Design - a Tufte decision

2006-12-28 Thread Rob Seaman

On Dec 27, 2006, at 12:02 AM, M. Warner Losh wrote:


Calculating time intervals for times 6+ months in the future can be
the least of one's worries when one tries to code up a library to deal
gracefully with these different failure modes.  The trivial case where
one has perfect knowledge of TAI-UTC and one can keep that knowledge
current is very simple in comparison.  Dealing with this case is very
simple, and is the way most people think about leap seconds.  But
dealing with the edge cases can be difficult because there are so
many, and so many that people forget to test or conceive of until the
call from the field comes in with a failure...


A lot of these edge cases are really firmly centered in issues of
real-time programming.  Few versions of Unix are equipped to deal
with real-time issues in even a rudimentary fashion.  In any event,
these cases have very little to do with leap seconds or any other
aspects of the representation of time quantities.

That said, I've found the current discussion immensely refreshing.
If there is to be any common ground found between the different
factions on this list (including the lurkers who actually have a vote
on ITU matters), it will be located by focusing on the actual
technical design process, not some quick fix gimmick.

   1) Who are the stakeholders for civil timekeeping?  (A discerning
eye might note that all this time we have NOT been arguing about TT,
etc.)

   2) What minimal inventory of timescales will satisfy all stakeholders?

   3) What economic, legal, historical, cultural, scientific, etc.,
requirements are placed on the delivery of said timescale(s)?

   4) What technical solution(s) satisfy the requirements?

   5) If change is deemed to be warranted, how best should it be
accomplished?  (Funded, scheduled, designed, implemented, deployed,
maintained, supported, etc?)

My initial position for #2 is that there must be at least two
timescales, representing interval time and time-of-day, but in the
extreme one could even imagine a coherent position stating that NO
common international civil timescale is needed at all.  (Whether one
holds this point of view may say more about ones view of civil
society than it does about civil timekeeping :–)

In the latter case, let UTC continue as it is, complete with leap
seconds.  Let facilities derived from ITU deliberations start
distributing, for example, a refinement of GPS time.  And let some
new consortium adopt the distribution of UTC, perhaps with many of
the improvements folks have suggested.  (This would provide a chance
to do over - wouldn't that be lovely?)  And then let the market
decide.

In the U.S., one would expect funding proposals for a new-and-
improved UTC to result.  Those of us who aren't Co-I's would likely
be referees...

Whatever the solution, implementing it is unlikely to prove a
panacea.  In the seven years this list has been in existence, we've
only scratched the surface of the complexities inherent in civil
timekeeping.  In short:

   6) Where should the lines of elegant design and rational compromise
be drawn?

Rob Seaman
NOAO


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

Poul-Henning Kamp wrote:


I seriously don't belive you do equality comparisons at the 1msec
level in real world software.  Please provide examples.


You know you're in trouble when PHK and I agree.  One would think a
(double precision) floating point epsilon test might be what you
want.  In those cases that demand some sort of archival query, an ISO
8601 string might be appropriate, but one would typically expect
queries to be issued on a window about the desired timestamp, or
perhaps given a range specification from 10:03:01.933 to
10:03:02.008 (whether a string, integer or floating point - binary
or sexagesimal or BCD for that matter).

Rob


Re: Design - a Tufte decision

2006-12-28 Thread M. Warner Losh
In message: [EMAIL PROTECTED]
Rob Seaman [EMAIL PROTECTED] writes:
: On Dec 27, 2006, at 12:02 AM, M. Warner Losh wrote:
:
:  Calculating time intervals for times 6+ months in the future can be
:  the least of one's worries when one tries to code up a library to deal
:  gracefully with these different failure modes.  The trivial case where
:  one has perfect knowledge of TAI-UTC and one can keep that knowledge
:  current is very simple in comparison.  Dealing with this case is very
:  simple, and is the way most people think about leap seconds.  But
:  dealing with the edge cases can be difficult because there are so
:  many, and so many that people forget to test or conceive of until the
:  call from the field comes in with a failure...
:
: A lot of these edge cases are really firmly centered in issues of
: real-time programming.  Few versions of Unix are equipped to deal
: with real-time issues in even a rudimentary fashion.  In any event,
: these cases have very little to do with leap seconds or any other
: aspects of the representation of time quantities.

