Re: Results of my test: Re: Friday 13th, try it yourself

Re: Results of my test: Re: Friday 13th, try it yourself

[James Gillespie]

    At the risk of prolonging this thread, there has been recent
discussion over how long a time period must be analysed to get a
correct distribution.  One value put forward was 4800 years.  While
this is very interesting in a theoretical way, what about the last
hundred years or so?  If Friday 13ths are unevenly spread through the
4800 years there must be local maxima and minima.  Are we currently in
an epoch in which there are a comparatively large number of Friday
13ths?

                Jim

Jim Gillespie      ,'_            "Happiness is being famous for your
jim@sbil.co.uk    / -.--.    ___   financial ability to indulge in
+44 171 721 2672 _~\  \__`--'_,-'  every form of excess"
                / /\\    `--'_-\\     -- Calvin
'94 ZZR600      \__/ `----' \__/  

Re: Results of my test: Re: Friday 13th, try it yourself

[Daan Sandee]

In article <bii3ezwnwlc.fsf@sbil.co.uk>, James Gillespie <jim.gillespie@sbil.co.uk> writes:
|>     At the risk of prolonging this thread, there has been recent
|> discussion over how long a time period must be analysed to get a
|> correct distribution.  One value put forward was 4800 years.  While
|> this is very interesting in a theoretical way, what about the last
|> hundred years or so?  If Friday 13ths are unevenly spread through the
|> 4800 years there must be local maxima and minima.  Are we currently in
|> an epoch in which there are a comparatively large number of Friday
|> 13ths?

Jim, this thread has already gone around the circle twice, and you are 
now starting a third iteration.  All this was thrashed out weeks ago.
The Gregorian calendar repeats the days of the week in a 400-year cycle
of 146,097 days or 20,871 weeks.  Of the 4,800 13ths in that 400-year
period, 688 are on a Friday, more than on any other day of the week.
This answers the original question, and all other answers are either
wrong or irrelevant.
Now can everyone go on to programming in their favorite language ?  And
can anyone remember who started this thread, so we can go back and
retroactively refuse him an account with Usenet access ?

Daan Sandee
Burlington, MA                                           sandee@think.com

Re: Results of my test: Re: Friday 13th, try it yourself

[Dr John Stockton]

In article <bii3ezwnwlc.fsf@sbil.co.uk> of Thu, 3 Oct 1996 11:58:07 in
comp.lang.pascal.misc, James Gillespie <jim.gillespie@sbil.co.uk> wrote:
>    At the risk of prolonging this thread, there has been recent
>discussion over how long a time period must be analysed to get a
>correct distribution.  One value put forward was 4800 years.  While
>this is very interesting in a theoretical way, what about the last
>hundred years or so?  If Friday 13ths are unevenly spread through the
>4800 years there must be local maxima and minima.  Are we currently in
>an epoch in which there are a comparatively large number of Friday
>13ths?
>
>                Jim
>
>Jim Gillespie      ,'_            "Happiness is being famous for your
>jim@sbil.co.uk    / -.--.    ___   financial ability to indulge in
>+44 171 721 2672 _~\  \__`--'_,-'  every form of excess"
>                / /\\    `--'_-\\     -- Calvin
>'94 ZZR600      \__/ `----' \__/  

No.  One seventh of 13ths fall on each day of the week, **BETWEEN** 1900
& 2100 AD.  The full Gregorian calendar repeats every 400 years, and a
repeat contains a slight excess if F13.  See URL below.  As I said
before.

Recommend you also read Son-of-RFC1036 sec 4.3.2 end re signature
separation, quoted in URL below +news-use.htm
-- 
John Stockton, Surrey, UK.  JRS@merlyn.demon.co.uk  Turnpike v1.12  MIME
    http://www.merlyn.demon.co.uk/

Re: Results of my test: Re: Friday 13th, try it yourself

[Paul Skoczylas]

James Gillespie wrote:
> 
>     At the risk of prolonging this thread, there has been recent
> discussion over how long a time period must be analysed to get a
> correct distribution.  One value put forward was 4800 years.

But if the calendar, as presently defined (whether that is the best
definition or not), repeats every four hundred years, why use anything
longer than that?  If you use 4800 yrs, the distribution will look
exactly like 400 yrs, but 12 times bigger.

Re: Friday 13th, try it yourself (was Language Wars..)

[Ken Pizzini]

In article <R.521pfp$kec@ns.ccsn.edu>,
Russell Mosemann <mose@ns.ccsn.edu> wrote:
>   I decided to write a script of my own for Solaris 2.4 and perl
>5.003 which calls cal for 1066 to 1996 and rips out the Fridays.  The
>following is the number of times a particular day of the month falls
>on a Friday.  The results are pretty evenly distributed, i.e. it is an
>Urban Legend.

Try again, avoiding years befor 1752.  The cal program on Solaris
uses the Julian calender for years before 1752, the Gregorian
calendar for years after, and the calendar that England and
her colonies used for 1752 itself.  Under the Julian calendar
the 13th of a month will be equidistributed among each of the
days of the week, but under the Gregorian calendar you will find
that some days fall on the 13th more frequently than others
over a 400 year cycle.  (Note that any pair of dates on the
Gregorian calendar that are exactly 400 years apart will
fall on the same day of the week.)

