Wednesday, September 10, 2014

:ב Why are we here?

תקנתם את רבו ואת עצמו לא תקנתם לישא שפחה אינו יכול בת חורין אינו יכול ליבטיל והלא לא נברא העולם אלא לפריה ורביה שנאמר לא תהו בראה לשבת יצרה
תוספות ד"ה לא תהו בראה. האי עשה אלים טפי מפרו ורבו כדאמר במגילה בפרק בתרא (דף כז.) מוכר אדם ס"ת לישא אשה וללמוד תורה ומייתי לא תהו בראה

Surely, the very first מצוה in the תורה is פרו ורבו. However, תוספות here indicate that the פסוק of לא תהו בראה is of some greater value. It doesn't seem that תוספות actually go into detail as to how that is, only to dispel the notion that this פסוק is used due to the absence of the real מצות פרו ורבו. 

I believe the following is the utility of the פסוק in ישעיה - either as an explanation of תוספות or an alternate approach: The main source for the מצוה is surely from בראשית. However, it is only one מצוה among 613. The פסוק in ישעיה is brought into play when the מצוה of פרו ורבו finds itself in a conflict with another מצוה, in order to establish the supremacy of the מצוה of פרו ורבו. Once we understand that the very purpose of the creation of the world was for us to inhabit it, the מצוה of פרו ורבו can take precedence over certain other מצוות.

As תוספות reference, one may sell a ספר תורה to enable the מצוה of פרו ורבו. In our case here, the emancipation of the second half of the servant is problematic with the מצוה of לעולם בהם תעבדו, prohibiting the freeing of an עבד כנעני. Neverheless, since פרו ורבו has been established as the "purpose of our creation," it is preferable to transgress לעולם בהם תעבדו or to sell a ספר תורה in order to enable its performance. 

Monday, August 11, 2014

.ל"א The reading for מחר חדש

חל להיות באחד בשבת מאתמול מפטירין ויאמר לו יהונתן מחר חדש

Yehonasan tells David that tomorrow is Rosh Chodesh and there will be a seudah. (For a discussion on how exactly Yehonasan knew it would be Rosh Chodesh since it was based on testimony, see AstroTorah.) They devise a whole plan to confirm whether Shaul still bears mortal enmity towards David. R' Shimon Schwab, in Maayan Beis HaShoeiva, is bothered, is it only because of the fact that Yehonasan mentions the words machar chodesh that we read this haftara? Surely there is a greater reason to push aside the regular haftara in favour of this one. 

Rav Schwab explains that Yehonasan's intentions in telling David not to escape until after the seudah of Rosh Chodesh were because Rosh Chodesh, as the moon enters a new cycle around the Earth, symbolizes a time of renewal, on opportunity for repentance and atonement. Yehonasan was telling David to wait and see if Rosh Chodesh will possibly have this positive effect on Shaul and he will change his mind. Therefore, we read this haftara to impress upon the masses this important aspect of Rosh Chodesh. Additionally, Rosh Chodesh is a time destined for geula which is why we recite in Mussaf, Mizbeach chadash b'Tzion tachin. And if Moshiach doesn't come, we are left wondering "why has ben Yishai not come, not yesterday and not today" (20:27, apasuk in the haftara.) The Navi remarks, vayipaked mekom David, David's place was vacant, an allusion to the fact that we, too, are lacking the presence of ben Yishai. And just as it was gratuitous hatred that caused David's absence from the party, it is exactly that that causes Moshiach to be absent today.

.ל"א What to read on חנוכה

בחנוכה בנשיאים ומפטירין בנרות דזכריה ואי מיקלעי שתי שבתות קמייתא בנרות דזכריה בתרייתא בנרות שלמה

If you had to choose which of these two הפטרות were more directly pertinent, which would you intuitively choose? Would it not be the מנורות of שלמה? After all, they do speak of actual מנורות in the בית המקדש whereas זכריה speaks only of a מנורה he saw in a dream. And wouldn't the "אחרונים" defer to the "ראשונים"? Why then is the הפטרה of זכריה given precedence and we only read that of שלמה if we have to שבתות חנוכה?

