The perpetual calendar [Math]

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From: PaulJK on 22 Feb 2010 01:48

Andrew Usher wrote:
> Brian M. Scott wrote:
>
>>>>> And the first day of the week is Sunday, not Monday - that
>>>>> is an incontrovertible fact.
>>
>>>> Don't be ridiculous: it's merely a convention. For many of
>>>> us Monday is unquestionably the first day of the week.
>>
>>> It's historically true. No one questioned it before modern times.
>>
>> Apparently you're not familiar with the Slavic and Baltic
>> day-names. For that matter, Sunday is the first day in
>> Jewish tradition for the same reason that Monday is the
>> first day for many of us today.
>
> The Slavic and Baltic day names come from Greek tradition (itself
> aberrant), not from Western tradition where it was always Sunday.

Where did you get that nonsense?

If you actually checked the Slavic/Baltic and Greek day
names you'd find that they obviously do NOT follow the same
tradition. Hey, what a surprise, Greek day names treat Sunday
as the day number one!

pjk

> In addition, it's probably true that the astrological week came before
> the Jews adopted it.
>
> Andrew Usher

From: Transfer Principle on 22 Feb 2010 01:58

On Feb 18, 8:13 pm, Andrew Usher <k_over_hb...(a)yahoo.com> wrote:
> Owing to the inconveniences which attend the shifting of the calendar,
> and attempting in passing to create a more perfect Church calendar, I
> say the following:

The notion of calendar reform has appeared on sci.math from time
to time. Some people may argue that the debate between those who
defend the standard Gregorian calendar and those who wish to
reform it is analogous to the debate between the standard set
theorists and the so-called "cranks." I'd argue that calendar
reform would fit Underwood Dudley's "eccentric" category more
than the "crank" category. But then again, the OP of this thread
(Andrew Usher) has already been considered a "crank" due to his
views on the standard ZFC set theory.

Compared to some calendar reformer's proposal's, Usher's is
relatively tame. He only proposes a new leap year rule and new
dates for the Christian holidays, as opposed to more radical
proposals (such as the 13-month calendar proposal mentioned
later in this thread).

> 1. That Christmas day should be fixed to a Sunday, and this should be
> the Sunday between Dec. 21 and 27, and that in all civilised countries
> the Monday should be considered a holiday, or the Saturday if not
> normally.

On one hand, the notion of Christmas always falling on a Sunday
sounds appealing, since it's the Christian sabbath (and thus
Christians are already in church anyway). Some of the previous
calendar reformers have also proposed having Christmas always
fall on a Sunday, since, as Usher points out, it allows the
holiday to fall on a three-day weekend and prevents workers
from wanting to take extra days off when Christmas is mid-week.

On the other hand, some workers are going to take off extra
days anyway. According to a certain game show (the second time
I've referenced game shows in an Usher thread), Christmas (and
not Thanksgiving as some may believe) is the most heavily
traveled holiday in the USA. Travelers are often forced to
leave several days before Christmas because the airlines are
booked on the days closer to the holiday. In years in which
Christmas is mid-week, the workers are likely to take those
extra days off anyway, but when Christmas is on a Sunday as
per Usher's proposal, workers don't necessarily wait until
Friday, December 23rd at 5PM to begin their holiday travel. So
workers may be as likely to take off extra days under Usher's
proposal as they are under the current Gregorian calendar.

(Also, Sunday Christmases often cause headaches for school
calendar planners as well. Some schools actually have school
all the way up until Friday, December 23rd, and then have low
attendance rates the last few days. One could have school end
a full week before Christmas instead, but then the standard
two-week winter break might end too close to New Year's Day,
or even before, since a December 21st Usher Christmas would
result in school resuming on Monday, December 29th, which is
before New Year's Day.)

Therefore I'm of two minds regarding the Usher Christmas Day.

> 2. That similarly Easter day should be fixed to the Sunday which is 15
> weeks following Christmas.

