seconds in a millennium
DGH
From alt.brainteasers:
Jim Rockwell wrote:
>
> How many seconds are in a millenium?
> 60*60=3600
> 3600*24=86400
> 86400*364.25=31471200
> 31471200*1000= 31471200000sec.
> IS THIS CORRECT?
Gerry Quinn
No, but it's close. 365.24 is more accurate as regards the number of
days in a year. That should give an answer correct to four or five
digits.
- Gerry
===========================================================
ger...@indigo.ie (Gerry Quinn)
http://indigo.ie/~gerryq
Original puzzlers for PC, Amiga, and Java
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LakeWin98
How many seconds are in a millenium?
>>> 60*60=3600
>>> 3600*24=86400
>>> 86400*364.25=31471200
>>> 31471200*1000= 31471200000sec.
>>> IS THIS CORRECT?
>
>No, but it's close. 365.24 is more accurate as regards the number of
>days in a year. That should give an answer correct to four or five
>digits.
There are 97 leap years every 400 years, so there are 365.2425 days per year.
Some millenia have 242 leap years, others have 243, so there are either
31,556,908,800 -or- 31,556,995,200 seconds.
Abigail
LakeWin98 (lake...@aol.com) wrote on MDCLXV September MCMXCIII in
<URL: news:199803230422...@ladder03.news.aol.com>:
++ How many seconds are in a millenium?
++ >>> 60*60=3600
++ >>> 3600*24=86400
++ >>> 86400*364.25=31471200
++ >>> 31471200*1000= 31471200000sec.
++ >>> IS THIS CORRECT?
++ >
++ >No, but it's close. 365.24 is more accurate as regards the number of
++ >days in a year. That should give an answer correct to four or five
++ >digits.
++
++ There are 97 leap years every 400 years, so there are 365.2425 days per year.
++
++ Some millenia have 242 leap years, others have 243, so there are either
++ 31,556,908,800 -or- 31,556,995,200 seconds.
I don't think we had a millenium with that number of seconds yet,
and the current one won't be one either.
How likely is it the next millenium won't see a calendar reform?
(What about leap seconds?)
Abigail
spam...@nil.nil
> >>> 3600*24=86400
> >>> 86400*364.25=31471200
> >>> 31471200*1000= 31471200000sec.
> >>> IS THIS CORRECT?
> >
> There are 97 leap years every 400 years, so there are 365.2425 days per year.
> Some millenia have 242 leap years, others have 243, so there are either
> 31,556,908,800 -or- 31,556,995,200 seconds.
and so it may have been when the second was defined as a fraction of a
tropical year (though its length would then change depending upon the
epoch!). With atomic clocks, and the (general) slowing up of the earth
(though some years it may speed up) one has to worry about leap seconds
(added or subtracted) (which is why no one can be *sure* of the number of
seconds from now to 00:00:00 GMT, 1/1/2000 -- one can predict
approximately the number of leap seconds to be added, but due to various
unpredictable effects, there may be one or more leap seconds that one
misses).
Timothy Reed
In article <199803230422...@ladder03.news.aol.com>,
lake...@aol.com (LakeWin98) wrote:
> How many seconds are in a millenium?
> >>> 60*60=3600
> >>> 3600*24=86400
> >>> 86400*364.25=31471200
> >>> 31471200*1000= 31471200000sec.
> >>> IS THIS CORRECT?
> >
> >No, but it's close. 365.24 is more accurate as regards the number of
> >days in a year. That should give an answer correct to four or five
> >digits.
>
> There are 97 leap years every 400 years, so there are 365.2425 days per year.
>
> Some millenia have 242 leap years, others have 243, so there are either
> 31,556,908,800 -or- 31,556,995,200 seconds.
In reality, the National Institute of Standards and Technology officially
adds a leap second to Coordinated Universal Time at midnight on January 1
or July 1 whenever UTC and solar time get out of sync. So for the current
and future millenia, neither of the above are necessary true.
Remove obvious spam protection from email address before replying
Abigail
Timothy Reed (treedREMOVEB...@ball.com) wrote on MDCLXV
September MCMXCIII in <URL: news:treedREMOVEBEFOREMAI...@treed.ball.com>:
++ In article <199803230422...@ladder03.news.aol.com>,
++ lake...@aol.com (LakeWin98) wrote:
++
++ > >>> 60*60=3600
++ > >>> 3600*24=86400
++ > >>> 86400*364.25=31471200
++ > >>> 31471200*1000= 31471200000sec.
++ > >>> IS THIS CORRECT?
++ > >
++ > >No, but it's close. 365.24 is more accurate as regards the number of
++ > >days in a year. That should give an answer correct to four or five
++ > >digits.
++ >
++ > There are 97 leap years every 400 years, so there are 365.2425 days per year.
++ >
++ > Some millenia have 242 leap years, others have 243, so there are either
++ > 31,556,908,800 -or- 31,556,995,200 seconds.
++ In reality, the National Institute of Standards and Technology officially
++ adds a leap second to Coordinated Universal Time at midnight on January 1
++ or July 1 whenever UTC and solar time get out of sync. So for the current
++ and future millenia, neither of the above are necessary true.
Not to mention that the rule of '97 leap years every 400 years'
has been in effect for less than half of the current century.
