Wednesday, January 31, 2018

korban - Why do we bring a sin offering on rosh chodesh, given the midrash about changing the size of the moon?


We bring a sin offering as a 'kapara' for hashem for decreasing the size of the moon. The story goes that the moon said we cant have two 'kings' the same size so I want to be bigger. Hashem says no you will be smaller but to make up for it I give you stars. It seems they didnt exist before that. The moon was still not satisfied it seems stars dont make up for 'size' so hashem says I have to bring a sin offering for decreasing the moon' size.


So the question is why not increase her size again and dont bring a sin offering. If it was right to decrease it shouldnt need a sin offering and if it was wrong then increase it again. This story is also mentioned regarding korach that if you ask for more even what you have got is taken away.


בי שמעון בן פזי רמי כתיב (בראשית א, טז) ויעש אלהים את שני המאורות הגדולים וכתיב את המאור הגדול ואת המאור הקטן אמרה ירח לפני הקב"ה רבש"ע אפשר לשני מלכים שישתמשו בכתר אחד אמר לה לכי ומעטי את עצמך


https://he.wikisource.org/wiki/%D7%97%D7%95%D7%9C%D7%99%D7%9F_%D7%A1_%D7%91




conjugations - What is the etymology of 〜ません(でした)?


I have always been interested in the negative polite (〜ません) and negative past-polite (〜ませんでした) inflections of verbs.



My understanding is that ます is an inflectable function word (助動詞), so I'm wondering why the negative form ends with ん. Is that a contraction of ぬ perhaps? (Also why is the 未然形 ませ rather than something more regular, like まさ?)


The really weird thing for me is でした (the past inflection of the polite copula), showing up for the negative past-polite form. Has this always been the way to handle this sort of semantics, even in Classical Japanese, or is this a recent introduction to the language?


Although I think there is probably no really satisfying answer to why things are like this, I do think it'd be interesting to know how things evolved through time, so any answers revealing some of that information are welcome!



Answer




My understanding is that ます is an inflectable function word (助動詞), so I'm wondering why the negative form ends with ん. Is that a contraction of ぬ perhaps?



Yes, the final -n is from negative -nu. This should make sense as -nu attaches to the irrealis, which is ma-se since mas- is サ変.



(Also why is the 未然形 ませ rather than something more regular, like まさ?)




masu is assigned the サ変 conjugation. As such, the irrealis is ma-se. Conjugation types can change over time, but サ変 is used in other words as well, so there is currently no motivation for such a change. That said, in the early stages of masu, there are a few extant usages of irrealis ma-sa indicating experimentation as a 四段 conjugation; though this form is rare and never prevailed.



The really weird thing for me is でした (the past inflection of the polite copula), showing up for the negative past-polite form. Has this always been the way to handle this sort of semantics, even in Classical Japanese, or is this a recent introduction to the language?



There were originally several competing negative past polite forms: masenkatta, masen datta, and masen desita. Early citations for masen desita appear around 1860s. As desu became more common and standard, the past polite standardized on masen desita by the 1890s. At this point, it is modern Japanese, not classical.


nevua prophecy - What is the qualitative difference between the revelation at Sinai and other miracles according to Rambam?


In Hilchot Yesodei HaTorah (8:1), Rambam writes:



משה רבינו לא האמינו בו ישראל מפני האותות שעשה שהמאמין על פי האותות יש בלבו דופי שאפשר שיעשה האות בלט וכשוף אלא כל האותות שעשה משה במדבר לפי הצורך עשאם לא להביא ראיה על הנבואה היה צריך להשקיע את המצריים קרע את הים והצלילן בתוכו צרכנו למזון הוריד לנו את המן צמאו בקע להן את האבן כפרו בו עדת קרח בלעה אותן הארץ וכן שאר כל האותות ובמה האמינו בו במעמד הר סיני שעינינו ראו ולא זר ואזנינו שמעו ולא אחר האש והקולות והלפידים והוא נגש אל הערפל והקול מדבר אליו ואנו שומעים משה משה לך אמור להן כך וכך וכן הוא אומר פנים בפנים דבר ה' עמכם ונאמר לא את אבותינו כרת ה' את הברית הזאת ומנין שמעמד הר סיני לבדו היא הראיה לנבואתו שהיא אמת שאין בו דופי שנאמר הנה אנכי בא אליך בעב הענן בעבור ישמע העם בדברי עמך וגם בך יאמינו לעולם מכלל שקודם דבר זה לא האמינו בו נאמנות שהיא עומדת לעולם אלא נאמנות שיש אחריה הרהור ומחשבה


The Jews did not believe in Moses, our teacher, because of the wonders that he performed. Whenever anyone's belief is based on wonders, [the commitment of] his heart has shortcomings, because it is possible to perform a wonder through magic or sorcery.


All the wonders performed by Moses in the desert were not intended to serve as proof [of the legitimacy] of his prophecy, but rather were performed for a purpose. It was necessary to drown the Egyptians, so he split the sea and sank them in it. We needed food, so he provided us with manna. We were thirsty, so he split the rock [providing us with water]. Korach's band mutinied against him, so the earth swallowed them up. The same applies to the other wonders.



