noon to noon or midnight to midnight is 24 hours.

The two longest time spans from noon to noon occur twice each year, around 20 June (24 hours plus 13 seconds) and 21 December (24 hours plus 30 seconds).

The shortest time spans occur twice each year, around 25 March (24 hours minus 18 seconds) and 13 September (24 hours minus 22 seconds).

https://en.m.wikipedia.org/wiki/Noon#Solar_noon

[retina]

Originally Posted by xilman

What's so magic about the day anyway?

The day is important IMO because our body processes are quite tightly synchronised to it. The year is important IMO for anyone living on the Earth if they want to ensure sustainable food sources. All other time scales IMO are not important except for historical, political or economic reasons.

[Dr Sardonicus]

Originally Posted by retina

The day is important IMO because our body processes are quite tightly synchronised to it. The year is important IMO for anyone living on the Earth if they want to ensure sustainable food sources. All other time scales IMO are not important except for historical, political or economic reasons.

The etymology of the word "month" indicates a close association with "moon," and, indeed, used to mean the lunar cycle -- the interval from one new moon to the next (about 29.5 days). The week is about a quarter of a month.

The magnitudes of tides are associated with the phases of the moon. Spring tides occur at new and full moons, while neap tides occur at first and third quarter.

Beyond the importance of tides for marine navigation (which, I suppose, you may dismiss as "merely economic"), there is also their everyday importance for people living in coastal areas, including significance WRT the height of storm surges, which can be a matter of survival.

A number of marine organisms have biological cycles that follow the lunar cycle. At least one human biological cycle is nearly the same length as the interval from new moon to new moon.

[xilman]

Originally Posted by retina

The day is important IMO because our body processes are quite tightly synchronised to it. The year is important IMO for anyone living on the Earth if they want to ensure sustainable food sources. All other time scales IMO are not important except for historical, political or economic reasons.

And how do you propose to reconcile the incommensurability of the day and the year?

[retina]

Originally Posted by Dr Sardonicus

The etymology of the word "month" indicates a close association with "moon," and, indeed, used to mean the lunar cycle -- the interval from one new moon to the next (about 29.5 days). The week is about a quarter of a month.

The magnitudes of tides are associated with the phases of the moon. Spring tides occur at new and full moons, while neap tides occur at first and third quarter.

Beyond the importance of tides for marine navigation (which, I suppose, you may dismiss as "merely economic"), there is also their everyday importance for people living in coastal areas, including significance WRT the height of storm surges, which can be a matter of survival.

A number of marine organisms have biological cycles that follow the lunar cycle. At least one human biological cycle is nearly the same length as the interval from new moon to new moon.

The "month" we have now in the most popular calendars isn't synchronised to the Lunar phases. Even the Chinese calendar adds leap months to get itself briefly synchronised with the year, but it rapidly shifts out of phase again.

Storm surges are not very predicable WRT to absolute magnitude. We will still need to plan for the highest magnitude events regardless of the moon phases. It isn't as though we can shift our storm survival strategies day to day based upon the current Moon phase.

Originally Posted by xilman

And how do you propose to reconcile the incommensurability of the day and the year?

That is why we have leap seconds and leap years. We will always need those no matter what fixed time period we choose for the second.

[xilman]

Originally Posted by retina

We will always need those no matter what fixed time period we choose for the second.

If and only if we still have those other units. Leap seconds in particular are a real PITA for those who care about accurate time-keeping over periods longer than 10Ms or so.

A major reason (perhaps the major reason) for metrology is to make measurements consistent between observers and to make models of the behaviour of physical phenomena as simple and reliable as possible. Take a well-known example: Newton's F=ma, better expressed as F=m d²x/dt². If the unit of time varies in an ad hoc manner, as the day and year does in your espoused system of units, it becomes impossible even in principle to compute the future trajectory of a body of constant mass being acted upon by a constant force. Please don't start wittering on about Newtonian mechanics being superseded by QM or relativity because exactly the same considerations apply there.

