language wars (results 13 September) last posting

language wars (results 13 September) last posting

[Roy Gardiner]

The Language Preference Grid (Friday 13th September 1996)
               1   2   3   4
|------------|---|---|---|---|
| Ada        | 17| 3 | 1 | 0 |
| apl        | 9 | 1 | 1 | 1 |
| C          | 9 | 14| 7 | 6 |
| perl       | 7 | 4 | 2 | 2 |
| C++        | 4 | 5 | 2 | 3 |
| Rexx       | 4 | 1 | 3 | 0 |
| smalltalk  | 4 | 0 | 1 | 0 |
| Ada-95     | 4 | 0 | 0 | 0 |
| pascal     | 3 | 16| 7 | 9 |
| PL/I       | 2 | 5 | 1 | 4 |
| fortran    | 2 | 3 | 4 | 7 | (no level specified)
| J          | 2 | 1 | 2 | 0 |
| fortran-90 | 2 | 1 | 0 | 0 |
| python     | 2 | 0 | 1 | 0 |
| Algol 68   | 2 | 0 | 0 | 0 |
| icon       | 1 | 2 | 0 | 2 |
| scheme     | 1 | 1 | 2 | 0 |
| Assembler  | 1 | 1 | 1 | 6 | (type not stated)
| ObjectRexx | 1 | 1 | 0 | 0 |
| fortran-77 | 1 | 1 | 0 | 1 |
| Ada-83     | 1 | 1 | 0 | 0 |
| VB         | 1 | 1 | 2 | 1 |
| modula-2   | 1 | 0 | 1 | 0 |
| turing     | 1 | 0 | 0 | 0 |
| Forth      | 1 | 0 | 0 | 0 |
|------------|---|---|---|---|
| prolog     | 0 | 2 | 2 | 0 |
| awk        | 0 | 2 | 0 | 1 |
| SNOBOL     | 0 | 1 | 0 | 1 |
| lisp       | 0 | 1 | 3 | 2 |
| bourne shell 0 | 1 | 0 | 1 |
| modula-3   | 0 | 1 | 0 | 1 |
| modula     | 0 | 1 | 0 | 2 |
| X86 BAL    | 0 | 1 | 1 | 2 |
| ML         | 0 | 1 | 0 | 0 | (is this the same as ML/1?)
| MATLAB     | 0 | 1 | 0 | 0 |
| Spitbol    | 0 | 1 | 0 | 0 |
| cybil      | 0 | 1 | 0 | 0 |
| cms pipelines  | 1 | 0 | 0 |
| bertrand   | 0 | 1 | 0 | 0 |
|------------|---|---|---|---|
| X80 BAL    | 0 | 0 | 2 | 0 |
| ML/1       | 0 | 0 | 1 | 0 |
| BASIC      | 0 | 0 | 2 | 1 |
| orwell     | 0 | 0 | 1 | 0 |
| Bliss      | 0 | 0 | 1 | 0 |
| Pick basic | 0 | 0 | 2 | 0 |
| NetRexx    | 0 | 0 | 1 | 0 |
| simula     | 0 | 0 | 1 | 0 |
| haskel     | 0 | 0 | 1 | 0 |
| algol-60   | 0 | 0 | 1 | 0 |
| COBOL      | 0 | 0 | 1 | 2 |
| tcl/tk     | 0 | 0 | 1 | 0 |
| java       | 0 | 0 | 1 | 1 |
| korn shell | 0 | 0 | 1 | 0 |
| HyperTalk  | 0 | 0 | 1 | 0 |
|------------|---|---|---|---|
| postScript | 0 | 0 | 1 | 2 |
| IDL        | 0 | 0 | 0 | 1 |
| Scan       | 0 | 0 | 0 | 1 |
| KSH        | 0 | 0 | 0 | 1 |
| occam      | 0 | 0 | 0 | 1 |
| ASM /360   | 0 | 0 | 0 | 1 |
| S+         | 0 | 0 | 0 | 1 |
| Clipper    | 0 | 0 | 0 | 1 |
| MC68009ASM | 0 | 0 | 0 | 1 |
| SETL       | 0 | 0 | 0 | 1 |
| DCL        | 0 | 0 | 0 | 1 |
| NewtonScript 0 | 0 | 0 | 1 |

96 responses in all.

One person voted for a language they invented; I could not disallow it 
because it was not their first language

I don't suppose much can be concluded. What surprised me was:

1) How cleanly Ada (not ada, as one correspondent corrected me) won it; 
not only by the number of 1st place votes (especially if you include 
dialects - votes for Ada95 and Ada83 were NOT included in the Ada list), 
but by how few votes were for 2nd or lower place.
2) What an incredible variety of languages are out there.

Some people voted (unprompted) for least favourite:

The Language (least favourite) Grid 
               1   2   3   4
|------------|---|---|---|---|
| C++        | 3 | 0 | 0 | 0 |
| C          | 2 | 0 | 0 | 0 |
| VB         | 1 | 0 | 0 | 0 |
| BASIC      | 1 | 0 | 0 | 0 |
| COBOL      | 1 | 0 | 0 | 0 |
| pascal     | 0 | 1 | 0 | 0 |
| Forth      | 0 | 1 | 0 | 0 |
| X86 BAL    | 0 | 0 | 1 | 0 |

and gave little comments.

-- I try to stay above C level,  I get C sick.

No more votes, please. Interesting comments to newsgroup(s).

Roy Gardiner

Re: language wars (results 13 September) last posting

[William Clodius]

As always it is difficult to make sense of such an evaluation. Such
biases are inevitable, but note the following:

1.  The voters are selected only from that set of people with an
interest in and access to internet language news groups in the summer.

2.  The voters are selected only from those interested in a few of the
more popular newsgroups, i.e., no comp.lang.c++, comp.lang.forth,
comp.lang.java, comp.lang.cobol, comp.lang.functional, comp.lang.lisp,
etc.  Votes for such languages are probably more meaningful than votes
for other languages. I suspect that a posting to comp.lang.c++, for
example, would have greatly increased the number of C++ votes, similarly
for comp.lang.java.

3.  No postings to the moderated newsgroups, which tend to attract more
knowledgeable posters.

4.  The disallowal of first languages implies, at least in the US,
reduced votes for Basic, Pascal, C, and Fortran which may bias results
in Ada's favor.

5.  There is no way to weight the voter's experience with a variety of
languages.

6.  There is no way to weight the voter's degree of preference.

I suspect that ML stands for SML (Standard Meta-Language), but it is
unclear whether IDL stands for the Interface Definition Language or the
Interactive Data Language.

-- 

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

Re: language wars (results 13 September) last posting

[Peter Seebach]

In article <323993D5.41C6@lanl.gov>,
William Clodius  <wclodius@lanl.gov> wrote:
>3.  No postings to the moderated newsgroups, which tend to attract more
>knowledgeable posters.

And we didn't get a submission, at least in clcm.  (Although I'd probably have
bounced it as a troll.)

