‘Nafkeh Mineh L’kedushin’ and The Quadratic Equation
Samuel Katz2010Every Yeshiva boy learns about Nafkeh Mineh L’kedushin at some point. Nafkeh Mineh L’kedushin is used to justify a perpetual Talmudic argument that has no practical implications. For example, if two guys are arguing as to what was the reasoning behind a specific Talmudic ruling and each of them comes up with a different explanation, yet both of those explanations lead to the same conclusion, then what would justify continuing to argue about something completely irrelevant? Nafkeh Mineh L’kedushin!
Nafkeh Mineh L’kedushin means ‘it makes a difference with regard to marriage.’ Meaning, if a man were to say to a woman, “you are engaged to me on the condition that explanation A is the correct explanation for the Talmudic statement,” it would be of utmost importance to know which of the two explanations is true. If A is true then this woman is considered a married woman. If however B is correct then the marriage would be invalid since the condition it specified was not fulfilled. And with that, a seemingly hypothetical debate becomes a legitimate problem with ralistic urgency. If I were to receive a dollar for every time someone used it, I could have repaid half the Madoff victims by now.
And so it was one Thursday night that I found myself working on my own Nafkeh Mineh L’kedushin. Thursday night was when I would stay awake for the whole night and write up my Sikum, a summary of all that we studied in the past two weeks, usually adding my own touch to it.
Thursday night was my favorite time. It was quiet and I had the whole library to myself. In my little cubicle I would have a Ritva and Ramban, my favorite amongst the primary Talmudic commentators. Alongside them I would have a Pnei Yeshuah and a Chidushei R’ Shimon Yehuda Hakohen, another favorite of mine. I would also have a Birkas Shmuel, not because I particularly liked him, but I liked not liking him. His twisted explanations were a pleasure to disagree with.
As my point on the globe would turn towards the sunlit part of our galaxy I would retire my writing equipment and fold up my notes. Sometimes I’d have had answered the questions I had at the beginning of the night, at other times I would at that point have questioned the answers I previously had. And sometimes I would have just been a kid on carrousel, circling around on the saddle of pontification in a cyclical ride of Talmudic jargon. But no matter what, what I did was a Nafkeh Mineh L’kedushin. It all mattered, it mattered for marriage.
In most cities you know that it is early morning when you see the newspaper boys delivering the papers, but not in my city. There you knew it was early morning when you began seeing elderly men head for the earliest minyan of the morning services. That is how you know you’re in an ultra-Orthodox city, fixated on its ideals of pre-war Europe, if the morning is marked not by those who have to wake up early to feed their kids, but by those who can’t sleep due to their nightmares of the Holocaust.
The services at that hour are quiet and sleepy. The elderly men who are its prime constituency wear expressions that profess sarcasm for life amplified by exhaustion. Their expressions say more about the vanity of life than the Book of Ecclesiastics itself. The prayers proceed smoothly, my tired eyes keep on closing and my head falls back. I’m exhausted because I was up all night making sense of something; these elderly men are exhausted because they gave up on making sense of anything.
Back in my room my mashgiach walks in to wake up the students for the morning services. “Asiti Mishmur” I tell him, explaining that I was up all night studying and therefore exempt from attending the morning period. He lets me go to bed. In bed I think about all I did. I juggled some serious Talmudic issues over the night and if some guy were to tell a woman one day, “You are married to me on the condition that the BIrkas Shmeul is wrong,” I might be able to help them. What I did all night mattered; it is a Nafkeh Mineh L’kedushin. I studied all night and wrote it all down; it mattered, it mattered for marriage.
Two years later I was in a library again about to do an all-nighter. This time the school was a university not a Yehsiva . I had a homework assignment for my calculus class due the next day and I couldn’t solve it. There was a variable that appeared twice in the equation but raised to different powers. By 2 am, when the library was about to close, I had estimated the answer to three decimal places, but I still didn’t have the right answer. I continued working on the problem the rest of the night without success.
When early morning came I looked out my window for signs that the day had started, but there weren’t any. The place was as dead as it was a few hours earlier. No old people running from their memories, no young people struggling for their bread. There is no urgency on a college campus.