[xilman]

Originally Posted by retina

We will always need those no matter what fixed time period we choose for the second.

I dispute the validity of the term "always". Martian colonists, let alone those living in another solar system, don't have any obvious reason to keep track of terrestrial days, months and years other than to chat with folk elsewhere in the solar system(s). Which month do you use on Mars, for instance? A Phobos month or a Deimos month?

As you note, the length of a day on Earth is not constant, whether civil, solar or sidereal. The civil day is particularly erratic and can vary between 82.8ks and 90ks depending on where you live and the epoch at which it is measured.

Regardless of where you live, which month do you choose, bearing in mind that all are subject to variation when measured in SI seconds? The tropical, sidereal, anomalistic, draconic or synodic? Something else? The numbers below are for the Earth.

• The tropical month is close to 2.360584512 Ms now.
• The sidereal month is close to 2.360591424 Ms now.
• The anomalistic month is close to 2.38071312 Ms now.
• The draconic month is close to 2.551442976 Ms now.
• The synodic month is close to 2.351135808 Ms now.

Likewise, which year? Options include Julian, tropical, sidereal, anomalistic, draconic and Gaussian but that is far from an exhaustive list. For instance, the Lunar year is in very widespread use. Once again, the numerical values are for the Earth.

• The Julian year is defined as 31.5576 Ms exactly.
• The tropical year is close to 31.556925216 Ms now.
• The sidereal year was 31.5581497635456 Ms at the epoch J2000.0; I don't know what it is now.
• The anomalistic year is close to 31.5584325504 Ms now.
• The draconic year is close to 29.947974.5562912 Ms now.
• The Gaussian year is close to 31.55819601312 Ms now.

[retina]

Originally Posted by xilman

I dispute the validity of the term "always". Martian colonists, let alone those living in another solar system, don't have any obvious reason to keep track of terrestrial days, months and years other than to chat with folk elsewhere in the solar system(s). Which month do you use on Mars, for instance? A Phobos month or a Deimos month?

As you note, the length of a day on Earth is not constant, whether civil, solar or sidereal. The civil day is particularly erratic and can vary between 82.8ks and 90ks depending on where you live and the epoch at which it is measured.

Regardless of where you live, which month do you choose, bearing in mind that all are subject to variation when measured in SI seconds? The tropical, sidereal, anomalistic, draconic or synodic? Something else? The numbers below are for the Earth.

• The tropical month is close to 2.360584512 Ms now.
• The sidereal month is close to 2.360591424 Ms now.
• The anomalistic month is close to 2.38071312 Ms now.
• The draconic month is close to 2.551442976 Ms now.
• The synodic month is close to 2.351135808 Ms now.

Likewise, which year? Options include Julian, tropical, sidereal, anomalistic, draconic and Gaussian but that is far from an exhaustive list. For instance, the Lunar year is in very widespread use. Once again, the numerical values are for the Earth.

• The Julian year is defined as 31.5576 Ms exactly.
• The tropical year is close to 31.556925216 Ms now.
• The sidereal year was 31.5581497635456 Ms at the epoch J2000.0; I don't know what it is now.
• The anomalistic year is close to 31.5584325504 Ms now.
• The draconic year is close to 29.947974.5562912 Ms now.
• The Gaussian year is close to 31.55819601312 Ms now.

I already stated that months are not important. And for years I mentioned the reason why people on Earth would find that important. But I guess Mars also has seasons, so perhaps if some intrepid explorers find a way to grow crops on Mars they might also find the year to be important. Naturally the Mars year would have more days, and their days would be longer. That would be for them to worry about.

[xilman]

Originally Posted by retina

I already stated that months are not important. And for years I mentioned the reason why people on Earth would find that important. But I guess Mars also has seasons, so perhaps if some intrepid explorers find a way to grow crops on Mars they might also find the year to be important. Naturally the Mars year would have more days, and their days would be longer. That would be for them to worry about.

Nonetheless, which day and year (and month if you wish) do you choose here and now for use by residents of the Earth? Why do you not choose the others?