# I Think I Have The Solution!

 Posts 29
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hotdog8
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Joined: Feb 21 2018, 01:52 PM
Look I am no genius - I may hold a degree in economics but I don't have honours, masters nor a doctorate. But I am an expert in common sense and simplicity and I truly believe that if we are to get the masses and different countries to accept the dozenal calendar it has to be simple to understand - and have some new benefit to them.

I independently arrived in thought as to a dozenal calendar late last year - it was only after I had myself invented a dozenal 10 month calendar each month comprised of 26 days, or 5 weeks of a 6-day week - 260 days of 10 months and 50 weeks, with 5 and a quarter days left over, that I did some research using google and the net to see if anyone else had invented it before me.Obviously I found out that such a calendar had already been proposed independently from me. BUT mine is slightly different in accounting for the remainder of the days left over from 10 totally symmetrical months than any proposal I have seen so far.

In a nutshell, what about if we add an extra week of 6 days to the dozenal calendar year mentioned above i.e. 266 days and 51 weeks in a year with the extra 6 days being split into an extra day in each other month - that is 27 days in each of February, April, June, August, October and December, with 26 days in each of the other months.

266 days dozenal is equivalent to 366 days decimal and we know that the Earth revolves around the Sun every 365 and a quarter days, so we are actually borrowing three-quarters of a day or 0;9 of a day. But what makes it so symmetrical is that every 8 years (0;9 x 8 = 6 days we have gained) we can repay the borrowed time of having a 'Leap Year' of exactly 10 dozenal months, each with exactly 50 weeks - 5 weeks of 6 days (or 26 days) each month - 260 days in that year!

The beauty of this calendar is that unlike the Gregorian calendar it is not short of a day and a quarter which causes the dates of different years to fall on different days in the week i.e. my calendar causes any day of the year to fall on the same day of the week as the previous year for seven years straight! Only every 8 years on a leap year will the dates and days be different than the other years BUT because the number of weeks completed in the year is whole the 9th year will have exactly the same days of dates as the first year!

This calendar will allow the masses to know exactly what day a date in the year is, so that is one benefit to the people. A second benefit would be to lobby each countries government to enshrine in law a work roster of 3 days on - 3 days off, but that is another topic which is quite complex in terms of worker productivity etc and is one I don't feel qualified to address - but the idea is out there!

Dozens Disciple
Shaun
Dozens Disciple
Joined: Aug 2 2005, 04:09 PM
The only problem I can see arising is the lack of provision for those religiously-minded for whom a 7-day unit is essential; they might be happy to have Easter fixed, though, and not forever meandering.
Three days on and three off - or four and two?

And welcome to the Forum!
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.

 Posts 29
Casual Member
hotdog8
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Joined: Feb 21 2018, 01:52 PM
Thanks Shaun! I feel so STUPID - somehow I counted in decimal the number of weeks in 260 days - I should have written 50 dozenal weeks and not 42 ! Any ideas how to correct my mistake without losing face?

 Posts 29
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hotdog8
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Joined: Feb 21 2018, 01:52 PM
It's ok Shaun - I found the 'Edit' feature for my post - what a wonderful, practical and powerful website you have - I am really glad to be on board!

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
hotdog8 @ Feb 21 2018, 05:57 PM wrote: Thanks Shaun! I feel so STUPID - somehow I counted in decimal the number of weeks in 260 days - I should have written 50 dozenal weeks and not 42 ! Any ideas how to correct my mistake without losing face?
It looks like you've already discovered or learned via private message that you can edit your own posts after the fact.

I might also suggest you adopt a method of annotating the bases of your numbers, besides just stating a base in prose, which gets awkward after a while. Several different methods have been proposed over the last 6 dozen years, and many of those have been discussed here and are actively used by their proponents.