Many schools and universities no longer tie their spring break
holidays to Easter since it floats so much. They often prefer
a break at a fixed point in the spring semester. Therefore, I
agree with the Usher Easter more than the Usher Christmas.

> 3. That the leap year rule be changed to have a leap year occur every
> fourth save that it be delayed when the leap year would start on a
> Thursday, and that this gives 7 leap years in every 29, which is near
> enough.

There's a huge problem with the Usher leap year plan here. I
can see why Usher would want to avoid leap years starting on
Thursdays, since Easter, being 15 weeks after Christmas,
would fall on April 4th such years, which is outside of the
April 5-11 range given by Usher elsewhere in this thread.

But suppose the Usher plan had been implemented in 2004, which
was the last time a leap year started on Thursday. Thus the
Usher leap year would have been 2005 instead. Now let's look
at a table of Usher New Year's Days and leap years:

2004: Thursday
2005: Friday (leap year)
2006: Sunday
2007: Monday
2008: Tuesday
2009: Wednesday (leap year)
2010: Friday
2011: Saturday
2012: Sunday
2013: Monday (leap year)
2014: Wednesday
2015: Thursday
2016: Friday
2017: Saturday (leap year)
2018: Monday
2019: Tuesday
2020: Wednesday
2021: Thursday (common year)
2022: Friday (leap year)
2023: Sunday

And now we see the problem. The resulting leap year cycle
isn't 7 leap years in 29 years, but rather 4 leap years in
only 17 years. This is because by skipping Thursday leap
years, Usher unwittingly skipped Tuesday and Sunday leap
years as well! And so the resulting mean year length is
only 365+4/17 = 365.2352941 days, which is less accurate
than the Gregorian leap year rule.

The idea of having occasional five-year periods between
leap year's isn't new. Wikipedia mentions the Jalaali
calendar, billed as the most accurate solar calendar in
the world, which has 8 leap years in 33 years, giving a
mean year length of 365+8/33=365.2424... years:

http://en.wikipedia.org/wiki/Iranian_calendar

> 4. That the perpetual calendar can be made, by considering the first
> day of the year of weeks to occur on the Sunday after the Assumption,
> and if this is the first possible calendar day, it is called week 1,
> and otherwise week 2, and every year runs through week 53. And this
> calendar ensures that everything can be fixed to a day of a certain
> week, in particular the American Thanksgiving must be made 31 days
> before Christmas.

There is already a similar week-numbering scheme:

http://en.wikipedia.org/wiki/ISO_week_date

Of course, the ISO week 1 occurs near New Year's Day, which
is unacceptable to Usher since he wants to avoid starting the
count during his 15 weeks between Christmas and Easter. So he
chose a different starting point. Also, the ISO weeks start
on Monday whereas Usher weeks start of Sunday (but this was
discussed by others elsewhere in the thread).

Notice that the current USA Labor Day (first Monday in
September) already occurs exactly 11 weeks and three days
before Usher Thanksgiving. As Usher points out later, this
is convenient for college football, which traditionally began
on Labor Day weekend and ended on Thanksgiving, with enough
time to play 11 games in between. (The recent practice of
playing 12 games instead of 11 occurred because in a recent
year when Labor Day and Thanksgiving were 12 weeks and three
days apart, colleges scheduled an extra game, then kept on
scheduling 12 games even when the period between the two
holidays switched back to 11 weeks and three days.)

Also, the current USA Memorial Day (last Monday in May)
already occurs exactly seven weeks and one day after the
Usher Easter. In other words, it's always Whit Monday. (For
those who are tired of all these USA holiday references,
note that the UK Spring Bank Holiday occurs on the same day
as USA Memorial Day, while the UK Summer Bank Holiday occurs
exactly one week before USA Labor Day.)

> 6. This is surely the best possible arrangement that can be made,
> without disturbing the cycle of weeks or that of calendar days
> inherited from the Romans.

I'm not sure whether this is the best possible calendar, but
it's certainly an interesting proposal.