What is the source of our belief in him? The [revelation] at Mount Sinai. Our eyes saw, and not a stranger's. Our ears heard, and not another's. There was fire, thunder, and lightning. He entered the thick clouds; the Voice spoke to him and we heard, "Moses, Moses, go tell them the following:...."


Thus, [Deuteronomy 5:4] relates: "Face to face, God spoke to you," and [Deuteronomy 5:3] states: "God did not make this covenant with our fathers, [but with us, who are all here alive today]."


How is it known that the [revelation] at Mount Sinai alone is proof of the truth of Moses' prophecy that leaves no shortcoming? [Exodus 19:9] states: "Behold, I will come to you in a thick cloud, so that the people will hear Me speaking to you, [so that] they will believe in you forever." It appears that before this happened, they did not believe in him with a faith that would last forever, but rather with a faith that allowed for suspicions and doubts. (Touger translation)



I am trying to figure out what the qualitative difference is between what happened at Sinai and any of the other wonders mentioned. The only things mentioned here that happened at Sinai are that "we" saw and heard thunder, lightning, Moshe entering the clouds, and a voice speaking to Moshe.


This does not appear to be qualitatively different from a regular miracle. In fact I'm not even sure it sounds quantitatively different from the other miracles. Moshe split the sea, brought food from the sky, produced water from a rock, and opened the earth. He also walked into clouds accompanied by thunder, lightning, and fire, and we heard a voice.


Rambam's point here is that miracles are not sufficient proof because one could argue that the miracles were somehow done by man himself and are not really from God. So if an onlooker would think that Moshe somehow split the sea, rained food from the sky, drew water from a rock, and split the earth on his own, why couldn't they think that he had produced the thunder, lightning, fire, and voice at Sinai on his own?


What was it about the events at Sinai that proved that it was a divine revelation and not merely another miracle?


Some people will undoubtedly answer that the difference is that at Sinai the people actually experienced the prophetic revelation as opposed to the other cases where they merely witnessed the miracles. Indeed this seems to be R. Yosef Albo's understanding of this point in Sefer HaIkkarim 1:18. However, even if we were to grant that experiencing a prophetic revelation is qualitatively different from witnessing a miracle, in that a prophet somehow knows with certainty that he is prophesying (which itself is a question), I don't think it would help us here. Rambam himself in Guide for the Perplexed explains at length that what the masses experienced at Sinai was not prophecy; indeed he writes that it is impossible for people who don't have the prerequisites of prophecy to prophesy.


Guide for the Perplexed 2:32




We hold that fools and ignorant people are unfit for this distinction. It is as impossible for any one of these to prophesy as it is for an ass or a frog; for prophecy is impossible without study and training; when these have created the possibility, then it depends on the will of God whether the possibility is to be turned into reality. (Friedlander translation)




As to the revelation on Mount Sinai, all saw the great fire, and heard the fearful thunderings, that caused such an extraordinary terror; but only those of them who were duly qualified were prophetically inspired, each one according to his capacities. Therefore it is said, "Come up unto the Lord, thou and Aaron, Nadab and Abihu." Moses rose to the highest degree of prophecy, according to the words, "And Moses alone shall come near the Lord." Aaron was below him, Nadab and Abihu below Aaron, and the seventy elders below Nadab and Abihu, and the rest below the latter, each one according to his degree of perfection. (Friedlander translation)



Guide for the Perplexed 2:33



IT is clear to me that what Moses experienced at the revelation on Mount Sinai was different from that which was experienced by all the other Israelites, for Moses alone was addressed by God, and for this reason the second person singular is used in the Ten Commandments; Moses then went down to the foot of the mount and told his fellow-men what he had heard. Comp., "I stood between the Lord and you at that time to tell you the word of the Lord" (Deut. v. 5). Again, "Moses spake, and God answered him with a loud voice" (Exod. xix. 19). In the Mechilta our Sages say distinctly that he brought to them every word as he had heard it. Furthermore, the words, "In order that the people hear when I speak with thee" (Exod. xix. 9), show that God spoke to Moses, and the people only heard the mighty sound, not distinct words. It is to the perception of this mighty sound that Scripture refers in the passage, "When ye hear the sound" (Deut. v. 20); again it is stated, "You heard a sound of words" (ibid. iv. 12), and it is not said "You heard words"; and even where the hearing of the words is mentioned, only the perception of the sound is meant. It was only Moses that heard the words, and he reported them to the people. (Friedlander translation, my emphasis)




Thus it seems that according to Rambam himself, the regular people only heard a sound. So in what sense is this different from other miracles? Here they witnessed a miraculous sound, and elsewhere they witnessed other miraculous phenomena. On what basis, then, does Rambam maintain that the revelation at Sinai was qualitatively different from other wonders, such that the former is a proof to Moshe being the messenger of God while the latter is not?


(I am aware of this related question, but I do not believe it is a duplicate. That question is simply asking how we know the revelation at Sinai wasn't a trick. My question is how Rambam distinguishes the believability of the revelation at Sinai from the believability of other miracles. Indeed, the answers to the other question would not work according to my portrayal of Rambam here. I am also aware of this related question, but that one only asks how magic could be faked according to Rambam, not what the difference was between the revelation at Sinai and other miracles.)