		--Ken Pizzini

Results of my test: Re: Friday 13th, try it yourself

[Lee Crites]

For the most part, I've ignored this friday the 13th thread.  However,
something someone said got my interest.  Basically the statement was that
the same date 400 years later would fall on the same day.  I thought I'd
check it out and see.  Unfortunately, it did not work on the dates I
checked. 

There was also another comment about having to stay after 1752.  So I
decided I could toss together a quick csh script to call cal for 400
years, strip out the Fridays, and use awk to summarize them into which
date happened most often -- if, in fact, any happened more often than
another. 

I *assume* the cal utility takes all of the funky leap-year triviality
into consideration.  If it doesn't, then my results are skewed.  I'm using
the assumption, though, that aix 4.1, which I have been told has had the
'year 2000' fix applied, would have a 'good' version of cal. 

In keeping with the 'show us your source' mindset, here's mine.  I've
tested this on a sun and an rs.  What I'm including is the rs/aix 4.1
version and output. 

This is the csh script that ran it all (No flames about me using csh will
be accepted; If you don't like csh, that's fine with me, please keep it to
yourself): 

#!/bin/csh -f

#
# get friday dates for 400 years
#
if (-e f13.out) then
  rm f13.out
endif

@ yr_base = 1752 # from Ken Pizzini
@ yr = 0

while ( $yr < 400 )

  @ yr ++
  @ year = $yr_base + $yr
  echo $year

  #
  # use cal to give me a calendar of the month in question, then
  # use cut to give me just the Fridays, tail to strip out the
  # cal header stuff, and awk to make sure we have valid numbers
  #
  @ month = 0
  while ( $month < 12 )
    @ month ++
    cal $month $year | \
      tail +2 | \
      cut -c21-22 | \
      awk '{x=int($0);if(x>0)print x}' >> f13.out
    end

  end

awk -f f13.awk f13.out > f13.rpt
cat f13.rpt

Just because it's there, here is a list of the first 20 entries in the
f13.out file (there were 20871 Fridays listed): 

5
12
19
26
2
9
16
23
2
9
16
23
30
6
13
20
27
4
11
18


This is the awk file used above:

BEGIN {
  cnt = 0
  x = 0
  for (x=1; x<32; x++) {
    dist[x] = 0
    }
}
{
  dist[$0]++
  cnt++
}
END {
  if (cnt==0) {
    printf("No values found\n")
  } else {
    printf("Summary of Friday dates for 400 years:\n")
    for (x=1; x<32; x++) {
      if (dist[x] > 0) {
        printf("%10d found %4d times\n", x, dist[x])
        }
      }
  }
}


And finally, here are the results of the run:

Summary of Friday dates for 400 years:
         1 found  687 times
         2 found  685 times
         3 found  685 times
         4 found  687 times
         5 found  684 times
         6 found  688 times
         7 found  684 times
         8 found  687 times
         9 found  685 times
        10 found  685 times
        11 found  687 times
        12 found  684 times
        13 found  688 times
        14 found  684 times
        15 found  687 times
        16 found  685 times
        17 found  685 times
        18 found  687 times
        19 found  684 times
        20 found  688 times
        21 found  684 times
        22 found  687 times
        23 found  685 times
        24 found  685 times
        25 found  687 times
        26 found  684 times
        27 found  688 times
        28 found  684 times
        29 found  643 times
        30 found  629 times
        31 found  399 times

If I'd made a wild guess of what the results would have been before I
started, I'd have come up with something similar to the above.  Uniform
distribution across all dates -- with diminished numbers from the 29th
through 31st. 

Realizing these results would not make the it's-not-uniform-distribution
group happy, I ran it again based upon 1800 instead of 1753, with exactly
the same results.  Since there will be those who want to analyze the cal
functionality, I've included the January calendar for the start of each
decade from 1760 through 2150 at the end of this message.  Knock yourself
out... 

I'm not stupid enough to believe this will settle the discussion
concerning the statistical nature of our calendar, but at least it's
something more concrete to work with.  And, as it is, I am satisfied with
the results. 

Lee Crites
Systems Consultant
Computer Mavericks
adonai@jump.net



       January 1760       
Sun Mon Tue Wed Thu Fri Sat  
         1   2   3   4   5
 6   7   8   9  10  11  12
13  14  15  16  17  18  19
20  21  22  23  24  25  26
27  28  29  30  31

       January 1770       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 1780       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 1790       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 1800       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 1810       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 1820       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 1830       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 1840       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 1850       
Sun Mon Tue Wed Thu Fri Sat  
         1   2   3   4   5
 6   7   8   9  10  11  12
13  14  15  16  17  18  19
20  21  22  23  24  25  26
27  28  29  30  31

       January 1860       
Sun Mon Tue Wed Thu Fri Sat  
 1   2   3   4   5   6   7
 8   9  10  11  12  13  14
15  16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31

