[HN Gopher] Lewis Carroll - computing the day of the week for an...
       ___________________________________________________________________
        
       Lewis Carroll - computing the day of the week for any given date
       (1887)
        
       Author : beardyw
       Score  : 147 points
       Date   : 2024-05-24 08:56 UTC (14 hours ago)
        
 (HTM) web link (www.futilitycloset.com)
 (TXT) w3m dump (www.futilitycloset.com)
        
       | beardyw wrote:
       | If he could do it in 20 seconds I would call that remarkable!
       | 
       | He didn't consider himself a "rapid computer".
        
         | defrost wrote:
         | His benchmark would have been _other_ Oxbridge Dons teaching
         | mathematics . .
        
       | ColinWright wrote:
       | This is very similar to the method I use and, after conversation
       | with him, the method Art Benjamin uses. It's trivial to do in 10
       | to 15 seconds, though it requires practice, a very small amount
       | of memorisation[0], and a small amount of mental arithmetic. I
       | use it regularly, partly to keep in practice, and partly because
       | once you have the skill you find it's surprisingly useful.
       | 
       | JH Conway used a different technique[1] which I have swutch to
       | when computing days in the current year. It's quicker and easier,
       | but I find that it's harder to compute "The Doomsday" for other
       | years (it's Thursday this year), so I revert to my standard
       | method[2].
       | 
       | Example: Today is 2024/05/24                   Years since 2012
       | is 12         Leap years is 12/4 = 3         Magic month number =
       | 2         Date is 24         Add mod 7 is (12+3+2+24) =
       | (-2)+3+2+3 = 6 = Friday
       | 
       | [0] A "magic number" for each month. There are mnemonics, and
       | they can be computed from first principles if needed. It's also
       | easy to remember a few and then compute the others.
       | 144 : Jan, Feb, Mar       025 : Apr, May, Jun       036 : Jul,
       | Aug, Sep       146 : Oct, Nov, Dec
       | 
       | [1] https://en.wikipedia.org/wiki/Doomsday_rule
       | 
       | [2] All values computed mod 7. Take years since 1900. Add number
       | of leap years since 1900 (so (YYYY-1900)/4 rounded down). Add the
       | magic number for the month. Add the day of the month. Then
       | Sunday=1, Wednesday=4, etc.
       | 
       | Because the calendar repeats every 28 years, for more recent
       | dates you can start with 2012 instead of 1900.
        
         | jihadjihad wrote:
         | > which I have swutch to
         | 
         | That's a past participle I've never seent before
        
           | purpleyhippo wrote:
           | Second guessed myself and had to look up whether this was
           | actually a word
        
             | OJFord wrote:
             | If it was phrased 'to which I have swutch' I don't think
             | I'd bat an eyelid!
             | 
             | (i.e. past perfect, I think?)
        
               | seabass-labrax wrote:
               | If 'swutch' is the (past) participle of 'to switch':
               | 
               | Perfect: "to which I have swutch"
               | 
               | Pluperfect/past perfect: "to which I had swutch"
        
             | mattmaroon wrote:
             | Google says the correct term is, in fact, Nintendo Switch.
        
               | lotsoweiners wrote:
               | I assume it lets you know where to buy one as well.
        
               | mattmaroon wrote:
               | How'd you guess?
        
               | yazzku wrote:
               | Trust Google with the facts.
        
           | smallnamespace wrote:
           | I find this all much ado ablaut nothing.
        
           | dvfjsdhgfv wrote:
           | maybe you haven't liveth long enough
        
           | jrochkind1 wrote:
           | For some reason part participles are particularly hard for me
           | too (native English speaker who speaks no other languages
           | fluently). (they must just be a mess in English? I can't
           | imagine how non-native speakers ever get any of them)
           | 
           | I'm going to go with swutcheted
        
             | cyberax wrote:
             | English verbs are pretty tame compared to Slavic verbs that
             | can be modified with all kinds of perfective prefixes.
             | 
             | On the other hand, Chinese verbs are even easier. They
             | don't even have a tense!
        
             | jjtheblunt wrote:
             | For entertainment look up Germanic string and weak verbs.
        