Discrete approximation to Gaussian filter


One method of producing a discrete approximation kernel to a Gaussian filter of variance $\sigma^2$ is to assume a cutoff of $5\sigma$. This seems to suggest the following procedure:




  1. Create a uniform grid $\mathbb{x}$ of size $11(=2*5+1)$ between $[-5\sigma,5\sigma]$

  2. Evaluate $\mathcal{N}(\mathbb{x};0,\sigma)$ and obtain the discrete approximation.


The blue lines in the second plot below depict the discretized values(for $\sigma=1.5$). In this case, the result is not a proper filter kernel since the sum of values is not $1$.


But MATLAB's fspecial does things a bit differently. For the call fspecial('gaussian',[1 11],sigma)



  1. Create a uniform grid $\mathbb{x}$ of size $11(=2*5+1)$ between $[-5,5]$

  2. Compute $\mathbb{x}'= e^{\frac{-\mathbb{x}^2}{2\sigma^2}}$

  3. Normalize $\mathbb{x}'$ so that it sums to $1$



The green lines in the first plot below the values as computed by MATLAB's fspecial(for $\sigma=1.5$).


enter image description here What is the difference between both methods ?



Answer



The first method involves computation of the Gaussian function including its normalization factor. The normalization factor is relevant for the full distribution. In fact, evaluating it at discrete points is not correct since it is meant to be used for a continuous distribution. However, even if we omit the normalization factor from the function, we could still use the uniformly discretized $[-5\sigma,5\sigma]$ to compute the filter. In fact, the first method has the nice property that filter values fall at intervals of $\sigma$.


Most likely, the second method(MATLAB's) is used since we are guaranteed to have uniform discretization (stepping in integer increments) unlike the first method.


However, while plotting, we do need to use the normalization factor to ensure the vertical lines(green,blue lines in plots shown) line up nicely.


downsampling - Downsample: resample vs antialias fitlering + decimation


I have a discrete signal sampled @Fs. I need to downsample it to Fs/k. Main reason is to reduce signal bandwidth and speed up computation : I'm only interested in a reduced bandwidth < Fs/2k. Some high frequency noise >> Fs/2k can exist : antialiasing is needed. From what I understand, I have several options :



  1. brute force : decimation (without taking care of aliasing problem!)

  2. antialiasing + decimation : I can use for example numpy decimate function


  3. frequency approach : FFT then truncation then IFFT, can be done using resample


Only solution 2- 3- help solving antialiasing issue. 3- filters in frequency domain, supposing signal is periodic. 2- filters with IIR/FIR filter.


I can always use decimate without questioning, but I would like to precisely understand limitations behind. What are drawbacks / advantages of using solution 2- versus 3-? Do you have some practical guidelines about downsampling? Some recommendations?




reference request - What are the most extreme chemicals?


Some chemicals certainly have extraordinary properties. One can consider them extreme in a sense, that they are the prime example for a concept, or they achieve the highest or lowest values in a certain area.


This Q&A attempts to compile a list of questions asked on this network, which have a background related to such extreme values or properties. we decided to add such a list because it is a popular search term.


It is a community effort, hence everybody with more than 100 reputation points can edit the answer. If you think something is missing in this list, just go ahead and add it. This post will be locked to prevent adding new answers, though. The corresponding discussion can be found on meta.chemistry.se. If you think there are some obvious points missing here, please go there and open a discussion.



Answer





Good external lists:



modulation - Gardner Timing Recovery for Repeated Symbols


I am implementing the Gardner Timing Error Detection algorithm for a QPSK signal. I understand the concepts behind it but I am curious as to what effect repeated signals can have on the phase lock.


If a symbol is repeated (maybe twice, maybe one hundred times) would the error not accumulate out of control? As I understand it the Gardner method looks at peaks and zero crossings to determine the timing error. If for, example, a symbol is repeated many times, would the algorithm not spiral out of control? If the symbol never changes, the algorithm would keep determining that there was symbol error and push the loop filter further and further from the true symbol timing; only fixing itself after a new lock in time when symbol transitions start occurring again.


Am I correct in thinking this will happen? If so, is it mitigated by the assumption that real world data will never (or very infrequently) repeat symbols more than a couple times in a row?


Thank you,




Answer



Your Gardner Loop would properly "Flywheel" in the absence of symbol transitions. So it would slowly drift off of synchronization, but would not spiral out of control as you describe. This is ideal for a control system with "missing updates"; to have the contributions for those updates with no additional information to contribute 0 to the accumulated error, resulting in a "flywheel" behavior. There are other detectors used to discriminate the control term in loops (such as a digital phase-frequency detector used in PLL implementations (such as this device: Maxim Phase Frequency Detector) that produce maximum error in the absence of transitions, and these systems would move off of lock at the maximum speed possible - this would be bad for timing recovery where we expect to have missing bits!


See my picture below demonstrating the operation of the Gardner Loop. In the absence of transitions, the Timing Error Detector would be zero on average as the Late and Early samples would be the same, and therefore $Late - Early = 0$.


enter image description here


Here is another post I made earlier with more information on the Gardner Loop:


Location of Matched Filter


number - Shemona Ve'arba'im Umatayim?