       January 1870       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 1880       
Sun Mon Tue Wed Thu Fri Sat  
                 1   2   3
 4   5   6   7   8   9  10
11  12  13  14  15  16  17
18  19  20  21  22  23  24
25  26  27  28  29  30  31

       January 1890       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 1900       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 1910       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 1920       
Sun Mon Tue Wed Thu Fri Sat  
                 1   2   3
 4   5   6   7   8   9  10
11  12  13  14  15  16  17
18  19  20  21  22  23  24
25  26  27  28  29  30  31

       January 1930       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 1940       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 1950       
Sun Mon Tue Wed Thu Fri Sat  
 1   2   3   4   5   6   7
 8   9  10  11  12  13  14
15  16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31

       January 1960       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 1970       
Sun Mon Tue Wed Thu Fri Sat  
                 1   2   3
 4   5   6   7   8   9  10
11  12  13  14  15  16  17
18  19  20  21  22  23  24
25  26  27  28  29  30  31

       January 1980       
Sun Mon Tue Wed Thu Fri Sat  
         1   2   3   4   5
 6   7   8   9  10  11  12
13  14  15  16  17  18  19
20  21  22  23  24  25  26
27  28  29  30  31

       January 1990       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 2000       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 2010       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 2020       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 2030       
Sun Mon Tue Wed Thu Fri Sat  
         1   2   3   4   5
 6   7   8   9  10  11  12
13  14  15  16  17  18  19
20  21  22  23  24  25  26
27  28  29  30  31

       January 2040       
Sun Mon Tue Wed Thu Fri Sat  
 1   2   3   4   5   6   7
 8   9  10  11  12  13  14
15  16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31

       January 2050       
Sun Mon Tue Wed Thu Fri Sat  
                         1
 2   3   4   5   6   7   8
 9  10  11  12  13  14  15
16  17  18  19  20  21  22
23  24  25  26  27  28  29
30  31
       January 2060       
Sun Mon Tue Wed Thu Fri Sat  
                 1   2   3
 4   5   6   7   8   9  10
11  12  13  14  15  16  17
18  19  20  21  22  23  24
25  26  27  28  29  30  31

       January 2070       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 2080       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 2090       
Sun Mon Tue Wed Thu Fri Sat  
 1   2   3   4   5   6   7
 8   9  10  11  12  13  14
15  16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31

       January 2100       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 2110       
Sun Mon Tue Wed Thu Fri Sat  
             1   2   3   4
 5   6   7   8   9  10  11
12  13  14  15  16  17  18
19  20  21  22  23  24  25
26  27  28  29  30  31

       January 2120       
Sun Mon Tue Wed Thu Fri Sat  
     1   2   3   4   5   6
 7   8   9  10  11  12  13
14  15  16  17  18  19  20
21  22  23  24  25  26  27
28  29  30  31

       January 2130       
Sun Mon Tue Wed Thu Fri Sat  
 1   2   3   4   5   6   7
 8   9  10  11  12  13  14
15  16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31

       January 2140       
Sun Mon Tue Wed Thu Fri Sat  
                     1   2
 3   4   5   6   7   8   9
10  11  12  13  14  15  16
17  18  19  20  21  22  23
24  25  26  27  28  29  30
31
       January 2150       
Sun Mon Tue Wed Thu Fri Sat  
                 1   2   3
 4   5   6   7   8   9  10
11  12  13  14  15  16  17
18  19  20  21  22  23  24
25  26  27  28  29  30  31

Re: Results of my test: Re: Friday 13th, try it yourself

[William Clodius]

Lee Crites wrote:
> 
> For the most part, I've ignored this friday the 13th thread.  However,
> something someone said got my interest.  Basically the statement was that
> the same date 400 years later would fall on the same day.  I thought I'd
> check it out and see.  Unfortunately, it did not work on the dates I
> checked.
> 
<snip>
> @ yr = 0
> 
> while ( $yr < 400 )
>
>  @ yr ++

<snip>

If you want to compare the starting weekday of year 1 with with that 400
years later, I believe this should be

while ( $yr < 401 )

depending on your starting index yours gives either years 0, 1, 2, ...,
399 or years 1, 2, 3, ..., 400, while the above gives years 0, 1, 2,
..., 400 or years 1, 2, 3, ..., 401, so that you can compare year 1 with
401 or 0 with 400.

-- 

William B. Clodius		Phone: (505)-665-9370
Los Alamos National Laboratory	Email: wclodius@lanl.gov
Los Alamos, NM 87545

Re: Results of my test: Re: Friday 13th, try it yourself

[Dik T. Winter]

In article <Pine.SOL.3.91.960925162108.6568A-100000@serv1.jump.net> Lee Crites <adonai@jump.net> writes:
...
 > Summary of Friday dates for 400 years:
...
 > If I'd made a wild guess of what the results would have been before I
 > started, I'd have come up with something similar to the above.  Uniform
 > distribution across all dates -- with diminished numbers from the 29th
 > through 31st. 

Yup, it looks uniform.  But because these are exact figures, valid for
every period of 400 years, they are *not* uniform but biased in favour
of Friday 13 (and 6, 20 and 27).