Perhaps there is more to the הפטרה of זכריה. On חנוכה we are not just celebrating the נס of the מנורה but also השם delivering us from the hands of the mighty Syrian Greeks who sought to completely destroy Judaism. The נבואה of זכריה foretells the eventual return to ירושלים and rebuilding of the second בית המקדש following the 70 bitter years of גלות בבל. Therein lies the message to never lose hope even in the darkest of days for השם's salvation is just around the corner, a pertinent theme indeed for חנוכה. 

Sunday, August 10, 2014

:ל What to read on הושענא רבה

רש"י ד"ה בקרבנות החג. ...יום ראשון של חול המועד שהוא ספק שני ספק שלישי קורא ראשון ביום השני ותניינא ביום השלישי תליתאה ביום הרביעי הרביעי שהוא נוסף בשביל חש"מ הוא קורא את ספיקי היום ומה הן ספיקי היום ביום השני וביום השלישי וכן למחר קורא ראשון ביום השלישי שני קורא ביום הרביעי שלישי קורא ביום החמישי והרביעי ביום השלישי וביום הרביעי שהן ספיקי היום וכן תמיד הרביעי קורא מה שקרא ראשון ושני חוץ מיום אחרון של חש"מ שא"א לקרות ביום השמיני לפי שאינו מימי החג אלא רגל לעצמו לפיכך יום ז' של חש"מ ראשון קורין ביום החמישי שני קורא ביום הששי שלישי קורא ביום השביעי והרביעי קורא ביום הששי וביום הז' שהן ספיקי היום:

A number of years ago, I was puzzled by this רש"י, specifically as it pertains to what we end up reading on הושענא רבה. I did receive some answers but I'm still unsure. See for yourself.

Saturday, July 26, 2014

.ט"ו Magic Number 48

ואמר ר"א אמר רבי חנינא כל האומר דבר בשם אומרו מביא גאולה לעולם שנאמר ותאמר אסתר למלך בשם מרדכי

This idea appears (anonymously, ironically) in פרקי אבות ו:ו as the very last of the 48 ways in which תורה is acquired. 48 - that should sound like a familiar number. Indeed, on .י"ד the גמרא declared that there were 48 נביאים. And according to רש"י's enumeration, #48 was none other than מרדכי!

Friday, July 25, 2014

.י"ד The Most Effective Rebuke

אמר רבי אבא בר כהנא גדולה הסרת טבעת יותר מארבעים ושמונה נביאים ושבע נביאות שנתנבאו להן לישראל שכולן לא החזירום למוטב ואילו הסרת טבעת החזירתן למוטב

This is one of my favourite shtikles. I usually just link back to the original but in this case I'll reinsert instead:

At first glance, this passage seems to be delivering a very simple message. Actions speak louder than words. בני ישראל were never able to internalize the messages of the prophets and act upon them accordingly. But when they saw their imminent extermination before their very eyes, they knew there was only one answer.

But there is a grave difficulty with this approach. The rebukes of the נביאים were indeed ignored, on the whole. But the destruction of בית המקדש did not happen overnight. There were many events that led to its destruction, many steps along the way where בני ישראל ought to have taken heed more so than they did to the mere words of the prophets. So one can understand why אחשורוש's actions sent a stronger message than the rebukes of the prophets. But what about the siege on ירושלים? What about the breeching of the walls? In what way were they less inspiring than the removal of the ring.

To establish a direction on this, we must consider the מהרש"א's commentary on the above passage. He asks why the removal of the ring is singled out by the גמרא. After all, it could simply have stated that the המן's evil decree was greater than the prophets. What is the true significance of the removal of the ring? He answers that when a purchase is made between two parties, it is common for the buyer to make a deposit to ensure the seller of his commitment to the transaction. In this case, the buyer would have been המן. He was "acquiring" the king's consent and approval for his evil plan. And yet, it was אחשורו who gave his ring to המן. This gesture showed אחשורוש's true feelings towards the Jews and המן's plan. It was more content than consent, as if he was now asking המן to carry it out, not allowing it. With the supreme ruler of the inhabited world against them, the Jews realized they were doomed.

