halacha - Are minor fasts obligatory?

Are "minor" fasts such as Taanit Esther ("Fast of Esther"; i.e. the day before Purim) or Tzom Gedaliyah ("Fast of Gedaliyah"; i.e. the day after Rosh Hashanah) optional or obligatory?

Under what conditions is one permitted to skip a minor fast?

history - Was Malbim an innovator?

The Malbim - Meir Leibush ben Yechiel Michel(1809 – 1879) - wrote a commentary on most of Tanach. In his introduction (to Yeshayahu) he writes the assumptions with which he operates in his commentary:

:עמודי התוך אשר הפירוש נשען עליהם הם שלשה

א) לא נמצא במליצות הנביאים כפל ענין במלות שונות, לא כפל ענין, לא כפל מאמר, ולא כפל מליצה, לא שני משפטים שענינם אחד, לא שני משלים שהנמשל אחד, ואף לא שני מלות כפולות

ב) לא נמצאו במליצות הנביאים ובמאמריהם הפשוטים או הכפולים, מלות או פעלים הונחו במקרה מבלתי כונה מיוחדת, על שכל המלות והשמות והפעלים שמהם הורכב כל מאמר, לא לבד שהם מוכרחים לבא במאמר ההוא, כי גם לא היה אפשר להמליץ האלהי להניח תחתיהם מלה אחרת,כי כל מלות המליצה האלהית שקולה במאזני החכמה והדעת, ערוכים ושמורים מנוים וספורים במדת החכמה העליונה, אשר אך היא לבדה תשגיב בכחה לדבר כן

ג) לא נמצא במליצות הנביאים קליפה בלא תוך גויה בלא נשמה, לבוש בלא מתלבש, מאמר רק מרעיון נשגב, דבור לא תשכון תבונה בו, כי דברות אלהים חיים כולם אל חי בקרבם, רוח חיים באפם רוח איום אביר אדיר ונורא

To summarize in English:

• 1) There are no two phrases or even two words that mean exactly the same thing. There is no such thing as "repetition of the same idea with different wording".


• 2) All words and phrases in Tanach are necessary. Not only would the idea that the author is trying to get across be deficient without the specific phrase he uses, but also that no other phrase with different wording could take its place and convey the same idea.


• 3) No phrase, verse, or section in Tanach is pointless. Everything that is written has profound meaning.

Anyone who had read part of Malbim's commentary can see how these "axioms" are incorporated. What has always bothered me, though, is that Malbim seems to be saying with (1) and (2) that Tanach is devoid of poetic style. The author did not have a choice with his wording, but rather used the only phrasology available to convey the exact point he was trying to make. Not only is this uncomfortable for me to accept, but it also seems to be in direct opposition to the multitude of Rishonim that wrote commentaries on Tanach.

Radak seems to be especially fond of saying that certain wordings are "כפל ענין במלות שונות" - "repetition of the same idea with a different wording."
Ibn Kaspi is especially well-known for saying that the way the Torah writes many things is a matter of style, and that anyone who tries to learn things from the fact that the Torah wrote something one way and not another way is attributing meaning to something that has none. Now, perhaps Ibn Kaspi is an extreme example, but I cannot find a single Rishon that would agree with Malbim's axioms (1) and (2).

Now, I have thought of several options to explain this phenomenon:

• Malbim is an innovator. He effectively rejects the approach of all those that came before him to introduce a completely novel approach to Tanach. The problem with this is that in general, the religious Jewish community is not fond of commentaries with approaches that are "too novel". I have often heard that certain newer commentaries should not be learned because they strayed from the path of the earlier commentaries in their approach. Malbim, however, is so popular, that it is difficult to find a set of Mikraot Gedolot on Nach that does not include his commentary.


• Malbim is not a p'shat commentary. Being that most of the Rishonim under question were of the p'shat approach, the earlier discussion would not pose a problem. Also, this can be seen by the fact that one of Malbim's main tasks is to justify Chazal's midrashim based on the text, especially the midrash halacha, which seems to be his entire commentary to Shemos through Devarim. And midrash halacha has, for the most part, already been identified as part of the d'rash approach, in opposition to p'shat, by such commentators as Ramban and Ibn Ezra.


• Malbim himself didn't really believe what he wrote. Historically, Malbim had a lot of trouble with the reform movement. Perhaps he wrote this commentary in opposition to the maskil philosophy, which perhaps emphasized the poetic nature of Tanach over its technical nature (that is, the messages being conveyed in the text). Perhaps, even though Malbim agreed with the earlier approach of the Rishonim, he wrote his commentary stressing the other extreme particularly for his time and place. (Generally, I don't like saying these types of explanations.)

I apologize for writing such a long question, but my question, succinctly, is:

How do you explain the Malbim's deviation from earlier commentators in light of his unbelievable popularity in the modern religious community?

Answer

To summarize (and perhaps embellish) Prof. Yaakov Elman's The Rebirth of Omnisignificant Biblical Exegesis in the Nineteenth and Twentieth Centuries, which addresses all this at length, Hazal seemed to assume that every word in the Torah was deliberate, meaningful, and not mere stylistic flourish. However, in response to Karaism, Rav Saadya Gaon greatly downplayed the role of exegesis, and promoted instead tradition as the true source of understanding of the text. This exegetical approach applied all the more so to non-legal matters. This methodology became popular among the Rishonim. However, the 19th century saw the rise of attack on the Written Law itself. To combat this, the Malbim and others resurrected the approach that each word in Scripture is deliberate and meaningful.

