The perpetual calendar [Math]

Prev: THE MIND OF MATHEMATICIANS PART 7 " SPATIAL MATHEMATICS , VALUE OF 1 and 3
Next: Exactly why the theories of relativity are complete nonsense- the basic mistake exposed!

From: Andrew Usher on 22 Feb 2010 21:02

Transfer Principle wrote:

> 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).

I see you've worked out yourself many of the implications I hinted at
in the original post and elsewhere. It's quite remarkable to me that
this all works!

> 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.

I think this is a valid point, but still it's clear that workers would
be less likely to take days off. Not everyone travels a great distance
for Christmas, nor is everyone allowed to take that many days off.

> (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.

Schools could end on the Thursday or Wednesday, then.

> 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.)

Many schools have a winter break not fixed in length already; they
resume on the weekday after New Year's and they still could. I would
rather, though, extend the break to the end of a full week.

> > 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.

Yes, Easter on Apr. 4 would throw the whole rest of the year off.
Having a rule like this seems not unreasonable; the Jewish calendar
has it (and more complicated, too).

> 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.

Yes, this was an error I found shortly after posting it. Doh.

One needs, to correct this, to sometimes have a shorter than 4-year
interval between leap years. This can be accomplished by inserting at
intervals, a shorter cycle as follows (using your notation):

Year 1: Friday (leap year)
Year 2: Sunday
Year 3: Monday
Year 4: Tuesday (leap year)
Year 5: Thursday
Year 6: Friday (leap year)

7 17-year cycles and 1 of these make 30 leap years in 124, or a year
of 365+30/124 = 365.2419 days.

> 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.)

My college football season would always have 13 weekends (rather than
13 or 14); whether 11 or 12 games is allowed is not my concern.

> 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.)

Indeed, and I had those in mind as well.

Andrew Usher

From: Evan Kirshenbaum on 22 Feb 2010 21:24

Andrew Usher <k_over_hbarc(a)yahoo.com> writes:

> Evan Kirshenbaum wrote:
>
>> > mine, yours, his, hers, its,ours, theirs.
>> >
>> > Not one possessive pronoun has an apostrophe.
>>
>> One should be sure of one's facts before making such assertions.
>> (Or should that be "ones"?)
>
> 'One' is not, grammatically, a pronoun. It is a nominalised
> adjective (the number one) that is used in place of a pronoun.

Both Merriam-Webster and the OED appear to disagree with you.

--
Evan Kirshenbaum +------------------------------------
HP Laboratories |You gotta know when to code,
1501 Page Mill Road, 1U, MS 1141 | Know when to log out,
Palo Alto, CA 94304 |Know when to single step,
| Know when you're through.
kirshenbaum(a)hpl.hp.com |You don't write your program
(650)857-7572 | When you're sittin' at the term'nal.
|There'll be time enough for writin'
http://www.kirshenbaum.net/ | When you're in the queue.

From: R H Draney on 22 Feb 2010 21:58

Michael Stemper filted:
>
>mine, yours, his, hers, its,ours, theirs.
>
>Not one possessive pronoun has an apostrophe.

That might just be somebody's opinion....r

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

From: Androcles on 22 Feb 2010 22:24

"R H Draney" <dadoctah(a)spamcop.net> wrote in message
news:hlvg8b02b4(a)drn.newsguy.com...
> Michael Stemper filted:
>>
>>mine, yours, his, hers, its,ours, theirs.
>>
>>Not one possessive pronoun has an apostrophe.
>
> That might just be somebody's opinion....r
>
>
Pigs might fly; but then they'd be pigeons.

From: Brian M. Scott on 22 Feb 2010 22:55

On Tue, 23 Feb 2010 09:37:43 +0800, Robert Bannister
<robban1(a)bigpond.com> wrote in
<news:7ugpr7Fll6U1(a)mid.individual.net> in
sci.math,sci.physics,sci.astro,sci.lang,alt.usage.english:

> Brian M. Scott wrote:

>> R H Draney wrote:

>> [...]

>>> 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

>> I like DST; my only objection is that we don't have it all
>> year round.

> I think you should go and live in Inverness until you
> change your mind.

I can't imagine why you think that I'd change my mind. As
far as I'm concerned, DST has no disadvantages at any time
of year in any climate at any latitude. In winter at higher
latitudes its advantages are minimal, but it still has no
disadvantages. I couldn't care less how dark it is in the
morning; it's in the afternoon and evening that I want the
benefit of as much daylight as possible.

Brian