Maybe it's about time for comp.lang.advocacy?

>4.  The disallowal of first languages implies, at least in the US,
>reduced votes for Basic, Pascal, C, and Fortran which may bias results
>in Ada's favor.

It also prevents people like me, who have no real memory of the order in which
we learned things, from answering.  It's also ill defined; does the fact that
I used to type "rogue" when I was about 9 years old mean Bourne shell was my
first language?

>5.  There is no way to weight the voter's experience with a variety of
>languages.

Certainly.  Would my failure to rank Ada be because it's not a language I
*would* like, or because GNAT doesn't support NetBSD/68k yet?

>6.  There is no way to weight the voter's degree of preference.

Or degree of bias.  I'm on XJ311.  Does this mean I'm biased towards C?  (Or
against it, for that matter.)

I mean, all we can really say is the only reason that TECO macros weren't the
winner is that no one has any respect for *REAL* programming any more.

-s
-- 
Peter Seebach - seebs@solon.com - Copyright 1996 - http://www.solon.com/~seebs
Unix/C Wizard - send mail for help, or send money for consulting!
The *other* C FAQ, the hacker FAQ, et al.  See web page above.
Unsolicited email (junk mail and ads) is unwelcome, and will be billed for.

Re: language wars (results 13 September) last posting

[Robert Dewar]

Reposting article removed by rogue canceller.

Peter mentioned

"Certainly.  Would my failure to rank Ada be because it's not a language I
*would* like, or because GNAT doesn't support NetBSD/68k yet?"

Please note that it would be quite straightforward to port GNAT to 
NetBSD/68k, so if anyone actually wants such a port, the unavailability
of Ada 95 for this platform should not stand in their way. It is however
fairly unlikely that this port will appear by magic, unless some 
NetBSD enthusiast out there contributes the port!

Re: language wars (results 13 September) last posting

[Robert Dewar]

Peter mentioned

"Certainly.  Would my failure to rank Ada be because it's not a language I
*would* like, or because GNAT doesn't support NetBSD/68k yet?"

Please note that it would be quite straightforward to port GNAT to 
NetBSD/68k, so if anyone actually wants such a port, the unavailability
of Ada 95 for this platform should not stand in their way. It is however
fairly unlikely that this port will appear by magic, unless some 
NetBSD enthusiast out there contributes the port!

Re: language wars (results 13 September) last posting

[Robert Fahey]

In article <51c6df$c23@solutions.solon.com>, Peter Seebach
<seebs@solutions.solon.com> writes

>Maybe it's about time for comp.lang.advocacy?
Quite possibly. Ah, it'd be fun to flame a few BASIC and C++ people from
time to time - all my mates use Pascal and think it is great anyway
(most of em migrated from C++) so there is no scope for a good argument
;-)

>>4.  The disallowal of first languages implies, at least in the US,
>>reduced votes for Basic, Pascal, C, and Fortran which may bias results
>>in Ada's favor.
Exactly my view. After all, who uses Ada seriously? Anyone? Okay, the
odd conservationist (odd being the meaningful word) but apart from that?

>>5.  There is no way to weight the voter's experience with a variety of
>>languages.
>
>Certainly.  Would my failure to rank Ada be because it's not a language I
>*would* like, or because GNAT doesn't support NetBSD/68k yet?
Similarly, did I not rank Modula-2 because I think its crap or because I
have only used it briefly?

>I mean, all we can really say is the only reason that TECO macros weren't the
>winner is that no one has any respect for *REAL* programming any more.
Hah, _real_ programming? Well, for plain stupid programming Forth takes
first prize, but for _real_ programming try doing a 3D game/demo in pure
80x86 asm!
>
>-s

Ciao,
Robert
=======================================================================
# Robert Fahey               |    Reality is for those                #
# robert@fbs1.demon.co.uk    |       who can't handle QUAKE           #
# --------------------------------------------------------------------#
# http://KOLA.DCU.IE/mlstrm  |         ALL DONE. BYE BYE.             #
=======================================================================

Re: language wars (results 13 September) last posting

[James Giles]

> > [...]
> > Skeptics are invited to write a program to do the calculation for
> > themselves.
> 
> Assuming that *you* have done so, please have the courtesy to run it
> 2800 years and note that the 13th is equidistributed in weekdays.
> Then you can come back and apologise.  You have to run it more than
> 400 years because you have to go through a complete cycle of exceptions
> to the century rule.

I find that I'm the one to apologise.  And i do.

The issue that confused me was the irrelevant statement the 12
wasn't divisible by 7.  That has nothing to do with it.  The issue
is entirely a matter of what day of the week a year begins on.
During the century, the days are equidistributed (and will be over
this next century change as well).  But, because of the 400 year
rule, 4 centuries *is* commensurate with 7 days.  This means that
centuries begin on one of four different days of the week: Sat,
Mon., Wed., or Fri..  That asymmetry is sufficient to distort
the distribution of days for 13ths of months.

J. Giles
Ricercar Software

Re: language wars (results 13 September) last posting

[Norman H. Cohen]

Andrew Gierth wrote:

> Useless (but true) factoid:
> 
> The 13th day of the month is more often Friday than any other day of the
> week.

I apologize for the off-topic posting (especially when it 
is cross-posted to so many newsgroups, and thus off so 
many topics at once), but it should be pointed out, 
before this becomes an urban legend, that this "factoid"
is patently false!

In any 2800-year cycle, the 13th will come out on each 
day of the week the same number of times.  In fact, this 
is true of any 28-year cycle that does not include a century 
year that is not a leap year (e.g. 1800, 1900, 2100, 2200).

-- 
Norman H. Cohen    ncohen@watson.ibm.com
                   http://www.research.ibm.com/people/n/ncohen/

Re: language wars (results 13 September) last posting

[Andrew Gierth]

>>>>> "Luke" == Luke Chao <ab470@freenet.hamilton.on.ca> writes:

 Luke> Roy Gardiner (gardinerr@dcslambert.agw.bt.co.uk) wrote:
 Luke> : The Language Preference Grid (Friday 13th September 1996)
 Luke>                                 ^^^^^^^^^^^
 Luke> I'm sure you could have picked a better day :)

Useless (but true) factoid:

The 13th day of the month is more often Friday than any other day of the
week. 

-- 
Andrew Gierth (andrewg@microlise.co.uk)

"Ceterum censeo Microsoftam delendam esse" - Alain Knaff in nanam

Re: language wars (results 13 September) last posting

[Luke Chao]

Roy Gardiner (gardinerr@dcslambert.agw.bt.co.uk) wrote:
: The Language Preference Grid (Friday 13th September 1996)
                                ^^^^^^^^^^^
I'm sure you could have picked a better day :)
--
____________________________________________

 Luke Chao of Hamilton, Ontario, Canada
 luke.chao@freenet.hamilton.on.ca
 http://www.freenet.hamilton.on.ca/~ab470/
____________________________________________

Re: language wars (results 13 September) last posting

[James Giles]

Andrew Gierth wrote:
> [...]
> However, 400 years is 4800 months, which is *not* divisible by 7.
> Therefore it is manifestly impossible for a specified day-of-the-month
> to fall equally on all days of the week. It so happens that the 13th
> falls most often on Friday.