Who knows two hundred forty-eight?


Please cite/link your sources, if possible. At some point at least twenty-four hours from now, I will:




  • Upvote all answers I consider relevant and interesting.





  • Accept the what I think is the "best" answer.




  • Go on to the next number.




The Race to Ramach starts now.



Answer



Hashem examined each word of the Tora 248 times before putting it in the Tora (whatever that means), corresponding to the 248 evarim (bones or something) of a person (source), which in turn correspond to the 248 words of sh'ma (source) and mitzvos ase (positive commands).


number - Sheloshim?


Who knows thirty?


Please cite/link your sources, if possible. After about one business day, I will:





  • Upvote all interesting answers.




  • Accept the best answer.




  • Go on to the next number.





Answer




At 30 years one attains full strength (Avot 5:25)


megillat esther - What is the source for writing names of Haman's sons in a separate column?


What is the source for writing names of Haman's sons in a separate column? We see that most megillos are written this way, but where can I find halacha? Shulchan Aruch doesn't seem to be discussing it?



Answer



The Talmud Yerushalmi (Megillah 3:7) says about the list that the word איש should be at the "head" of the column and ואת should be at the "end" of it. Some versions (see Masekhet Sofrim 13:6) also mention that עשרת should be at the "end" of the column. The remarks about איש and עשרת are important because we may have thought the song structure didn't include those words and, for example, the last line could read ויזתא עשרת בני המן בן without any gaps.


Now it's clear from the fact that every ואת [and עשרת] can't all be at the bottom of the column that either "דפא -- column" here means row, or that "head" and "end" mean the right and left sides respectively. Many Rishonim note this explicitly (Haghot Maymoniot Megillah 2:12 quoting Ri and Maharam, Haghot Ashiri Megillah 1:9, Or Zarua 373, Semag Asin Derabanan 4, Raavyah 253 in the name of the Bahag, Beit Yosef 691, and more). This is the practice in ancient Esther manuscripts.


The practice of writing the names in their own column is a "stringency" so that איש can literally be at the top of the column and עשרת can be at the literal bottom. This practice presents a number of Halakhic problems in terms of spacing and font sizes (eg. Beiur HaGra OC 691), but it remains quite popular (see the valiant defense of the Nishmat Adam 155). The Vilna Gaon, 3rd Lubavitcher Rebbe, Chatam Sofer, Aruch leNer and others did not write the sons of Haman in a separate column.


The earliest source I'm aware of that mentions matching the top or bottom of the column is the Orchot Chayim (Megillah 17) who mentions "some" who put עשרת at the bottom of the column because of קבלה (tradition?). (It seems from his wording that he views this as an alternative to what he viewed as the "mainstream" tradition of placing איש at the top of the column, not that he advocated doing both and stretching the letters (cf. his comments in 18 about stretching the letter ו in ויזתא).)


The source that most gets quoted through in the Acharonim is the Keneset HaGedolah (OC 691) who develops a theory that while the above proof shows that ואת needs only to be at the end of the row, the extra claim of עשרת at the end of the column found in Masekhet Soferim is to be taken as the bottom of the column not the end of the row. He thus ruled that we should be stringent not to read from a Megillah where עשרת is not at the bottom of the column, even though the Tur doesn't even mention that extra claim regarding עשרת, since many Rishonim (including many of those listed above as explaining "end" as "left side") did mention the extra claim of עשרת at the end. He argues that the Tur must not have seen Masekhet Sofrim's expanded version and he definitely would have ruled like it if had. Many didn't find this convincing (Beit Ephraim OC 70, Chatam Sofer OC 190, Ginat Veradim 4:12). Even the Keneset HaGedolah agreed that if you already read from a scroll that didn't have עשרת at the bottom of the column that you don't need to read it again.


The only Rishon I'm aware of who explicitly indicates that איש must be at the top of the column and עשרת at the bottom is the Piskei Tosfot (Megillah #30).



Tuesday, January 30, 2018

sampling - Oversampled polyphase filter banks


i would a confirm of this: with polyphase structure is possible only design a filter bank with a INTEGER oversampling ratio? For non-integer i've seen the weighted overlap-add metod, is right?


thanks S.




halacha - eBay Judaica auctions


I occasionally check eBay for assorted items; this is typically for the science half of my life, but I sometimes find Judaica which probably should not be sold there. For example, I know that in the case of a sefer torah, there is an obligation to purchase, rather than letting it go to a non-Jew. Does this always apply and furthermore, does it apply to purchasing other sta"m (holy scribe-written) products?




Minhag to wear wedding ring on the right hand


I don't have much background on this question--it's simply that I've seen some married Chabad women wearing their rings on the right hand. Why?


Is it because the right hand is considered "preferable" by Judaism? ...Because the ring is put on the right hand under the chuppah? ...Because that is how rings were (and are) worn in Russia?



Also, who and which groups have this custom?




lowpass filter - Differences between filtering and polynomial regression smoothing?