           | aidenn0 wrote:
           | Like the joke of the guy returning to Boston after being away
           | for years; asks his cab driver "Do you know where I can get
           | scrod" and the driver says "Sure, but I've never heard that
           | in the past perfect before!"
        
             | xorbax wrote:
             | This might be the first time I get a joke's punchline but
             | not the setup
        
               | aidenn0 wrote:
               | Scrod is the name for a small whitefish; he was looking
               | for a seafood restaurant.
        
         | jgrahamc wrote:
         | I assume by                 144 : Jan, Feb, Mar       025 :
         | Apr, May, Jun       036 : Jul, Aug, Sep       146 : Oct, Nov,
         | Dec
         | 
         | You mean: Jan = 1, Feb = 4, Mar = 4, etc.
        
           | chongli wrote:
           | Yeah, since they're all mod 7.
        
           | ColinWright wrote:
           | Exactly so.
           | 
           | I remember them in this table because they are squares
           | (except for December), as well as "highlights" ... May=2 and
           | August=3 are two that I have "to hand".
        
         | reedf1 wrote:
         | I am struggling to understand the advantages over the Lewis
         | Carroll method, which I find very simple and quick. It seems to
         | add quite a lot of complexity.
        
           | jgrahamc wrote:
           | Really? Colin's method seems pretty simple to memorize and
           | work with. Especially since it's all addition mod 7. Given
           | that the mod operator distributes over addition you can work
           | answers out easily while working with small numbers.
           | 
           | For example, what day of week was September 2, 1945?
           | 45/4 = 11 (mod 7 = 4)         45 mod 7 = 3 (easy to work out
           | from 7 times table)         September = 6         2
           | 
           | So you've got 4 + 3 (disappears under mod 7) and 6 + 2 mod 7
           | = 1. So, the second world war ended on a Sunday.
        
           | ColinWright wrote:
           | I'm struggling to see why you think this is more complex ...
           | the methods seem completely equivalent to me. The Carroll
           | method does:
           | 
           | 1: A calculation for the Century-Item ... divide by 4, take
           | overplus from 3, multiply remainder by 2.
           | 
           | 2: A calculation for the Year-Item ... Add together the
           | number of dozens, the overplus, and the number of 4's in the
           | overplus.
           | 
           | 3: A calculation for the Month-Item ... alternatively,
           | memorise a table: the required final numbers after division
           | by 7 are January, 0; February, 3; March, 3; April, 6; May, 1;
           | June, 4; July, 6; August 2; September, 5; October, 0;
           | November, 3; and December, 5.
           | 
           | Note that these numbers are exactly those in my table, minus
           | 1.
           | 
           | 4: Include the Day-Item.
           | 
           | Then add them all (mod 7) and convert the number to a month.
           | 
           | It's _exactly_ equivalent to what I described, except the
           | Carroll method has additional calculations for the year.
        
             | reedf1 wrote:
             | Possibly it was in the clarity of his explanation. That
             | makes sense, thank you.
        
           | ColinWright wrote:
           | I think it's unreasonable for you to have been downvoted, and
           | I've given you an upvote to do what I can to balance that.
           | Expressing confusion over something like this is perfectly
           | reasonable.
        
         | fifilura wrote:
         | A little pressed with time, but does it handle leap years
         | properly? Since every year divisible by 100 is not a leap year,
         | unless it is also divisible by 400?
         | 
         | (E.g. 1900 is not a leap year but 2000 is)
        
           | ColinWright wrote:
           | There is a small correction needed for January and February
           | in leap years, and I haven't included the corrections for
           | pre-1900. The Carroll method does deal with these issues and
           | I have internalised them, but I find I never use them, so I
           | retain only the simpler version.
        
             | OscarCunningham wrote:
             | One simple way to do January and February is to treat them
             | as part of the previous year (with an adjustment for the
             | constant you remember for those months).
        
         | b_emery wrote:
         | > partly because once you have the skill you find it's
         | surprisingly useful.
         | 
         | A statement I find to be true in general.
        