The day of the week that the 13th of any month falls upon is entirely
dependent on the day of the week the first of that year falls upon and
on whether the year is a leap year or not.  It does not depend on
whether the number of months is divisible by 12.

> [...]
> Skeptics are invited to write a program to do the calculation for
> themselves.

Assuming that *you* have done so, please have the courtesy to run it
2800 years and note that the 13th is equidistributed in weekdays.
Then you can come back and apologise.  You have to run it more than
400 years because you have to go through a complete cycle of exceptions
to the century rule.

J. Giles
Ricercar Software

Re: language wars (results 13 September) last posting

[Daniel J. Long]

James Giles wrote (with deletions) :
>
> > Skeptics are invited to write a program to do the calculation for
> > themselves.
> 
> Assuming that *you* have done so, please have the courtesy to run it
> 2800 years and note that the 13th is equidistributed in weekdays.
> Then you can come back and apologise.  You have to run it more than
> 400 years because you have to go through a complete cycle of exceptions
> to the century rule.
> 
> J. Giles
> Ricercar Software


Ok, here is my program, written in Smalltalk, to calculate the
distribution
of Friday the 13ths for a 2800 year period from 1996 to 4795.  BTW,
Friday did
turn out to be the most likely 13th.

Dan


| anArray |
anArray := Array new: 7 withAll: 0.
1996 to: 4795 do: [:year |
	1 to: 12 do: [:month | | day |
		day := (Date newDay: 13 monthNumber: month year: year) weekdayIndex.
		anArray at: day put: ((anArray at: day) + 1)]].
anArray inspect

Result:  Mon  Tues Wed  Thur Fri  Sat  Sun
       #(4795 4795 4809 4788 4816 4788 4809)

Re: language wars (results 13 September) last posting

[Ken Pizzini]

In article <32414A27.14E@cat.com>, Daniel J. Long <longdj@cat.com> wrote:
>Ok, here is my program, written in Smalltalk, to calculate the
>distribution
>of Friday the 13ths for a 2800 year period from 1996 to 4795.  BTW,
>Friday did
>turn out to be the most likely 13th.
...
>| anArray |
>anArray := Array new: 7 withAll: 0.
>1996 to: 4795 do: [:year |
>	1 to: 12 do: [:month | | day |
>		day := (Date newDay: 13 monthNumber: month year: year) weekdayIndex.
>		anArray at: day put: ((anArray at: day) + 1)]].
>anArray inspect
>
>Result:  Mon  Tues Wed  Thur Fri  Sat  Sun
>       #(4795 4795 4809 4788 4816 4788 4809)

What is the impentation of Date and/or weekdayIndex?  I think this shows
that at least one of them has a bug...

		--Ken Pizzini

Re: language wars (results 13 September) last posting

[Art Schwarz]

(Sorry about entering a private conversation :)

Just to provide a basis for settling the discussion, why not contribute
your procedure to generate the appropriate statistics and contribute a
summary of the statistics. It seems that the conjecture that Friday the
13th (or any other day) occurs more frequently / less frequently than
anything is demonstrable, so demonstrate.

To be more contentious, there have been 2 (?) postings of algorithms.
Before questions are levied on implementation or language features,
post an algorithm which demonstrates your case.

art schwarz

(I have no opinions. They belong to someone else.)

Re: language wars (results 13 September) last posting

[Matthew D. Healy]

In article <528lab$6af@mill.gdls.com>, schwarza@gdls.com wrote:

> summary of the statistics. It seems that the conjecture that Friday the
> 13th (or any other day) occurs more frequently / less frequently than
> anything is demonstrable, so demonstrate.
> 

But it is not possible, fundamentally not possible, that a general answer
to this debate could exist!  In most flavors of Unix, you get the
following result when you say "cal 9 1752"

   September 1752
 S  M Tu  W Th  F  S
       1  2 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

because it was in 1752 that the British Empire (including of course
their American Colonies) changed from the old Julian calendar -- leap
year every fourth year -- to the current Gregorian calendar -- a year
ending in 00 is a leap year if and only if it is a multiple of 400
because 365.25 days is a little bit too long.  However, the change
was made at different dates in different countries, ranging from the
sixteenth century to the twentieth country*.  Thus, whatever the
answer may be, for, say, the English-speaking countries in the period
1500-2100, IT WILL BE DIFFERENT FOR OTHER COUNTRIES.

*The Tsars of Russia stuck to the Julian calendar; one of the many
changes made by the Soviets was the calendar.  This is the reason
why the "October Revolution" was in November.

---------
Matthew.Healy@yale.edu
http://paella.med.yale.edu/~healy
"Any content-based regulation of the Internet could burn down the
global village to roast the pig."  -- Judge Dalzell, on the CDA

Re: language wars (results 13 September) last posting

[Randy MacDonald]

Matthew D. Healy wrote:
 
> *The Tsars of Russia stuck to the Julian calendar; one of the many
> changes made by the Soviets was the calendar.  This is the reason
> why the "October Revolution" was in November.

No, it was in (their) October. 
Didn't you learn anything from Einstein? ;)
It's like saying Pearl Harbour was bombed on 1941.12.07, but the
Japanese bombed it on 1941.12.08.

--
|\/| Randy A MacDonald       |"We ARE the weirdos, mister!"
|\\| randy@godin.on.ca       |        Fairuza Balk "The Craft"
     BSc(Math) UNBF '83      | APL: If you can say it, it's done.
     Natural Born APL'er     | *** GLi Info: info@godin.on.ca ***
     I use Real J            | Also http://www.godin.com/godin/
------------------------------------------------<-NTP>----{ gnat }-

Re: language wars (results 13 September) last posting

[galina.kasminskaya]

In article <324E0230.72DF@godin.on.ca>,
   Randy MacDonald <randy@godin.on.ca> wrote:
>Matthew D. Healy wrote:
> 
>> *The Tsars of Russia stuck to the Julian calendar; one of the many
>> changes made by the Soviets was the calendar.  This is the reason
>> why the "October Revolution" was in November.
>
>No, it was in (their) October. 
>Didn't you learn anything from Einstein? ;)
>It's like saying Pearl Harbour was bombed on 1941.12.07, but the
>Japanese bombed it on 1941.12.08.
>

Re: language wars (results 13 September) last posting

[Dave Tholen]

galina.kasminskaya@ksu.ru writes:

> It's like saying Pearl Harbour was bombed on 1941.12.07, but the
> Japanese bombed it on 1941.12.08.