As for the subject of dozenal calendars, bravo for working out some ideas on your own, but realize that it is a well-trodden subject so your ideas may not be entirely novel. For instance our own Paul Rapoport has developed a calendar that incorporates 6-day weeks (among other distinct novelties), and is even attempting to live by it! Not for the faint of heart, in this 7-day-a-week world.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 29
Casual Member
hotdog8
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Joined: Feb 21 2018, 01:52 PM
That’s a beautiful avatar you have drafted Kodegadulo - it is not two opposing trinity’s / triangles pulling in opposite directions as the Star of David purports but rather like the Pentagram it is harmoniously free-flowing and eternal - the pencil begins to draw and then never needs to be lifted at all to complete the picture- they are both uniting and harmonious and everlasting! Anyhow thank you for the advice - I will keep my eyes open on the blog and also in DSA publications for better and simpler ways to express dozenal vs decimal numbers.

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Followed up the comment about my avatar somewhere else, where my reply would be more on-topic.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
[quote="hotdog8 @ Feb 21 2018, 05:04 PM"]The beauty of this calendar is that unlike the Gregorian calendar it is not short of a day and a quarter which causes the dates of different years to fall on different days in the week i.e. my calendar causes any day of the year to fall on the same day of the week as the previous year for seven years straight! Only every 8 years on a leap year will the dates and days be different than the other years BUT because the number of weeks completed in the year is whole the 9th year will have exactly the same days of dates as the first year![/quote] There are "perennial calendars" which can be used [i]every[/i] year, so that a given date always lands on the same day of the week. Such calendars are short a day most years but then add a leap [i]week[/i] every few years. But they generally keep to the traditional 7-day week, which is so ingrained in our culture (both secular and religious) that I doubt it could ever be dislodged. From [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=666&view=findpost&p=22086580]this post[/url]: [quote="Kodegadulo @ Apr 17 2013, 12:54 PM"] [/quote] hotdog8 it might make it clearer what you are proposing if you laid out your own calendar like this, to show us what you mean. Sounds like your calendar would make most years approx 3/4 day too long, so 8 years would be 6 days too long, so you would "leap" by dropping a 6-day week from the last year, rather than adding a "leap week". Okay, what month would lose a week? Don't make it during Christmas or you'll have the "masses" revolting -- not to mention the retailers! :) (Just a bit of common sense there. ;) ) (P.S. I just noticed that the perennial calendar above places Christmas -- December 21[sub]z[/sub]=25[sub]d[/sub] -- on a Thursday, every year. So likely businesses would just give employees the day off on the Friday as well, which would be traditional "Boxing Day" December 22[sub]z[/sub]=26[sub]d[/sub]. Great day to hit the mall and exchange all those clothing gifts that don't fit. ;) So in the US there would be two major 4-day weekends near the end of the year: (1) American Thanksgiving, likely on Thursday November 21[sub]z[/sub]=25[sub]d[/sub] every year, with the following day known as "Black Friday" because it's the biggest shopping day of the year, putting most retailers "in the black" on their ledgers. (2) Christmas-Day/Boxing-Day weekend. Actually most years that would be a [i]5[/i]-day weekend, because the following Monday would be New Year's Day! But on a Leap Year, every 5 or 6 years or so, there would be a whole week in between.)
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 33
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Einmaleins
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Joined: Feb 12 2018, 06:58 AM
You can also consider the original Wold Calendar idea - four quatres each of 77z days with months days 26, 26, 27 in each quarter. Four x 77 = 264z, and add a "World Day" (unnumbered, bank holiday) at end of year. No need for elaborate leap weeks, just add a Leap Day (also unnumbered) at mid-year.

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Well, the advantage of a Bromberg-style Perennial calendar is that every month and every year always starts on a Monday and is always a whole number of weeks long. So you only need to print one version of the calendar and can use it every year. For any date you always know exactly what day of the week that will be. To me, that sounds simple rather than elaborate. The disadvantage, though, is that the years drift by as much as a week from alignment with the seasons, and the correction is to add a whole leap week. The formula for that is a bit more elaborate than the simple Gregorian pattern.

