The secular day begins at 12:00 AM and ends at 11:59 PM -a convention useful for coordinating soc... more The secular day begins at 12:00 AM and ends at 11:59 PM -a convention useful for coordinating society, but arbitrary by any natural measure. Jewish law takes a different approach: each day is calculated independently, reflective of its own astronomical reality. Sunrise and sunset are not merely representations of social activity or pretty sights; they are the legal boundaries within which time-bound commandments operate. The milestones within that range -midday, the afternoon offering, the latest time for the evening Shema -are all proportionally derived from those endpoints. After the Talmudic Sages codified ובשכבך ובקומך to establish individual timeframes for reciting the Shem'a, further end-times were imposed within the day and night, each one dependent on knowing where the day itself begins and ends. The stakes of getting this right are therefore high. Every time-dependent ruling is built proportionally on top of the endpoints; define them incorrectly, and the entire structure shifts with themat worst, causing Shabbat desecration without the observer even realizing it. Defining those endpoints, however, is anything but simple. The question of when the day begins and ends has been debated across centuries, drawing in astronomy, manuscript variants, legal precedent, and the limits of pre-modern timekeeping. Our responsibility is to be equipped with enough data (both practical and theoretical) to decide on our own, through all the different assertions and opinions. We begin with an Aggadah (a non-literal Talmudic text) that poses a deceptively simple question: how far can an average person walk in a day? The answer it gives is ten parsaot -it's a distance measuring unit where each individual parsa encompasses 4 individual mil (another measuring unit; could be further broken up to each mil encompassing 2000 amot). Distance, however, is only meant here as a unit for time keeping (since the text never cared about this distance) -measure the time correspondence for this distance unit (using the average person's walking speed), and you have your day. How is this day structured? There are 4 times of importance: dawn, sunrise, sunset, and הכוכבים .צאת Dawn and הכוכבים צאת are the edges of the day, where they mark the beginning and end of the 40 mil. Although their definitions are reflective of astronomy rather than time, their usage to start and end the day naturally causes their occurrence to become measured, and thus the basis of time. The measurements are done through the known variables: its length and the offset point. When you subtract its length from sunrise (the first visibility moment of the sun's solar sphere), you arrive at Dawn. To contrast this with the end of the day, when you add its length to sunset (the last visibility moment of the sun's solar sphere), that's when הכוכבים צאת occurs. With consistent definitions of sunrise, sunset, and the two in-between lengths (called "twilight" in English), the day's symmetry is consistent -the middle of the day is the midpoint of the sun's traversal in the sky, regardless of how long twilight is. How long is it? Within the answer of the 40 mil day, we know that both twilight periods reserve a minimum of 10% each -that is, at least 4 mil before sunrise and at least 4 mil after sunset. The dispute between R' Yoḥanan and R' Yehuda is about whether twilight extends beyond that minimum. R' Yehuda holds that the day occupies the full remaining 80%, allocating 32 mil to the sunrise-to-sunset period and leaving exactly 4 mil for each twilight period -the minimum. R' Yoḥanan disagrees, holding that the day occupies only 75%, allocating 30 mil to the sunrise-to-sunset period and extending each twilight period to 5 mil. The distinction between the two positions is therefore not about the length of the day itself -that remains a constant we will assign shortly -but about how much of the remaining time twilight is permitted to claim. Although our available text of the Talmud rules like R' Yehuda, we will see why that may be irrelevant for the final determination of twilight's length. By expressing the inner mil as a percentage of the larger "40 mil" unit, we could use the process of variable substitution to determine how long a singular mil (and thus, twilight) is. The consequences of
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