Ah, memories!  I was a member of my college living group's Campus Quiz
Bowl team, and one of the questions that year was "When did the Japanese
bomb Pearl Harbor?".  One of my teammates (and also roommate) was the
first to hit the buzzer, so he got to try the answer:  "Well, one date
was December 7, 1941."  The moderator confirmed "That's correct", but
looking puzzled by the answer, continued by asking "Do you have another
date?", to which my teammate casually replied "Well, in Japan, it was
December 8!"  The audience erupted in laughter.

Oh, by the way, we won the competition that year, by a landslide.

Re: language wars (results 13 September) last posting

[Ken Pizzini]

In article <528lab$6af@mill.gdls.com>, Art Schwarz <schwarza@gdls.com> wrote:
>Just to provide a basis for settling the discussion, why not contribute
>your procedure to generate the appropriate statistics and contribute a
>summary of the statistics. It seems that the conjecture that Friday the
>13th (or any other day) occurs more frequently / less frequently than
>anything is demonstrable, so demonstrate.
>
>To be more contentious, there have been 2 (?) postings of algorithms.
>Before questions are levied on implementation or language features,
>post an algorithm which demonstrates your case.

I'm not sure, but I suspect that this posting was prompted by my
ill-considered posting where I unfairly hinted at the possibility
that someone's Smalltalk implementation was flawed.  I was basing
my claim on a mathematical proof, which unfortunately depended on a
lemma which I failed to prove, and which turned out to be false.  I
canceled that article twice -- once shortly after posting, when I
realized my error, and again after someone re-posted my article in
an attempt to clean-up after a rogue canceler.

For the benifit of other mathematically inclined calendar watchers,
the lemma was that a 400-year interval had a number of days which
is not divisible by 7.  Other simple lemmata about the calendar and
a dash of group theory would then show that the 13th of a month
will be equidistributed across the days of the week over any
multiple of 2800 years.  (The "proof" I had would not rule out
shorter periods, but the existence of such a period was sufficient
for the question at hand.)  Unfortunately for my proof, the number
of days in any 400 year interval on the Gregorian calendar *is* a
multiple of 7, and thus some other form of analysis is required
to determine what the distribution of the days of the week that
the 13th of a month fall on is.

		--Ken Pizzini

Re: language wars (results 13 September) last posting

[Paul Gilmartin]

Ken Pizzini (ken@coho.halcyon.com) wrote:
: for the question at hand.)  Unfortunately for my proof, the number
: of days in any 400 year interval on the Gregorian calendar *is* a
: multiple of 7, and thus some other form of analysis is required
: to determine what the distribution of the days of the week that
: the 13th of a month fall on is.

You're almost there.  The number of 13th's in a period is 12*400,
which is not a multiple of 7, so they can not be equidistributed
among days of the week.  Beyond that, it's a simple matter
to count them.

-- gil

Re: language wars (results 13 September) last posting

[Ken Pizzini]

Reposting article removed by rogue canceller.

In article <32414A27.14E@cat.com>, Daniel J. Long <longdj@cat.com> wrote:
>Ok, here is my program, written in Smalltalk, to calculate the
>distribution
>of Friday the 13ths for a 2800 year period from 1996 to 4795.  BTW,
>Friday did
>turn out to be the most likely 13th.
...
>| anArray |
>anArray := Array new: 7 withAll: 0.
>1996 to: 4795 do: [:year |
>	1 to: 12 do: [:month | | day |
>		day := (Date newDay: 13 monthNumber: month year: year) weekdayIndex.
>		anArray at: day put: ((anArray at: day) + 1)]].
>anArray inspect
>
>Result:  Mon  Tues Wed  Thur Fri  Sat  Sun
>       #(4795 4795 4809 4788 4816 4788 4809)

What is the impentation of Date and/or weekdayIndex?  I think this shows
that at least one of them has a bug...

		--Ken Pizzini

Re: language wars (results 13 September) last posting

[Norman H. Cohen]

Andrew Gierth wrote:

>  Norman> In any 2800-year cycle, the 13th will come out on each day of
>  Norman> the week the same number of times.  In fact, this is true of
>  Norman> any 28-year cycle that does not include a century year that
>  Norman> is not a leap year (e.g. 1800, 1900, 2100, 2200).
> 
> You have missed, however, the fact that the calendar repeats every *400*
> years, not every 2800. 400 years is 146097 days, which is 20871 weeks
> precisely.

My goodness, your're right! My apologies.

-- 
Norman H. Cohen    
mailto:ncohen@watson.ibm.com
http://www.research.ibm.com/people/n/ncohen/

Re: language wars (results 13 September) last posting

[Andrew Gierth]

>>>>> "Norman" == Norman H Cohen <ncohen@watson.ibm.com> writes:

 > Andrew Gierth wrote:
 >> Useless (but true) factoid:
 >> 
 >> The 13th day of the month is more often Friday than any other day
 >> of the week.

 Norman> I apologize for the off-topic posting (especially when it is
 Norman> cross-posted to so many newsgroups, and thus off so many
 Norman> topics at once), but it should be pointed out, before this
 Norman> becomes an urban legend, that this "factoid" is patently
 Norman> false!

Oh dear. I don't have alt.folklore.urban on my server, or I might take
this discussion there; in the absence of any obvious other place to
direct followups to, we will have to stay off-topic for the time
being. Email might be a good move...

 Norman> In any 2800-year cycle, the 13th will come out on each day of
 Norman> the week the same number of times.  In fact, this is true of
 Norman> any 28-year cycle that does not include a century year that
 Norman> is not a leap year (e.g. 1800, 1900, 2100, 2200).

You have missed, however, the fact that the calendar repeats every *400*
years, not every 2800. 400 years is 146097 days, which is 20871 weeks
precisely.

However, 400 years is 4800 months, which is *not* divisible by 7. 
Therefore it is manifestly impossible for a specified day-of-the-month
to fall equally on all days of the week. It so happens that the 13th
falls most often on Friday.

Skeptics are invited to write a program to do the calculation for
themselves.

-- 
Andrew Gierth (andrewg@microlise.co.uk)

"Ceterum censeo Microsoftam delendam esse" - Alain Knaff in nanam

Re: language wars (results 13 September) last posting

[John Girash]

James Giles (JGiles@cris.com) wrote:

: Assuming that *you* have done so, please have the courtesy to run it
: 2800 years and note that the 13th is equidistributed in weekdays.
: Then you can come back and apologise.  You have to run it more than
: 400 years because you have to go through a complete cycle of exceptions
: to the century rule.

Ah, but in a 400-year cycle, the number of *days* (146 097) is evenly
divisible by 7, so in fact each 400-year cycle starts on the same day of
the week and is equivalent to all others.  Running it for 2800 years shouldn't
do anything but quadruple the 400-year counts, without smoothing them out.

