Accuracy and precision are related -- but different -- concepts. Accuracy is how well you can stay on target, precision is how well you can hit a certain point. To illustrate, in an physics lab we once needed a beam pipe (a vacuum pipe in which charged particles travel while being accelerated and then directed to targets -- physicist toy). We worked with a manufacturer who said they could give us the 100 m of pipe we needed in 100 sections, one meter each. We specified a tolerance of 0.1%, and they agreed. We took delivery and it didn't work. When we assembled our beam pipe, it was short by 10 cm! We complained, "We specified very tight accuracy; you messed up!" They replied, "No, you specified a tolerance of 0.1%, or one mm out of each meter section. We made each one precisely 999 mm; just one mm short."
There is a lot to learn from that story, but the lesson that interests me is that being more precise does not necessarily make you more accurate. Precision is certainly an important factor, but it has to be weighed with other factors when actually implementing a plan.
There are many times when Chazal extended a rule with לא פלוג רבנן/Chazal didn't make a distinction. For example, one is not allowed to roll a ball or marbles on the bare ground. That is a protective rule so one does not come to smooth the path, thus transgressing aTorah prohibition. Chazal also forbade rolling a ball or marbles on a paved surface -- לא פלוג רבנן -- so people wouldn't get confused about when the rule applies and when it doesn't. Similarly, one is not allowed to sweep a dirt floor; and analagously that rule is extended -- לא פלוג רבנן -- to all floors, even when covered. (It is a matter of halachic dispute nowadays how this applies to our indoor floors, since we no longer have dirt floors at all. CYLOR)
What I find even more fascinating is that Chazal sometimes intentionally used a round number for a similar reason. For example, regard the transmission of טומא via a roof, that roof needs to be at least one טפח (about four inches, give or take). When the roof is round (such as a pole), then the measurement is three טפחים in circumference. Obviously, Chazal knew that the circumference of of a circle that is one טפח in diameter is larger than three טפחים, but the decree was made to make things livable.
Here's another example. The Jewish calendar is a solar years with lunar months. (That is the correct way to state how we keep time.) There are not, however, and even number of months in a year, nor days in a year or a month. On the other hand, we are required by Torah law to have an integral number of days in a month and months in a year. That gives rise to our complicated calendrical system. We also have seasonal changes, each season being called a תקופה.
The halacha is that each תקופה (there are four per year) is 91 days, 7 hours, 540 חלקים (there are 1080 חלקים per hour). That is known as the תקופה of Shmuel. There is another תקופה, known as the תקופה of Rav Adda bar Ahava, that is 91 days, 7 hours, 519 חלקים, and 20 רגעים (there are 76 רגעים per חלק). In fact, the תקופה of Rav Adda bar Ahava is more precise; that is, it matches to the modern astronomical measurements. Because we use the תקופה of Shmuel, therefore, the calendar "drifts" a bit. Which is why the date of switching to request rain in the Shmone Esrei is now Dec 4/5, but if you look in older writings from over a century ago, you'll see Dec 3/4.
Why use Shmuel's תקופה when that of Rav Adda bar Ahava is more precise? In fact, you can even ask why each has a name... the תקופה is the תקופה, right? The answer is that Shmuel very clearly knew the more precise value, but he ruled that halachically we would use the less precise value. Why? Because the system is complicated enough, and the consequences of making a mistake are dire -- eating on Yom Kippur or chameitz on Pesach! We rule in accordance with Shmuel, so that becomes the appropriate date for our holidays.
Wait! Am I really saying that nature will accommodate our halichic rulings! Indeed I am. The Torah is no longer in heaven, and heaven is bound by the halachic decisions made by our Sages. That might require a bit of explanation...
There is a lot to learn from that story, but the lesson that interests me is that being more precise does not necessarily make you more accurate. Precision is certainly an important factor, but it has to be weighed with other factors when actually implementing a plan.
There are many times when Chazal extended a rule with לא פלוג רבנן/Chazal didn't make a distinction. For example, one is not allowed to roll a ball or marbles on the bare ground. That is a protective rule so one does not come to smooth the path, thus transgressing aTorah prohibition. Chazal also forbade rolling a ball or marbles on a paved surface -- לא פלוג רבנן -- so people wouldn't get confused about when the rule applies and when it doesn't. Similarly, one is not allowed to sweep a dirt floor; and analagously that rule is extended -- לא פלוג רבנן -- to all floors, even when covered. (It is a matter of halachic dispute nowadays how this applies to our indoor floors, since we no longer have dirt floors at all. CYLOR)
What I find even more fascinating is that Chazal sometimes intentionally used a round number for a similar reason. For example, regard the transmission of טומא via a roof, that roof needs to be at least one טפח (about four inches, give or take). When the roof is round (such as a pole), then the measurement is three טפחים in circumference. Obviously, Chazal knew that the circumference of of a circle that is one טפח in diameter is larger than three טפחים, but the decree was made to make things livable.
Here's another example. The Jewish calendar is a solar years with lunar months. (That is the correct way to state how we keep time.) There are not, however, and even number of months in a year, nor days in a year or a month. On the other hand, we are required by Torah law to have an integral number of days in a month and months in a year. That gives rise to our complicated calendrical system. We also have seasonal changes, each season being called a תקופה.
The halacha is that each תקופה (there are four per year) is 91 days, 7 hours, 540 חלקים (there are 1080 חלקים per hour). That is known as the תקופה of Shmuel. There is another תקופה, known as the תקופה of Rav Adda bar Ahava, that is 91 days, 7 hours, 519 חלקים, and 20 רגעים (there are 76 רגעים per חלק). In fact, the תקופה of Rav Adda bar Ahava is more precise; that is, it matches to the modern astronomical measurements. Because we use the תקופה of Shmuel, therefore, the calendar "drifts" a bit. Which is why the date of switching to request rain in the Shmone Esrei is now Dec 4/5, but if you look in older writings from over a century ago, you'll see Dec 3/4.
Why use Shmuel's תקופה when that of Rav Adda bar Ahava is more precise? In fact, you can even ask why each has a name... the תקופה is the תקופה, right? The answer is that Shmuel very clearly knew the more precise value, but he ruled that halachically we would use the less precise value. Why? Because the system is complicated enough, and the consequences of making a mistake are dire -- eating on Yom Kippur or chameitz on Pesach! We rule in accordance with Shmuel, so that becomes the appropriate date for our holidays.
Wait! Am I really saying that nature will accommodate our halichic rulings! Indeed I am. The Torah is no longer in heaven, and heaven is bound by the halachic decisions made by our Sages. That might require a bit of explanation...
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