From: R H Draney on 22 Feb 2010 03:34

Transfer Principle filted:
>
>The notion of calendar reform has appeared on sci.math from time
>to time. Some people may argue that the debate between those who
>defend the standard Gregorian calendar and those who wish to
>reform it is analogous to the debate between the standard set
>theorists and the so-called "cranks." I'd argue that calendar
>reform would fit Underwood Dudley's "eccentric" category more
>than the "crank" category.

If you want a crank, find the person who came up with Daylight Saving Time....

Then find his successor who decided that DST should apply for more of the year
than "Standard" time....r

--
"Oy! A cat made of lead cannot fly."
- Mark Brader declaims a basic scientific principle

From: Trond Engen on 22 Feb 2010 04:42

Brian M. Scott skrev:

> On Mon, 22 Feb 2010 01:27:05 -0000, Androcles
> <Headmaster(a)Hogwarts.physics_u> wrote in
> <news:U3lgn.67724$3E5.39843(a)newsfe18.ams2> in
> sci.math,sci.physics,sci.astro,sci.lang:
>
>> "alan" <in_flagrante(a)hotmail.com> wrote in message
>> news:hlsls1$294$1(a)news.eternal-september.org...
>>
>>> "Androcles" <Headmaster(a)Hogwarts.physics_u> wrote
>>>
>>>> Observing the planets as gods goes back to prehistory
>>>> and are the basis of the seven day week.
>>>
>>> The strcit 7 day week actually had its origins with the Jews.
>>
>> IN FACT the seven day week ACTUALLY has its origin in
>> prehistory, as I've explained. [...]
>
> In fact you've done nothing of the kind: you've made an
> unsupported assertion.

IN FACT argument-by-capitalization makes him sound AWFULLY like another
LOON with a Greek NICKNAME.

--
Trond Engen

From: Cheryl on 22 Feb 2010 07:14

Peter T. Daniels wrote:
> On Feb 21, 4:17 pm, Cheryl <cperk...(a)mun.ca> wrote:
>> Peter T. Daniels wrote:
>>> On Feb 21, 10:59 am, Mike Barnes <mikebar...(a)bluebottle.com> wrote:
>>>> Yusuf B Gursey <y...(a)theworld.com>:
>>>>> On Feb 19, 11:25 am, Mike Barnes <mikebar...(a)bluebottle.com> wrote:
>>>>>> But I thought that for most people the whole point of Easter is that
>>>>>> they get time off work.
>>>>> not in the US, at least not in my state.
>>>> So I now understand. Here in England, Friday and Monday are holidays,
>>>> and school terms fit around them. That's the problem with Easter. I
>>>> think it's fair to say that many people here would be happy if they
>>>> fixed the dates of the public holidays (e.g. second weekend in April)
>>>> and allowed the holy day to shift as it will. I don't if or why
>>>> disconnecting them would matter to anyone.
>>> That's because you're stuck with a state religion.
>>> In NYC, parking regulations are suspended for just about anyone's
>>> religious holidays.
>> Hey, we get to take some religious holidays (Christmas Day and Good
>> Friday) off work even without a state religion! I'm ecumenical; I'd take
>> ANY religious holidays. I suspect that there's some rule that you have
>> to be a member of the religion in question in order to not work that
>> aren't also legal or secular holidays, but that could be fixed by making
>> them ALL legal holidays. My home province ended up cancelling some of
>> the religious (ie Christian) holidays from the list of legal days off in
>> the interests of increased productivity, but some workers still have the
>> old list embodied in their contracts. Now, of course, some of them get
>> "Mid-March" and "Mid-July" off rather than religious holidays.
>
> What "religious holiday" does "Mid-July" accommodate?

I was thinking St. George's Day, but when I checked, it was Orangemen's
Day.

When all these were drawn up, people of both Irish Catholic and English
Protestant ancestry had to be accommodated, but I'd forgotten that the
Protestant got two days to the Catholic's single St. Patrick's Day.

--
Cheryl