Π and Other Precise Measurements in Halacha

Π (pi) is an irrational number 3.14159... and it never ends. There is discussion in the literature (I haven't read any of it) whether 22/7 (=3.14285...) was the value of pi used by the Ancient Israelites and Greeks, which is not mathematically too close to the actual value.

There are at least two halachos in which Π plays an important role (excluding astronomy): Sukkah and Tefillin. In Sukkah the issue is the area of a [round] sukkah, and in Menachos the discussion is what is square, because our tefillin must be square. Recall the Pythagorean theorem which states that a^2 + b^2 = c^2, that is the square of the hypotenuse of a right triangle is equal to the sum of the square of the sides. That means that the length of the hypotenuse equals the square root of a^2+b^2. For a right triangle where the sides are 1 amah (or any unit), the hypotenuse equals the square root of 2=1.414. Critics claim, because the Gemara (Sukkah 8a; see also Shulchan Aruch O"C 32:39 from Menachos 35a) says that this hypotenuse equals 1.4 amos ("an amah and a fifth of an amah") that Chazal had an imprecise value of irrational numbers such as the square root of 2 and pi.

Dr. David Medved in his book "Hidden Light: Science Secrets of the Bible" quotes sources that Chazal had an extremely accurate measurement of pi; so accurate, in fact, that a more accurate value was not found for another 1000 years. While the vort he quotes, dealing with the word kav in Melachim and Divrei Hayamim, seems to be a cute vort but not pshat, I am willing to agree that Chazal may have had an accurate value, but they publicized a less accurate but far simpler value to use in calculations when needed.

Several prominent Torah personalities, such as Harav Chaim Zimmerman zt"l held that Chazal knew all scientific discoveries that would ever be found. Some of Rav Chaim Zimmerman's ideas on this topic might be found in his book "Torah and Reason," which I have not read, but I heard his views from several of his talmidim. (Rabbeinu Avraham ben HaRambam, in his famous essay on aggadah, found at the beginning of Ein Yaakov clearly disagrees with this view and says Chazal could have made mistakes in science.)

I believe I can prove that Chazal made use of less accurate values even when they knew of more accurate values, to keep things simple. When calculating the tekufos, the solar seasons, we have two values: the tekufa of Shmuel and the tekufa of Rav Adda. Shmuel holds (Eruvin 56a) each season lasts 91 days and 7.5 hours. Rav Adda holds the tekufa is 1 1/8 minutes shorter than Shmuel's tekufa. (See Rabbi J. David Bleich, "Bircas Hachammah," 1st edition, ArtScroll, p.49 for the calculation). It is a very involved calculation, especially compared to Shmuel's calculation.

Rav Bleich writes:
"This does not mean that Shmuel must have been ignorant of Rav Adda's method of calculation. Despite acceptance of Hillel's calendar based upon the divergent calculations of Rav Adda, Shmuel is depicted in the Gemara, Brachos 58b, as being familiar with the "paths of the sky" as he was with the alleys of his own city of Nehardea. It may be assumed that Shmuel adopted a simpler method of calculation in order to avoid the necessity of manipulating fractions. This is noted by so early an authority as R. Abraham Ibn Ezra who states in Sefer haIbbur, p. 8, that the tekufah of Shmuel is not the true tekufa, and, moreover, that Shmuel knew his announced calculations to be imprecise. Nevertheless, Shmuel chose a close approximation because of the difficulty which most people have in working in fractions. The same explanation is also advanced by the 17th-century Sephardic scholar, R. David Nieto in his Kuzari Sheni, Vikuach Chamishi, no. 146."

I feel they held people could use easy fractions like 2/5 and 1/4, but uglier fractions were more difficult to use.

Rav Bleich then brings another interesting and very logical possibility in regard to the use of Shmuel's tekufa in the calendar, but it is not so relevent to the simpler value of pi.

Adar Fun

As we are in the last day of Adar, I have a humorous post to share.



I cooked an old family recipe from me Bubby. You can see it on the right.

I invited guests - the MacGraggers. They posed for a picture, here:










This year we don't have to worry about that serious shailah of what if March 17th falls on a Friday? There's a heter for that:
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Corned beef gets blessing for St. Pat's
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Chicago Tribune (IL)-March 16, 2006
Author: Manya A. Brachear, Tribune staff reporter.

Tipping his red hat to Chicago's Irish Catholic heritage, Cardinal Francis George has again taken action to resolve a St. Patrick's Day dilemma:

Every few years, the holiday falls on a Friday during Lent, when consuming meat is traditionally forbidden. But what would St. Patrick's Day be without corned beef and cabbage?

So George has declared an exception that permits his flock to eat meat on Friday. At least 76 other U.S. bishops reportedly have granted similar dispensations, including Joliet Bishop Joseph Imesch.

While eating meat on a lenten Friday isn't a mortal sin, many look to the church for guidance before bending the rule.

"So many of the oldest Irish are faithful to the sacrifice the faith asks them to make," said Rev. Dan Brandt, pastor of Nativity of Our Lord parish in Bridgeport, where Celtic crosses are etched into the doors and walls and the pews are filled with O'Malleys, O'Donnells and Slatterys. "They need to hear a dispensation has been granted before they keep their tradition."

Both George and Imesch have asked Catholics who choose to eat meat on Friday to substitute another act of penance or abstain on a different day.