 > Realizing these results would not make the it's-not-uniform-distribution
 > group happy, I ran it again based upon 1800 instead of 1753, with exactly
 > the same results.

Which ought to have shown you that the figures are exact for every period
of 400 years.  The situation is similar to a pseudo-random number generator
that repeats a sequence of 100 digits 0 and 1 with 49 occurrences of 0
and 51 of 1.  When you look at it without background information it looks
uniform, but because you know it repeats you know also that it is biased
in favour of 1 and so not uniform.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/

Re: Results of my test: Re: Friday 13th, try it yourself

[Dik T. Winter]

In article <52qpqt$1b3l@ilx018.iil.intel.com> Uri Raz <uraz@iil.intel.com> writes:
 >   Read sci.astro's FAQ
 >    http://astrosun.tn.cornell.edu/students/lazio/sci.astro.3.FAQ
 >   The four hundred years cycle is inaccurate, as following it would add three
 >   days to each 10,000 years, and thus the cycle does not repeat it self.

As the Gregorian calendar has not been changed by the sci.astro's FAQ the
cycle repeats itself.  It is possible of course that in the next hundred
years the calendar will be changed again, but currently we are living with
the Gregorian calendar.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/

Re: Results of my test: Re: Friday 13th, try it yourself

[Ken Pizzini]

In article <52qpqt$1b3l@ilx018.iil.intel.com>,
Uri Raz  <uraz@iil.intel.com> wrote:
>dik@cwi.nl (Dik T. Winter) wrote:
>> Which ought to have shown you that the figures are exact for every period
>> of 400 years.  The situation is similar to a pseudo-random number generator
>> that repeats a sequence of 100 digits 0 and 1 with 49 occurrences of 0
>> and 51 of 1.  When you look at it without background information it looks
>> uniform, but because you know it repeats you know also that it is biased
>> in favour of 1 and so not uniform.
>>
>  Read sci.astro's FAQ
>   http://astrosun.tn.cornell.edu/students/lazio/sci.astro.3.FAQ
>  The four hundred years cycle is inaccurate, as following it would add three
>  days to each 10,000 years, and thus the cycle does not repeat it self.

By our calendar, *as it is currently defined*, there is a 400 year
cycle.  I';ll even quote the sci.astro FAQ:

|The error in the Gregorian calendar will build up to a full day in
|roughly 3000 years, by which time another reform will be necessary.
|Various schemes have been proposed, some taking account of the changing
|lengths of the day and/or the tropical year, but none has been
|internationally recognized.  Leaving a reform to our descendants seems
|reasonable, since there is no obvious need to make a correction now.

*When* the next calendar reform happens, the 400-year cycle will
be altered.  But from the adoption of the Gregorian calendar
(the year varying with the political unit; 1753 was the first
full year for England and her colonies) until such time as the
eventual adjustment is made, the 400 cycle will exist.  And who
knows?  Maybe our descendants won't care about maintaining some
preconceived notion about keeping celestial events and the
calendar in sync and the cycle will never be broken.

		--Ken Pizzini

Re: Results of my test: Re: Friday 13th, try it yourself

[Dr John Stockton]

In article <Pine.SOL.3.91.960925162108.6568A-100000@serv1.jump.net> of
Wed, 25 Sep 1996 16:25:19 in comp.lang.pascal.misc, Lee Crites
<adonai@jump.net> wrote:
>
>For the most part, I've ignored this friday the 13th thread.  However,
>something someone said got my interest.  Basically the statement was that
>the same date 400 years later would fall on the same day.  I thought I'd
>check it out and see.  Unfortunately, it did not work on the dates I
>checked. 

SNIP


Too complex.  Just consider 400 years
        400 * 365       Taking all years as ordinary
            + 100       but every fourth is leap
            -   4       apart from the centuries
            +   1       except for every fourth.
        =========
           146097 ;
   * 1/7 => 20871.0 = integer weeks in 400 years.

The calendar therefore repeats every 400 years.

This calculation can be done in one's head, without even a calculator.

In 400 years there are 4800 months each containing one 13th.  Some are
Sunday, some ... ...Saturday; but 4800/7 is not an integer, so the 13ths
cannot be evenly distributed among the days of the week.

I think it is now necessary to do a little real work; there are 14 types
of year (Leap or not, starting Sun .. Sat), and the number of each type
in 400 years can be counted; and each type contributes a certain number
of 13ths.

It might be easier to consider the year as starting on March 1st; there
are now only 7 types of year for 13th-counting.
-- 
John Stockton, Surrey, UK.  JRS@merlyn.demon.co.uk  Turnpike v1.12  MIME
    http://www.merlyn.demon.co.uk/

Re: Results of my test: Re: Friday 13th, try it yourself

[Dr John Stockton]

In article <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net> of
Thu, 26 Sep 1996 13:14:53 in comp.lang.pascal.misc, Lee Crites
<adonai@jump.net> wrote:

>As they say, a little knowledge is a dangerous thing.  

Y

I make no comment on the script,

>This is the csh script that ran it:

but your results, repeated below, are correct, by impeccable authority.