Thus: was Malbim an innovator? Yes as his approach was in contradistinction to that of the previous millennium of Bible commentary. But it largely followed the approach of Hazal.

---

Some relevant quotations and paraphrasing from Elman:

One passage that relates to omnisignificance is the rabbinic interpretation of Deut 32 47: “For it is not an empty thing for you it is your very life. And if [it appears] devoid [of moral or halakhic meaning] it is you [who have not worked out its moral or legal significance]." (Yerushalmi Ketubot 8:11).

Rav Saadya Gaon attacks Karaite methods of biblical exegesis, in particular their use of analogy. Since many midrashic middot may be categorized as forms of analogy (hekesh, gezerah shavah, binyan av or mah matzinu) or work by analogy (kelal u-ferat and its near relations, ribbuy and micut, etc.), we may understand his strategic retreat from this battleground and his insistence on tradition alone. Depriving halakhic midrash of real authority prepared the ground for his counterattack on Karaite legal exegesis. This view continued to exercise influence so long as Karaism remained a threat, and its traces are to be found in the works of later Geonim, R. Shmuel ha-Nagid, R. Yehudah ha-Levi, and Ibn Ezra.

That is Rav Saadya Gaon minimized the textual role played even by halakhic portions of the Torah, explaining the ultimate source for the derived laws as being the tradition.

Thus, when faced with the anti-rabbinic challenges of nineteenth-century heterodox movements, one influential representative of Orthodox thinking on the matter, R. Y. I. Halevy Rabinowitz (1847-1914), author of Dorot Rishonim, took a similar stance. Note the following, from a volume published in 1875/6.

All the derashot in the Talmud [intended] to provide proof-texts (lehasmikh) for the words of the Mishnah are only hints in the biblical texts, ...And the derashah is nothing but a hint for the matter...for from biblical proof-texts (derashah di-qeraei) we learn nothing.

However, the modern challenge was far more serious. While the Karaites rejected rabbinic interpretation and authority, nineteenth-century thought challenged those and more; scriptural authority and divinity were eventually threatened as well. The new challenge thus required a response broader than R. Saadiah's polemics against Karaism.

It thus fell to the lot of nineteenth-century scholars such as R. Yaakov Zevi Mecklenberg (1785-1865), R. Meir Leibush Weiser (1809-1879, known by the acronym Malbim), and Samson Rafael Hirsch (1808-1888) to attempt to come to grips with omnisignificance again.

Regarding Malbim's approach to peshat in contradistinction to that of his predecessors:

It differs from Nahmanides' revival of the omnisignificant program in the Middle Ages. Nahmanides dealt with issues of proportion, repetition and sequence, as I have shown elsewhere. But he did so within a context that allowed for peshat as an independent area of interpretation, a point that Malbim is at pains to disavow. For Malbim, the medieval distinction between peshat and derash is all but obliterated; in his oft-quoted phrase, to use Harris rendering, the peshat that accords with the true and clear rules of language is only to be found in [what we conventionally refer to as] the derash.

Regarding whether Malbim himself was 100% serious with all of this:

Kugel, in his history of the study of parallelism, notes that Malbim was clearly aware of the binary structure and semantic pairing of parallelism..., [but] he frequently stated that repetition as such did not exist. He rejected utterly the approach to biblical style that had been adopted increasingly by Jews and Christians since the Renaissance.

Elman further documents examples where Malbim extends Hazal's exegetical techniques. Thus, he was certainly an especially when compared with Rishonim, but his approach was broadly consistent with his contemporaries such as Rav Hirsch, and was broadly based on Hazal.

history - How many Maccabees were there and what were their names?

How many Maccabees were there and what were their names?

Answer

Megillas Antiochus lists five sons of Matisyahu: Yehudah, Shimon, Yochanan, Yonasan, and Elazar.

I Maccabees has the same names, but in rearranged order: Yochanan, Shimon, Yehudah, Elazar, and Yonasan. (It also gives their respective nicknames or cognomens: respectively, Gaddi, Thassi, Maccabeus, Avaran and Apphus.)

Rashi (to Deut. 33:11) mentions "twelve sons of Chashmonai and Elazar," but doesn't give names.

time - Precise Zemanim?

This site (see the paragraph starting with "accuracy") says that no one can predict the times for sunrise and sunset to within a minute accurately for a given location because of certain atmospheric fluctuations. If so, how do some people predict zemanim (times of day with halachik significance) to a number of seconds, or even the end of shabbat to within a minute? Also, I have been to hanetz minyanim who are very careful to start at the moment of sunrise. But according to this, that's impossible to predict!

I suppose my question is really just looking for some justification for the common practice. Do any rabbis discuss this phenomenon? Do they say if it matters or not?