Sorry to not cull the followups line, but I'm not sure what would be best 
to remove {-;


-- 
"don't listen when you're told about the best days in your life      Spirit of
 a useless old expression, it means passing time until you die."      the West
 -----------------------------------------------------------------------------
  -- John Girash --- girash@cfa.harvard.edu --- http://skyron.harvard.edu/ --

Re: language wars (results 13 September) last posting

[John Girash]

John Girash (girash@skyron.harvard.edu) wrote:
: James Giles (JGiles@cris.com) wrote:
: 
: : Assuming that *you* have done so, please have the courtesy to run it
: : 2800 years and note that the 13th is equidistributed in weekdays.
: : Then you can come back and apologise.  You have to run it more than
: : 400 years because you have to go through a complete cycle of exceptions
: : to the century rule.
: 
: Ah, but in a 400-year cycle, the number of *days* (146 097) is evenly
: divisible by 7, so in fact each 400-year cycle starts on the same day of the
: week and is equivalent to all others.  Running it for 2800 years shouldn't
: do anything but quadruple the 400-year counts, without smoothing them out.

of course, I meant "septuple".  If anyone has found my long-lost language
skills, please send them back to me (postage-due is fine ;-)

: Sorry to not cull the followups line, but I'm not sure what would be best 
: to remove {-;

-- 
"don't listen when you're told about the best days in your life      Spirit of
 a useless old expression, it means passing time until you die."      the West
 -----------------------------------------------------------------------------
  -- John Girash --- girash@cfa.harvard.edu --- http://skyron.harvard.edu/ --

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

[Clinton Pierce]

Andrew Gierth wrote:
> 
> >>>>> "Norman" == Norman H Cohen <ncohen@watson.ibm.com> writes:
> 
>  > Andrew Gierth wrote:
>  >> The 13th day of the month is more often Friday than any other day
>  >> of the week.
>  Norman> I apologize for the off-topic posting (especially when it is
>  Norman> cross-posted to so many newsgroups, and thus off so many
>  Norman> topics at once), but it should be pointed out, before this
>  Norman> becomes an urban legend, that this "factoid" is patently
>  Norman> false!
> Oh dear. I don't have alt.folklore.urban on my server, or I might take
> this discussion there; in the absence of any obvious other place to
> direct followups to, we will have to stay off-topic for the time
> being. Email might be a good move...
> 
> Skeptics are invited to write a program to do the calculation for
> themselves.
> 

Let's get back on Topic, for comp.lang.perl at least.  

See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
Gregorian/Julian switch etc..etc... This Perl script will show you the Truth:


#!/usr/bin/perl4

foreach $year (1066...1996) {
        $FRIDAYS=`cal $year | cut -c20-24,50-53 | grep [0-9]`;
        while($FRIDAYS=~/\d+/g) {
                $DAYOFMONTH{$&}++;
        }
}
foreach(1..31) {
        print "Day of month: $_ Freq: $DAYOFMONTH{$_}\n";
}

Just make sure that your vendor's implementation of 'cal' puts Fridays in the
specified columns.  Use 'cal 1996 | cut -c20-24,50-53' and make sure you just
get Fridays as output.

-- 
----------------------------------------------------------------------o------
    Clinton A. Pierce       |    "If you rush a Miracle Man     |  \ / \ /
    cpierce1@ford.com       |      you get rotten miracles."    |   \ G /
 DCI, Inc. on loan to Ford. | --Miracle Max, The Princess Bride |  / \ / \
------------------------------------------------------------------Freemason--
Geek Code: GCM/GCSd-(++)s+:+a-C++UA++++$UIS+++$UL+++P++++L++E---W++N++w---O
(Revised!)  t++(+++)5+X+R-tv-b+++DI++++G++e+>++h----r+++y+++(--)>y*
I'll be a Speaking Geek at LISA '96.  Catch me on Wed AM, 11:30.  Topic: Igor

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

[Russell Mosemann]

Clinton Pierce <cpierce1@ford.com> writes:

>See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
>UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
>Gregorian/Julian switch etc..etc... This Perl script will show you the Truth:

   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.

Day of month: 1 Freq: 1600
Day of month: 2 Freq: 1594
Day of month: 3 Freq: 1596
Day of month: 4 Freq: 1594
Day of month: 5 Freq: 1593
Day of month: 6 Freq: 1601
Day of month: 7 Freq: 1593
Day of month: 8 Freq: 1600
Day of month: 9 Freq: 1594
Day of month: 10 Freq: 1596
Day of month: 11 Freq: 1594
Day of month: 12 Freq: 1593
Day of month: 13 Freq: 1601
Day of month: 14 Freq: 1593
Day of month: 15 Freq: 1601
Day of month: 16 Freq: 1594
Day of month: 17 Freq: 1596
Day of month: 18 Freq: 1594
Day of month: 19 Freq: 1593
Day of month: 20 Freq: 1601
Day of month: 21 Freq: 1593
Day of month: 22 Freq: 1601
Day of month: 23 Freq: 1594
Day of month: 24 Freq: 1596
Day of month: 25 Freq: 1594
Day of month: 26 Freq: 1593
Day of month: 27 Freq: 1601
Day of month: 28 Freq: 1593
Day of month: 29 Freq: 1499
Day of month: 30 Freq: 1461
Day of month: 31 Freq: 930


    The script is
   

#!/usr/bin/perl

@dom = ();
for ($year = 1066; $year <= 1996; $year++)
{
    open(CAL, "cal $year |");
    $row = <CAL>;                   # Get rid of year
    $row = <CAL>;                   # A blank line
    while($row = <CAL>)
    {
        for ($cols = 0; $cols < 3; $cols++)
        {
            $day = substr($row, 15 + ($cols * 23), 2);
            $dom[$day]++ if $day =~ m/^( |\d)\d$/;
        }
    }
    close(CAL);
}
for ($day = 1; $day <= 31; $day++)
{
    print "Day of month: $day Freq: $dom[$day]\n";
}
-- 
Russell Mosemann     Concordia College      Voice: (402) 643-7445
Computing Center     Seward, NE 68434       Fax:   (402) 643-4073
"If Teflon is non-stick, how do they get it to stick to the pan?"

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

[Russell Mosemann]

Reposting article removed by rogue canceller.

Clinton Pierce <cpierce1@ford.com> writes:

>See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
>UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
>Gregorian/Julian switch etc..etc... This Perl script will show you the Truth:

   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.