A World Calendar, like the current Gregorian calendar, would drift no more than a day from alignment with the seasons, and the correction is just a single leap day. But that is at the expense of needing twizeen (a dozen-two, or fourteen) different versions of the calendar, to accommodate every possibility of which day of the week the year might start on, and whether or not it includes a leap day. Months wind up starting on all sorts of days of the week. Predicting what day of the week a given date might fall on is not a simple and intuitive thing. But it keeps printers in business printing out calendars every year, and calendar apps give people another excuse to bury their noses in their mobile phones.

A six-day week would make this all different of course. Except that six days isn't really a "week". Most people are still going to think of a "week" as 7 days, approximately a quarter-month, not a fifth. So let's use a different word, perhaps "stint", for a cycle of 6 days. So every month could consist of exactly 5 stints, with "extra" days, not part of any stint but rather between stints, once every season/quarter, once every year, and once every leap cycle. If civil authorities imposed such a stint-based calendar, the religiously-inclined are still going to follow their 7-day weekly cycles at the same time. Just imagine how elaborate that would get!
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 33
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Einmaleins
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Joined: Feb 12 2018, 06:58 AM
"f civil authorities imposed such a stint-based calendar, the religiously-inclined are still going to follow their 7-day weekly cycles at the same time. Just imagine how elaborate that would get! "

You will never sell the idea to them; it gives the, something new to fight and squabel over.

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Of course I don't imagine any civil authorities will ever be imposing a new calendar nor do I advocate it. But there can be no objection to someone voluntarily adopting a new calendar and providing interactive tools for others to try it out. See Paul Rapoport's Dozenal Solstice Calendar interactive appointment book. You can see that it is based on months of five 6-day "stints" (as I've been calling them) starting on the summer solstice (northern hemisphere) with extra "S" days interspersed between the months/stints to keep the seasons aligned, accounting for the eccentricity of the Earth's orbit. Because none of this divides neatly by 7, you can see that each day in the calendar must be individually labeled with an abbreviation for the traditional day of the week.

Calendar reform seems to be a ... perennially ... favorite topic around here. But frankly I see little that the subject offers in the way of clear advantages for one numeric base or another. It's just a fact of nature that the number of Earth days in an Earth year is just not a round number in any convenient base. It's not even a whole number. If one is seeking slam-dunk advantages offered by dozenal, one must look elsewhere...
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 29
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hotdog8
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Joined: Feb 21 2018, 01:52 PM
Well Kodegadulo the Bromberg "Perennial" calendar appears at first glance to be symmetrical and perennial but a deeper analysis reveals that in fact it's not!

Using its seven day week dozenally it is only perennial for 264 dozenal (dozenal numbers here on after labelled with a 'z'). which is 364 days decimal (decimal numbers here on labelled with an 'x'). That leaves in both cases 1;3z days or 1.25x days short of the astronomical year that is 265;3z days or 365.25x days long, as we all know! So how often should we have a leap week in the Bromberg concept of a calendar? Every 2 years? In this case we have only lost 2.5x days or 2;6z days, so we cant add an extra 7 days. What about every 4 years? Again we are over the mark by adding an extra 7 days for a leap week when we have only lost 5 days - the calendar of the days of the week would shift by 2 days! What if we have a leap week every 6 years? Well we would have lost 7.5x days or 7;6 days equivalent but we would only be giving back 7 days - so over time this particular calendar would slowly drift us out of allignment with astronomical solstices and equinoxes by half a day every seven years.

Kodegadulo if i possessed the software and knowledge and skill to show you my calendar graphically - like your graphical posting of the Bromberg calendar - I would do so so as to make it easier for people to see and hence grasp the concept. BUT from what I have read in your reply posts you already have grasped my concept of a dozenal calendar that is perennial and whole - the only thing is, to answer your question, no we would NOT be taking a whole week off of any particular month! In a leap year of exactly 10z months (each month comprised of 5 weeks of 6 days or 26z days) making 260z days of exactly 50z weeks, we would remove the extra week that we have been slowly accumulating for the past 8 years by simply removing each of the 27th day that have been falling on every-other month in every 'normal' year (i.e. February, April, June, August, October and December all have 27z days in a normal year) - that gives us the 6 days we are giving back! Every leap year would be symmetrical, perennial and whole, as would the whole calendar overall.