         | ternaryoperator wrote:
         | You don't have to take the mod 7 of each of the values. You can
         | sum them into one number and take its mod 7. You'll get the
         | same result.
        
           | ColinWright wrote:
           | You can take mod 7 anywhere you like as you go. It's a tool
           | to make the arithmetic easier.
           | 
           | No, you don't need to do it relentlessly as you go, but it
           | can be used in an _ad hoc_ manner to keep the numbers small.
           | 
           | Having said that, if you have 24, you can reduce it (mod 7)
           | to 10, which you might find it easier to work with rather
           | than reducing it to 3. Similarly if you start with 27 you can
           | reduce it to -1 (mod 7). You don't always need to reduce
           | things to the range [0..7).
           | 
           | (Note, by convention the square bracket implies "included"
           | and the round bracket implies "excluded", so [0..7) is the
           | collection {0,1,2,3,4,5,6}.)
        
         | aidenn0 wrote:
         | Judging by that table (month numbers being the same for Feb +
         | March in 2024), you have to adjust -1 for dates before March in
         | leap years?
        
           | tzs wrote:
           | Yup. The designers of these kind of day of the week systems
           | generally design as if the year started on March 1, so leap
           | year shenanigans just mess with the last day of the year.
           | They take that into account in their formulas for the
           | century-based and year-based terms of the formulas so that
           | each March 1 will be the right number of days after the
           | previous March 1.
           | 
           | That way when using the system you don't have to care about
           | leap years except during January and February. The formulas
           | always give February 28th as the day before March 1 which in
           | leap years is one day too late because of February 29th, and
           | so as you surmised you need to adjust by -1 for dates in
           | those months.
        
         | hn8305823 wrote:
         | Why is it called "doomsday"? Neither the wiki article nor MW
         | dictionary definition explain this etnymology/usage.
         | 
         | https://www.merriam-webster.com/dictionary/doomsday
        
           | ColinWright wrote:
           | _" When I taught at Princeton five years ago, I asked my old
           | college roommate to get to John Conway and ask. To my
           | surprise it took 3, not 2, degrees of separation to get to
           | him. He said he wanted the name to end in "-day" and "Dooms"
           | popped into his head."_
           | 
           | -- https://www.rudy.ca/doomsday.html
           | 
           | Likely that sprung to mind because of the "Domesday Book":
           | 
           |  _" Domesday Book (/'du:mzdeI/ DOOMZ-day; the Middle English
           | spelling of "Doomsday Book") is a manuscript record of the
           | Great Survey of much of England and parts of Wales completed
           | in 1086 at the behest of King William the Conqueror."_
           | 
           | -- https://en.wikipedia.org/wiki/Domesday_Book
        
         | tzs wrote:
         | > A "magic number" for each month. There are mnemonics, and
         | they can be computed from first principles if needed. It's also
         | easy to remember a few and then compute the others.
         | > 144 : Jan, Feb, Mar         025 : Apr, May, Jun         036 :
         | Jul, Aug, Sep         146 : Oct, Nov, Dec
         | 
         | It can be useful to combine mnemonics and computation. Consider
         | this sequence:                 0, 1, -1, 0, 0, 1, 1, 2, 3, 3,
         | 4, 4
         | 
         | It is the offset between the day of the year of the 1st of each
         | month and the day of the year the 1st would be if the preceding
         | months had all been 30 day months. For example if the first 11
         | months had all been 30 day months Christmas, December 25, would
         | be day 30 x 11 + 25 = 355. Add the 12th item from the offset
         | sequence, 4, to that to get the real day of the year for
         | December 25th, which is 359.
         | 
         | The offset sequence is fairly easy to memorize.
         | 
         | Once you have that sequence memorized its easy to get the month
         | magic numbers for day of week calculations. There are a few
         | different sets of month magic numbers in use, but for all of
         | them:                 Magic(n) = 2 n + Offset(n) + c
         | 
         | where Magic(n) is the magic number for month n (1 <= n <= 12),
         | Offset(n) is the n'th item in the offset sequence, and c is a
         | constant that depends on just what set of magic month numbers
         | you use. For the 1 4 4 0 2 5 0 3 6 1 4 6 magic numbers c = -1.
         | 
         | For example for month 12, December, we get 2 x 12 + 4 + -1 = 6
         | mod 7.
         | 
         | By memorizing the offset sequence and using that to get the
         | month magic numbers you get, at the cost a small amount of
         | calculation to get the month numbers, easy day of year and days
         | between dates calculations.
         | 
         | Of course it works both ways. Given memorized month magic
         | numbers you can compute Magic(n) - 2 n - c and that will equal
         | Offset(n) mod 7. As long as you remember that Offset(n) is in
         | [-1,4] and so adjust anything outside that range by
         | adding/subtracting multiples of 7 to get into range it should
         | be fine.
        