Day of month: 1 Freq: 1600
Day of month: 2 Freq: 1594
Day of month: 3 Freq: 1596
Day of month: 4 Freq: 1594
Day of month: 5 Freq: 1593
Day of month: 6 Freq: 1601
Day of month: 7 Freq: 1593
Day of month: 8 Freq: 1600
Day of month: 9 Freq: 1594
Day of month: 10 Freq: 1596
Day of month: 11 Freq: 1594
Day of month: 12 Freq: 1593
Day of month: 13 Freq: 1601
Day of month: 14 Freq: 1593
Day of month: 15 Freq: 1601
Day of month: 16 Freq: 1594
Day of month: 17 Freq: 1596
Day of month: 18 Freq: 1594
Day of month: 19 Freq: 1593
Day of month: 20 Freq: 1601
Day of month: 21 Freq: 1593
Day of month: 22 Freq: 1601
Day of month: 23 Freq: 1594
Day of month: 24 Freq: 1596
Day of month: 25 Freq: 1594
Day of month: 26 Freq: 1593
Day of month: 27 Freq: 1601
Day of month: 28 Freq: 1593
Day of month: 29 Freq: 1499
Day of month: 30 Freq: 1461
Day of month: 31 Freq: 930


    The script is
   

#!/usr/bin/perl

@dom = ();
for ($year = 1066; $year <= 1996; $year++)
{
    open(CAL, "cal $year |");
    $row = <CAL>;                   # Get rid of year
    $row = <CAL>;                   # A blank line
    while($row = <CAL>)
    {
        for ($cols = 0; $cols < 3; $cols++)
        {
            $day = substr($row, 15 + ($cols * 23), 2);
            $dom[$day]++ if $day =~ m/^( |\d)\d$/;
        }
    }
    close(CAL);
}
for ($day = 1; $day <= 31; $day++)
{
    print "Day of month: $day Freq: $dom[$day]\n";
}
-- 
Russell Mosemann     Concordia College      Voice: (402) 643-7445
Computing Center     Seward, NE 68434       Fax:   (402) 643-4073
"If Teflon is non-stick, how do they get it to stick to the pan?"

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

[Barrie Walker]

In article <R.521pfp$kec@ns.ccsn.edu>, mose@ns.ccsn.edu says...
>
>Reposting article removed by rogue canceller.
>
>Clinton Pierce <cpierce1@ford.com> writes:
>
>>See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
>>UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
>>Gregorian/Julian switch etc..etc... This Perl script will show you the 
Truth:
>
>   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.

I think you have caught hold of the wrong end of the stick.

The observation doesn't claim
1	that 13ths have a monopoly on Fridays -
	6ths, 20ths and 27ths fall on just as many Fridays.
2	that the uneven distribution is restricted to Fridays -
	months are more likely to begin (1sts) on Sundays.
3	to work with anything but the current inplementation
	of the Gregorian calendar.

Try the following script and tell me what's wrong with it.
It suggests(?) that the 13th's distribution over the cycle is exactly:
       Sun     Mon     Tue     Wed     Thu     Fri     Sat
13     687     685     685     687     684   * 688     684
Now this is only _one_ (1) more than Sunday or Wednesday gets but "more" it 
certainly is.

#! perl

#start somewhere
($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = gmtime( 0);

for ($y=0; $y<400; $y++)
{        
  printf "%d\r", $y;
  for ($m=1; $m<=12; $m++)
  {
    $D = &days( $m, $y+1900+$year);
    for ($d=1; $d<=$D; $d++)
    {
      $k{$d,$wday}++;
      $wday++;
      $wday %= 7;
    }
  }
}

sub days
{
  local( $m, $y) = @_;
  return 29 if $m==2 && (!($y%400) || ($y%100) && !($y%4));
  (31,28,31,30,31,30,31,31,30,31,30,31)[$m-1];
}


$D = (reverse sort values %k)[0];
print "$D\n";
for (keys %k)
{
  $k{$_} = '* '.$k{$_} if $k{$_}==$D;
}

printf "%2s %7s %7s %7s %7s %7s %7s %7s\n", "", 
"Sun","Mon","Tue","Wed","Thu","Fri","Sat";
for ($d=1; $d<=31; $d++)
{
  printf "%2s %7s %7s %7s %7s %7s %7s %7s\n", $d, $k{$d,0}, $k{$d,1}, 
$k{$d,2}, $k{$d,3}, $k{$d,4}, $k{$d,5}, $k{$d,6};
}

-- 
Barrie
Edinburgh, Scotland                       http://www.csl.co.uk

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

[Jim Shapiro]

Barrie Walker (bwalker@csl.co.uk) wrote:
: In article <R.521pfp$kec@ns.ccsn.edu>, mose@ns.ccsn.edu says...
: >
: >Reposting article removed by rogue canceller.
: >
: >Clinton Pierce <cpierce1@ford.com> writes:
: >
: >>See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
: >>UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
: >>Gregorian/Julian switch etc..etc... This Perl script will show you the 
: Truth:
: >
: >   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.

: I think you have caught hold of the wrong end of the stick.

: The observation doesn't claim
: 1	that 13ths have a monopoly on Fridays -
: 	6ths, 20ths and 27ths fall on just as many Fridays.
: 2	that the uneven distribution is restricted to Fridays -
: 	months are more likely to begin (1sts) on Sundays.
: 3	to work with anything but the current inplementation
: 	of the Gregorian calendar.

[well written Perl code deleted]

I ran your program and got the same results, then I realized that this whole
argument is silly.  Suppose, for the sake of argument and with no loss in
in generality, we look at the day of the week the first of each month falls
on.  If January starts on say a Monday, the days for the remaining 11 months
depend only on the number of days in each month.  If all the months were 28
days (or any number that is congruent to 0 (mod 7) then _all_ the firsts would
be on Monday!  Given the odd ball number of days in each month (a number which
even changes with the year, for some years) the firsts of each month will
be divided among the days of the week in some _deterministic_ fashion.  Over
a 400 year interval it does not come out exactly evenly distributed.  That is
all there is to it.  Why does anyone think that firsts or thirteenths or any
day should be equally likely to be on any one weekday over any other in the
first place?

I guess it is a little counterintuitive, sort of like the famous birthday
problem, one which I will not introduce to keep the thread length in check.

: -- 
: Barrie
: Edinburgh, Scotland                       http://www.csl.co.uk

--
Hope this helps,
Jim Shapiro

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

[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

[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

[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

[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

[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

[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]

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

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

[Matthew D. Healy]

In article <3242D1EB.3F54@ford.com>, Clinton Pierce <cpierce1@ford.com> wrote:

> 
> See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
> UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
> Gregorian/Julian switch etc..etc... This Perl script will show you the Truth:
> 

But this will be modulo your country, because different countries did
the Julian/Gregorian change in different years, ranging from the sixteenth
to the twentieth* centuries.  Most flavors of Unix cal do it when the
British and their colonies did.  Dunno whether customers in, say,
Sweden can get one where cal works for their country.

PS: About six months ago when I entered a thread on different dates of
Julian/Gregorian switching in another newsgroup, I got email from an
astronomer somewhere in Europe who told me his country (forget which
one) did a _really_ strange number on this: instead of stepping in
a single year, they had half a century with no leap years until
they were in sync with the Gregorian calendar!  Stick _that_ in cal's
pipe and smoke it!

*Yes, twentieth.  Until the last Tsar fell, Russia was still on the
Julian calendar.  That's why the "October revolution" took place in
November.