What are the differences between classical low-pass filtering (with an IIR or FIR), and "smoothing" by localized Nth degree polynomial regression and/or interpolation (in the case of upsampling), specifically in the case where N is greater than 1 but less than the local number of points used in the regression fit.



Answer



Both low pass filtering and polynomial regression smoothing could be seen as approximations of a function. However, the means of doing this are different. The key question to ask here is "Can you do one in terms of the other?" and the short answer is "not always", for reasons that are explained below.


When smoothing by filtering the key operation is convolution where $y(n)=x(n)*h(n)$, which in the frequency domain translates to $y=F^{-1}(F(x)F(h))$ where $F$ denotes the Discrete Fourier Transform (and $F^{-1}$ the inverse). The Discrete Fourier Transform (e.g. $F(x)$) offers an approximation of $x$ as a sum of trigonometric functions. When $h$ is a low pass filter, a smaller number of low frequency components are retained and the abrupt changes in $x$ are smoothed out. This sets low-pass filtering in the context of function approximation by using trigonometric functions as the basis functions, but it is worth revisiting the convolution formula to note that when filtering, y(n) (the output of the filter) depends on $x(n)$ as well as a weighted sum of past samples of $x$ (the weighting here determined by the "shape" of $h$). (similar considerations hold for IIR filters of course with the addition of past values of $y(n)$ as well)


When smoothing by some n-degree polynomial though, the output of the interpolant depends only on $x(n)$ and a mixture of (different) basis functions (also called monomials). What are these different basis functions? It's a constant ($a_0x^0$), a line ($a_1x$), a parabola ($a_2x^2$) and so on (please refer to this for a nice illustration). Usually though, when dealing with equi-distant samples in time and for reasons to do with accuracy, what is used is Newton's form of the polynomial. The reason i am citing this is because through that it is easy to see that when performing linear interpolation you could construct a filter kernel that returns a linearly weighted sum of available samples, just as a low order interpolation polynomial would use "lines" to interpolate between two samples. But at higher degrees, the two approximation methods would return different results (due to the differences in the basis functions).



As i wrote above, not taking into account past values of $x(n)$ is not strict. This is a subtle point. Because usually, when building a polynomial the values outside the given interval ("past" and "future" of a signal) are not considered. It is however possible to include these by fixing the derivatives at the edges of the interval. And if this is done repeatedly (like a non-overlapping sliding window) then effectively, the "past samples" of x(n) would be taken into account. (This is the trick that splines use and in-fact there is a convolution expression for bicubic interpolation. However, please note here that the interpretation of $x$ is different when talking about splines -note the point about normalisation-)


The reason for using filtering as interpolation some times, say for instance in the case of "Sinc Interpolation", is because it also makes sense from a physical point of view. The idealised representation of a band-limited system (e.g. a (linear) amplifier or lens in an optical system) in time domain is the sinc pulse. The frequency domain representation of a sinc pulse is a rectangle "pulse". Therefore, with very few assumptions we expect a missing value to be more or less near its neighbours (of course, within limits). If this was performed with some n-order polynomial (for higher n) then in a way we "fix" the way that a missing value is related to its neighbours which might not always be realistic (why should the sound-pressure values of a wave-front hitting a microphone be fixed to have the shape of a $x^3$ for example? It puts an assumption on how the sound-source behaves which might not always be true. Please note that i do not imply any suitability of an interpolation scheme from a psychophysics point of view here, which involves the processing of the brain (see Lanczos resampling for example). I am strictly speaking about constraints imposed by interpolation when one tries to "guess" objectively missing values.


There is no universal "best method", it pretty much depends on the interpolation problem you are faced with.


I hope this helps.


P.S. (The artifacts generated by each of the two approximation methods are different as well, see for example the Gibbs Phenomenon and overfitting, although overfitting is "at the other side" of your question.)


christianity - Did the Vilna Gaon study Torah on Christmas?


I'm looking for some information (sourced) about the Vilna Gaon and Nittelnacht. Did the Vilna Gaon avoid the study of Torah on the night of Nittel (Christmas) as was done by some European communities or was that minhag not followed by the Gaon?




halacha - Brewing fresh coffee for Shabbos with a time clock


May one prepare coffee ingredients in a brewer such as this one on Friday and set the timer to brew the coffee for 8:00 Shabbos morning?




Answer



The Sefer Yerushas Pleita (Siman 16) brings from a sefer called Matta Yerushalayim that quotes in the name of the Chasam Sofer that it was common for people to set up a fire on Erev Shabbos in a way that would burn along a path until shabbos morning where it would reach the stove that had a coffee pot sitting on top and it would cook it.


Based off this the Shearim Metzuyanim Behalacha (Vol. 2. Siman 72 note 42) says that to set a timer for the coffee is not a problem. For although the electricity is lit on Shabbos, it is not any worse than the practice quoted above.


Of course the water and the coffee are already prepared in the pot before shabbos.


As noted in other answers here Rav Moshe Feinstein, as well as other prominent Poskim, forbade this practice.


This is not to be relied upon for practical halacha.


tefilla - Why summarize m'nachos in musaf?



In every musaf prayer service, we read an excerpt from Bamidbar delineating the musaf animal sacrifices of the day. While each day's passage in Bamidbar includes also a description of the flour and oil offerings brought along with the animals, we don't read that excerpt, instead summarizing it; we use the same (or almost the same) wording every musaf prayer.