With this important point, we can suggest an approach to answer our question above. The prophets' warnings and calls for repentance leading up to the destruction of the בית המקדש were all during a time when בני ישראל were an autonomous nation in their homeland. They were facing invasion and incursion from forces from the outside. Even when נבוכדנצר was banging down the doors and ירושלים was ready to fall, this position gave them the false hope to believe that somehow they could simply beat back the invading forces. They were therefore unable to appreciate the true urgency and necessity for תשובה.

The circumstances were vastly different during the era of אסתר. They were strangers in a strange land.They didn't have their own leaders, their own army or their own land. They were fully aware that they were at the whim of their rulers. When they saw that the supreme ruler was bent on their destruction, they knew there was simply nothing they could possibly do - except תשובה!

This is, of course, a very important and prevalent lesson today. We certainly need an army as any other country does. We even need to invest in the Iron Dome and pursue the protection of our nation in every normal way. We simply cannot rely on these institutions and believe that everything will be okay because they are in place. We must understand that is השם who grants triumph to these endeavours and it is our תפלה and תשובה that fuels their continued success.

Thursday, July 24, 2014

.י"ג Weight a Minute

אם על המלך טוב יכתב לאבדם ועשרת אלפים ככר כסף וגו' אמר ריש לקיש גלוי וידוע לפני מי שאמר והיה העולם שעתיד המן לשקול שקלים על ישראל לפיכך הקדים שקליהן לשקליו והיינו דתנן באחד באדר משמיעין על השקלים ועל הכלאים
תוס' ט"ז. ד"ה דחי עשרה אלפי ככרי כספא. שמעתי שעשרה אלפי ככר כסף עולין חצי שקל לכל אחד מישראל שהיו שש מאות אלף כשיצאו ממצרים ואמר שיתן לאחשורוש כל פדיונם (ה) ודוק ותשכח:

A fascinating piece attempting to unlock the mystery of this תוספות.
(Get out your calculators.)

.י"ג Provincial Beauty

ותהי אסתר נשאת חן [בעיני כל ראיה] אר"א מלמד שלכל אחד ואחד נדמתה לו כאומתו
What is the גמרא getting at here? From where do we see that the פסוק would insinuate such a miracle? Is it not possible that she simply found favour in everyone's eyes? The גמרא is conveying a very simple idea. אחשורוש ruled over the entire world. The capital was most certainly populated by people from all nationalities and walks of life, each with their own standards of beauty and pleasantness based on the culture of their homeland. It was therefore unfathomable that all of these individuals would each have a similarly favourable opinion of אסתר. Therefore, by means of a miracle, she appeared to each and every person as one of their own.

A woman recently explored this phenomenon in an intriguing 21st century way. She took a simple picture of herself and then commissioned individuals from all walks of life all over the world to digitally beautify her. As expected, the results were staggeringly diverse each reflecting the artists own definition of beauty as influenced by their local society.

.י"ג Provisional Beauty

ר' יהושע בן קרחה אמר אסתר ירקרוקת היתה וחוט של חסד משוך עליה
So, אסתר was not the most beautiful woman in the land? What would compel ר' יהושע בן קרחה to say that? The גר"א brilliantly points out that in the discussion (:בבא בתרא ט"ו) of what era the character איוב lived (if at all) ר' יהושע בן קרחה's opinion is that he lived in the time of אחשורוש. And it says (איוב מ"ב:ט"ו) that איוב's daughters were the most beautiful in the entire land. Therefore, according to ר' יהושע בן קרחה it could not possibly be that אסתר was the most beautiful. Certainly, there was some special Divine Providence at play here.

Wednesday, July 23, 2014

.י"ב Delayed Response?

שאלו תלמידיו את רשב"י מפני מה נתחייבו שונאיהן של ישראל שבאותו הדור כליה... אמר להם מפני שהשתחוו לצלם
רש"י ד"ה שהשתחוו לצלם. בימי נבוכדנצר:

As I have previously written in a פורים shtikle, there are two difficulties with this, both of which stem fro the simple historical fact that Nevuchadnezzar's reign was many decades before the story of Purim. As we know from the previous דף, Nevuchadnezzar reigned approximately 26 years after the חורבן. If they deserved to be destroyed, why did it take so long for this punishment to (almost) be meted out? Furthermore, this generation was not the one that sinned in the days of Nevuchadnezzar. Why does the גמרא list this as the reason why the Jews of that generation deserved to be destroyed?