At 9 am I went to my professor’s office and said, “I was up all night trying to solve it,” showing him three pages of approximations and graphs, “but how do I get rid of a variable raised to two different powers?” My professor looked at me skeptically. “The quadratic equation,” he said, “You learned that in high school.”
Oops.
“Oh,” I said. Ten minutes later I solved the problem we were assigned and along with all the high school graduates in my class I turned in my homework; the homework that cost me a night’s sleep.
What I did all night, endlessly approximating an equation that lends itself easily to a precise formula, didn’t matter, not even for marriage. If some man would tell a woman, you are married to me on the condition that this equation can be solved, he won’t need my hours of labor. He will have the quadratic equation. It has no Nafkeh Mineh L’kedushin, it doesn’t matter.
I proceeded to the cafeteria and enjoyed a late breakfast. I took a newspaper that was dropped off earlier by the newspaper guy and spread it across my table. A girl I knew noticed me and came over and pulled up a chair. “Where were you last night?” she asked. I told her I was up all night approximating and graphing a problem and that I was clueless about a shortcut I could have used.
She laughed and said: “Nerd.”
I guess my work the night before did matter; it even mattered for something similar to marriage.
30 Responses
Yonadab — forget about Quadratic Equations. We want to know more about the girl!
Beautiful piece!
Nice!
“we awake and they awake…”
It’s all a popular myth. The nafka mina l’kidushin rationale is only raised when the subject argued considers material value. If A is correct, the subject is worth pruta. If B is correct it’s worthless.
Thanks HR and LH.
And PH, I’m not sure what you are trying to say.
Excellent piece.
Thanks, Hedyot.
how did u estimated the answer to three decimal places? what was the the answer, some damn root?
it might not matter for marrige, but it will sure matter for ur exam…
btw where did u learn the quadratic formula?
the question was:
How many lines which are tangent to the curve y=x/(x+1) pass through the point (1, 3)? Where do they touch the curve?
Since it can only be one line it is possible to estimate, I don’t remember the answer in the end, and I’m lazy to do it now.
As for when I learned it, I never really learned it, I just heard of it and how it should be used. It just wasn’t in my bag of tricks at the time.
Your writings, both the content and style,are a piece of art.
Thanks Hoezen.
You Never Cease To Amaze Me!!! Nice Work….
“Since it can only be one line it is possible to estimate”
Actually I think there are two tangent lines of x/(x+1) that pass through (1,3); one at x=(-3+sqrt(5))/2 and one at x=(-3-sqrt(5))/2.
Those are two points which connect to be one line.
>A girl I knew noticed me and came over and pulled up a chair.
Solid foundations are important. I hope this was on a Friday too.
“Those are two points which connect to be one line.”
No, they are two distinct tangent lines, see here:
http://tinypic.com/view.php?pic=jtscwm&s=6
I’ve been in the same situation, knowing all the college-level stuff, but not knowing any of the high-school level stuff. Eventually you’ll catch up (except for the stuff they teach in high school but you don’t use in college, like binomial theorem).
Beautiful piece. The idea, the content, the style, the mechanics, your talent as a writer jumps off the screen! Keep it up!
I can relate to everything you wrote. I do have a couple of bones to pick with you though.
I agree on the Ramba”n, but how could you forsake the Rash”bu? In my humble opinion, there is no greater Talmudic exegesist (among the Rishonim) than the Rash”bu.
Also, agreed on Reb Shimon, he is truly great. But how can you slander Reb Boruch Ber? I dont know where you learnt, but judging from your writing you are probably an estimable talmid chuchem and a lamden, so you should know that you can’t open a Birkas Shmuel and read it like any other sefer. Birkas Shmuel was intentionally written in a cryptic fashion. It is quite apparent that R’ B”B wanted people to toil and immerse themselves in the depth of the suggya and use his chidushim to shed light on complex matters. He didn’t intend his book to be a handbook of lumdes. His direction is extremely complicated, and one can never be completely sure as to what he is alluring to. But I can tell you this much, he wasn’t twisted. There is a method how to learn Birkas Shmuel. There exists an oral tradition around every shtikel toireh, I’m not kidding you. Certain Yeshivot that have direct lineage to R’ B”B have the study of Birkas Shmuel almost down to a science. I agree it’s almost impossible to understand him purely form his sefer. He is very sweet though if you handle him with the proper tools.