  • Why do we summarize instead of finishing up the quotation we've started?

  • Are there any nuschaos (versions) that do (or did) include the entire quotation rather than a summary?


The one exception is the musaf of Shabas, whose passage in Bamidbar we quote entire and do not summarize.



  • Does the reason I seek above for summarizing not apply to Shabas? If it does apply, why don't we summarize the passage of Shabas also?

  • Are there any nuschaos (versions) that do (or did) summarize the passage of Shabas as other days'?





On later reflection: The reason we don't summarize the musaf of Shabas (my third bulleted question) is presumably that it'd require quoting half a pasuk a verbatim. But a source for that would be nice; and, anyway, that doesn't answer my first two (and last) bulleted questions.



Answer



According to this article, in Eretz Yisrael in ancient times they did recite the entire section for each Yom Tov (including the verses describing the menachos and nesachim). But because it's difficult to remember them (particularly before siddurim began to be written), in Babylonia the ומנחתם ונסכיהם paragraph was created to regularize the description of that part of the korban (which in the Torah has various subtle variations from day to day).


[Other Geonim held (based on Rosh Hashanan 35a, see Rashi there ד"ה כיון and אין צריך) that even that's not necessary; the Sephardic nusach to this day follows suit, and omits the pesukim of the korbanos (and ומנחתם ונסכיהם) entirely. On the other hand, Rashi eventually accepted the position of R. Meir Shliach Tzibbur (the author of Akdamus) that they should be recited, and this became the Ashkenazic practice.]


As for Shabbos, Rashi writes that its pesukim were always recited in Ashkenazic communities even before R. Meir came along, "because they are constant and [therefore] familiar." So there was probably also less of a need to use ומנחתם ונסכיהם to replace any part of those two pesukim. (Also, anyway it would be factually incorrect - דובר שקרים - to use it in its standard form, since there is no שעיר לכפר on Shabbos.)


Monday, January 29, 2018

grammar - What kind of verbs can the suffix たて (立て) attach to?


Why can -たて attach to some verbs and not others? What is a more precise definition of how to use it?



I had been aware of the suffix -たて as meaning 'an action just/newly completed/occurred' for a while but I covered it in my textbook more formally today. It attaches in the form of 連用形+たて. For example,
焼きたて = freshly baked
とりたて = freshly picked
ペンキ塗りたて = newly painted


However, my book also stated that you can't say the following.
読みたて
寝たて
食べたて


If the definition above was correct, I should be able to use it for those words. That definition is also supported by the dictionaries I've looked it up in:
Yahoo! Jisho "動詞の連用形に付いて、その動作が終わったばかりであることを表す"

Jisho.org "indicates activity only just occurred; just (done)"




historical figures - Is Pinchas of Balak/Pinchas same Pinchas as Shoftim?


Is the Pinchas from the generation that left Egypt the same as the Pinchas mentioned in Shoftim 20?


Pinchas's zealotry earns him an eternal priesthood because of going above the letter of the law and risking his own life (al pi Rashi) to exact judgement.


The Pinchas of Shoftim calls on Israel to battle Binyomin to the point of nearly exterminating the tribe. In this case the zealotry isn't a positive choice and because of this error causes thousands of Jews to perish.


I am interested in anyones findings in the Gemara, Commentary on Tanach, etc. that connect these two Pinchas individuals as the same and also discuss the topic of zealotry.





physical chemistry - Testing a sodium aluminate solution


I prepared some sodium aluminate by reacting a strong $NaOH$ solution with aluminium foil and filtering the result. I now have a clear solution and I'm not sure what it is. I stopped adding aluminium when the reaction rate showed down dramatically in a hot water bath. Basically what I'm asking is what are the properties of sodium aluminate since Wikipedia is severely lacking in information on sodium aluminate



Answer



There are multiple reactions going on simultaneously. Aluminum metal reacts with the oxygen in surrounding air in order to create a plating of aluminum (III) oxide.


$$\ce{4Al(s) + 3O2(l) -> 2Al2O3(s)}$$


Upon addition of sodium hydroxide, the oxide layer reacts with the base, leaving the aluminum free to attack by water for instance.


$$\ce{2 Al + 6 H2O -> 2 Al(OH)3 + 3 H2}$$ $$\ce{Al(OH)3 + NaOH -> Na+ + [Al(OH)4]-}$$


In summary, we can write the sum of the reactions as:


$$\ce{2Al(s) + 2NaOH(aq) + 6H2O(l) -> 2Na+(aq) + 2[Al(OH)4]- + 3H2(g)}$$



The reason why the reaction proceeded slowly at first was due to the aluminum (III) oxide layer covering the aluminum metal.


From this link, http://www2.uni-siegen.de/~pci/versuche/english/v44-10.html:



This reaction is used in drain cleaners. They are mostly made out of strong alkalis, to which alumunim or zinc has been added. The alkalis break down organic residues chemically. In addition, the formation of hydrogen leads to a bubbling effect which adds an additional mechanical cleaning mechanism.