Actually, they can have a great deal to do with it.  The absolute need
to deal properly with these edge cases can, at times, lead to design
decisions that aren't the 'simplest'.  I also disagree that Unix is
ill-equipted to deal with real-time issues.  While one does need to
take care, I have successfully deployed over a dozen different types
of timing systems over the past 7 years on FreeBSD.  My familiarity
with these edge cases, the customers that expect them to work and the
different sources of time has been learned through these experiences.
The nature of these customers also means that they are less well
connected to networks than one would like, which also complicates
matters.

The salient point from my ramblings is that different time scales may
become available at different points in time because data about them
is available at different points in time to the application/os.  If
there's only one time scale, then once you know the time, you are
done.  If there's more than one, then you need to either discover both
times, or you need to discover one time and the transforms to that
time to know the others.

Warner


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Tony Finch
On Wed, 27 Dec 2006, John Cowan wrote:

 If we confine ourselves to the Gregorian calendar, a time interval can
 be safely represented as a triple of months, minutes, and seconds.

It seems to me that that would put too much complexity at too low a level
but still without enough complexity to deal with the whole problem. How
does your proposal deal with local time zone changes, e.g. same time
tomorrow, or times based on weeks, e.g. last thursday in the month? I
don't see much point in having an intermediate stage between day counts
and fully broken down dates. Similarly for times, I favour a split between
interval time (which the RTC would produce) and broken-down time of day
plus day count (with leap seconds and local time handled in the latter
layer).

Tony.
--
f.a.n.finch  [EMAIL PROTECTED]  http://dotat.at/
FISHER GERMAN BIGHT HUMBER: NORTHWEST BACKING SOUTH 4 OR 5, INCREASING 6 OR 7.
SLIGHT OR MODERATE, OCCASIONALLY ROUGH LATER. OCCASIONAL RAIN. MODERATE OR
GOOD.


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Tony Finch
On Thu, 28 Dec 2006, John Cowan wrote:

 Distinguo.  I am talking about time intervals; you are talking about
 periodic events.  Two different things.

Still, your minute/month system does not deal with variable-length days.

Tony.
--
f.a.n.finch  [EMAIL PROTECTED]  http://dotat.at/
SHANNON: SOUTH BECOMING CYCLONIC 7 TO SEVERE GALE 9, OCCASIONALLY STORM 10,
PERHAPS VIOLENT STORM 11 LATER. VERY ROUGH OCCASIONALLY HIGH. RAIN OR SHOWERS.
MODERATE OR GOOD.


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread John Cowan
Tony Finch scripsit:

 Still, your minute/month system does not deal with variable-length days.

I assume you mean 23-hour or 25-hour LCT days?  True.  It does work
against UCT days, though, since they are uniformly 1440 minutes long.

--
Overhead, without any fuss, the stars were going out.
--Arthur C. Clarke, The Nine Billion Names of God
John Cowan [EMAIL PROTECTED]


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

John Cowan wrote:


I assume you mean 23-hour or 25-hour LCT days?  True.  It does work
against UCT days, though, since they are uniformly 1440 minutes long.


Not should leap hours replace leap seconds.


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

I am talking about time intervals; you are talking about periodic
events.  Two different things.


Amen!


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

M. Warner Losh wrote:


And avoiding the ugly 61 or 59 second minutes to define away the
problem...


It was the time lords who decreed that rubber minutes were prettier
than rubber seconds.  We're now to skip right over rubber hours to
rubber days?  Their aesthetic sense seems strangely malleable.

Problems that are merely defined away rarely stay away.

Rob


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Poul-Henning Kamp
In message [EMAIL PROTECTED], Rob Seaman writes:
M. Warner Losh wrote:

 And avoiding the ugly 61 or 59 second minutes to define away the
 problem...

It was the time lords who decreed that rubber minutes were prettier
than rubber seconds.  We're now to skip right over rubber hours to
rubber days?  Their aesthetic sense seems strangely malleable.

It is not an æsthetic issue, it is an issue of practical implementation.