Note: I know most zemanim services will say "Please don't rely on this till this last moment; these may not be exact" but that sounds more like a legal disclaimer than a statement of fact.

halacha - Contract Law and Intentions

If two parties write a contract with two clauses A and B, such that if the conditions of the first clause A, are not fulfilled then the contract defaults to the second clause B, and both parties have the intention at the time of signing that the conditions in clause A will not be fulfilled and / or write clause A so that it's impossible or nearly impossible to fulfill it's conditions, is clause A a valid part of the contract, or is clause B effectively the whole contract?

The assumption is that it is clear to everyone, including witnesses to the signing, that clause A is meant to be symbolic only, such that if either side were to try and fulfill the conditions in clause A the other side would fight against it's enforcement in Beit Din and try to prove it either invalid or unenforceable.

Edit

I just realized that this is an example of the logical construct known as empty truth or vacuous truth.

The heter iska agreement is one example of such a construct in halacha, and I don't understand why this is acceptable as it seems to contradict the idea of Torat Emet as I understand it in it's p'shat meaning ( which may be incomplete I admit ).

I could for example say:

If I am a chicken, then this pig is a cow.

Both are logically equivalent, yet no one would accept this statement as valid even though it is logically true.

Specifically, people assume that the logical truthfulness of the overall statement implies that "this pig is a cow" is truthful, which is clearly ( and logically ) not the case. The known truthfulness of "If P Then Q" implies nothing about the truthfulness of Q.

So when I say:

If ( some impossible condition ) Then ( the money I pay you is profit and not interest )

It seems that the above is what is happening, i.e. that people assume that the overall logical truthfulness of the statement necessarily implies that the second part of the structure is true, which is not the case.

minhag - Origin of Spilling Wine by 10 Plagues

The custom among all Jews (as far as I know) is to spill a drip of wine for each of the plagues as they are mentioned in a list in the haggadah. This custom is not mentioned anywhere in the Talmud (as far as I know). What is the earliest source to mention this custom? Does it encourage or discourage the practice? What reason does it give?

Answer

The דרכי משה ( in אורח חיים ס' תעד ס'ק יח ) brings the custom based on the מהרי'ל and the custom of the מהר'ש. He also states that the מהר'ש based it on the ספר אבי'ה - presumably the ראבי'ה. There are two things being symbolized. The use of the finger symbolizes the 'finger of G-d' and the number of times has a gematria of 16. The דרכי משה explains this to be referring to the faces of the חיות or a gematria linking it to G-d's sword. The משנה ברורה (in ס'ק עד on that סימן) has it referring to the name of G-d (י-ו). The specific finger to use is brought by the מגן אברהם (in ס'ק כח) as the קמיצה (ring finger) based on a מדרש that G-d used his ring finger to deliver the plagues. The שער הציון on that piece also says that it's better to spill from the cup if you will be disgusted drinking from a glass you put your finger in and that some authorities say that its preferable to spill whatever the case.

minhag - reason for black lines on wool talis katan

What is the reason why wool talis katanim have black lines on them? Why don't talis katanim of other materials have them also?

frequency - Can I run a GA to optimize wavelet transform?

I am running a wavelet transform (cmor) to estimate damping and frequencies that exists in a signal.cmor has 2 parameters that I can change them to get more accurate results. center frequency(Fc) and bandwidth frequency(Fb). If I construct a signal with few freqs and damping then I can measure the error of my estimation(fig 2). but in actual case I have a signal and I don't know its freqs and dampings so I can't measure the error.so a friend in here suggested me to reconstruct the signal and find error by measuring the difference between the original and reconstructed signal e(t)=|x(t)−x^(t)|. so my question is:
Does anyone know a better function to find the error between reconstructed and original signal,rather than e(t)=|x(t)−x^(t)|.
can I use GA to search for Fb and Fc? or do you know a better search method?
Hope this picture shows what I mean, the actual case is last one. others are for explanations

Thanks in advance

suffixes - What is 方 used for (when attached to a た-verb)?

I have the following sentence:

• 早く行った方が良かったでしょう。

Here, if we take it apart we shall have:

• 早く(Adverb) 行った(Verb, Past tense) 方(?) が(GA, Subject particle) 良かったでしょう(Verb, Past tense) 。

What is the function of 方 in this position? I've read that it can be suffix, suffix of what?

Answer

A方{ほう}がB means "more B if A" or "Ber if A":

早く行った方が良かったでしょう。
It would have been better [more good] if (we/you/I etc) had gone early, would it not?

The 方 here indicates a direction/side when comparing 2 or more things ([3] （イ） of this definition at Daijirin), in this case implying going early would have been better than going later.

word choice - Which is the correct phrase to say saving money?

I like to tell that I am saving money to buy Mac Book . So two sentence come to my mind , which one is more suitable to use ..

1. 僕はMACBOOKを買うためにお金を貯金しています。


2. 僕はMACBOOKを買うためにお金を節約しています。

frequency spectrum - Why so many methods of computing PSD?

Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in Matlab I see:

• PSD using Burg method


• PSD using covariance method


• PSD using periodogram


• PSD using modified covariance method


• PSD using multitaper method (MTM)


• PSD using Welch's method



• PSD using Yule-Walker AR method


• Spectrogram using short-time Fourier transform


• Spectral estimation

What are the advantages of these various methods? As a practical question, when would I want to use something other than Welch's method?