Forget calculus, go back to the oitzer and devote yourself to understanding R’ B”B!! (JK of course)
Where in shas did you have a נפק”מ לקידושין like you described?
Thanks R&C.
I liked Ritv”a because (I found) his ideas always to be half way between Rash”i and Tosfos, so it was always unique yet familiar. And Ramba”n I found was the most original of them all. As for the Rashb”a personally I felt like he was another Tosfos. I agree he is at times critical, but I didn’t find in him the novelty I found in the Ramba”n. I don’t mention him not because I didn’t use him, but because I just don’t remember him as fondly as the others. That’s just me.
As for Birkas Shmuel. I agree with you that he is a special style and I don’t claim to have mastered him. My problem with him was that he was the second generation of a particular analytical approach. The brisker derech halimud.” If you read R’Chaim, he see that he is very lengthy, which is common for a new approach, paradigm shift if you will, (if you are into the Kuhn thing.) As the words have not been fine tuned for the new understanding. It was R’Boruch Ber, who chose the keywords that defined the approach. And at times I found his choice to be arbitrary or at least debatable. At times I found that if you choose different points in R’Chaim’s text as the central idea you evade many of the criticisms opponents of R’Chaim had.
I noticed that when I was working on the sugyes of “Mezakeh L’ibur Lifnai Moisoi” and “Bechor Shemes” (If we meet, I would gladly share with you the papers I wrote on those)
I might not be familiar with the proper way to learn Birkas Shmuel, but I found it a rewarding exercise to challenge his reading of R’Chaim (who I acknowledge, R’Boruch Ber had personal access to and I didn’t) and other options.
And when you learn in Yeshiva, a rewarding exercise is the most you can hope for.
Oh, and I learnned in Bnai Barack, does that explain anything?
The Ramban is very profound and difficult to learn. He measures his words and is somewhat cryptic. It seems to me that similar to what you are saying about R’ Chaiyim and R’ B”B, is true about the Ramban. He seems to have an air of originality because after all a lot of the other Rishonim were his disciples, and descend from his school of Talmudic interpretation. His school of disciples (such as Rashba, Ritva and Ran) further developed and improved his original ideas. That is also exactly why I disliked the Ritv”a. To me it seems like he is only expounding on what the earlier Rishonim, such as Rashi and Toisfes, wrote. He seems to be an accumulator of the previous Rishonim. When he does add his owntwist, he just complicates matters most of the time. The truth is that the Rishonim were great, and I’m sure you are well aware, that it is over simplistic and reductionist to attribute individualistic styles to them. Every suggya has its fundamental Rishon. Sometimes it’s Rashi, sometimes it’s the Rif, or the Ran. Yet, you’re allowed to have personal favorites, mine was the Rashba and yours was the Ramban and Ritva. I’m cool with that.
You might be on to something with the Rashb”a being similar to toisfes. The Mharshal in his preface to “Yam Shel Shlome” (I think on B”K) is critical on the editors of the early Shas for the inclusion of Toisfes in the main text. He claims that the Rashb”a could have served the same purpose as Toisfes and is even better than Toisfes at explaining contradicting suggyos and so on.
As for Birkas Shmuel, true he is the second generation of the new approach as taught by the great R’ Chayim, but I don’t attribute the discrepancy seen between R’ Chayim’s writing and R’ B”B’s to that. It is known that R’ Chayim had unbelievable powers of explanation. The same has been said about R’ B”B. It could simply be that R’ Chyim knew how to transpose his thoughts into written form and R’ B”B didn’t. Some say that R’ B”B intentionally wrote his treatise in a difficult style, who knows. Although R’ B”B is a second generation Brisker, I think there is a profound shift between him and his master. With R’ Chayim the suggya is not of utmost importance; it’s all about the “Vort”. He doesn’t haggle, and is not preoccupied with satisfying every little “kneytch”- if you will- in the suggya. For R’ Chayim it’s all about the big theme; it’s about the suggya as a whole. The masterfulness of R’ B”B is, that he deals with the nitty gritty of the suggya while at the same time he doesn’t abandon the big theme.