In days no more than 100 clocks worldwide were precise enough to
care about rubber seconds, they were acceptable.

In days where no more than 1000 clocks worldwide were seriously
affected by leap seconds, they were acceptable.

In these days of heavily computerized infrastructure, we need more
than half a years warning about discontinuities in the timescale.

We can get that only by increasing the DUT tolerance.

As Warner, I and others have repeatedly emphasized:  It is not the
step size that is the problem, it is the 6 month warning.

I don't care if you want to implement leap-milliseconds, as long
as you tell me 10 years in advance when they happen.

--
Poul-Henning Kamp   | UNIX since Zilog Zeus 3.20
[EMAIL PROTECTED] | TCP/IP since RFC 956
FreeBSD committer   | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread M. Warner Losh
In message: [EMAIL PROTECTED]
Poul-Henning Kamp [EMAIL PROTECTED] writes:
: We can get that only by increasing the DUT tolerance.

Yes.  Letting DUT be bounded by +- 10s rather than +- 0.9s is going to
affect a tiny number of users.  Having leapseconds only known 6 months
in advance affects a lot more users...

: As Warner, I and others have repeatedly emphasized:  It is not the
: step size that is the problem, it is the 6 month warning.
:
: I don't care if you want to implement leap-milliseconds, as long
: as you tell me 10 years in advance when they happen.

While my preference would be to never see another leap second, I know
that's likely not an option.

For many practical reasons, scheduling them out 10 years would help
ameliorate the costs of leap seconds and allow for better long term
planning.

Warner


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

Poul-Henning Kamp wrote:


It is not an æsthetic issue, it is an issue of practical
implementation.


Well, it's both.  The big question is practical implementation of what?


In these days of heavily computerized infrastructure, we need more
than half a years warning about discontinuities in the timescale.


We've had this discussion before.  There are no discontinuities in
the timescale.  Leap seconds are a question of data representation.
I'm not trying to minimize the issues by saying that, rather to point
out that we can't solve a problem until we state it correctly.


We can get that only by increasing the DUT tolerance.


We all understand the trade-offs.  Presumably the guys who have
suggested degrading the tolerance to the point that it will outlive
our grandchildren's grandchildren - and simultaneously removed any
requirement for the ITU to distribute DUT corrections - understand
the trade-offs, too.


I don't care if you want to implement leap-milliseconds, as long
as you tell me 10 years in advance when they happen.


Again - with no intent to minimize the issues - what supports this
assertion?  Is there any reason to believe that 10 years advance
notice would encourage projects and vendors to do anything other than
ignore the requirement entirely?  A statement that 10 years, or 600
years, notice is all that is needed to resolve all the problems,
smooth over all the complications, is entirely too glib.

Rather than starting from a bunker mentality of repeatedly fending
off an absurd non-solution, perhaps it would be better to design from
clearly stated use cases, responsive requirements, coherent risk
analyses, a reasonable deployment schedule, a fair-minded budget.
We're not going to successfully define the real world out of existence.

Rob Seaman
NOAO


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread John Cowan
Rob Seaman scripsit:

 I don't care if you want to implement leap-milliseconds, as long
 as you tell me 10 years in advance when they happen.

 Again - with no intent to minimize the issues - what supports this
 assertion?  Is there any reason to believe that 10 years advance notice
 would encourage projects and vendors to do anything other than ignore
 the requirement entirely?  A statement that 10 years, or 600 years,
 notice is all that is needed to resolve all the problems, smooth over
 all the complications, is entirely too glib.

You are confusing the question of fixity (which is what notice is
about) with granularity.  It's true that probably no one would bother
to implement the ALHP.  However, if computer technologists were handed a
list of leap seconds from now until 2015, and told Implement these, it
wouldn't matter how many or how few leap seconds there were.  But since
you astronomers insist on a fixed maximum for |DUT1|, no such table
can exist.

The proposal is this:  look at the trends, take your best shot at
working out a leap-year schedule for 10 years in the future, and then
live with it.