Dozens Demigod
Double sharp
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Joined: Sep 19 2015, 11:02 AM
hotdog8 @ Feb 25 2018, 02:58 PM wrote: Well Kodegadulo the Bromberg "Perennial" calendar appears at first glance to be symmetrical and perennial but a deeper analysis reveals that in fact it's not!

Using its seven day week dozenally it is only perennial for 264 dozenal (dozenal numbers here on after labelled with a 'z'). which is 364 days decimal (decimal numbers here on labelled with an 'x'). That leaves in both cases 1;3z days or 1.25x days short of the astronomical year that is 265;3z days or 365.25x days long, as we all know! So how often should we have a leap week in the Bromberg concept of a calendar? Every 2 years? In this case we have only lost 2.5x days or 2;6z days, so we cant add an extra 7 days. What about every 4 years? Again we are over the mark by adding an extra 7 days for a leap week when we have only lost 5 days - the calendar of the days of the week would shift by 2 days! What if we have a leap week every 7 years? Well we would have lost 7.5x days or 7;6 days equivalent but we would only be giving back 7 days - so over time this particular calendar would slowly drift us out of allignment with astronomical solstices and equinoxes by half a day every seven years.
{a} default decimal

It's more complicated than that; there's a regular pattern of leap years (link) in Bromberg's calendar that has 52 leap years per every 293-year cycle. A year is a leap year if the remainder of (52*year + 146)/293 < 52. So the leap years sometimes come five years apart, and sometimes come six.

Personally I don't much like this sort of solution, because the complications of such a leap-year rule seem to negate all the gains of a perpetual calendar. In effect, it swaps the difficulty of telling what day of the week a particular date fell on for the difficulty of telling if a year was a leap year or not, and I do not think that's a very good swap (especially since 293 is prime and this cycle won't match easily with any sensible base).

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Double sharp we are in violent agreement. The point I am making is that it's a no-win proposition. There seems to be a law of conservation of complexity when it comes to Earth calendars. Simplifying one aspect merely concentrates the complexity somewhere else. There is very little to nothing that one base or another does to improve the situation. So calendar reform, as fun as it might be, offers little to recommend one base over another.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 634
Dozens Disciple
Paul Rapoport
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Joined: Dec 26 2012, 01:59 AM
Calendar reform is indeed intractable, and as discussed, not just with regard to number base. All I've done is the best I can while assuming dozenal is the base. The trade off between easily knowing the day of a date and easily knowing which are leap years, I've chosen to resolve in favor of the former. I find it much more useful in practice, especially because in my calendar the leap years are every 4 except rarely when they have one gap of 5. I'd bet that there's a way of determining where the gaps of 5 years occur. I'd like someone to look at that possibility.

Whether the weeks are 7 days or stints of 6 (another terminological invention I like), the basic problem remains what to do with the extra days. If the year were exactly 365.25 decimal days, life would be easy. The complications making it not so require the human calendar to keep pace with astronomic incongruences, irregularities, and drift over long periods. One way to do that is simply to declare the year's beginning on an equinox or solstice. (I prefer to start the year in December in the northern hemisphere, while at least one other person prefers June.)

The balance is always between astronomic accuracy and ease of use. I've chosen what seems an easy position on that issue. Others are equally valid, probably. They all have advantages and disadvantages. I don't find having an additional day every second month to be accurate enough.

Another approach with 6-day stints is dozenal 13 "months" a year, plus extra days. Those 20-day periods may also need their own name. I don't recall whether they've been given one yet.

 Posts 29
Casual Member
hotdog8
Casual Member
Joined: Feb 21 2018, 01:52 PM
Kodegadulo I am now in possession of a spreadsheet graphic of my calendar. If you would like to see it posted then I shall ask you for a small favour. Could you write me and post me the steps for importing an excel format document to this blog from an Apple iPhone 8 - I have wi-fi available to me.

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
Just start a new post and actually take a look at the editor features. Can't you see a little button labeled Choose File? It's not that hard to figure out these things...

