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Conference hydra::dejavu

Title:Psychic Phenomena
Notice:Please read note 1.0-1.* before writing
Moderator:JARETH::PAINTER
Created:Wed Jan 22 1986
Last Modified:Tue May 27 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2143
Total number of notes:41773

310.0. "How often Friday, the 13th full moons?" by PBSVAX::COOPER (Topher Cooper) Thu Feb 19 1987 22:15

    My daughter was born last Friday night.  This was both a "Friday
    the 13th" and the day of the full moon.  I wondered how often these
    occur together, and did a quick calculation to get an estimate.
    I thought readers might be interested.
    
    Step 1. The probability that a given day will be a Friday is 1/7.
    
    Step 2. In a four year period, the number of days is 365+365+365+366
    which equals 1461 days.  In that same period there will be 12*4
    or 48 thirteenths.  Thus the probability of a randomly selected
    day being a thirteenth is 48/1461 = 16/487.
    
    Step 3. (This parts a little bit sophisticated) Since the length
    of time between Friday's and that between thirteenths (on the average)
    don't divide each other, the probability that an arbitrary day is
    a Friday is "independent" of the probability that it is a 13th.
    This means that the probability that any particular day (such as
    a full moon day) is 1/7 * 16/487 = 16/3409.  This means that, on
    the average, out of 3409 full moons, 16 of them will occur on Friday
    the thirteenth.
    
    Step 4. The average time between full moons (the length of the
    "synodic" month) is 29.5 days.  If it were *one* full moon out of
    3409 then the average times between them would be 29.5*3409 days.
    But it is 16 of those 3409 full moons, so the average time is
    
    			29.5*3409
    			--------- days
    			   16
    
    between full moon Friday the thirteenths on the average.  This comes
    to roughly 6285 days or about 17.2 years between full moon Friday
    the thirteenth's on the average.
    
    NOTE: This caculates an average.  Since we are dealing with a periodic
    (in the case of the 13ths, a complicated periodic) phenomena, we
    might actually tend to get clustering, i.e., a bunch of such events
    all together, and then none for a very long time.  I don't know.
     But this should be an accurate estimate of the *average* time between
    them.
    
    			Topher
    
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310.1Three firday the 13's this year.NEXUS::MORGANOrganized Religion? Just say NO!Fri Feb 20 1987 04:316
    I was watching STARHUSTLER on PBS and the old guy said that any
    year that's not a leap year that starts on thursday will have 3
    friday the 13's in that year.  Now I know that is not what you are
    asking about but I had to chime in anyway.
    
      Mikie?
310.2How wonderful for you.MANTIS::PAREFri Feb 20 1987 13:324
    Congratulations on the birth of your daughter!!!  How wonderful
    for you.  I have a feeling that this child, born on that day under
    a full moon, will have a very special role to play in life.  Take
    good care of her.
310.3Some _good_ luck for Fri the 13th, tooNATASH::BUTCHARTFri Feb 20 1987 19:3319
    Friday the 13th on a full moon does seem especially auspicious for
    the birth of a daughter.  Reasons being, in ancient (_really_ ancient)
    mythology, the deity worshipped was the Triple Goddess, who was
    considered to be manifested in the waxing and waning of the moon.
    There are 13 (not 12) lunar months in a single year; therefore the
    number 13 was considered somewhat sacred, especially to the triple
    goddess.  And Friday is a day that has, in some goddess religions,
    been associated with her.  So a Friday the 13th was actually considered
    a day of great spiritual significance and good luck.  To have a
    full moon occur on this day would probably have been considered
    extremely special, since the full moon phase represents the goddess
    in her mother role.  (Interesting note:  the really ancient ideas
    of the moon gave it 3 phases, not 4; the Maiden phase was the new
    to gibbous waxing moon, the Mother phase was the gibbous to full to 
    gibbous moon, and the Crone phase was the waning to new moon.)
    
    A very good day to become a mother . . .
    
    Marcia
310.4TGIFPBSVAX::COOPERTopher CooperFri Feb 20 1987 23:1816
RE: .3
    
    One doesn't have to look very far to find that Friday is sacred
    to (or at least "ruled" by) the Goddess.  The word "Friday" comes
    from the Old English "Frigedaeg" (with a bar over the i).  Frige
    is a form of the Old English goddess Freo (with a bar over the e).
    For Norse mythology fans she corresponds to Freya.  She is associated
    with Venus.  Venus/Freya/Freo are versions of the triune Goddess
    (there are others, e.g., Juno) as absorbed into the broader pantheons
    of the religions they are associated with.  They are all multi-aspected
    though, probably because of their association with the Morning/Evening
    Star, the Crone aspect is played down.  Note that in French, the
    word for Friday is "vendredi" or "Venus's day" (and similarly for
    other Latin based languages).
    
    				Topher
310.5When Friday the 13'th occurs.PBSVAX::COOPERTopher CooperWed Feb 25 1987 21:2245
RE: .1
        
    Knowing the day of the week on which the year starts and whether or not it
is a leap year is always sufficient to determine what day of the week any
date of that year is on, and therefore how many (and which) Friday the
13'ths there are.  Roughly speaking, assign numbers to the days of the week
as follows: Sunday = 0, Monday =1, ... Saturday=6.  To find out the day of
the week for any date, calculate the day of the *year* for that date (using
"30 days hath ...").  For example Feb. 1 will be day 32 of the year.  Add
the number for the starting day of the week for Jan. 1, divide by 7 and
take the remainder.  That remainder will be the day of the week for that
date (there are some shortcuts).  I used this technique to build the
following tables -- 

		Non-leap years
	J F M A M J J A S O N D	    #	NY
       ------------------------------------
    Su  X                 X    	    2	Mo
    Mo        X     X		    2	Tu
    Tu                  X     X	    2	We
    We            X            	    1	Th
    Th    X X               X  	    3	Fr
    Fr                X        	    1	Sa
    Sa          X              	    1	Su

		  Leap years
 	J F M A M J J A S O N D	    #	NY
       ------------------------------------
    Su  X     X     X          	    3	Tu
    Mo               	X     X     2	We
    Tu            X            	    1	Th
    We      X               X  	    2	Fr
    Th    X           X        	    2	Sa
    Fr          X              	    1	Su
    Sa                    X    	    1	Mo

The rows in these two tables represent the days of the week on which the
year starts.  The first twelve columns represent the twelve months of the
year.  An "X" indicates that the thirteenth of that month on a year
starting on the given day of the week will occur on a Friday.  The column
headed "#" is the number of Friday the thirteenths which will occur in a
year starting on that day of the week.  The column headed "NY" gives the
day of the week which the Next Year will start on. 

				Topher