--
Newbies always ask: John Cowan
  Elements or attributes?  http://www.ccil.org/~cowan
Which will serve me best?  [EMAIL PROTECTED]
  Those who know roar like lions;
  Wise hackers smile like tigers.   --a tanka, or extended haiku


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread M. Warner Losh
In message: [EMAIL PROTECTED]
John Cowan [EMAIL PROTECTED] writes:
: Rob Seaman scripsit:
:
:  I don't care if you want to implement leap-milliseconds, as long
:  as you tell me 10 years in advance when they happen.
: 
:  Again - with no intent to minimize the issues - what supports this
:  assertion?  Is there any reason to believe that 10 years advance notice
:  would encourage projects and vendors to do anything other than ignore
:  the requirement entirely?  A statement that 10 years, or 600 years,
:  notice is all that is needed to resolve all the problems, smooth over
:  all the complications, is entirely too glib.
:
: You are confusing the question of fixity (which is what notice is
: about) with granularity.  It's true that probably no one would bother
: to implement the ALHP.  However, if computer technologists were handed a
: list of leap seconds from now until 2015, and told Implement these, it
: wouldn't matter how many or how few leap seconds there were.  But since
: you astronomers insist on a fixed maximum for |DUT1|, no such table
: can exist.
:
: The proposal is this:  look at the trends, take your best shot at
: working out a leap-year schedule for 10 years in the future, and then
: live with it.

Let's turn the question around.  What would the harm be if |DUT1| were
1.1s?  1.5s?  2.0s?  Contrast this with the harm and difficulty that
the current 6 month scheduling window affords.

Warner


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

M. Warner Losh wrote:


Let's turn the question around.  What would the harm be if |DUT1| were
1.1s?  1.5s?  2.0s?  Contrast this with the harm and difficulty that
the current 6 month scheduling window affords.


Indeed.  Go for it.  I look forward to reading your report.  Who and
what interests are adversely affected in each case?  How are these
effects mitigated as a function of the limit on DUT1?  Also, contrast
what benefits accrue.  One would think that the responsibility for
quantifying the implications of a change to a standard would fall on
the parties proposing said change.

Rob


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread John Cowan
Rob Seaman scripsit:

 Indeed.  Go for it.  I look forward to reading your report.  Who and
 what interests are adversely affected in each case?  How are these
 effects mitigated as a function of the limit on DUT1?  Also, contrast
 what benefits accrue.  One would think that the responsibility for
 quantifying the implications of a change to a standard would fall on
 the parties proposing said change.

It can't possibly be.  Nobody can know what a change is going to
cost except those who are going to have to pay for it (or not
pay for it).  And even their word cannot necessarily be trusted.

In this case there are really two questions:  how much it would
cost to loosen DUT1 but leave it bounded, and how much it would
cost if it were only statistically, not absolutely, bounded.

--
Don't be so humble.  You're not that great. John Cowan
--Golda Meir[EMAIL PROTECTED]


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

John Cowan wrote:


It can't possibly be.  Nobody can know what a change is going to
cost except those who are going to have to pay for it (or not
pay for it).


Are you really suggesting that the planning of technical projects is
impossible?  One might expect some investment of time and money in
standard planning activities to be made first, rather than
immediately jumping to a narrowly and rather randomly conceived
notional position unsupported by even the slimmest of white papers.
It is crazily unprofessional to abjure any responsibility for
quantifying costs, benefits and risks.


And even their word cannot necessarily be trusted.


Um.  Which edge of the sword are we talking about here?

Rob


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread M. Warner Losh
In message: [EMAIL PROTECTED]
Rob Seaman [EMAIL PROTECTED] writes:
: M. Warner Losh wrote:
:
:  Let's turn the question around.  What would the harm be if |DUT1| were
:  1.1s?  1.5s?  2.0s?  Contrast this with the harm and difficulty that
:  the current 6 month scheduling window affords.
:
: Indeed.  Go for it.  I look forward to reading your report.  Who and
: what interests are adversely affected in each case?  How are these
: effects mitigated as a function of the limit on DUT1?  Also, contrast
: what benefits accrue.  One would think that the responsibility for
: quantifying the implications of a change to a standard would fall on
: the parties proposing said change.