         | schoen wrote:
         | > Then Sunday=1, Wednesday=4, etc.
         | 
         | That's a helpful encoding because it matches up with numbering
         | that's routinely used in Portuguese, Hebrew, Greek, and by
         | Quakers, among many others.
         | 
         | https://en.wikipedia.org/wiki/Names_of_the_days_of_the_week#...
         | 
         | These are mostly ultimately because of the Hebrew Bible account
         | in which Sunday is the first day of creation (e.g. Genesis 1:5,
         | 1:8, 1:13, ...).
        
       | throwaway211 wrote:
       | Reading the article, I wandered into the difference of Old Style
       | and New Style dates and what happened in 1752.
       | 
       | From [1]: By the 18th century, the English legal year - used for
       | legal, financial and other civil purposes - had for centuries
       | begun on 25 March, or Lady Day.[13][i] Thus, for example, 24
       | March 1707 was immediately followed by 25 March 1708, while the
       | day following 31 December 1708 was 1 January 1708, with 1709
       | still nearly three months away.
       | 
       | Thank goodness that happened.
       | 
       | [1]
       | https://en.m.wikipedia.org/wiki/Calendar_(New_Style)_Act_175...
        
         | beardyw wrote:
         | Yes, I have been following Pepys (17th century) and the dates
         | confused me a lot until I got the hang of it.
        
         | tomoyoirl wrote:
         | The Romans also used the March-based year; that's why February
         | has fewer days and why October is literally the eighth month
        
         | omoikane wrote:
         | The linux `cal` utility has special handling to recognize
         | September 1752:
         | 
         | https://github.com/util-linux/util-linux/blob/9f15d2de811773...
        
         | andyjohnson0 wrote:
         | To this day the UK tax year still begins on April 6th, for
         | reasons [1] that have to do with the migration from Julian to
         | Gregorian calendars almost 300 years ago. I wonder if other
         | countries have so many of these legacy patches from ye olden
         | times.
         | 
         | [1] https://theconversation.com/why-the-uk-tax-year-begins-on-
         | ap...
        
         | anonymousiam wrote:
         | I just typed "cal 1752" and got a calendar with a September
         | that has no dates between Wednesday the 2nd and Thursday the
         | 14th.
         | 
         | Although disputed by some, apparently the switch to the
         | Gregorian calendar is also the basis for "April Fools' Day."
         | 
         | https://en.wikipedia.org/wiki/April_Fools%27_Day
         | 
         | https://en.wikipedia.org/wiki/Gregorian_calendar
        
           | schoen wrote:
           | I've been amused by this for a while, although I think when I
           | first saw it I didn't realize that there was so much country-
           | to-country variation in what year the Gregorian calendar was
           | legally adopted.
           | 
           | Maybe a better (or much worse!) behavior would be to show the
           | switch _in the current locale_ , so in ru_RU it happens in
           | 1918, but in es_ES (or es_MX, es_CO, es_AR, es_PY, ...) it
           | happens in 1582.
        
         | interroboink wrote:
         | Though note the wiki page for Carroll's method[1] states:
         | 1676, February 23         ...         Dates before 1752 would
         | in England be given Old Style with 25 March as the
         | first day of the new year. Carroll's method however assumes 1
         | January as         the first day of the year, thus he fails to
         | arrive at the correct answer,         namely "Friday".
         | ...         It is noteworthy that those who have republished
         | Carroll's method have         failed to point out his error"
         | 
         | Indeed, the linked article has this flaw, too (:
         | 
         | [1]
         | https://en.wikipedia.org/wiki/Determination_of_the_day_of_th...
        