>Summary of days which the 13th happen on:
>
>      4800 total items
>
>       Sun found  687 times
>       Mon found  685 times
>       Tue found  685 times
>       Wed found  687 times
>       Thu found  684 times
>       Fri found  688 times
>       Sat found  684 times
>     error found    0 times

-- 
John Stockton, Surrey, UK.  JRS@merlyn.demon.co.uk  Turnpike v1.12  MIME
    http://www.merlyn.demon.co.uk/

Re: Results of my test: Re: Friday 13th, try it yourself

[Lee Crites]

As they say, a little knowledge is a dangerous thing.  I guess I went out 
of my way to prove something nobody cared about.  I got a message telling 
me I was proving the wrong thing.  The discussion was not "how frequently 
does each date happen on a Friday," but was "how frequently is the 13th a 
Friday."  The argument, as I understand it, is that the 13th is a Friday 
more often than some other day because of some statistical glitch in the 
calendar.

My initial proof showed that each date happened on each day of the week 
basically as often as any other.  I would think that would be enough to 
close the topic.  However, I was requested to test it the other way -- 
tell me how often the 13th happens on each day of the week.  Fine.  I 
went in and changed my scripts to do so.  I've included them here just as 
I did before.

However, the results are no different.  Basically, the 13th falls 
uniformily across each day of the week.

Now the same disclaimer still applies.  I'm using aix 4.1's cal utility to
give me the calendar data.  If IF is wrong, then I am also wrong.  Before
you stomp on the data again, though, you'd better be able to tell me which
of the calendar entries I sent out earlier is in error.

If you can't find an error in my scripts below, or an error in the
calendar entries I sent out earlier, then it is settled.  There is a
uniform distribution of dates across the day of the week AND a uniform
distribution of days of the week across dates. 


Lee Crites

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

This is the csh script that ran it:

#!/bin/csh -f

#
# get 13th dates for 400 years
#
if (-e w13.out) then
  rm w13.out
endif

#
# for those who can't follow the logic, yr is going from
# 0 to 399 at the while statement, incremented (so it will
# be 1 to 400) BEFORE it is used, then ADDED to yr_base,
# which will then go from 1753 to 2152
#
@ yr_base = 1752 # from Ken Pizzini
@ yr = 0

# we will be going from 0 to 399 at the while statement
while ( $yr < 400 )

  # increment the yr counter, so it will go from 1 to 400 here
  @ yr ++

  # add the yr counter to the yr_base
  @ year = $yr_base + $yr

  # show me the year we are working with
  echo $year

  # initialize month counter
  @ month = 0

  # again, we are going from 0 to 11 at the while statement
  while ( $month < 12 )

    # increment the month counter, so it will go from 1 to 12 here
    @ month ++

    # get the calendar for the month, strip out the line with 13 in it
    cal $month $year | grep "13" >> w13.out

    end

  end

# strip out invalid entries -- e.g. January 1913, March 2130, etc
grep -iv "y" w13.out | grep -iv "a" | grep -iv "e" | \
  awk -f w13.awk > w13.rpt
cat w13.rpt

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

Just because it's there, here is a list of the first 20 entries in
the w13.out:

 7   8   9  10  11  12  13
11  12  13  14  15  16  17
11  12  13  14  15  16  17
 8   9  10  11  12  13  14
13  14  15  16  17  18  19
10  11  12  13  14  15  16
 8   9  10  11  12  13  14
12  13  14  15  16  17  18
 9  10  11  12  13  14  15
 7   8   9  10  11  12  13
11  12  13  14  15  16  17
 9  10  11  12  13  14  15
13  14  15  16  17  18  19
10  11  12  13  14  15  16
10  11  12  13  14  15  16
 7   8   9  10  11  12  13
12  13  14  15  16  17  18
 9  10  11  12  13  14  15
 7   8   9  10  11  12  13
11  12  13  14  15  16  17

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

This is the awk file used above:

BEGIN {
  cnt = 0
  x = 0
  for (x=1; x<9; x++) {
    cntr[x] = 0
    }
}
{
  cnt++
  if ($1 == 13) {
    cntr[1]++
    continue
    }
  if ($2 == 13) {
    cntr[2]++
    continue
    }
  if ($3 == 13) {
    cntr[3]++
    continue
    }
  if ($4 == 13) {
    cntr[4]++
    continue
    }
  if ($5 == 13) {
    cntr[5]++
    continue
    }
  if ($6 == 13) {
    cntr[6]++
    continue
    }
  if ($7 == 13) {
    cntr[7]++
    continue
    }
  cntr[8]++
}
END {
  printf("Summary of days which the 13th happen on:\n")
  printf("\n")
  printf("%10s total items\n", cnt)
  printf("\n")
  printf("%10s found %4d times\n", "Sun", cntr[1])
  printf("%10s found %4d times\n", "Mon", cntr[2])
  printf("%10s found %4d times\n", "Tue", cntr[3])
  printf("%10s found %4d times\n", "Wed", cntr[4])
  printf("%10s found %4d times\n", "Thu", cntr[5])
  printf("%10s found %4d times\n", "Fri", cntr[6])
  printf("%10s found %4d times\n", "Sat", cntr[7])
  printf("%10s found %4d times\n", "error", cntr[8])
}