I know the benefits, but nobody has yet produced a study on why 0.9s
was chosen.  Some vague rumblings about astronomical software needing
to be rewritten, and some vague notions about 'hearty souls' that do
celestial navigation with atomic clocks for high accuracy have been
offered, but who really would be hurt by this change?  Since you are
an astronomer, I thought you might be able to give some insight into
at least one of these users of time.  Daylight savings time and time
zones prove that society at large has a very high tolerance for
variations between the mean solar time at an arbitrary location, maybe
hundreds of miles away, and the local time.  Only specialized users of
time would be affected.  Who are they and how do we find out the cost
of change?

The world has changed from having maybe a few dozen or tens of dozen
atomic clocks when leap seconds started to having GPS with cheap,
disciplined oscillators that number in the hundreds of thousands.
These little devices have obviated the need, in many cases, for
celestial navigation.  Given that change, the cost benefit analysis
that was done in 1972 likely needs updating.

Warner


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Rob Seaman

M. Warner Losh wrote:


vague rumblings about astronomical software needing to be rewritten,


Unlike Y2K, there is no solid public proposal for astronomers to cost
against, but the cost is likely to dwarf Y2K in our community, since
algorithms and deployed services would have to change, not just
retrofitting two digit years.

Folks keep fretting here about retrieving lists of leap seconds
autonomously, although no specific use case is proffered about why
one needs to use UTC to measure intervals across various and sundry
leap second events.  On the other hand, astronomers have quite
reasonably coded their systems to take advantage of the original (and
current) definition of UTC:  GMT may be regarded as the general
equivalent of UT.  One second of time is 15 seconds of arc on the
celestial equator - this is many times greater than the resolution of
any O/IR telescope.

The proposal really amounts to trading the need to track leap seconds
to convert from time-of-day to intervals, for the need to track the
equivalent of leap seconds to convert from interval time to time-of-day.


Daylight savings time and time
zones prove that society at large has a very high tolerance for
variations between the mean solar time at an arbitrary location, maybe
hundreds of miles away, and the local time.


This is a static offset.  Leap seconds are one mechanism to address a
secular drift - a rate, that is, not a constant.  Local time -
daylight, standard, mean, apparent - has been raised as an issue
innumerable times - it has been irrelevant every one of them.  We're
not talking about mucking with local time, we're talking about
subverting the mother of all solar time.


Only specialized users of time would be affected.
Who are they and how do we find out the cost of change?


If this is true, you can find out by actually seeking them out,
rather than hiding a proposal with worldwide implications away in
some squirrelly little bureaucratic committee.

However, the suggestion has been implicitly made that everybody is a
potential victim of leap seconds - that airplanes will drop from the
sky, even though they haven't done so through 23 prior
opportunities.  That suggestion opens the possibility that
generalized users, i.e., people might be affected by civil
timekeeping issues in subtle ways.  The way to find out the cost of
change is to spend some time and money characterizing this.

For example, I set my workstation's clock forward eleven years (to
match Gregorian calendars) for a couple of years prior to Y2K to
provide a platform for our Y2K remediation activities.  We set clocks
forward at the telescopes and some of them started to track the sky
backwards.  Surely a Y2K-like inventory could be performed for
certain key industries to get a sense for what dependencies might
lurk?  We've long since established that different countries have
different legal civil time standards, e.g., GMT versus UTC.  What
happens should this discrepancy continue as UTC diverges from GMT?

The proposal on the supersecret ITU-R table is to discard an
international standard that has been in effect for more than a
century and that pervades every aspect of our technical, cultural,
legal, economic, etc., world.  One might expect somebody might have
thought to submit a proposal for a few hundred thousand dollars to
conduct a proper pilot study before even beginning to speculate about
discarding mean solar time as a basis for civil timekeeping.


These little devices have obviated the need, in many cases, for
celestial navigation.


In many cases?  That will be comforting to the folks that really need
a backup when their GPS goes out.  Whatever the solution should be,
the one thing it should not be is brittle.


Given that change, the cost benefit analysis
that was done in 1972 likely needs updating.


It sounds like we agree on this point.


Seems like a logical leap for leap seconds to follow, if the costs
aren't
prohibitive.  Chances are that one person knows all the users of time
that still need DUT1 to be less than 1s.