I do not have a definite, clear approach to this but perhaps part of the answer may lie in the ensuing exchange:
אמרו לו וכי משוא פנים יש בדבר אמר להם הם לא עשו אלא לפנים אף הקב"ה לא עשה עמהן אלא לפנים
While רש"י explains they were asking why they merited the miracle and being saved from the evil decree, perhaps they were also asking why the punishment was so delayed. Perhaps the Jews in the time of Nevuchadnezzar were excused due to the extreme duress and circumstances of their transgressions. As the story of the מגילה begins, the Jews were certainly enjoying more relaxed treatment and perhaps they were not showing an adequate desire to abandon the practices of the previous generation.

Tuesday, July 22, 2014

:י"א The Man Who's Been Through It All

אמר איהו מיטעא טעי אנא חשיבנא ולא טעינא מי כתיב למלכות בבל לבבל כתיב מאי לבבל לגלות בבל כמה בצירן תמני חשיב ועייל חילופייהו חדא דבלשצר וחמש דדריוש וכורש ותרתי דידיה הא שבעין כיון דחזי דמלו שבעין ולא איפרוק אמר השתא ודאי תו לא מיפרקי אפיק מאני דבי מקדשא ואשתמש בהו בא שטן וריקד ביניהן והרג את ושתי והא שפיר חשיב איהו נמי מיטעא טעי דאיבעי ליה למימני מחרבות ירושלים

As I was going through this I had a thought about a פסוק at the beginning of the מגילה.
אֲשֶׁר הָגְלָה מִירוּשָׁלַיִם עִם הַגֹּלָה אֲשֶׁר הָגְלְתָה עִם יְכָנְיָה מֶלֶךְ יְהוּדָה אֲשֶׁר הֶגְלָה נְבוּכַדְנֶצַּר מֶלֶךְ בָּבֶל
One might ask why this extensive introduction is necessary? This does give us an insight into מרדכי's approximate age. And perhaps it is noteworthy that he went through the גלות of Nevuchadnezzar. But we are also told that he was with the גלות of יכניה. But after all the above calculations, we understand that the story begins 70 years after the first exile, that of יכניה. (Well, a little less than 70 years as we soon find out.) That's why it is significant that מרדכי was part of the first exile, not the second and this is what positions מרדכי to be the leader that he was. He had already endured almost 70 years of exile. He could sense that the end was near. His yearning for the impending redemption was one that could not be fully experienced or appreciated by a younger Jew from a later generation.

Wednesday, July 16, 2014

:ה All Sides

היינו טעמא דמספקא ליה משום דחד גיסא שורא דימא
A very loose connection to the פרשה: It appears טבריא was protected by a wall on all sides but one. We find in the מדרש that we were commanded to attack מדין from all sides but one.

Sunday, July 13, 2014

.ב No More, No Less

מתני' מגילה נקראת בי"א בי"ב בי"ג בי"ד בט"ו לא פחות ולא יותר
How about a nice piece of דרוש to start off the מסכתא. From the גר"א in שדה אליהו:
If you add up the גמטריא of the days on which the מגילה can be read, it equals 65. (Sorry if you were already in the middle of using the Gauss method.) This is the same as the גמטריא of השם’s name, א-ד-נ-י. This name is associated with השם’s more hidden Providence which, as we know, was behind the story of פורים.
But here’s where it gets cute. The name י-ה-ו-ה is associated with השם’s more blatant and obvious השגחה, which we did not merit to see in the story of פורים. The גמטריא of that name is 26. The משנה states that the מגילה cannot be read before the 11th or after the 15th. Therefore, the days on which it cannot be read are 10 and 16. Add them up and what do you get? 26!!

Tuesday, July 8, 2014

:כ"ז Similar Raffles

וחלקום והעמידום על עשרים וארבעה בללום ונתנום בקלפי בא ידעיה ונטל חלקו וחלק חבריו שש בא [חרים] ונטל חלקו וחלק חבריו שש וכן פשחור וכן אימר

How fitting that this גמרא falls out in פרשת פינחס. In an installment of על פי חשבון, I attempted to calculate the probability of the Divinely "rigged" גורל falling out exactly like it did. So, then, what would be the odds of this one coming out like it did without the obvious Divine intervention?