Answer

I have no familiarity with the Multitaper method. That said, you've asked quite a question. In pursuit of my MSEE degree, I took an entire course that covered PSD estimation. The course covered all of what you listed (with exception to the Multitaper method), and also subspace methods. Even this only covers some of the main ideas, and there are many methods stemming from these concepts.

For starters, there are two main methods of power spectral density estimation: non-parametric and parametric.

Non-parametric methods are used when little is known about the signal ahead of time. They typically have less computational complexity than parametric models. Methods in this group are further divided into two categories: periodograms and correlograms. Periodograms are also sometimes referred to as direct methods, as they result in a direct transformation of the data . These include the sample spectrum, Bartlett's method, Welch's method, and the Daniell Periodogram. Correlograms are sometimes referred to as indirect methods, as they exploit the Wiener-Khinchin theorem. Therefore these methods are based on taking the Fourier transform of some sort of estimate of the autocorrelation sequence. Because of the high amount of variance associated with higher order lags (due to a small amount of data samples used in the correlations), windowing is used. The Blackman-Tukey method generalizes the correlogram methods.

Parametric methods typically assume some sort of signal model prior to calculation of the power spectral density estimate. Therefore, it is assumed that some knowledge of the signal is known ahead of time. There are two main parametric method categories: autoregressive methods and subspace methods.

Autoregressive methods assume that the signal can be modeled as the output of an autoregressive filter (such as an IIR filter) driven by a white noise sequence. Therefore all of these methods attempt to solve for the IIR coefficients, whereby the resulting power spectral density is easily calculated. The model order (or number of taps), however, must be determined. If the model order is too small, the spectrum will be highly smoothed, and lack resolution. If the model order is too high, false peaks from an abundant amount of poles begin to appear. If the signal may be modeled by an AR process of model 'p', then the output of the filter of order >= p driven by the signal will produce white noise. There are hundreds of metrics for model order selection. Note that these methods are excellent for high-to-moderate SNR, narrowband signals. The former is because the model breaks down in significant noise, and is better modeled as an ARMA process. The latter is due to the impulsive nature of the resulting spectrum from the poles in the Fourier transform of the resulting model. AR methods are based on linear prediction, which is what's used to extrapolate the signal outside of it's known values. As a result, they do not suffer from sidelobes and require no windowing.

Subspace methods decompose the signal into a signal subspace and noise subspace. Exploiting orthogonality between the two subspaces allows a pseudospectrum to be formed where large peaks at narrowband components can appear. These methods work very well in low SNR environments, but are computationally very expensive. They can be grouped into two categories: noise subspace methods and signal subspace methods.

Both categories can be utilized in one of two ways: eigenvalue decomposition of the autocorrelation matrix or singular value decomposition of the data matrix.

Noise subspace methods attempt to solve for 1 or more of the noise subspace eigenvectors. Then, the orthogonality between the noise subspace and the signal subspace produces zeros in the denominator of the resulting spectrum estimates, resulting in large values or spikes at true signal components. The number of discrete sinusoids, or the rank of the signal subspace, must be determined/estimated, or known ahead of time.

Signal subspace methods attempt to discard the noise subspace prior to spectral estimation, improving the SNR. A reduced rank autocorrelation matrix is formed with only the eigenvectors determined to belong to the signal subspace (again, a model order problem), and the reduced rank matrix is used in any one of the other methods.

Now, I'll try to quickly cover your list:

• 
  

  PSD using Burg method: The Burg method leverages the Levinson recursion slightly differently than the Yule-Walker method, in that it estimates the reflection coefficients by minimizing the average of the forward and backward linear prediction error. This results in a harmonic mean of the partial correlation coefficients of the forward and backward linear prediction error. It produces very high resolution estimates, like all autoregressive methods, because it uses linear prediction to extrapolate the signal outside of its known data record. This effectively removes all sidelobe phenomena. It is superior to the YW method for short data records, and also removes the tradeoff between utilizing the biased and unbiased autocorrelation estimates, as the weighting factors divide out. One disadvantage is that it can exhibit spectral line splitting. In addition, it suffers from the same problems all AR methods have. That is, low to moderate SNR severely degrades the performance, as it is no longer properly modeled by an AR process, but rather an ARMA process. ARMA methods are rarely used as they generally result in a nonlinear set of equations with respect to the moving average parameters.

  
  



• 
  

  PSD using covariance method: The covariance method is a special case of the least-squares method, whereby the windowed portion of the linear prediction errors is discarded. This has superior performance to the Burg method, but unlike the YW method, the matrix inverse to be solved for is not Hermitian Toeplitz in general, but rather the product of two Toeplitz matrices. Therefore, the Levinson recursion cannot be used to solve for the coefficients. In addition, the filter generated by this method is not guaranteed to be stable. However, for spectral estimation this is a good thing, resulting in very large peaks for sinusoidal content.

  
  


• 
  

  PSD using periodogram: This is one of the worst estimators, and is a special case of Welch's method with a single segment, rectangular or triangular windowing (depending on which autocorrelation estimate is used, biased or unbiased), and no overlap. However, it's one of the "cheapest" computationally speaking. The resulting variance can be quite high.