---------
Matthew.Healy@yale.edu
http://paella.med.yale.edu/~healy
"Any content-based regulation of the Internet could burn down the
global village to roast the pig."  -- Judge Dalzell, on the CDA

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

[Dik T. Winter]

In article <Matthew.Healy-2309960924350001@pudding.med.yale.edu> Matthew.Healy@yale.edu (Matthew D. Healy) writes:
 > PS: About six months ago when I entered a thread on different dates of
 > Julian/Gregorian switching in another newsgroup, I got email from an
 > astronomer somewhere in Europe who told me his country (forget which
 > one) did a _really_ strange number on this: instead of stepping in
 > a single year, they had half a century with no leap years until
 > they were in sync with the Gregorian calendar!

From Sweden probably and told wrong.  It was the intention that starting
1700 they would omit leap years until they were in sync with the Gregorian
calendar.  So 1700 was not a leap year.  But they forgot about that or
something and they made 1704 and 1708 leap years, so they did not gain
on the Gregorian calendar and were one day out of sync with the Julian
calendar.  In 1712 they got back in sync with Julian by adding a
February 30.  They finally changed later that century (1768 if I remember
right).

But what this is doing in all those newsgroups...
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924098
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/

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

[Paul Gilmartin]

Matthew D. Healy (Matthew.Healy@yale.edu) wrote:

: PS: About six months ago when I entered a thread on different dates of
: Julian/Gregorian switching in another newsgroup, I got email from an
: astronomer somewhere in Europe who told me his country (forget which

(quite likely Paul Schlyter :-)

: one) did a _really_ strange number on this: instead of stepping in
: a single year, they had half a century with no leap years until
: they were in sync with the Gregorian calendar!  Stick _that_ in cal's
: pipe and smoke it!

From:    
   Linkname: Calendar FAQ
        URL: ftp://login.dknet.dk/pub/ct/calendar.faq

        This document is Copyright (C) 1996 by Claus Tondering.
        E-mail: ct@login.dknet.dk.

Sweden has a curious history. Sweden decided to make a gradual change
from the Julian to the Gregorian calendar. By dropping every leap year
from 1700 through 1740 the eleven superfluous days would be omitted  
and from 1 Mar 1740 they would be in sync with the Gregorian 
calendar. (But in the meantime they would be in sync with nobody!)   
 
So 1700 (which should have been a leap year in the Julian calendar)  
was not a leap year in Sweden. However, by mistake 1704 and 1708
became leap years. This left Sweden out of synchronisation with both
the Julian and the Gregorian world, so they decided to go *back* to
the Julian calendar. In order to do this, they inserted an extra day
in 1712, making that year a double leap year! So in 1712, February had
30 days in Sweden.        

Later, in 1753 Sweden changed to the Gregorian calendar by dropping 11
days like everyone else.

--gil

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

[Dr John Stockton]

In article <521pfp$kec@ns.ccsn.edu> of Sat, 21 Sep 1996 17:16:25 in
comp.lang.pascal.misc, Russell Mosemann <mose@ns.ccsn.edu> wrote:
>Clinton Pierce <cpierce1@ford.com> writes:
>
>>See for yourself if the "Friday the 13th" thing is just a UL.  If you trust
>>UNIX's 'cal' program, and that it does the Right Thing with Leap Years, the
>>Gregorian/Julian switch etc..etc... This Perl script will show you the Truth:
>
>   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.
...

You need to test over 400 years, rather than over a more-or-less
arbitrary period, because in the Gregorian calendar the length-of-month
rule repeats every 400 years, and 400 years happens to be an integer
number of weeks.

You will then find that Friday 13th is slightly more common that one
might at first expect.  Authority for this is excellent.


A.D. 2000 is a leap year. After (in the U.K.) 1752, every year divisible
by 4 is leap,
        EXCEPT if it is divisible by 100 but not by 400; so that:

Leap := (Year mod 4 = 0) xor (Year mod 100 = 0) xor (Year mod 400 = 0) ; 

For proof, read any of the following :
RGO, UK : 
  http://www.ast.cam.ac.uk:80/pubinfo/leaflets/leapyear/leapyear.html
  http://www.ast.cam.ac.uk:80/pubinfo/leaflets/2000/2000.html 
  http://www.ast.cam.ac.uk:80/pubinfo/leaflets/calendar/calendar.html 
Claus Tondering :
  ftp://login.dknet.dk/pub/ct/calendar.faq
  ftp://garbo.uwasa.fi/pc/doc-net/calfaq.zip
Prof. Timo Salmi :
  ftp://garbo.uwasa.fi/pc/link/tsfaqp.zip
any reputable encyclopaedia; 
or even Windows Calendar, set to Feb 2000.

The Gregorian Calendar repeats every 400 years, which is 146097 days (in
Octal, 435261 days) or exactly 20871 (Octal, 50607) weeks.

BTW, February 29th, in a "century" year, is always Tuesday 29/02/00.


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

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

[Randy MacDonald]

I've reposted this message from Roger Hui, since his access to
the newsgroup didn't allow for posting to the other groups.
With apologies to the comp.lang.apl folk...

<BEGIN>

Subject: Re: Triskaidekanalysis
       Date: 21 Sep 96 05:35:19 GMT
       From: Roger Hui <Roger.Hui@SYMPATICO.CA>
Organization: UofNB News Gateway, Fredericton, CANADA
  Newsgroups:comp.lang.apl


A more recent and complete leap year rule specifies that years
divisible by 4000 are common (not leap) years.  In J, the following
verb is 1 if the argument is a leap year, and 0 if it is common:

   leapyear=: 0&(~:/ . =) @ (4000 400 100 4&(|/))

In words: Compute the remainder of division by 4000, 400, 100,
and 4.  If the number of 0 remainders is odd, then it is
a leap year; if even, then it is a common year.

The additional 4000-year rule is described in Guy Ottewell's
"The Astronomical Companion", 1979, Furman University, Greenville,
SC, USA, Telephone (803) 294-2208.  The reason for having the rule
is to bring the average calendar year closer to the tropical year
(within one day in 20000 years):

   1460969 days % 4000 years = 365.24225 days/year  (4000 year rule)
   146097  days % 400  years = 365.2425  days/year  (400  year rule)

Therefore, to determine the distribution of the 13-th day over
the days of the week, it is necessary to consider not just a
400 year cycle, but a 28000 year cycle.  (Actually the first
should be a 2800 year cycle, with a short cut to 400 years made
possible by the fact that 146097 is divisible by 7.)