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

And finally, here are the results of the run:

Summary of days which the 13th happen on:

      4800 total items

       Sun found  687 times
       Mon found  685 times
       Tue found  685 times
       Wed found  687 times
       Thu found  684 times
       Fri found  688 times
       Sat found  684 times
     error found    0 times

Re: Results of my test: Re: Friday 13th, try it yourself

[John Winters]

In article <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net>,
Lee Crites  <adonai@jump.net> wrote:
>
[snip]
>However, the results are no different.  Basically, the 13th falls 
>uniformily across each day of the week.
>
[snip]
>If you can't find an error in my scripts below, or an error in the
>calendar entries I sent out earlier, then it is settled.  There is a
>uniform distribution of dates across the day of the week AND a uniform
>distribution of days of the week across dates. 
[snip]
>And finally, here are the results of the run:
>
>Summary of days which the 13th happen on:
>
>      4800 total items
>
>       Sun found  687 times
>       Mon found  685 times
>       Tue found  685 times
>       Wed found  687 times
>       Thu found  684 times
>       Fri found  688 times
>       Sat found  684 times
>     error found    0 times

What a stunning bit of reasoning!  "I want to conclude that there is
no unevenness in the distribution.  My results clearly demonstrate that
there *is*.  Therefore I will assert that my required result is
proven."

Don't ring us, we'll ring you.

John
(Follow ups set appropriately.)
-- 
John Winters.  Wallingford, Oxon, England.

Re: Results of my test: Re: Friday 13th, try it yourself

[Daan Sandee]

In article <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net>, Lee Crites <adonai@jump.net> writes:

[repeats attempts already made by others and posted here ad nauseam]

|> However, the results are no different.  Basically, the 13th falls 
|> uniformily across each day of the week.

As your table shows, the 13th is a Friday more often that any other day
of the week.  Which was the original claim.  The claim was not "much
more often".  The numbers you have calculated are exact and repeatable
(others have produced them with totally different programs.)  You can
call these numbers "basically uniform" if you like, but the claim that
Friday occurs more often is correct.

|> And finally, here are the results of the run:
|> 
|> Summary of days which the 13th happen on:
|> 
|>       4800 total items
|> 
|>        Sun found  687 times
|>        Mon found  685 times
|>        Tue found  685 times
|>        Wed found  687 times
|>        Thu found  684 times
|>        Fri found  688 times
|>        Sat found  684 times

(Anyone wanting to repeat the attempt should remember to use the
Gregorian calendar for 400 consecutive years.  That is a necessary
and sufficient requirement.  If you use Unix 'cal', start after 1752.)

Daan Sandee
Burlington, MA                                           sandee@think.com

Re: Results of my test: Re: Friday 13th, try it yourself

[Jeff Drummond]

In article <52ej16$ite@bone.think.com>, sandee@Think.COM (Daan Sandee) writes:
> In article <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net>, Lee Crites <adonai@jump.net> writes:
>
> [repeats attempts already made by others and posted here ad nauseam]
>
> |> However, the results are no different.  Basically, the 13th falls 
> |> uniformily across each day of the week.
>
> As your table shows, the 13th is a Friday more often that any other day
> of the week.  Which was the original claim.  The claim was not "much
> more often".  The numbers you have calculated are exact and repeatable
> (others have produced them with totally different programs.)  You can
> call these numbers "basically uniform" if you like, but the claim that
> Friday occurs more often is correct.

Yes, but is this linguistic nit-picking or statistical nit-picking?    :-)

-Jeff    jjd@cray.com    .02% is close enough for me...
--
Kitman's Law: Pure drivel tends to drive out ordinary drivel.

Re: Results of my test: Re: Friday 13th, try it yourself

[Ray Dunn]

In referenced article, Jeff Drummond says...
>-Jeff    jjd@cray.com    .02% is close enough for me...
>--
>Kitman's Law: Pure drivel tends to drive out ordinary drivel.

That's true enough, Jeff.  I tell you what, send me a million dollars, 
and I'll send you back $999,800.  Don't have a million dollars?  OK, 
let's keep it simple - just you send me $200.  Close enough, eh?
-- 
Ray Dunn (opinions are my own) | Phone: (514) 938 9050
Montreal                       | Phax : (514) 938 5225
ray@ultimate-tech.com          | Home : (514) 630 3749

Re: Results of my test: Re: Friday 13th, try it yourself

[Adam Beneschan]

Lee Crites <adonai@jump.net> writes:

 >As they say, a little knowledge is a dangerous thing.  I guess I went out 
 >of my way to prove something nobody cared about.  I got a message telling 
 >me I was proving the wrong thing.  The discussion was not "how frequently 
 >does each date happen on a Friday," but was "how frequently is the 13th a 
 >Friday."  The argument, as I understand it, is that the 13th is a Friday 
 >more often than some other day because of some statistical glitch in the 
 >calendar.
 >
 >My initial proof showed that each date happened on each day of the week 
 >basically as often as any other.  I would think that would be enough to 
 >close the topic.  However, I was requested to test it the other way -- 
 >tell me how often the 13th happens on each day of the week.  Fine.  I 
 >went in and changed my scripts to do so.  I've included them here just as 
 >I did before.
 >
 >However, the results are no different.  Basically, the 13th falls 
 >uniformily across each day of the week.
 