I have to admit, I'm not sure I fully understand the exact process and exactly who picked what. I also have not investigated the מפרשים sufficiently. So I will keep it as simple as possible. Therefore, we will assume that the one picked for each משמר did not have to pick the name of the משמר first. In other words, ידעיה picked first. He came up with 6 names, all of which belonged to the ידעיה family but one was actually named ידעיה. Let us assume that he picked all 6 at the same time*. Using simple nCr notation, there would be 24C6 different possible combinations for ידעיה. For the uninitiated, that is simply a fanyc way of expressing the following: 24! / (24-6)! x 6! Simply put, the different possible combinations ar
24 x 23 x 22 x 21 x 20 x 19
6 x 5 x 4 x 3 x 2 x 1
The reason we have to divide by 6 x 5 x 4...  is because order doesn't matter, so there are that many different combination which are essentially one in the same.

I probably have not sufficiently explained the above concept for those who are not familiar but if we move on, I believe the probability can be expressed thusly:
1
24C6 x 18C6 x 12C6
The probability of the final group is essentially 1 since there are only those 6 tickets left so we really only need examine the probability of the first three groups. That computes to
1
134596 x 18564 x 924
Which is 1 in 2,308,743,493,056. Although both this and the גורל of פינחס both involved 24 tickets, since this one was drawn in groups of 6, the probability is in fact nearly 100,000 greater than that of פינחס. Nevertheless, as was discussed in my parallel calculation of פינחס, the odds would still be close those of getting fatally hit by lightning twice in one year! Again, this is a veritable testimony to the extent of the miracle that occurred and the Divinity of the raffle.

*Well I just looked a little deeper into this.:רש"י ערכין י"ב explains that the raffle happened exactly the way I just assumed that it didn't. So first the head of the משמר picked his own name and then the other 5. This complicated things slightly. The probability would therefore be:
1
24 x 23C5 x 18 x 17C5 x 12 x 11C5

Which - let's just skip to the end - is 1 in 498,688,594,500,096, or over 200 times less probable than originally thought.

You want to simplify all this? According to רש"ש, there was nothing particularly miraculous going on here at all. There were in fact 4 separate raffles of 6 whereby each of the 4 משמרות would draw to determine the order of their respective subdivisions.




Thursday, July 3, 2014

.כ"ב Righteous Clowns

אתו הנך תרי אתי א"ל הנך נמי בני עלמא דאתי נינהו אזל לגבייהו אמר להו מאי עובדייכו אמרו ליה אינשי בדוחי אנן מבדחינן עציבי
For those who are not aware, there is actually a troupe of medical clowns in Israel. They are not simply trained as clowns, they are trained as clowning therapists and operate in most of the hospitals to help cheer people up. This גמרא leaves little doubt as to their portion in the World to Come.

Wednesday, July 2, 2014

:כ"א Death Frequency

דרוקרת עיר המוציאה חמש מאות רגלי הוה ויצאו ממנה שלשה מתים ביום אחד גזר רב נחמן בר רב חסדא תעניתא אמר רב נחמן בר יצחק כמאן כר'מ דאמר ריחק נגיחותיו חייב קירב נגיחותיו לא כ"ש

See this Shtikle from שמיני עצרת on the well-known tactic of reciting משיב הרוח ומוריד הגשם enough times such that one is considered accustomed to saying it. The conclusion there is that despite the fact that the הלכה follows ר' יהודה in בבא קמא that the three gores must occur in three days, that is only based on the specific wording of the פסוק from which ר' יהודה derives his position. However, he certainly subscribes to ר' מאיר's reasoning in general. This passage from our גמרא, however, would seem to challenge that. For if it were so, not only ר' מאיר but even ר' יהודה would agree that three deaths in one day constitute דבר.

Tuesday, April 1, 2014

What is your name?