Considering the properties of aluminates, one can go to PubChem hosted by the NIH which has a lot of information for almost every single compound necessary as well as literature linked to the specific compound in question:


http://pubchem.ncbi.nlm.nih.gov/summary/summary.cgi?cid=14766&loc=ec_rcs


enter image description here


physical chemistry - Derivation of the Heisenberg uncertainty principle


The Heisenberg uncertainty principle states that


$$\Delta x \Delta p \geq \frac{\hbar}{2}$$


where
$\Delta x$ is the uncertainty in the position,

$\Delta p$ is the uncertainty in linear momentum, and
$\hbar = 1.054571800(13) \times 10^{-34}\ \mathrm{J\ s}$[source] is the reduced Planck constant


This means that, regardless of what quantum mechanical state the particle is in, we cannot simultaneously measure its position and momentum with perfect precision. I read that this is intrinsically linked to the fact that the position and momentum operators do not commute: $[\hat{x},\hat{p}] = \mathrm{i}\hbar$.


How can I derive the uncertainty principle, as given above?



Answer



The proof I will use is taken from Griffiths, Introduction to Quantum Mechanics, 2nd ed., pp 110-111.


Defining "uncertainty"


Let's assume that the normalised state $|\psi\rangle$ of a particle can be expanded as a linear combination of energy eigenstates $|n\rangle$, with $\hat{H}|n\rangle = E_n |n\rangle$.


$$| \psi \rangle = \sum_n c_n |n\rangle \tag{1}$$


The expectation value (the "mean") of a quantity, such as energy, is given by



$$\begin{align} \langle E\rangle &= \langle \psi | H | \psi \rangle \tag{2} \end{align}$$


and the variance of the energy can be defined analogously to that used in statistics, which for a continuous variable $x$ is simply the expectation value of $(x - \bar{x})^2$:


$$\sigma_E^2 = \left\langle (E - \langle E\rangle)^2 \right\rangle \tag{3}$$


The standard deviation is the square root of the variance, and the "uncertainty" refers to the standard deviation. It's more proper to use $\sigma$ as the symbol, instead of $\Delta$, and this is what you will see in most "proper" texts.


$$\sigma_E = \sqrt{\left\langle (E - \langle E\rangle)^2 \right\rangle} \tag{4}$$


However, it's much easier to stick to the variance in the proof. Let's generalise this now to any generic observable, $A$, which is necessarily represented by a hermitian operator, $\hat{A}$. The expectation value of $A$ is merely a number, so let's use the small letter $a$ to refer to it. With that, we have


$$\begin{align} \sigma_A^2 &= \left\langle (A - a)^2 \right\rangle \tag{5} \\ &= \left\langle \psi \middle| (\hat{A} - a)^2 \middle| \psi \right\rangle \tag{6} \\ &= \left\langle \psi \middle| (\hat{A} - a) \middle| (\hat{A} - a)\psi \right\rangle \tag{7} \\ &= \left\langle (\hat{A} - a)\psi \middle| (\hat{A} - a) \middle| \psi \right\rangle \tag{8} \\ &= \left\langle (\hat{A} - a)\psi \middle| (\hat{A} - a)\psi \right\rangle \tag{9} \end{align}$$


where, in going from $(7)$ to $(8)$, I have invoked the hermiticity of $(\hat{A} - a)$ (since $\hat{A}$ is hermitian and $a$ is only a constant). Likewise, for a second observable $B$ with $\langle B \rangle = b$,


$$\sigma_B^2 = \left\langle (\hat{B} - b)\psi \middle| (\hat{B} - b)\psi \right\rangle \tag{10}$$


The Cauchy-Schwarz inequality



...states that, for all vectors $f$ and $g$ belonging to an inner product space (suffice it to say that functions in quantum mechanics satisfy this condition),


$$\langle f | f \rangle \langle g | g \rangle \geq |\langle f | g \rangle|^2 \tag{11}$$


In general, $\langle f | g \rangle$ is a complex number, which is why we need to take the modulus. By the definition of the inner product,


$$\langle f | g \rangle = \langle g | f \rangle^* \tag{12}$$


For a generic complex number $z = x + \mathrm{i}y$, we have


$$|z|^2 = x^2 + y^2 \geq y^2 \qquad \qquad \text{(since }x^2 \geq 0\text{)} \tag{13}$$


But $z^* = x - \mathrm{i}y$ means that


$$\begin{align} y &= \frac{z - z^*}{2\mathrm{i}} \tag{14} \\ |z|^2 &\geq \left(\frac{z - z^*}{2\mathrm{i}}\right)^2 \tag{15} \end{align}$$


and plugging $z = \langle f | g \rangle$ into equation $(15)$, we get


$$|\langle f | g \rangle|^2 \geq \left[\frac{1}{2\mathrm{i}}(\langle f | g \rangle - \langle g | f \rangle) \right]^2 \tag{16}$$



Now, if we let $| f \rangle = | (\hat{A} - a)\psi \rangle$ and $| g \rangle = | (\hat{B} - B)\psi \rangle$, we can combine equations $(9)$, $(10)$, $(11)$, and $(16)$ to get:


$$\begin{align} \sigma_A^2 \sigma_B^2 &= \langle f | f \rangle \langle g | g \rangle \tag{17} \\ &\geq |\langle f | g \rangle|^2 \tag{18} \\ &\geq \left[\frac{1}{2\mathrm{i}}(\langle f | g \rangle - \langle g | f \rangle) \right]^2 \tag{19} \end{align}$$


Expanding the brackets


If you've made it this far - great job - take a breather before you continue, because there's more maths coming.