The analysis can be done in J as follows:

   p=: 31 28,10$5$31 30       NB. days in month in common years
   q=: 31 29,10$5$31 30       NB. days in month in leap   years
   +/,(leapyear i.4000){p,:q  NB. # days in 4000 years
1460969

   y=: i.28000                NB. year numbers from 0 to 27999.

   d=: (leapyear y){p,:q      NB. # of days in each month in y
   $d                         NB. d is a 28000 by 12 matrix
28000 12
   5{.d                       NB. first 5 rows of d
31 28 31 30 31 30 31 31 30 31 30 31
31 28 31 30 31 30 31 31 30 31 30 31
31 28 31 30 31 30 31 31 30 31 30 31
31 28 31 30 31 30 31 31 30 31 30 31
31 29 31 30 31 30 31 31 30 31 30 31

   w=: 7| +/\ ,d              NB. day-of-week of every 13-th day of
month
   20 {. w                    NB. first 20 entries in w
3 3 6 1 4 6 2 5 0 3 5 1 4 4 0 2 5 0 3 6

   t=: /:~ (~.w) ,. #/.~ w    NB. sorted table of day-of-week, #
occurrences
   t
0 48000
1 48000
2 48000
3 48000
4 48000
5 48000
6 48000

The next example shows that a 4000-year cycle exhibits uneven
distribution.
Since the number of days in 4000 years (1460969) is not divisible by 7,
the unevenness is smoothed out when the cycle is lengthen by a factor of
7,
as above.

   /:~ (~.w) ,. #/.~ w=: 7 | +/\ , (leapyear i.4000){p,:q
0 6880
1 6840
2 6869
3 6851
4 6850
5 6870
6 6840

<END>

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

[Dik T. Winter]

In article <32462521.76DD@godin.on.ca> randy@godin.on.ca writes:
 > The additional 4000-year rule is described in Guy Ottewell's
 > "The Astronomical Companion", 1979, Furman University, Greenville,
 > SC, USA, Telephone (803) 294-2208.

That it is described there does not make it a rule.  It has been a
proposal by the American Astronomical Society, but it *never*
made it to a rule (although some older editions of the Encyclopedia
Brittanica mention it as a rule).
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924098
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/

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

[John Harper]

In article <32462521.76DD@godin.on.ca>,
Randy MacDonald  <randy@godin.on.ca> wrote:
>       From: Roger Hui <Roger.Hui@SYMPATICO.CA>
>Organization: UofNB News Gateway, Fredericton, CANADA
>  Newsgroups:comp.lang.apl
>
>A more recent and complete leap year rule specifies that years
>divisible by 4000 are common (not leap) years. 

No point considering this one yet. Calendars are legal matters (they
determine when payments are due, when public holidays are, and so on)
Unless and until some government incorporates the 4000-year rule in its
laws, we may as well go on using the Gregorian rule (except of course
that there is a Greek? rule that has a 2-exceptions-every-900-years
rule instead of 1-exception-every-400-years.

John Harper Mathematics Dept. Victoria University Wellington New Zealand

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

[jupiter]

In <52a2d6$4v7@totara.its.vuw.ac.nz>, harper@kauri.vuw.ac.nz (John Harper) writes:
>Randy MacDonald  <randy@godin.on.ca> wrote:
>>A more recent and complete leap year rule specifies that years
>>divisible by 4000 are common (not leap) years. 
>
>No point considering this one yet. Calendars are legal matters (they
>determine when payments are due, when public holidays are, and so on)
>Unless and until some government incorporates the 4000-year rule in its
>laws, we may as well go on using the Gregorian rule

Isn't it true that the Soviet Union adopted the 4000-year rule legally?
I've read about it in one of Asimov's papers.
How is the current situation in Russia?
I assume they wouldn't have bothered to revert to the strictly 
Gregorian calendar, specially since their version gets rid of that 
3 days displacement every 10000 years.

Manuel Alfonseca, Universidad Autonoma Madrid

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

[Dr John Stockton]

In article <32462521.76DD@godin.on.ca> of Mon, 23 Sep 1996 01:50:25 in
comp.lang.pascal.misc, Randy MacDonald <randy@godin.on.ca> wrote:
>I've reposted this message from Roger Hui, since his access to
>the newsgroup didn't allow for posting to the other groups.
>With apologies to the comp.lang.apl folk...
>
> ...
>
>A more recent and complete leap year rule specifies that years
>divisible by 4000 are common (not leap) years. 
> ...

That is a reasonable proposal - though AFAIR 3200 might be better than
4000 - but it has NO AUTHORITY.

The present calendar has a 400-year cycle.  Links to some references are
via the URL below.

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

Re: language wars (results 13 September) last posting

[Andrew Gierth]

>>>>> "Ken" == Ken Pizzini <ken@chinook.halcyon.com> writes:

 > In article <32414A27.14E@cat.com>, Daniel J. Long <longdj@cat.com> wrote:
 >> Ok, here is my program, written in Smalltalk, to calculate the
 >> distribution
 >> of Friday the 13ths for a 2800 year period from 1996 to 4795.  BTW,
 >> Friday did
 >> turn out to be the most likely 13th.
[code snipped]
 >> 
 >> Result:  Mon  Tues Wed  Thur Fri  Sat  Sun
 >> #(4795 4795 4809 4788 4816 4788 4809)

 Ken> What is the impentation of Date and/or weekdayIndex?  I think
 Ken> this shows that at least one of them has a bug...

Why do you say that?

OK, so my smalltalk is nonexistent, but the code given looks ok, and here
for your delectation is my version in Emacs Lisp, and my results:

(require 'calendar)

(defun day-of-13th (month year) (calendar-day-of-week (list month 13 year)))

(defun d13-one-year (v year)
  (mapcar (lambda (month)
            (let ((day (day-of-13th month year)))
              (aset v day (1+ (aref v day)))))
   '(1 2 3 4 5 6 7 8 9 10 11 12)) 
  v)

(defun d13-range (first count)
  (let ((v (vector 0 0 0 0 0 0 0)) 
	(y first) 
	(lim (+ first count)))
    (while (< y lim)
      (setq v (d13-one-year v y)) 
      (setq y (1+ y))) 
    v))

(d13-range 1996 2800)
[4809 4795 4795 4809 4788 4816 4788]

Note - this code uses 0=Sunday. So, my results agree with Mr. Long's.

Incidentally, for the curious, I first came across this obscure fact in an
exercise in a book (exactly *which* book I forget, but I vaguely recall that
it might have been Richards (?) & Whitby-Strevens (sp?) book on BCPL). The
exercise simply said "Write a program to prove that the 13th falls more
often on Friday than any other day of the week". So I did (but not in BCPL).

-- 
Andrew Gierth (andrewg@microlise.co.uk)

"Ceterum censeo Microsoftam delendam esse" - Alain Knaff in nanam

Re: language wars (results 13 September) last posting

[Art Schwarz]

It appears that the number of Friday the 13th's is determinable given that
we know what day Jan 1 falls on and whether the year is a leap year or not.
Adding these numbers for each year being considered provides an answer to
the ubiquitous question "is Friday the 13th more frequently occurring than
any other day". But what do I know? :} (This is a metaphorical question
relating my own experiences to the philsophical and transcendental plane of
corporeal existence and hence, not needing a response.)


As time permits I will perform the necessary calculations and provide the
algorithm. 


art schwarz

(No opinion is worth it's salt unless my wife approves it.)