"Fridays during Lent are days of discipline," Brandt said. "We try to do something to remind ourselves of the excess in which we live."

Though there are no official records, the archbishop of Chicago has granted the dispensation as far back as anyone with the archdiocese can remember. The last time was in 2000.

The dispensation applies only to parishioners within the archdiocese. Catholics traveling outside the boundaries would seek permission from the bishop of their destination diocese or abstain from meat as usual.

Technically, Catholics could take advantage of the one-day dispensation to indulge in other meaty delicacies, whether fried chicken, pigs' feet or steak. In fact, the cardinal also granted a dispensation to the Young Irish Fellowship's annual banquet last Friday where chefs prepared filet mignon.

Still, Brandt said the St. Patrick's Day dispensation was meant to recognize a time-honored Irish-American tradition--not to give Catholics in the Chicago area a "get out of jail free" card.

"The spirit of the dispensation was in keeping with Irish roots, so those for whom it is a tradition to eat corned beef and cabbage on Friday can go ahead and do it," said Brandt.

Brandt also said it's important to keep the act of penance in perspective, saying that any good deed or act of self-denial can serve the same purpose as abstaining from meat, which in reality is not much to ask.

"Crab cakes, tuna melts--it's really no great sacrifice," Brandt said. "It makes us mindful perhaps that we are a country of excess. It helps us relate to those who aren't so fortunate."

Before the Vatican II Council in the 1960s, Roman Catholics were prohibited from eating meat every Friday. The council recommended that the abstention be limited to Fridays during Lent instead.

Some theologians say a bishop's dispensation is not strictly required for a Catholic to eat meat on the holiday--that believers can make an exception if circumstances call for it. Others say there are rules and only local bishops have the authority to bend them.

Few seem to object to making an exception for St. Patrick. Even Bill Donohue, president of the conservative Catholic League, commended George's decision.

"It's one of the church's manmade rules having nothing to with dogma," Donohue said. "It would be imprudent for Cardinal George not to cede to this reality that corned beef and cabbage and green beer are the staples to an Irishman's diet on St. Patrick's Day."

In Ireland, where the holiday is considered more a day to lift a saint up rather than let the hair down, dispensations are routinely granted, according to the Irish consulate in Chicago.

Corned beef is more of an Irish-American tradition, and Catholics in Ireland would be more likely to indulge in boiled bacon, said Rev. Tom Reynolds, an Irish-born priest who helps run the Missionary Society of St. Columbine in Rogers Park.

"St. Patrick would take to drink in heaven if he thought we weren't eating meat on his feast day," Reynolds joshed.

But since his arrival, Reynolds added, he has developed a taste for corned beef.

"I was delighted when I came to the states and tasted it for the first time," he said. "I can't imagine not eating corned beef on St. Patrick's Day."

St. Patrick is best known as the man who converted Ireland to Christianity. Born in Scotland in 387, Patrick was made a bishop by the pope and dispatched from Rome to Ireland as a missionary. Using the three leaves and single stem of the shamrock, Patrick illustrated the concept of the trinity--"even as there are three leaves on this one stem so there are three persons in one God."

For many Americans, Irish and otherwise, the holiday has evolved into an excuse to celebrate the onset of spring with parades, a platter of corned beef and a pitcher of green beer.

For that reason, Brandt said, he will still be making a sacrifice this Friday. "I gave up beer for Lent," he said. "I'd rather drink beer than eat corned beef any day of the week."

Rev. Jim Donovan, pastor of Our Lady of Loretto parish in Hometown, sees nothing wrong with a little revelry, as long as the reason behind it is remembered.

"We're celebrating our faith. We get so far away from why we're doing things," Donovan said. "It's more than just a party. It's about our faith and identity as a Christian people."

"In the grand scheme of things, one day every other year is not that big of a deal," he said of the cardinal's dispensation.

Even Christ liked to live it up at times, Donovan said. "What would Jesus say? He turned the water into wine."
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דרשו ה' בהמצאו

I See Him
by Dr. Samuel Soloveichik zt"l (1908-1966)

I see Him in a sick's recovery
In a scientific discovery.
I see Him in creative tension,
Realization, materialization, and invention.

I see Him in the voice of our Tano'im,
In the discussion of the Amoraim.
I see Him in the Rishonim's debate,
And in my ancestor's faith.

I see Him in my mother's devotion,
In a little girl's emotion.
I see Him in Beethoven's inspiration
And in a doctor's devotion.

I see Him in a gale's soar,
In the sea's mighty roar.
I see Him in heaven's silence
And in nature's thundering violence.

I see Him in Jewish History,
Highly complex and full of mystery.
I see the Great Sire,
Even in Treblinka's and Oswiecim's fire.

On a rainy day I see Him on the cloud's roof,
Cold, far distant, aloof.
And on a warm day, in prayer I see Him clear,
Glorious, majestic and yet close and near.

I see G-d the Universe Creator,
In science, the innovator.
I see G-d the Great Judge,
in human misery and grudge.

I believe in the uniqueness of our religion and race,
I believe in the righteousness of our case.
When I see the weak's survival,
I am sure of the Messiah's ultimate arrival.

I believe that all people are of one stock,
Yet I am aware that I am of the minority block.
A lost sheep of Jacob's flock,
And G-d is my fortress and rock.