How Six Hundred Thousand Is Calculated
The arithmetic of shishim ribo is simple only after the halachic question has been defined. Six hundred thousand is an exact number. What is not automatic is the unit to which that number applies.
A calculation of people crossing one point is one kind of test. A calculation of the public presence throughout a city is another. A residential population test is different again. Using exact arithmetic with the wrong unit produces a precise answer to the wrong question.
If 600,000 means passage through one point
Suppose, only for purposes of calculation, that the requirement means 600,000 people must physically pass a particular point during one day.
There are exactly 86,400 seconds in twenty-four hours. There are exactly 43,200 seconds in twelve hours.
| Period | Required total | Average per hour | Average per minute | Average per second |
|---|---|---|---|---|
| 24 hours | 600,000 | 25,000 | 416.67 | 6.94 |
| 12 hours | 600,000 | 50,000 | 833.33 | 13.89 |
If passage were perfectly continuous and people were counted only in whole persons, a rate of at least 7 people per second for all twenty-four hours would exceed 600,000. Over twelve hours, a rate of at least 14 people per second would exceed 600,000.
These figures are mathematical conversions, not a halachic ruling that the count must be performed this way. They show only what the literal single-point interpretation would require numerically.
Rabbi Levin's arithmetic
Rabbi Sholom Dovber Levin uses this kind of calculation to argue that the phrase “six hundred thousand pass through it every day” should not be understood as requiring all 600,000 to cross the same narrow place.
In his 2019 pamphlet on eruvin in large cities, he first acknowledges the surface reading:
נראה לכאורה הפירוש שצריך שיעברו ס' רבוא בכל יום ברחוב הזה עצמו
“It appears at first that the meaning is that six hundred thousand must pass every day through this street itself.”
He then argues that such a reading is not realistic. His illustration says that a full twenty-four hours contains “84 thousand seconds,” that twelve daytime hours contain “42 thousand seconds,” and that 600,000 passages would therefore require 15 people to pass every second. He describes the image as fifteen rows crowded within sixteen amos and moving continuously “like a marathon.”
Those numbers should be quoted as his illustration, not silently converted into exact clock values. A twenty-four-hour day actually contains 86,400 seconds, and twelve hours contain 43,200 seconds. The exact average over twelve hours is about 13.89 people per second. If one instead uses Rabbi Levin's rounded figure of 42,000 seconds, 600,000 divided by 42,000 is about 14.29, which rounds upward to 15 whole people per second.
The arithmetic therefore supports the general scale of his illustration, while his stated 84,000 and 42,000 seconds are rounded and not the exact number of seconds in those periods.
The arithmetic does not decide the interpretation
The calculation above cannot establish that the single-point interpretation is halachically correct or incorrect by itself. It only reveals what follows if that interpretation is assumed.
The Mishnah Berurah already notes a textual reason to be cautious about treating “every day” as a straightforward point-count rule. He writes that he searched the Rishonim who require shishim ribo and did not find the daily condition in their formulations, only that six hundred thousand be commonly found there.
Rashi in Eruvin 59a speaks of six hundred thousand regularly entering a city. The Ritva, explaining Rashi, says they need not all be settled residents. Rav Moshe Feinstein later distinguishes between a road and a city, while Rabbi Levin argues for a resident-city reading. Those are interpretive questions. Arithmetic comes afterward.
Rav Moshe's city calculation uses an estimate, not one counter
Rav Moshe's treatment in Igros Moshe changes what must be calculated.
For an independent road, he says that the required number must pass along that road. A daily traffic count can therefore be relevant to the road itself.
For a city, however, he rejects the need for six hundred thousand on every street. In Orach Chaim IV:87 he describes the relevant figure as six hundred thousand found throughout the streets of the city during the ordinary times people go out. He speaks of an umdana, an estimate, based on the number of residents and the proportion likely to be in the streets.
He also says that people entering from other cities must be added. This means that a city-wide calculation may require at least three distinct factual inputs:
- the resident population of the relevant area;
- an estimate of how many are in the public streets during the relevant period;
- people entering from outside who are likewise part of that public presence.
Rav Moshe does not provide a modern statistical formula for deduplicating commuters, passengers, repeated journeys, or people moving between neighborhoods. Those are factual measurement problems that must be handled honestly when modern datasets are applied to his rule.
A resident-city calculation asks a different question
Rabbi Levin's published formulation is that six hundred thousand “live there and use the streets.” Under that approach, the central base figure is the residential population of the city or relevant urban unit. The streets need not each receive a separate count of 600,000 passages.
This model can therefore produce a very different result from the single-point calculation. A street with 100,000 daily passages could still be a street of a city that satisfies a resident-city shishim ribo test. Conversely, a road outside a smaller city could have extraordinary traffic even though the city's resident population is below 600,000.
Neither number can be substituted for the other without first stating which halachic model is being used.
Repeated traffic is not automatically unique people
Modern transportation data often counts trips, vehicles, boardings, station entries, or crossings. Shishim ribo, however, is expressed in the sources as people.
This creates several obvious arithmetic traps:
- 600,000 vehicle movements do not necessarily mean 600,000 people.
- 600,000 passenger trips do not necessarily mean 600,000 unique passengers.
- the same commuter can appear in an inbound count and an outbound count;
- the same person can cross several traffic counters during one journey;
- an annual or average-weekday figure is not automatically the same as the period required by a particular halachic interpretation.
A modern calculation must therefore identify its denominator and counting unit. “Traffic” by itself is not a sufficient statistic.
The geographical unit matters too
The area being counted must also match the halachic question. Rav Moshe discusses a city and, in connection with the Midbar, a bounded area corresponding to the encampment. He also distinguishes the city from a separate road. Rabbi Levin speaks of the city whose residents use its streets.
It is therefore not enough to produce a population number without stating whether it refers to New York City, Brooklyn, a borough subdivision, a neighborhood, a twelve-by-twelve-mil area, or some other unit. The factual boundary can change the number dramatically, while the halachic source determines which boundary is relevant.
The detailed geographic and statistical application to New York and Brooklyn is treated on New York and Brooklyn: Population, Commuters, and Visitors.
The calculation should follow the halacha
A sound shishim ribo calculation therefore proceeds in this order:
- identify whether the Posek requires shishim ribo at all;
- identify whether the relevant unit is one road, the city as a whole, the city's residents, or public presence throughout the city;
- identify whether entrants from outside are included;
- identify the relevant time period;
- only then choose the modern dataset and perform the arithmetic.
This order prevents a numerical figure from appearing more decisive than it is. The number 600,000 is fixed. The halachic question is what, exactly, must reach that number.