Uh, your own results prove that the 13th falls on Friday more often
than on other days of the week.  Yes, the numbers are "basically" the
same, but no one has been arguing that there's a big difference, have
they?  No one has claimed that the 13th is a Friday 25% more often
than a Monday, or anything like that.

Next time the Lakers beat the Bullets 104-103 or something, are you
going to say that they should score it as a tie in the standings,
because the two teams got basically the same number of points?  :-)
:-) :-)

                                -- Adam


[snip] 
 >And finally, here are the results of the run:
 >
 >Summary of days which the 13th happen on:
 >
 >      4800 total items
 >
 >       Sun found  687 times
 >       Mon found  685 times
 >       Tue found  685 times
 >       Wed found  687 times
 >       Thu found  684 times
 >       Fri found  688 times
 >       Sat found  684 times
 >     error found    0 times

Re: Results of my test: Re: Friday 13th, try it yourself

[Glen Clark]

Adam Beneschan wrote:
> 
> Lee Crites <adonai@jump.net> writes:
> 
>  >I got a message telling
>  >me I was proving the wrong thing.  The discussion was not "how frequently
>  >does each date happen on a Friday," but was "how frequently is the 13th a
>  >Friday."  
> 
> Uh, your own results prove that the 13th falls on Friday more often
> than on other days of the week.  No one has claimed that the 13th is a
> Friday 25% more often
> than a Monday, or anything like that.
 

I am baffled at the amount of bandwidth that has been consumed
arguing about how many Friday the 13ths fit on the head of a
pin. In the news business, they talk about whether a story has
"legs". If it has legs, it means the public wants more of it.
This discussion about Friday the 13th has incredible legs. If
I remember right, it started out three titles ago under the 
heading of Publishing Scholarly Works on the Net several weeks
back. And it's cross-posted to no fewer than eight newsgroups.

Is this a spoof?

-- 
Glen Clark
glen@clarkcom.com

Re: Results of my test: Re: Friday 13th, try it yourself

[CHI Research, Inc.]

In <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net> Lee Crites
<adonai@jump.net> writes: 
>
>

[snip]

>
>However, the results are no different.  Basically, the 13th falls 
>uniformily across each day of the week.
>
>       Sun found  687 times
>       Mon found  685 times
>       Tue found  685 times
>       Wed found  687 times
>       Thu found  684 times
>       Fri found  688 times
>       Sat found  684 times
>     error found    0 times
>
>

Something is really wrong here.  The results show the opposite of the
poster's conclusions.  No?

Dom Olivastro

Re: Results of my test: Re: Friday 13th, try it yourself

[Lee Crites]

> >However, the results are no different.  Basically, the 13th falls 
> >uniformily across each day of the week.
> >
> >       Sun found  687 times
> >       Mon found  685 times
> >       Tue found  685 times
> >       Wed found  687 times
> >       Thu found  684 times
> >       Fri found  688 times
> >       Sat found  684 times
> >     error found    0 times
> 
> Something is really wrong here.  The results show the opposite of the
> poster's conclusions.  No?

No.

It's all fine and good to try to be precise.  But there comes a time when
overprecision is uncalled for.  This is one of them.  "Basically, the 13th
falls uniformally across each day of the week" is an accurate statement. 
Not only is something *not* wrong, it is not 'really wrong.'

Sorry guys, but I'd forgotten how truly anal some of these discussions can
become. 

I find it amazing that I'd be taken to task for saying that "basically"
these results show a uniform distribution -- I figured anyone with 
sense enough to read the message in the first place could understand 
the term 'basically.'  I guess I am wrong on that -- so I guess there 
WAS something 'really wrong' with my original message!

It's my guess that if everyone knew there was only one more from the
beginning, this discussion would have probably never happened!  In fact, 
I guess if ANYONE knew the above distribution, this discussion wouldn't 
have happened.

And for those dozen or more people who tried to point out some 'obvious'
error (like the fact I set the initial date to 1752 or checked for < 400),
go back through the scripts with as fine a tooth comb as you are using in
interpreting the data, and then tell me what was wrong. 

After all, if you are going to be anal, do it right.  (including looking
up that term so you don't show more stupidity by trying to say anal=ass)

Lee

Re: Results of my test: Re: Friday 13th, try it yourself

[John Winters]

In article <Pine.SOL.3.91.960927175816.8469B-100000@serv1.jump.net>,
Lee Crites  <adonai@jump.net> wrote:
>> >However, the results are no different.  Basically, the 13th falls 
>> >uniformily across each day of the week.
>> >
>> >       Sun found  687 times
>> >       Mon found  685 times
>> >       Tue found  685 times
>> >       Wed found  687 times
>> >       Thu found  684 times
>> >       Fri found  688 times
>> >       Sat found  684 times
>> >     error found    0 times
>> 
>> Something is really wrong here.  The results show the opposite of the
>> poster's conclusions.  No?
>
>No.