  
  


• 
  

  PSD using modified covariance method: This improves on both the covariance method and the Burg method. It can be compared to the Burg method, whereby the Burg method only minimizes the average forward/backward linear prediction error with respect to the reflection coefficient, the MC method minimizes it with respect to ALL of the AR coefficients. In addition, it does not suffer from spectral line splitting, and provides much less distortion than the previously listed methods. In addition, while it does not guarantee a stable IIR filter, it's lattice filter realization is stable. It is more computationally demanding than the other two methods as well.

  
  


• 
  
  

  PSD using Welch's method: Welch's method improves upon the periodogram by addressing the lack of the ensemble averaging which is present in the true PSD formula. It generalizes Barlett's method by using overlap and windowing to provide more PSD "samples" for the pseudo-ensemble average. It can be a cheap, effective method depending on the application. However, if you have a situation with closely spaced sinusoids, AR methods may be better suited. However, it does not require estimating the model order like AR methods, so if little is known about your spectrum a priori, it can be an excellent starting point.

  
  


• 
  

  PSD using Yule-Walker AR method: This is a special case of the least squares method where the complete error residuals are utilized. This results in diminished performance compared to the covariance methods, but may be efficiently solved using the Levinson recursion. It's also known as the autocorrelation method.

  
  


• 
  

  Spectrogram using short-time Fourier transform: Now you're crossing into a different domain. This is used for time-varying spectra. That is, one whose spectrum changes with time. This opens up a whole other can of worms, and there are just as many methods as you have listed for time-frequency analysis. This is certainly the cheapest, which is why its so frequently used.

  
  


• 
  

  Spectral estimation: This is not a method, but a blanket term for the rest of your post. Sometimes the Periodogram is referred to as the "sample spectrum" or the "Schuster Periodogram", the former of which may be what you're referring to.

  
  
  

If your interested, you may also look into subspace methods such as MUSIC and Pisarenko Harmonic Decomposition. These decompose the signal into signal and noise subspace, and exploits the orthogonality between the noise subspace and the signal subspace eigenvectors to produce a pseudospectrum. Much like the AR methods, you may not get a "true" PSD estimate, in that power most likely is not conserved, and the amplitudes between spectral components is relative. However, it all depends on your application.

Cheers

tefilin - Allowed to change Tefillin minhag?

So is it allowed to change the way/minhag you wrap your Tefillin? Because I want to wrap my Tefillin on the the temani way, but I follow another tradition. Would that be any problem if I changed the way how I wrap the Shel Yad in a different way? Thanks

parshanut torah comment - Source for manna being natural

What interpretations (sources) claim the falling of manna were not meant to be taken literally in the Exodus? It was a natural event but exaggerated like the split of the Sea of Reeds. This does not make them any less miraculous.

What do “rational” Jews (rabbis) or even midrash say regarding this?

Answer

A helpful source in this discussion is (the ever-rational) Ibn Ezra, in his second commentary to Shemot 16:13:

ירקב שם חיוי שאמר כי המן הוא הנקרא בלשון פרס: תרנגבין, ובלשון ערב: מן, ובלשון לעז: מנא. כי קושיות רבות יעמדו עליו: האחד – כי אינו יורד היום במדבר סיני, כי ההר ידוע. ואני ראיתי זה הדומה למן במלכות אלנצי״ר, והוא יורד בניסן ובאייר, לא בחדשים אחרים. ועוד: אם תשימהו לשמש לא ימס. ועוד: כי בלילה לא יבאש. ועוד: כי איננו חזק, ואין צריך שידוכנו אדם במדוכה שיעשה ממנו עוגות. ועוד: כאשר יושם בלשון ימס. ועוד: כי איננו משביע שיוליד דם, רק הוא נכנס ברפואות. ועוד: כי ביום הששי היה יורד משנה. ועוד: כי לא היה יורד בשבת. ועוד: כי יורד לכל מקום שיחנו. ועוד: כי עבר עמהם הירדן, ולא שבת עד חצי ניסן, על דרך הפשט.‏

Let the name of Chivi rot, as he said that the Man is that which is called in Persian “Tarnagvin”, and in Arab “Man”, and in the vernacular “Manna”, as many questions will rise over him. Firstly, it does not descend today in the Sinai desert, and the mountain is known. I saw this [substance] which is similar to Man in Al-Nasir [?], and it descends in Nissan and Iyar, not in other months. Additionally, if you put it in the sun, it does not melt. Additionally, at night it does not rot. Additionally, it is not strong, and there is no need to grind it in mortars to make cakes from it. Additionally, when it is put on the tongue it will melt. Additionally, it does not satisfy [to the point of] creating blood, it only enters medicines. Additionally, on Friday double would descend. Additionally, none would descend on Shabbat. Additionally, it would fall in every place that they camped. Additionally, it crossed the Jordan with them, and did not cease until halfway through Nissan, according to the method of Peshat.

He is no nicer in his first commentary two verses later:

ישתחקו עצמות חיוי הפושע וכל הזונים אחריו שיאמרו כי מנהג זה המן לרדת עד היום במדבר...ולא התבישו אלה...והנה איננו כאשר דמו.

May the bones of Chivi the sinner and all those who turn away following him be beaten, [since] they said that it is the practice of the Man to descend until this day in the desert… Are they not embarrassed?... And behold, it is not as they thought.