There is certainly no shortage of מסכתות whose properly pronounced name is a matter of discussion. Is it Yuma or Yoma? Erchin or Arachin? I've even heard a suggestion that Yavmus is the proper pronunciation of what most of us know as Yevamos. But while those are more of a simple matter of word structure, the story behind how to pronounce our current מסכתא's name is quite a bit more rich. I searched around for some detailed write-up of the issue and found the following.
(Source: http://www.dafyomi.co.il/sanhedrin/insites/sn-dt-005.htm)

3) "BEITZAH" OR "BEI'A" OPINIONS: The Gemara relates that Rebbi visited a town and saw everyone kneading dough in impure vessels. When he inquired about their actions, the people of the town told him that "a certain Talmid told us that Mei Betza'im (water of swamps) does not have the ability to make a food susceptible to Tum'ah." They assumed, therefore, that since their dough was made with such water it could not become Tamei from their vessels. 
This was an outright mistake, as the Talmid actually had said "Mei Beitzim" (the liquid of eggs), and not "Mei Betza'im," swamp water. The people did not realize their mistake, and they even cited support for it from the Mishnah in Parah (8:10). The Mishnah there states that certain types of waters cannot be used for the Mei Chatas, the sprinkling of the ashes of the Parah Adumah, because they are swamp waters. They erroneously reasoned that the Mishnah there was the source for the Talmid's ruling: since such water is not usable for the Parah Adamah, it also must not be suitable to make something capable of becoming Tamei. As a result of that incident, the Chachamim decreed that a Talmid may not issue a ruling unless he has received permission from his Rebbi to do so. 
The Acharonim cite this Gemara when they discuss whether it is preferable to pronounce the word "Beitzah" (egg) as "Bei'a" (the Aramaic word for "egg"). 
(a) The MAGEN AVRAHAM (end of OC 156) in the name of the MAHARSHAL (Yam Shel Shlomo, Bava Kama 4:11) writes that "it is proper to say ['Bei'a' or] 'Bei'im' instead of ['Beitzah' or] Beitzim,' in order to maintain a high standard of purity of speech." (The word "Beitzah" is used by the Chachamim to connote part of the male reproductive system, and thus it is improper to utter it unnecessarily, as the Gemara in Pesachim (3a) teaches that one should accustom himself not to speak in an improper manner.) Based on this, many people have the custom to refer to Maseches Beitzah as "Bei'a," which is the Aramaic term for "egg." 
(b) The IYEI HA'YAM (cited by the Likutim on the Mishnayos), however, refutes this practice. He points out that there is no source anywhere in Shas that indicates that the Chachamim refrained from pronouncing the word as "Beitzah" or that they classified the word as improper speech. In fact, the Chachamim even used the word to describe many oblong objects (such as "Beitzas ha'Gir," Beitzah 15a). 
Furthermore, he argues, what does one gain by merely translating the Hebrew word to Aramaic if it has the same meaning in both languages? (See, however, BEIS EFRAIM, Teshuvos OC 15.) As clear proof that the word was pronounced "Beitzim" in the times of the Chachamim, he cites the Gemara here in Sanhedrin. Had the Talmid, when he referred to the liquid of eggs, not used the term "Betza'im" but rather "Bei'im," no mistake would have resulted. The townspeople would not have confused "Bei'im" with "Betza'im." (TOSFOS even has difficulty with how the townspeople confused the word "Beitzim" with "Betza'im." He explains that they thought that they heard the Talmid say "Bitzim" which they assumed was "Betza'im." Nonetheless, they would never have made this mistake had the Talmid said, "Bei'im.") 
(c) These arguments prompt the TIFERES YISRAEL (introduction to Beitzah) to suggest that the practice of not pronouncing the word as "Beitzah" is unrelated to concern for improper speech. Rather, he explains that since an error in Halachah was made because of the similarity between the words "Beitzim" and "Betza'im," the practice arose to pronounce the word "Bei'a" when used in a Halachic context in order to prevent such mistakes from happening again.
Nowadays, the generally-accepted practice is to pronounce the word "Beitzah," except in reference to the name of the Maseches, which some refer to as "Bei'a." Although the Iyei ha'Yam quotes the son of the Vilna Ga'on who testifies that the Vilna Ga'on called the Maseches "Beitzah" in contrast to the practice of the Magen Avraham, many continue to pronounce it "Bei'a" today. In defense of this practice, it may be suggested that the source for this pronunciation is the Gemara in Bava Kama (3b) which explains that the word "Mav'eh" (from the root "Ba'a") has two meanings: it connotes either praying or eating. The Gemara in Beitzah (15b) quotes Rebbi Yehoshua who maintains that one must divide the day of Yom Tov into two parts and dedicate half of the day "Lachem" ("for you," for culinary pleasure) and half of the day "la'Hashem" ("for Hash-m," for spiritual pursuits such as prayer and Torah study). Since both of these practices are alluded to in the word "Bei'a" as described by the Gemara in Bava Kama, it is an appropriate name for the Maseches which discusses the laws of Yom Tov. (M. Kornfeld)