       | gcanyon wrote:
       | I did a write-up of (what I think is) a more straightforward way
       | to do this here:
       | https://gcanyon.wordpress.com/2013/04/09/a-better-way-to-cal...
        
       | ColinWright wrote:
       | It's really interesting watching Art Benjamin do this in his TED
       | talk[0] ... if you watch closely you can see him keeping track of
       | the intermediate calculations in his hand movements.
       | 
       | Very clever, and obvious once you know.
       | 
       | [0]
       | https://www.ted.com/talks/arthur_benjamin_a_performance_of_m...
       | ... starts at 7:47
        
       | llm_trw wrote:
       | To people who say that notation doesn't matter, this is what all
       | mathematics was like before we got our new better notation.
       | 
       | I'd go as far as saying that in mathematics little other than
       | notation matters and the same is true in computer science.
       | 
       | This is why lisp like languages are the obvious choice when
       | variables are explicit.
        
         | tzs wrote:
         | Chess was like that too. Consider a game where the first move
         | was for white to move the knight that is closest to the white
         | king to the square that is two squares forward and one square
         | to the left of where the knight started.
         | 
         | Here's how that move would have been written at various times
         | from the 17th century to the present [1].
         | 
         | Early 1600s: The white king commands his owne knight into the
         | third house before his owne bishop.
         | 
         | Mid-1700s: K. knight to His Bishop's 3d.
         | 
         | Early 1800s: K.Kt. to B.third sq.
         | 
         | Around 1850: K.Kt to B's 3rd.
         | 
         | Around 1860: K.Kt to B. 3d.
         | 
         | Around 1870: K.Kt to B3.
         | 
         | Around 1890: KKt-B3.
         | 
         | Early 1900s: Kt-KB3.
         | 
         | Mid 1900s: N-KB3.
         | 
         | Last quarter of 1900s to present: Nf3 or if you want to avoid
         | language-specific piece names f3.
         | 
         | [1]
         | https://www.knightschessclub.org/the_history_of_notation.htm...
        
       | SamBam wrote:
       | So Lewis Carroll's method for today (May 24 2024):
       | 
       | The Century-Item:
       | 
       | The year is 2024. The century is 20.
       | 
       | 20/4 = 5, with no remainder. Overplus is 0. 3-0 = 3. 3x2 = 6.
       | 
       | The Year-Item:
       | 
       | The year part is 24. Number of dozens: 2
       | 
       | 24/12=2. Overplus: 24 mod 12 = 0. Number of 4's in the overplus:
       | 0. 2+0+0 = 2.
       | 
       | The Month-Item: May: 1 (from the text).
       | 
       | The Day-Item: The day is 24.
       | 
       | Adding all items:
       | 
       | 6+2+1+24=33. 33 mod 7 = 5, which is Friday.
        
         | digging wrote:
         | > The Month-Item: May: 1 (from the text).
         | 
         | This was the part I as hoping you'd write out :) I can't make
         | heads or tails of the explanation.
        
           | SamBam wrote:
           | Agreed. I don't get from the explanation how March is 3 and
           | May is 1, as they are both 31 days and neither begins nor end
           | with a vowel. I assumed there was some missing text about
           | what to do if the month _doesn 't_ begin or end with a vowel.
        
       | ot1138 wrote:
       | Neat but what is this useful for?
        
         | Andruru wrote:
         | What do you mean, what knowing the day of week a date is useful
         | for ?
        
           | ot1138 wrote:
           | Yes, that's what people typically use a calendar for. So you
           | agree that this trick isn't useful for anything?
        
         | IncreasePosts wrote:
         | Making people think you're smarter than you are. That's about
         | it.
        
       | bumbledraven wrote:
       | Carroll's algorithm has evolved over the years. The First Sunday
       | Doomsday Algorithm
       | (https://firstsundaydoomsday.blogspot.com/2009/12/quick-start...)
       | includes all the improvements published as of 2023, including
       | Fong & Walters' nifty "odd+11" rule for calculating the year code
       | (https://arxiv.org/abs/1010.0765).
        