“I noticed that when I was working on the sugyes of “Mezakeh L’ibur Lifnai Moisoi” and “Bechor Shemes” – Oh, how far I am removed from these sublime concepts. I would love to see your papers on these subjects. (We have met, we just didnt speak. Next time we will)
Learning in Yeshivah is tremendous brain exercise. But you have to be real. If you’re doing it only for brain exercise you won’t get the desired results. You have to be really devoted to understand and explore the depths of the Talmud in order for it to have an effect. Herein lays the problem too. For someone who devalues the study as a relevant discipline, it is almost impossible to study with fierce vigor. You have to shut your logical part of the brain and pretend that it all matters. I was somewhat successful at that.
B”B is a muk’oiym teyreh. Where did you learn? In the main cthedral?
I didn’t learn in the main cathedral, I learned on the other city on a hill, the one criticised by the past Rosh Yeshivah of the cathedral.If you receive my meaning.(and since I have written a post about the Rosh Yeshiva of the school, this is as far as I will go with hinting which school I attended)
We have met? Please identify yourself next time we do.
As for what you write in your last paragrap, I have struggled with that. Maybe in the future I’ll write about it.
Or you can.
The pontiff of the basilica, of blessed memory, criticized almost evry other cleric in the world. At least the ones that he saw as a threat to his papacy. I have an incling as to whom you’re reffering to, but I wont push the envelope due to the reason you have mentioned before.
We met very briefly. I knew who you were, you didnt know who I was. We didnt speak. We will meet one day, and I’ll identify myself.
Do write about it. You write great. I would love to hear your thoughts on the matter. Maybe I’ll write too and we’ll compare notes. We’ll do a mishmar on it, in some dusty, grimy, forsaken oitzer.
When my non mathematical friend told me about this blog and article, I told him “gotte be the quadratic equation.”
Now, had quadratic equation been introduced in yeshivah, we would have spent a semester about it,attempting to understand, among many other issues, why it’s called quadratic not triploric?
The Berchas Shmuel would then get into the depth of why the rambam mentions not the equation? It would be explained as follows: and behold my dear rabbi may rest in peace said that the above equation, unlike other equations, is not of real equal weight, for it produces more then one answer, which cannot be of the same value e.g. +1,-1. It is the action of the equation that results in the unequal. Hence, it doesn’t qualify as such.
Adds now RBB as follows, I will attempt to use his precious language. “and if we where to say that the deed of the equation results through the equation itself, then the paper on which it was written becomes a Cheftza of an equation and writing it creates a solution, which is indeed impossible. That is what my late rabbi meant that it is not an equation altogether.” Briske rav would put it in simple terms: “a paper of an equation is an equation not.”
All this talk is indeed a nafke minah le’kidition, e.g. If someone is mekadesh on the condition that it is considered an equation only to the extent that it happens through the chetzah of the paper itself. Consequently, learning Quadratic Equations in yeshivah would help. Or would it?
Elegant
Thanks Mosmed, I’m flattered to hear that my post was discussed, and your loimdus isto yeshivish for me to follow.
Andthanks BSM.
mosmed, i enjoyed your triploric peregrination to the second power–which, if you look carefully, is really 11 because 1+1=2. i very much look forward to more of your explorations of “the depth of why.”
I enjoyed reading your piece a lot! Very creative, interesting and fun.
In case it makes you feel any better:
> What I did all night, endlessly approximating an equation that lends itself easily to a precise formula, didn’t matter, not even for marriage. If some man would tell a woman, you are married to me on the condition that this equation can be solved, he won’t need my hours of labor. He will have the quadratic equation. It has no Nafkeh Mineh L’kedushin, it doesn’t matter.
Actually, if the man phrases his marriage proposal correctly, it *would* matter. For example suppose he says to the woman: You are married to me on condition that this equation can be solved to within three decimal places of accuracy *without using the quadratic equation*.
Kol tuv!