In general, if you want to figure out how people are using BBCode and/or HTML to accomplish things in their posts, try just hitting Quote, and then study the raw text of their post in your Quote editor.

But if you want to share a spreadsheet with folks, just do it in Google sheets and share the link here.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 29
Casual Member
hotdog8
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Joined: Feb 21 2018, 01:52 PM

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
hotdog8 @ Feb 27 2018, 11:30 AM wrote: To view a graphic calendar of my dozenal calendar please follow the link below:
So, 51z ("fivzy-one", or "five-dozen-one") whole stints of 6 days each, yielding a year that is too long, 266z ("two zandred sixzy-six", or "two-gross, six-dozen-six") days long. That means you periodically must "unleap" by removing a whole stint from somewhere in this calendar for an "unleap" year. (That is, if you really mean for this to be a perennial calendar, and not have it degenerate into a dozen different calendars covering every possible day-of-the-stint that the year might start on.) So which stint, in which month, is going to be sacrificed? Realize that people getting salaries by the stint, but paying rents by the month, are going to be up in arms whenever they have one less paycheck contributing to the rent. And they will all know who to blame ...

I suppose an "unleap" year could just drop the 27thz ("twenzy-seventh", or "two-dozen-seventh") day off the even months, for a 260z ("two-zandred-sixzy" or "two-gross six-dozen") day year. But then it's not precisely a "perennial" calendar. It's two calendars, one for longer years and one for "unleap" years.

You're going to have a lot of trouble with people wondering what happened to their Sundays, though...
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
hotdog I would've gotten rid of *Monday* myself... let's just say Monday had it comin' ; )

kode, let's rename the "leap week" (snore) "PARTAY! week!" I think we'd get more buy-in. Think of all the work that wouldn't get done the following week?

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
I don't even think the day-of-the-week names are appropriate labels for days-of-the-stint. You really need to reserve those for labelling the days in true 7-day weeks. What you need is a completely different set if day-names reflecting their positions within 6-day stints. Just for the sake of argument, call them Alphaday, Betaday, Gammaday, Deltaday, Epsilonday, Zetaday (or come up with something else). Then you can do something like Paul's calendar, which labels each date box with its day of the week, regardless of which day-of-the-stint column it appears in.

So you might see a month starting on an Alphaday Monday. But one stint later the Alphday would be a Sunday, and it would be Monday on Betaday. A stint later, Alphaday would be a Saturday, and Gammaday would be a Monday. And so forth.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

 Posts 634
Dozens Disciple
Paul Rapoport
Dozens Disciple
Joined: Dec 26 2012, 01:59 AM
In the proposed calendar, the first day of the month creeps forward throughout the year. I've thought it better to avoid that, although some may think that using days with no weekday name attached to them is at best odd and at worst a kind of cheating.

I think it's good cheating How it would work in practice is still up for discussion.

Also in my calendar (created equally by Sunny of this forum), there are three types of year rather than two (one leap, two non-leap). That's a tradeoff to keep the start of winter and start of summer always in their respective places, at month beginnings. I suspect for most people that tradeoff is questionable, because they don't care (or even acknowledge) when the seasons start. I prefer to keep more connected to solar reality

One of the functions of a perpetual calendar (or small group of calendars) is to keep it from drifting against the seasons/sun. At least I've managed that There's never any drift, so no approximation is needed to get seasonal accuracy, meaning: there's no leap-year rule.

What you choose depends on your priorities.

One of the odd discoveries (made by Sunny) is that for the most accuracy, if the year's extra days above 260z go at month ends, they must do so in consecutive months. So in the current year I see months with these numbers of days:

26 26 26 26
26+1 26+1 26+1 26+1 26+1
26 26 26

wendy.krieger
wendy.krieger
I am not really fond of calendars that have the dates on the same day of the year.  In one case, a person born on Tuesday, would always have their birthday on tuesday, which would never be on a weekend.  A person born on sunday, would always have their birthday on sunday.

None the less, the calendar can be simplified, to make the week-shift more evident from the calendar.