       | tzs wrote:
       | For the part that depends on the last two digits of the year I
       | use a method that I've not seen anywhere else. It is
       | algorithmically more work than Conway's method (Y + Y//4, where Y
       | is the last two digits of the year and // is integer division
       | rounding positive results down), but I think is easier for quick
       | mental computation for most people.
       | 
       | Let Y = 10 T + U, i.e., T is the first digit of the two digit
       | year and U is the second digit.
       | 
       | If T is even, the year part is:                 2 T + U       if
       | U = 0, 1, 2, or 3       2 T + U + 1   if U = 4, 5, 6, or 7
       | 2 T + U + 2   if U = 8 or 9
       | 
       | If T is odd:                 3 + 2 T + U       if U = 0 or 1
       | 3 + 2 T + U + 1   if U = 2, 3, 4, or 5       3 + 2 T + U + 2   if
       | U = 6, 7, 8 or 9
       | 
       | Algorithmically I compute it something like this:
       | Compute 2 T + U       If T is even           Add 1 if T >= 4 and
       | add another 1 if T >= 8       else           Add 3           Add
       | 1 if T >= 2 and add another 1 if T >= 6
       | 
       | Those add 1s come from the way leap years are distributed within
       | decades. The 2 T + U takes into account any leap years when U =
       | 0. The add 1s are to take care of the leap years that happen when
       | U != 0. In even decades those occur at 4 and 8, and in odd
       | decades they occur at 2 and 6.
       | 
       | Example: for 2024, T=2 and U=4. Mentally my train of thought
       | would be:                 2 doubles to 4, plus 4 = 8 = 1 mod 7,
       | even decade so add 1 for 4 <= T < 8 giving 2.
       | 
       | For that example there is not really easier than Conway's Y +
       | Y//4, which would be 24 + 6 = 30 = 2 mod 7.
       | 
       | Example: for 2099, T = 9 and U = 9. Mentally that goes something
       | like this:                 9 = 2 mod 7 doubles to 4, add 9 = 2
       | mod 7 giving 6       T was odd so add 3 giving 9 = 2 mod 7
       | T was odd so the so there were leap years at 2 and 6, which each
       | add 1       That gives us 4
       | 
       | I find that easier that Conway's 99 + 99/4. I can do that, and at
       | decent speed, but I can make mistakes.
       | 
       | With my method you never have to deal with a number above 32, and
       | that's only if you do no reductions mod 7 along the way. If you
       | reduce mod 7 whenever you can you never have to deal with
       | anything above 12.
       | 
       | Note: when reducing mod 7 along the way it is crucial to remember
       | that whether you take the T is even case or the T is odd case
       | depends on the actual value of T. E.g., when I am doing 2099 I
       | reduce both T and U to 2 right away but first note that 9 is odd
       | so will need to take the odd case.
        