Seems like?  Chances are?  Pick some other random technical issue
- say, automobile airbags, standardized educational testing, the lead
content of pigment in children's crayons, and so forth and so on.
Would seems like and chances are be phrases you would want to see
in a white paper discussing the costs, benefits and risks of these?
Oh yeah - that's right.  After seven years there is not one single
white paper discussing issues related to the decision-making of the
ITU-R WP-7A.  (And if there were, we presumably would not be able to
read it.)

There are several thousand professional astronomers in the world and
many times this number of amateurs.  All of them ultimately care
about the subtle concepts underlying the notion of DUT1.  It seems
bizarre to dismiss their concerns precisely because they might have a
more personal interest than some others.

It may be naively convenient to assume that the only risks are with
poorly 

Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Steve Allen
On Thu 2006-12-28T22:07:08 -0700, M. Warner Losh hath writ:
 I know the benefits, but nobody has yet produced a study on why 0.9s
 was chosen.

That's pretty easy.  In 1969 the CCIR subcommittee was preparing its
unilateral decision to switch from rubber seconds and 200 ms steps
to leap seconds.  They were disregarding the other international
scientific organizations who had called for a multi-lateral meeting
on how to deal with time and frequency broadcasts.

When the CCIR plenipotentiary voted in early 1970 their resolution
said the limit was 0.7 seconds.  When the IAU met in the middle of
that year they had no correspondence from the CCIR, so they could take
no action and provide no response to give input before the 1972 deadline.

The limit of 0.7 was somebody's idea of how well the astronomers
could do on a six month schedule given the observing techniques and
telecomm and computational means available in 1970.  Unfortunately at
that time the earth rotation was almost as slow as it has ever been,
so it seemed likely that there would have to be a lot of leap seconds,
and whoever was in charge tended to jump the gun on inserting them such
that the DUT1 value was often very close to the 0.7 s limit.
In 1973 the IAU did have standing to respond to the CCIR and recommended
0.9 s, which the CCIR then implemented despite the fact that the WWV
coding for DUT1 could not go past 0.7 s.

So the indications are that 0.7, and then 0.9 was as close as
anyone believed was possible in the early 1970s on a semi-annual
schedule.  It was a compromise then, and a few people were very,
very upset about the situation, but so far as I know no ships
ran aground as a result.  The subject of leap seconds causing
planes to crash was raised then, too, and that didn't happen
either.

This story may not be exactly right, but the existing public documents
make it seem pretty close to the truth.
Who exactly the principals were in these cases is still obscure;
some of them have died, and others have not.  Maybe the future will
have access to existing memoirs of some of the dead folks, and maybe
some of those living can be exhorted to leave their views behind.

So we don't really need a study of the history of why 0.9 because
the record of what happened and who did what when is pretty good
and that's all kindof moot for solving the dissatisfaction now.

The point of keeping DUT1 small was mainly for consistency
with existing navigation practices, and also for ease of
broadcasting that difference.  I don't think that either of
these constraints is relevant anymore.

--
Steve Allen [EMAIL PROTECTED]WGS-84 (GPS)
UCO/Lick ObservatoryNatural Sciences II, Room 165Lat  +36.99858
University of CaliforniaVoice: +1 831 459 3046   Lng -122.06014
Santa Cruz, CA 95064http://www.ucolick.org/~sla/ Hgt +250 m


Re: Mechanism to provide tai-utc.dat locally

2006-12-28 Thread Tony Finch
On Thu, 28 Dec 2006, M. Warner Losh wrote:

 We've accepted a statistical solution for the leap-day problem now for
 about 500 years.

The Julian calendar reform was in 46 BC. Astronomers still count Julian
years (365.25 days instead of exact years) when dealing with long MJD
intervals.

Tony.
--
f.a.n.finch  [EMAIL PROTECTED]  http://dotat.at/
HUMBER THAMES DOVER WIGHT PORTLAND: SOUTHERLY 7 OR GALE 8, OCCASIONALLY SEVERE
GALE 9. ROUGH OR VERY ROUGH. RAIN THEN SQUALLY SHOWERS. MODERATE, OCCASIONALLY
POOR.