Some Data Analysis Methodologies From the Gemara
A data geek's dream: three economics problems on a single daf!
The Gemara happens to discuss three very loosely connected “data analytics” problems on a single daf (Ta’anis 19 - with a follow-up on 21a): actuarial rates, measuring inflation, and economies of scale. Given that my private daf yomi schedule just hit that page, you could hardly expect to escape a new article.
But first, speaking of applying data analytics to public policy questions, I just launched a new publication called The Audit. I understand that very few of you will be even remotely interested in articles focused on “holding public officials and institutions accountable using data-driven investigative journalism”. But in case any of you share my unfortunate (and untreated) compulsion for diving down data-lined rabbit holes, do drop by.
Now let’s look at those passages one at a time:
Quantifying Mortality Rates
Here’s the Mishna:
איזהו דבר עיר המוציאה חמש מאות רגלי ויצאו ממנה ג' מתים בג' ימים זה אחר זה הרי זה דבר פחות מכאן אין זה דבר
Which could be read as something like this:
What qualifies as a plague? A city that produces 500 men from whom three die over three days. Less than that, isn’t a plague.
We care about this threshold because only qualifying plague events will trigger the halachic need for public fasting and coronet (חצוצרות) blowing. I might think that this is a simple calculation: if the deaths were to continue at that rate - where one out of every 500 people dies each day - you would lose your entire population after around 16 months. So it’s time to get God involved.
But that’s definitely not what’s going on here. Because the Gemara itself adds an alternative illustration:
ת"ר עיר המוציאה חמש מאות ואלף רגלי כגון כפר עכו ויצאו הימנה תשעה מתים בשלשה ימים זה אחר זה הרי זה דבר ביום אחד או בד' ימים אין זה דבר
A city of 1,500 men…that loses nine men over three days: that is a plague…
Since the time span for nine deaths out of 1,500 is three days (rather than nine), it’s clearly not about a simple death rate.
So what exactly are we measuring? First of all, according to the Kesef Mishna to the Rambam (תעניות ב:ה) those numbers only refer to adult males, since illness in women, children, and older people is more likely even under normal conditions. Also, if three people would die in a single day, only Rabbi Meir would classify it as a plague (see Ta’anis 21a). By contrast, according to Rashi on the Mishna, the majority opinion teaches that such deaths are simply random (“אקראי בעלמא”).
All this leads to some interesting assumptions:
Specific symptoms or pathological diagnoses don’t seem to matter: only the death count.
Under normal conditions, women and children die at a higher rate than military-aged men. (This could possibly be explained by higher infant mortality and pregnancy-related death rates in the ancient world.)
Halacha does not require special treatment for predictable - “random” - events like the occasional death or any death of women, old people, and children. Those, it would seem, are just nature taking its course.
Fasting and coronets, is seems, are only required for events with a measurably supernatural origin.
Defining “Dangerous” Inflation
Extreme economic conditions can also trigger a halachic communal response. But, as this next Gemara shows, you need to precisely define those conditions. According to Meiri a status of drought (בצורתא) would require only public fasting, but a full famine would require also blowing coronets.
סאה בסלע ושכיחא בצורתא ארבעה ולא שכיחא כפנא א"ר יוחנן לא שנו אלא בזמן שהמעות בזול ופירות ביוקר אבל מעות ביוקר ופירות בזול מתריעין עליה מיד דא"ר יוחנן נהירנא כד הוו קיימי ד' סאין בסלע והוו נפישי נפיחי כפן בטבריא מדלית איסר
If a seah [measure of wheat] sells for a selah, but it’s easily available, [that’s a sign that you’re experiencing] a drought (בצורתא). [But if a selah will buy four seah] but it’s not available, that’s a famine (כפנא)…
Rabbi Yochanan continues by qualifying the drought case: the lighter (fasting-only) status will only apply when money is widely available, but when money is hard to come by (מעות ביוקר) then - even when grain prices are low - one must immediately initiate a cycle of fasts.
So it seems that there are two kinds of inflation:
The price of basic goods is high but there are ways to cover the cost (loans? charity?)
The price of basic goods is high but no one can access funds to purchase them
Of course, “no one can access funds” might mean that none of the locals can afford to buy, so the producers are moving into other markets. Alternatively, if the entire consumer economy collapses, producers will have no choice but to stop producing altogether.
The added words of Rabbi Yochanan (“I remember once when you could get four seah of grain for a sela but there were people dying of starvation in Tiberius because there was no sela”) suggests that at least that event was localized and specific to Tiberius. But the second - global - possibility would seem to signal a broad political breakdown in society where a currency itself had failed.
Identifying Economies of Scale
יש שנה שגשמיה מרובין ויש שנה שגשמיה מועטין יש שנה שגשמיה יורדין בזמנן ויש שנה שאין גשמיה יורדין בזמנן
“Some years receive plenty of rain and some years receive minimal rain. Some years the rain falls in the right time and some years the rain does not fall at the right time”
The Gemara illustrates each of those four possibilities with its own analogy:
Rain falling at the proper time is like a slave whose master provides his full week’s supply of grain on Sundays, allowing the slave to both bake and consume his bread appropriately
Rain that falls at the wrong time is like a slave whose master provides his supply on Friday, meaning both the slave’s preparations and consumption will be flawed (presumably because of the time constraints under which he’s working)
Years of plentiful rain are like a slave whose master provides his needs all at once so that “the mill will grind from a kur what it would (otherwise) grind from a kav; and a dough will consume from a kur what it would (otherwise) consume from a kav”
Years of limited rain are like a slave whose master provides his needs in small incremental portions so that “what the mill would grind from a kur it would grind from a kav; and a dough that would be consumed from a kur it would consume from a kav”
The last two illustrations seem to be describing the economies of scale. "Economies of scale" refer to the cost advantage achieved when a company increases production volume, leading to a decrease in the cost per unit. This happens because fixed costs are spread over more units, operational efficiencies improve, and bulk purchasing may reduce material costs.
By receiving his grain in bulk, the slave can grind it into flour and then knead it into a dough while encountering only minimal, one-time “fixed costs” of loss to the mill and kneading bowl. But when the slave is forced to process grain and then flour in smaller, daily units, he’ll lose the fixed cost wastage for each processing run - multiplying his losses by six.