For further discussion, I would suggest reading Abarbanel (Shemot 16:14), Shadal (same location), and RDZ Hoffman (16:36), all of whom approach this topic, and all of whom would be considered "rational" (and some/all were Rabbis).

prayer book - Why is there an Aramaic line after "Hashem yimloch l'olam va'ed" in Az Yashir?

Directly after the phrase "Hashem yimloch l'olam va'ed" ^* in the paragraph of Az Yashir in the siddur, the phrase is translated into Aramaic: "Hashem malchutei ka'eim l'alam ul'almei alma".

Why is this so?

My personal speculation would that be that the line is left over from when the majority of the Jewish world spoke Aramaic, in order that the person praying would understand what they were saying. I'm not sure about this, though.

---

^{* To understand why the phrase "Hashem yimloch l'olam va'ed" is repeated twice, see here.}

Answer

I don't know if this will satisfy you but your siddur is following what the Arizal says to do, brought by the Mishnah Berurah.

Rema 51:7

וְכוֹפְלִין פָּסוּק כָּל הַנְּשָׁמָה תְּהַלֵּל יָהּ לְפִי שֶׁהוּא סוֹף פְּסוּקֵי דְּזִמְרָה (טוּר) וְכֵן פָּסוּק ה' יִמְלֹךְ לְעוֹלָם וָעֶד (אַבּוּדַרְהַם)‏

And we say the verse "And we shall praise Hashem" at the end of the Ashrei ("A Psalm of David") (Tur and the Kol Bo), and we double-recite the verse "Let every living soul praise God" because it is the conclusion of "The Psalms of Praise" (Tur), and so too for the verse "Hashem will rule forever and ever (Abudraham).

Mishnah Berurah sk 17

‏ (יז) לעולם ועד - ובשם האר"י כתבו שיש לומר ג"כ תרגום פסוק זה דהיינו שנים יאמר מקרא ואחד תרגום

In the name of the Arizal they wrote to say in addition the pasuk in Aramaic, so you'll have shnayim mikrah veechad targum

organic chemistry - Comparing acidities of substituted and aromatic carboxylic acids

When comparing the acidities of carboxylic acids, we primarily see the electropositivity of the carboxylic acid carbons, i.e. we see how effectively the negative charge on the carboxylate ion is dispersed upon ionization. Electron withdrawing groups increase the acidity by stabilising the anion via electron withdrawal.

Now consider the following two comparisons:-

1. Formic acid ($\ce{HCOOH}$) and benzoic acid($\ce{C6H5COOH}$)


2. Benzoic acid and 3-chloropropanoic acid ($\ce{ClCH2CH2COOH}$)

$$\begin{array}{c|c} \hline \text{Species} & \mathrm{p}K_\mathrm{a} \\ \hline \ce{HCOOH} & 3.75\mathrm{-}3.77 \\ \ce{PhCOOH} & 4.19 \\ \ce{ClCH2CH2COOH} & 3.98 \\ \hline \end{array}$$

(source)

My questions:

1. 
   

   Why is 3-chloropropanoic acid less acidic than formic acid. The negative inductive effect of chlorine helps in dispersing the negative charge on the carboxylate ion. It is not conjugated and too far to exert positive mesomeric effect. Therefore, the negative inductive effect should increase the acidity by improving the stability of the conjugate base.

   
   


2. 
   

   Why is benzoic acid weaker than formic acid? Unless I am mistaken, in several other places, the phenylic moiety is treated as slightly electron withdrawing, as in case of alcohol acidity, acidity of hydrogens in base catalysed reactions etc. I am unable to understand the resonance here or any other factor, that might cause this anomaly.

   
   

Answer

In the case of 3-chloropropanoic acid vs. formic acid, I suspect the disparity in expected acidity can mostly be explained by solvation effects. The 3-chloropropanoic acid is much bulkier than formic acid, and hence interacts with solvent molecules differently than formic acid does. There are two essential components to the thermodynamics of solvation:

1. Due to steric hindrance, it may be the case that the negative charge is less accessible to solvent molecules, and thus more weakly stabilized. I suspect the difference in enthalpy here is actually negligible, but I'm not able to find a reference at this time.


2. Perhaps more importantly, there is an entropic effect, in that larger molecules tend to require a larger number of solvent molecules to solvate them. These solvent molecules form highly ordered, cage-like structures, which is entropically unfavorable. I believe similar underlying mechanisms are at work in, e.g., the hydrophobic effect, micellization, protein folding, etc.

As Klaus Warzecha points out, if the chlorine were not as far-removed from the carboxylate moiety (since induction rapidly diminishes with growing distance), the strength of the inductive effect would trump the solvent effects.

In the case of benzoic acid, there are probably similar solvent effects occurring. Additionally, the benzene ring is actually electron-donating within the $\pi$-electron system of the molecule, which can only be destabilizing to the carboxylate conjugate base. Unlike in, e.g., phenol or aniline, the excess negative charge cannot actually be delocalized into the ring. Experimentally, the electron-donating effect of the ring (equivalently, the electron-withdrawing effect of the carboxylate) is confirmed by the fact that benzoic acid is severely deactivated in electrophilic aromatic substitution reactions by comparison to ordinary benzene. The benzene ring's electron-withdrawing effect within the $\sigma$-framework (rationalized, according to valence bond theory, by the greater s-character of $\mathrm{sp^2}$ carbons) of the molecule is probably quite weak. There may also be Coulombic destabilization between the strong $\delta^+$ of the carboxylate carbon atom and the $\mathrm{sp^2}$ carbons of the aromatic ring, again due to greater s-character, although that's speculative.

grammar - What's the meaning of もの in this sentence?