Tuesday, February 11, 2014

.ח Easy as Pi

אמר ליה רב אסי לרב אשי לעולם גברא באמתא יתיב ורבי יוחנן מקום גברי לא קחשיב כמה הוו להו תמני סרי בשיבסר נכי חומשא סגיא היינו דלא דק ולחומרא לא דק

A "mathy" guy like myself can't help but be curious to examine the precise math behind this גמרא. The results are quite fascinating.

Let's start with what the precise הלכה would be:
If we do, in fact, require a circle that encompasses a 4x4 square, the radius of that circle would be √(32) by the Pythagorean Theorem. That would make the circumference of that circle √(32)π which is approximately 17.7715 אמות circumference. 

Now, let's examine ר' יוחנן's statement according to רב אסי. The גמרא assumes based on its loose interpretation of π that if we made a circle of 24 men, the circle inside of that ring would be 18 אמות circumference. We could end right here and declare that the margin of לא דק is even more narrow than the גמרא suggested. But let's try to get a little more precise. A circle of 24 אמות circumference would have a diameter of 24/π. The men take up exactly one אמה so the inner circle would then have a radius of 24/π - 2. The circumference of that inner circle would then be (24/π -2) x π which comes out to 17.7168 !!! So ר' יוחנן's statement is off by only 0.0547 אמות !!! The only issue, of course is that it is לא דק לקולא but at that minuscule amount, that should be allowable. 

Monday, February 10, 2014

:ז Pi in the ... תורה

רש"י ד"ה באמתא יתיב. כל אחד מקומו אמה נמצא הקיפה כ"ד אמות וקיימא לן (עירובין דף יג:) כל עגול שיש בהקיפו ג' טפחים יש ברחבו טפח דכתיב (דה"ב ד) בים שעשה שלמה עשר באמה משפתו אל שפתו עגול סביב וקו שלשים באמה יסוב אותו סביב לעשר אמות רוחב שלשים אמה היקף אלמא הכא נמי בתריסר אמות היקף סגי דנהוי פותיא ארבעה:

Since רש"י references the ים של שלמה, it would seem appropriate to reference the גר"א's famous פשט on that.
Read more here.

Wednesday, February 5, 2014

:ב Cutting off the Angles

First off, מזל טוב to all who recently completed מסכת יומא.

At the very beginning of סוכה we have the familiar discussion surrounding the 20 אמה walls. A number of years ago there was an interesting discussion on two of my other blogs regarding the interpretation of ר' זירא's position that 20 אמה  walls are not a problem with a סוכה larger than 4x4 אמות.
Please see R' Ari Storch's post on AstroTorah and my follow up on AlPiCheshbon.


Friday, January 10, 2014

:ס"ב The ט"ו בשבט Connection

Ok, this is a little bit of a stretch...

מיעוט צפרים שנים *שתים

I was initially intrigued by the הגהה. Really? ציפור is feminine? Certainly there are other words that don't give off any apparent evidence of being feminine but are, nevertheless. But I wanted to double-check it. As I was approaching the חומשים where I would confirm that it most definitely is feminine - החיה, השחותה, אותה, etc. - it hit me that the ubiquitous ט"ו בשבט ditty as well indicates that it is so. Here are the words:

השקדיה פורחת
ושמש פז זורחת,
צפורים מראש כל גג
מבשרות את בוא החג.

ט"ו בשבט הגיע חג לאילנות.
ט"ו בשבט הגיע חג לאילנות.