Yes.

>
>It's all fine and good to try to be precise.  But there comes a time when
>overprecision is uncalled for.

Presumably your definition of "overprecision" is "pointing out that
I'm wrong".  You contradicted a perfectly correct statement, now you
try to salve your ego by saying you weren't very wrong.  The original
statement was "only just" correct.

>Sorry guys, but I'd forgotten how truly anal some of these discussions can
>become. 

Ah.  New definition of "anal" too.  (Why is anal becoming such a
fashionable insult these days?)  Every time anyone makes him or herself
look a fool on a newgroup, he/she ends up calling the opposition "anal".

Pathetic.

John

-- 
John Winters.  Wallingford, Oxon, England.

Re: Results of my test: Re: Friday 13th, try it yourself

[Adam Beneschan]

Lee Crites <adonai@jump.net> writes:

 >I find it amazing that I'd be taken to task for saying that "basically"
 >these results show a uniform distribution -- I figured anyone with 
 >sense enough to read the message in the first place could understand 
 >the term 'basically.'  I guess I am wrong on that -- so I guess there 
 >WAS something 'really wrong' with my original message!
 >
 >It's my guess that if everyone knew there was only one more from the
 >beginning, this discussion would have probably never happened!  In fact, 
 >I guess if ANYONE knew the above distribution, this discussion wouldn't 
 >have happened.

The problem here is that you've completely misunderstood the whole
discussion.  The person who originally brought this up said simply
that the 13th occurs on a Friday more often than any other day.  He
didn't say "a lot more often" or "significantly more often", just
"more often", which is of course a true statement.  The objections to
this statement came at first from people who believed that this was
mathematically impossible (until they figured out that the pattern
repeated after 400 years, not 2800).  NOBODY was arguing that there
was a difference of more than one, and nobody except you understood
the argument to be about that.  So your "guess" in the second
paragraph I quoted above is incorrect.  Yes, the discussion is
definitely about something that is completely irrelevant to anyone's
life, but that happens a lot on USENET.

                                -- Adam

Re: Results of my test: Re: Friday 13th, try it yourself

[Mike McCarty]

In article <52hb32$ns5@sjx-ixn3.ix.netcom.com>,
CHI Research, Inc.  <chirsrch@ix.netcom.com> wrote:
)In <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net> Lee Crites
)<adonai@jump.net> writes: 
)>
)>
)
)[snip]
)
)>
)>However, the results are no different.  Basically, the 13th falls 
)>uniformily across each day of the week.
)>
)>       Sun found  687 times
)>       Mon found  685 times
)>       Tue found  685 times
)>       Wed found  687 times
)>       Thu found  684 times
)>       Fri found  688 times
)>       Sat found  684 times
)>     error found    0 times
)>
)>
)
)Something is really wrong here.  The results show the opposite of the
)poster's conclusions.  No?
)
)Dom Olivastro


NO! They show remarkable agreement with a constant distribution with the
expected value 685.7 indeed.

Mik
-- 
----
char *p="char *p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}

I don't speak for DSC.         <- They make me say that.

Re: Results of my test: Re: Friday 13th, try it yourself

[Lee Crites]

On Tue, 1 Oct 1996, John Harper wrote:

> In article <Pine.SOL.3.91.960926130011.17641E-100000@serv1.jump.net> you write:
> >
> >However, the results are no different.  Basically, the 13th falls 
> >uniformily across each day of the week.
> >
> >Summary of days which the 13th happen on:
> >
> >      4800 total items
> >
> >       Sun found  687 times
> >       Mon found  685 times
> >       Tue found  685 times
> >       Wed found  687 times
> >       Thu found  684 times
> >       Fri found  688 times
> >       Sat found  684 times
> >     error found    0 times
> >
> Your claim was that the distribution was uniform. Other people claimed
> that the 13th was a Friday most often. You have just proved the other
> people were right. 688 really is bigger than 684, 685 or 687. (You did
> not claim that the distribution was nearly uniform; the other people
> did not claim that the 13th was a Friday very much more often.)  

Yes I *did* claim it was 'nearly uniform.'

That is what "Basically, this is a uniform distribution" means.  I even
admitted the numbers showed what they show -- that Friday happened more
often, but that "basically" they are the same. 

And they are.

If your mother was 687 mile walk one way and your spouse`s mother was 688
mile walk the other way, they'd be "basically as far apart."  In fact, if
*I* tried to fixate on the fact that you'd have to walk one more mile to
your spouses mother, you'd think I was as nuts as I think the several of
you are that are trying to tell *ME* how stupid *I* am for saying they are
"basically" the same. 

Now, I'll say again, these numbers are "basically" the same.  There's no 
real statistical slant towards Friday the 13th.  That 10 to 15 
generations of your children will pass before there is one more Friday 
the 13th than there was Sunday the 13th, notwithstanding.

The numbers show there to be exactly one more Friday the 13th than any 
other day.  This is fine.  In fact, for *any* 400 year time period (after 
1752, that is), this exact same set of results happen.  I admit, as I did 
up front, there is one more Friday.

Now, can you guys give it a rest?

Lee