てっきり、兄{あに}は腰{こし}を下{お}ろすものだと思{おも}っていた。

I have no clue about what it could mean.

Answer

「Phrase/Mini-Sentence + ものだと思っていた」

is probably better if you remembered it as a fixed expression meaning:

"I just took it for granted that (Phrase/Mini-Sentence)."

"I never had the slightest doubt that (Phrase/Mini-Sentence)."

It would be practically impossible to translate the 「もの」 all by itself here, but it is being used to refer to an "assumed fact".

「てっきり、兄{あに}は腰{こし}を下{お}ろすものだと思{おも}っていた。」

therefore means:

"Without thinking, I simply had assumed that my older brother would sit down."

physical chemistry - Why are C6 dispersion forces named C6?

I'm reading about water models and their dispersion coefficients, and going back to S. C. Wang's work according to the citation of an equation (Google books here)

As you can see one citation's to a biographical work, and the other to a German work.

Nowhere in the chapter I'm reading (chapter 5, ‘Resolution’, in Rowlinson’s 2002 Cohesion: A Scientific History of Intermolecular Forces) does it say what $C_6$ stands for, and it doesn't seem to be a series of $C_n$, so I'm a little confused.

There's the equation, apparently a Casimir-Polder integral

$$E_\mathrm{DS} = ‒\sum_{n=6,8,10,...} \left(\frac{C_n}{r_n}\right)$$

in something else I'm reading, but it's biochemistry and so they're skipping over actually defining these things (so I can see DFT would be density functional theory but can't actually figure out what either $E_\mathrm{DS}$ is, nor the meaning of a $C_6$ coefficient. Looking for $E_\mathrm{DS}$ is just bringing up a bunch of articles' editors in search results (Eds.).

Can anyone enlighten me as to the latter - the meaning of a $C_6$ coefficient with respect to [London] dispersion forces?

My own answer to this after more reading

The oscillating electrons in a molecule generate not only instantaneous dipoles but also quadrupoles and higher multipoles. It is to be expected, therefore, that the London dispersion energy is only the first term in a series expansion for the attractive energy

that starts in $$u(r) = −C_6r^{−6}$$

The term comes originally from the wave equation (as Rowlinson's text does eventually describe), the number six arising from a Cartesian coordinate system for each of the two interaction partners

Answer

From Calculation of Coefficients in the Power Series Expansion of the Long‐Range Dispersion Force between Atoms J. Chem. Phys. 56, 2801 (1972)

Highly accurate calculations of $C_6$, the coefficient of the $R^{-6}$ term, resulting from an induced dipole-induced dipole interaction, have been made for many atomic systems, while values of $C_8$ (dipole-quadrupole interaction) and $C_{10}$ (dipoleoctopole plus quadrupole-quadrupole interactions) are...

In other words, in London dispersion interaction is usually represented as induced dipole - induced dipole interaction, the energy of which is proportional to $R^{-6}$, but there are other components of the interaction.

inorganic chemistry - Is shielding of electrons really best described as shielding or is it really Coulombic repulsion between electrons?

For example, take the 2s electron in lithium - is the reason that it's ionisation energy is lower than would be expected if "shielding" didn't occur at all because the 1s electrons shield the attractive coulombic force from the nucleus or because the 2s electron is repelled by the 1s electrons? Is it possibly a mixture of the two?

To me, shielding seems to be a model to help conceptualize what is actually happening; am I wrong about this? What is actually going on?

Answer

The shielding model works as follows:

(source)

So it is a mixture of attraction and pushing from protons and non-valence electrons, in accord with the Coulomb's law. The prediction of the effective core charge is not an easy task - you will have to use quantum chemistry methods (e.g. Hartree-Fock) to predict those, like its done in this reference.

I think its best viewed as a pragmatic model to boil down the higher, not very graphic, quantum theories, to one number, the effective nuclear charge: $$ Z_\text{eff} = Z - S$$

chasidut hasidism - Who are the chassidei klali?

I've heard of these people who wear chasidic garments, pray nusach sfard, and learn chassidus but don't follow one chassidus exclusively or have one rebbe they follow. Does this fit in with a normal chasidic system? Is this a new thing? I just want clarification because I am a chussid, have a rebbe and I follow one chassidus or I learn from other chassidusen (whatever my rebbe thinks is appropriate for me).

syntax - 「が」vs「の」 with possessives

I know that the normal possessive form is usually formed subject+「の」+object. Though, in one instance, I found が being used in 天は我が物. I know that 「が」 can be used to express possession, though is there a certain way it can be used.

Answer

が for possession was more common in old Japanese.

But it's rare today and it only remains in proverbs (e.g. [人間]{にんげん}[万事]{ばんじ}[塞翁]{さいおう}が[馬]{うま}) and other fixed phrases.

One exception is [我]{わ}が. Usages as follows is common today.

• 我が社, 我が国, 我が母校, etc.