Abigail
Seth Breidbart
In article <6f79bt$j6v$1...@client3.news.psi.net>,
Abigail <abi...@fnx.com> wrote:
>Not to mention that the rule of '97 leap years every 400 years'
>has been in effect for less than half of the current century.
Where? In most countries it went into effect as of the missing 11 (or
so) days.
Seth
Abigail
Seth Breidbart (se...@panix.com) wrote on MDCLXXI September MCMXCIII in
<URL: news:6fku4h$r...@panix3.panix.com>:
++ In article <6f79bt$j6v$1...@client3.news.psi.net>,
++ Abigail <abi...@fnx.com> wrote:
++
++ >Not to mention that the rule of '97 leap years every 400 years'
++ >has been in effect for less than half of the current century.
++
++ Where? In most countries it went into effect as of the missing 11 (or
++ so) days.
I meant of course 'less than half of the current millennium'.
Abigail
David A Karr
>[...] 'less than half of the current millennium'.
But more than a full 400-year cycle, and I don't think it's at all
unreasonable to assume it will last another few cycles, at least
another millennium. After all, the Pope no longer has as much power
to change it. (But I wouldn't be surprised if the calculation of
Easter changed before the end of *its* cycle.)
Still, leap seconds will continue to be inserted into the calendar
in what is essentially an unpredictable process (and I wouldn't be
suprised if the rules for inserting them changed as well), so there
must be quite a few seconds' uncertainty in the length of the coming
millennium even under optimistic assumptions.
But since we can't predict the future that accurately, what about an
answer to the following:
How many seconds were there in the millennium that ended at noon GMT
on 1998 March 31 CE?
--
David A. Karr "Groups of guitars are on the way out, Mr. Epstein."
ka...@shore.net --Decca executive Dick Rowe, 1962
Adechert
ka...@shore.net (David A Karr) wrote,
>But more than a full 400-year cycle, and I don't think it's at all
>unreasonable to assume it will last another few cycles, at least
>another millennium. After all, the Pope no longer has as much power
>to change it. (But I wouldn't be surprised if the calculation of
>Easter changed before the end of *its* cycle.)
>
>Still, leap seconds will continue to be inserted into the calendar
>in what is essentially an unpredictable process (and I wouldn't be
>suprised if the rules for inserting them changed as well), so there
>must be quite a few seconds' uncertainty in the length of the coming
>millennium even under optimistic assumptions.
>
>But since we can't predict the future that accurately, what about an
>answer to the following:
>
>How many seconds were there in the millennium that ended at noon GMT
>on 1998 March 31 CE?
Okay, so the best answer depends on how you define a millennium (and how a year
is defined, and how a second is defined). A second is now established as
9,192,631,770 periods of the radiation corresponding to the transition between
the two hyperfine levels of cesium-133
A "natural year" (or "tropical year") is the time between successive vernal
equinoxes. If you say a millennium is a thousand successive natural years,
regardless of where you choose to define the end point (or beginning), then you
start to have a handle on the problem.
Unfortunately, due to the precession and nutation of the Earth's axis (and
other orbital irregularities) the number of seconds in a year varies. So much
so, that it would be impossible to accurately determine how many seconds in a
any millennium. The number of seconds in each of the past several years is
known within a fraction of a second, however, we simply do not have enough data
on the past thousand or so years to come up with an accurate number (we could
probably come close, however).
Above, I describe a scientific millennium. There could also be a "civil
millennium" which depends on when the beginning and end of a millennia were
recognized. In order to say the current millennium ends 12/31/99, you need to
show that 1000 was considered the beginning of this millennium. This is
dubious because the current year-numbering that is world-standard was, a
thousand years ago, only beginning to take hold in Europe. Some people thought
1000 was the new millennium but, clearly, most people in the world knew nothing
about this at the time.
Suffice it to say, there is some confusion over this matter. However, it seems
clear that 01/01/00 will be the popular beginning of the next millennium.
Actually, we have a unique opportunity to clarify the matter: call it Year Zero
and declare it a new epoch. Such a proposal exists called the Global Era
Calendar Resolution.
Consider this: The world has changed drastically from what it was a century
ago. Further, almost nothing is recognizable from civilization of 2000 years
ago. The Global Era Calendar Resolution simply asknowledges what has already
happened: we are living in a different era altogether, entering a new epoch.
see www.go2zero.com
cheers, Alan Dechert
David A Karr
Adechert <adec...@aol.com> wrote:
>Unfortunately, due to the precession and nutation of the Earth's axis
>(and other orbital irregularities) the number of seconds in a
>accurately determine how many seconds in a any millennium. The
>number of seconds in each of the past several years is known within a
>fraction of a second, however, we simply do not have enough data on
>the past thousand or so years to come up with an accurate number (we
>could probably come close, however).
I agree. I wouldn't mind seeing someone try, though.
>Above, I describe a scientific millennium. There could also be a "civil
>millennium" which depends on when the beginning and end of a millennia were
>recognized. In order to say the current millennium ends 12/31/99,
Ah, but I specifically asked for the millennium ending 1998 March 31
CE at 1200 GMT. I chose that date simply since it was when I posted.
I think if I had asked about the _year_ ending at that instant, there
would have been little doubt what I meant.
Your other points are well taken, but the puzzle is really about
making reasonable interpretations of "second" and "millennium" that
allow a number to be computed. I have my own favorite interpretation
but I would be happy to see others.