       | thyrsus wrote:
       | I'm having trouble following the algorithm for the month number.
       | 
       | From the article:
       | 
       | The Month-Item. -- If it begins or ends with a vowel, subtract
       | the number, denoting its place in the year, from 10. This, plus
       | its number of days, gives the item for the following month. The
       | item for January is '0'; for February or March (the 3rd month),
       | '3'; for December (the 12th month), '12.' [So, for clarity, the
       | required final numbers after division by 7 are January, 0;
       | February, 3; March, 3; April, 6; May, 1; June, 4; July, 6; August
       | 2; September, 5; October, 0; November, 3; and December, 5.]
       | 
       | My attempt to implement:
       | 
       | For January, the preceding month is December, which neither
       | begins nor ends with a vowel, so I do not subtract 10. The days
       | in December are 31, so 12+31 = 43 mod 7 = 1, not the 0 of the
       | article.
       | 
       | For February, the preceding month is January, which ends in a
       | vowel, so I subtract 1 from 10, giving 9, add the days in January
       | 1+31 = 32 mod 7 = 4, not the 3 of the article.
       | 
       | For March, the preceding month is February, which ends in a
       | vowel, so I subtract 2 from 10 giving 8 and add February's 28
       | days 8+28 = 36 mod 7 = 1, not the 3 of the article. Had I used a
       | leap year 29 for the days in February at this step the result
       | would be 2, which still does not match the article result. Since
       | the article has a constant result for March, it is either always
       | using 28 or always using 29 days in February.
       | 
       | For April, the preceding month is March, which neither begins nor
       | ends in a vowel so I do not subtract it from 10. 31 days in March
       | gives 3+31 = 34 mod 7 = 6, which does match the article result.
       | 
       | For May, the preceding month is April, which starts with a vowel,
       | so I subtract its position from 10, 10-4 = 6, add April's 30 days
       | 6+30 = 36 mod 7 = 1 which does match the article.
       | 
       | For June, the preceding month is May, ending in a vowel, so I
       | subtract May's 5 from 10, and adding May's 31 days gives 5+31= 36
       | mod 7 = 1 which does not match the article.
       | 
       | This should suffice to illustrate my misunderstanding; what have
       | I got wrong?
       | 
       | [edit: typos]
        
         | rrgmitchell wrote:
         | I struggled with this too. The best understanding I've been
         | able to come to is this:
         | 
         | 1. Every month's item number can be calculated from the
         | preceding month's _item number_ by the method given. I.e. add
         | the number of days in the preceding month to the preceding
         | month 's _item number_ then take mod 7.
         | 
         | 2. For January we take it that _there is no preceding month_.
         | Therefore the numbers in such a calculation are all zero, so we
         | end up with zero.
         | 
         | 3. For later months you don't need to start at January and go
         | month by month to the month you want; you can start at a month
         | with a start- or end-vowel and use the shortcut that such a
         | month's item number is ten minus the month number.
         | 
         | 4. For the purposes of 3, 'y' does not count as a vowel.
         | 
         | Or maybe it's easier just to learn them!
        
         | v8xi wrote:
         | Also had this issue. I even tried a bunch of different
         | reformulations/reinterpretation of the provided formula and
         | nothing helped :(
        
           | xorbax wrote:
           | Perhaps if someone who gets the language did it for today's
           | date, we'd both get some clarity. I've tried working
           | backwards but the labyrinthine explanation doesn't project
        
         | rhdunn wrote:
         | January -- The item for January is '0' = 0
         | 
         | February, March -- The item ... for February or March (the 3rd
         | month), '3' = 3
         | 
         | December -- The item ... for December (the 12th month), '12.'
         | 
         | So these all use fixed values.
         | 
         | The `(10-place)+days mod 7` logic works for May, July,
         | September, and November using the previous month's values --
         | effectively every other month. The vowel trick is likely a
         | nmemonic for not having to remember which months to do this
         | for.
         | 
         | The other months are the previous month's `item+days mod 7`,
         | although it is unclear where this interpretation is deduced. --
         | The "If it begins or ends with a vowel, subtract the number,
         | denoting its place in the year, from 10." text does not apply,
         | so I would have assumed that is was 0 not the calculated item
         | value. Thus, I would have expected it to just use the days in
         | month.
        
       | roland35 wrote:
       | This is why we need the international fixed calendar!!
       | 
       | https://en.m.wikipedia.org/wiki/International_Fixed_Calendar
        
       | hasbriwn23 wrote:
       | I made an app to learn this -
       | https://grantas33.github.io/Doomsday-algorithm-practice/
        
       | shhsshs wrote:
       | https://benjoffe.com/weekle
        
       | bee_rider wrote:
       | What a pain.
       | 
       | We really should just declared the year to be 360 days long, with
       | 12 months, 30 days each, split into 6 day long weeks. The extra 5
       | days? Everybody take a vacation. Leap days go in there too
       | somehow. Every month starts with a Monday and ends with a Sunday.
       | Wednesday will be removed because it was no good anyway.
        
         | dylan604 wrote:
         | I love very confident explanations that use the word "somehow"
         | as if we're just supposed to ignore it. It adds to the humor
        
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