• 我が物顔


• [我]{わ}が[家]{や}

我が is still old-fashioned has a bit arrogant nuance, so if someone is using 我が unlimitedly, I feel like he is playing a role of [魔王]{まおう}.

I recommend you to use が for possession only in such fixed phrases.

zemanim - Why is twilight called "Bein Hashmashot"?

Inspired by this question, I'm curious why halachic literature calls twilight בין השמשות, which means, literally, "between the two suns"? The sun has set, and there is just one sun, anyway. What do they mean by saying "two suns"?

I understand that the twighlight period is considered safek (doubtful) day or night. But, night is the absence of the sun. What does it mean by referring to "two suns" and being "between" them?

Answer

1. 
   
   

   According to Kipa here the reason is that it is after the sun ("Shemesh of the day") finishes lighting up the sky and before the moon ("Shemesh of the night") lights up the sky. Therefore, this time period is between the "two suns".

   
   

   This name makes perfect sense, as the "sun of the day" is not fully gone, but the "sun of the night" hasn't fully arrived, so it is a Safek if it is the time of the old Shemesh (of the day), or the new Shemesh (of the night).

   
   


2. 
   

   According to Wikishiva here, it is between when the sun disappears, and when it's light goes away:

   
   

   
   

   ביאור השם "בין השמשות" הוא: הזמן שבין שקיעת גוף השמש ובין העלם אור השמש, כלומר: בין שתי "שמשות"‏

   
   

   
   

   This would also make sense - the setting of the sun could be the end of the day, and darkness could be the beginning of the night.

   
   

halacha - Pirating software

I have heard from numerous people that there are opinions within Orthodox halacha that permit using pirated computer software. I have never seen this sourced or printed anywhere but only things like "I spoke to a rabbi once" or "my friend researched this extensively and it's ok.".

Can anyone share sources or names of poskim who are on record allowing use of pirated computer software?

names - What is the greatest number of pages (daf) you can go in the Babylonian Talmud without encountering Abayei or Rava?

What is the greatest number of pages (daf) you can go in the Babylonian Talmud without encountering Abayei or Rava? I've heard it was 3?

minhag - What are the major regions relevant to Ashkenazi minhagim?

Motivating this question are the instructions in the ArtScroll Siddur for the two versions of kel erekh apayim, said on weekdays before taking out the sefer torah: one is identified as “נוסח אשכנז, פיהם, ופולין קטן”, the other as “נוסח פולין גדל וליטא”. Similarly, selichos are listed as “מנהג פולין” or “מנהג ליטא”.

My question is in two parts:

• What do “פיהם”‎, “פולין גדל”‎, “פולין קטן”‎, “ליטא”‎, etc. specifically refer to? and (more importantly)


• When classifying Ashkenazi minhagim, which regions of Europe are significant?

(By “significant” I might [for example] include Frankfurt am Main [ק״ק פפד״מ] since its minhagim were historically important and distinct from elsewhere in the Germanies, but the simple fact that the one-horse town of Magyaslozckin had some unique minhagim of its own would not rate it a mention.)

gentiles - Who do B'nei Noach turn to for psak?

My understanding is that there are a few organized groups of non-Jews who strive to follow the Noahide laws. Just like Jews, B'nei Noach might have situations where the correct action to take is unclear. When Jews have such a problem, they ask a competent halachic authority their question. Presumably, there must be an equivalent type of "posek" who can answer the questions of the non-Jews and determine what their halacha is.

Are there any people who are known as prominent poskim for non-Jews? Are these poskim rabbis or are they non-Jews?

Answer

There are a number of Rabbis, mostly Chabad, involved in teaching Bnei Noach and answering their halachic questions. One of the more prominent ones is Rabbi Yaakov Rogalsky, co-author of Path of the Righteous Gentile. Another is Rabbi Chaim Richman.

halacha - What do you do if you forgot to turn off the refrigerator light before Shabbat?

The first time you open a fridge on Shabbat, you notice the light is on. Your intention is to take out food, not turn on the light. Is closing the fridge a problem? Can I open it again? Is it better to just unscrew the light once rather than turn it on and off each time you open and close the fridge the rest of Shabbat?

(Of course, CYLOR.)

halacha - May I daven wearing headphones?

There are many paths to concentration. I have known students who doodle because it helps them focus on a lecture more effectively. Others like to listen to music while they study either to help them focus, or to drown out other noises. If my kavana is increased by the removal of distractions, may I put headphones on while I daven my shmoneh esrei? [related, but about learning]

Would it make a difference if

a. I had ear plugs in

b. I wore headphones but nothing came through them

c. the noise I listened to was ambient/environmental (rain, waves, white noise) as opposed to instrumental music (and is that any better/worse than music with lyrics)?

I know that one should be able to hear himself davening but even with headphones on, one can hear his own voice.

One answer I have heard repeatedly is that we should conduct ourselves in a way which would be appropriate were we talking to a head of state. If I wouldn't address the president wearing headphones, then I shouldn't when I daven. But I also wouldn't address the president with a shawl on my head, or wearing leather straps, or shuckling so that equivalence is not exact.

If the goal is to increase my kavana is there any limit to what I can and can't do (barring actions which explicitly violate other halachot) to increase my focus and concentration?