Do more fasts fall out on monday and thursday, or does it just feel that way

Question

On Monday and Thursday, we say a longer Tachanun. On a fast day (where the weekday prayers are still said), Selichot are said in addition to Tachanun.

It feels like there are many more fasts that fall out on Monday and Thursday. Is this statistically true, or does it just feel that way because I always remember having to say the longer Tachanun in addition to the Selichot? (availability bias)

Answer 1

Considering Monica's point about year distributions, here's a refinement of Gershon's data (using the frequency table on Remy Landau's Hebrew Calendar page, here):

• Tzom Gedaliah falls on Monday or Thursday in the year types גכה, זחא, זשג, גכז, זחג, זשה. This is 40.08% of all years.

• Asarah B'Teves can't occur on Monday, but it can be on Thursday, only in the year type הכז. This happens to be the single most common keviah, occurring in 18.05% of all years.

• Taanis Esther can be on Monday or Thursday quite often (largely because of the cases where it is moved up from Shabbos) - indeed, the only time it's not is when Purim itself is on Thursday, which is in the year types הכז, בשז, גכז. The fast is therefore on Monday or Thursday 71.97% of the time.

• Shiva Asar B'Tammuz can't fall on Monday, but it can be on Thursday, in the year types בשה, גכה, בחה, זשה. These are 28.57% of all years.

• Same thing for Tisha B'Av: it's on Thursday in 28.57% of all years.

So the only one that occurs on Monday or Thursday a majority of the time is Taanis Esther, with Tzom Gedaliah being a distant second.

All told, if you consider the full Hebrew calendar cycle of 689472 years, with five fasts in each one, then you'll have that a fast occurs on Monday or Thursday 37.45% of the time.

Answer 2

I used the data from hebcal.com/hebcal and the linux command line to see how many times the various fasts actually fell on Monday or Thursday.

• First, I downloaded the Event Lists for the years 5514 through 5572. I started from 5514 because, according to the website, results for year 1752 C.E. and before may not be accurate. "Hebcal does not take into account a correction of ten days that was introduced by Pope Gregory XIII known as the Gregorian Reformation."

  This is 229 years of data.

  for i in `seq 5514 5772`; do 
   wget -c "http://www.hebcal.com/hebcal/?year=${i};month=x;yt=H;v=1;nh=on;nx=on;mf=on;ss=on;i=off;lg=s;c=off;geo=zip" -O $i
  done
  

• Then I searched for the number of instances the fasts fell on Monday or Thursday

   for i in Gedalia Asara Esther "Tzom Tammuz" ;do 
        COUNT=`cat 5* |grep "$i" |egrep "Mon|Thu" |wc -l`
        TOTAL=`ls 5* |wc -l`
        echo -e "$i\t\t== $COUNT / $TOTAL == `echo "scale=4; $COUNT/$TOTAL"|bc`"
   done
  

• This gave me the following results:

    Gedalia   == 93 / 229 == .4061
    Asara     == 41 / 229 == .1790
    Esther    == 166 / 229 == .7248
    Tzom Tammuz   == 65 / 229 == .2838
  

These are almost exactly the same numbers that Alex got.

---

And this code:

for i in Gedalia Asara Esther "Tzom Tammuz" ;do 
    for j in Sun Mon Tue Wed Thu Fri Sat
    do
        DAY_COUNT=`cat 5* |grep "$i" |grep "$j" |wc -l`
        echo -e "${i}:\t${j}\t==\t$DAY_COUNT"
    done
    echo "----------------------------------------------"
done

gave me the break down for each of the fasts by days of the week:

Gedalia:    Sun ==  74
Gedalia:    Mon ==  66
Gedalia:    Tue ==  0
Gedalia:    Wed ==  62
Gedalia:    Thu ==  27
Gedalia:    Fri ==  0
Gedalia:    Sat ==  0
----------------------------------------------
Asara:  Sun ==  68
Asara:  Mon ==  0
Asara:  Tue ==  64
Asara:  Wed ==  10
Asara:  Thu ==  41
Asara:  Fri ==  46
Asara:  Sat ==  0
----------------------------------------------
Esther: Sun ==  0
Esther: Mon ==  65
Esther: Tue ==  0
Esther: Wed ==  63
Esther: Thu ==  101
Esther: Fri ==  0
Esther: Sat ==  0
----------------------------------------------
Tzom Tammuz:    Sun ==  90
Tzom Tammuz:    Mon ==  0
Tzom Tammuz:    Tue ==  74
Tzom Tammuz:    Wed ==  0
Tzom Tammuz:    Thu ==  65
Tzom Tammuz:    Fri ==  0
Tzom Tammuz:    Sat ==  0
----------------------------------------------

Answer 3

No! It just feels that way. - Analyzing from 5761-5772 35 times not on Monday or Thursday and 25 times on a Monday or Thursday.

Tisha B'Av & Shiva Asar B'Tamuz can only come out on either Sunday, Tuesday, Thursday, or Shabbos and then it is observed on Sunday - so for these two fasts it is impossible to fall out on Monday and more likely to fall out on another day of the week.

Tzom Gedalya can only come out on Monday, Wednesday, Thursday, or Shabbos and then it is observed on Sunday - so it has a 50/50 chance of falling out on Monday or Thursday. (analyzing 5761-5790 - 30 year period - 16 times not on Monday or Thursday / 14 times on a Monday or Thursday)

Taanis Esther can only come out on Monday, Wednesday, Thursday, or Shabbos and then it is observed on Thursday - so there is a 75% chance of falling out on Monday or Thursday.

Asara B'Teveis can only fall out on Sunday, Tuesday, Wednesday, Thursday or Friday - so there is no chance of it happening on a Monday and only a 20% chance of it falling on a Thursday. (analyzing 5761-5790 - 30 year period - 26 times not on Monday or Thursday / 4 times on a Thursday)