We have1


$$\begin{align} \langle f | g \rangle &= \left\langle (\hat{A} - a)\psi \middle| (\hat{B} - b)\psi \right\rangle \tag{20} \\ &= \langle \hat{A}\psi |\hat{B}\psi \rangle - \langle a\psi |\hat{B}\psi \rangle - \langle \hat{A}\psi | b\psi \rangle + \langle a\psi |b\psi \rangle \tag{21} \\ &= \langle \psi |\hat{A}\hat{B}|\psi \rangle - a\langle \psi |\hat{B}\psi \rangle - b\langle \hat{A}\psi | \psi \rangle + ab\langle \psi |\psi \rangle \tag{22} \\ &= \langle \psi |\hat{A}\hat{B}|\psi \rangle - ab - ab + ab \tag{23} \\ &= \langle \psi |\hat{A}\hat{B}|\psi \rangle - ab \tag{24} \end{align}$$


Likewise,


$$\langle g | f \rangle = \langle \psi |\hat{B}\hat{A}|\psi \rangle - ab \tag{25}$$


So, substituting $(24)$ and $(25)$ into $(19)$,


$$\begin{align} \sigma_A^2 \sigma_B^2 &\geq \left[\frac{1}{2\mathrm{i}}(\langle\psi |\hat{A}\hat{B}|\psi \rangle - \langle \psi |\hat{B}\hat{A}|\psi\rangle) \right]^2 \tag{26} \\ &= \left[\frac{1}{2\mathrm{i}}(\langle\psi |\hat{A}\hat{B} - \hat{B}\hat{A}|\psi \rangle ) \right]^2 \tag{27} \end{align}$$



The commutator of two operators is defined as


$$[\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \tag{28}$$


So, the term in parentheses in equation $(27)$ is simply the expectation value of the commutator, and we have reached the Robertson uncertainty relation:


$$\sigma_A^2 \sigma_B^2 \geq \left(\frac{1}{2\mathrm{i}}\langle[\hat{A},\hat{B} ]\rangle \right)^2 \tag{29}$$


This inequality can be applied to any pair of observables $A$ and $B$.2


The Heisenberg uncertainty principle


Simply substituting in $A = x$ and $B = p$ gives us


$$\sigma_x^2 \sigma_p^2 \geq \left(\frac{1}{2\mathrm{i}}\langle[\hat{x},\hat{p} ]\rangle \right)^2 \tag{30}$$


The commutator of $\hat{x}$ and $\hat{p}$ is famously $\mathrm{i}\hbar$,3 and the expectation value of $\mathrm{i}\hbar$ is of course none other than $\mathrm{i}\hbar$. This completes the proof:


$$\begin{align} \sigma_x^2 \sigma_p^2 &\geq \left(\frac{1}{2\mathrm{i}}\cdot\mathrm{i}\hbar \right)^2 \tag{31} \\ &= \left(\frac{\hbar}{2}\right)^2 \tag{32} \\ \sigma_x \sigma_p &\geq \frac{\hbar}{2} \tag{33} \end{align}$$



where we have simply "removed the square" on both sides because as standard deviations, $\sigma_x$ and $\sigma_p$ are always positive.




Notes


1 I have skipped some stuff. Namely, $\langle \hat{A}\psi |\hat{B}\psi \rangle = \langle \psi |\hat{A}\hat{B}|\psi \rangle$ which is quite straightforward to prove using the hermiticity of both operators; $\langle \psi |\hat{A}|\psi \rangle = a$; $\langle \psi |\hat{B}|\psi \rangle = b$; and $a = a^*$ since it is the expectation value of a physical observable, which must be real.


2 This does not apply to, and cannot be used to derive, the energy-time uncertainty principle. There is no time operator in quantum mechanics, and time is not a measurable observable, it is only a parameter.


3 Technically, it is a postulate of quantum mechanics. (If I am not wrong, it derives from the Schrodinger equation, which is itself a postulate.)


halacha - What is the source for the mitzvah of kiruv?


Is kiruv a mitzvah? Is it biblical or rabbinic? Is there any reason it should supersede other mitzvot? what are the sources in chazal and halacha relating to kiruv?


related: Kiruv and halachik compromise




Minhag of married women shaving during marriage


The custom for married women to shave their heads is, evidently, a fairly widespread custom that exists at least amongst (certain) Hasidim. I have heard a variety of supposed, non-authoritative explanations for this practice, but, hitherto, I have been unable to find an explicit, written source. It would be greatly appreciated if some light were shed on this subject matter, particularly the following questions:




  1. What is the source/origin of this minhag? What is the underlying reasoning behind it? Is it primarily halakhic? Kabbalistic? Cultural? Historically speaking, how old is it?

  2. Sociologically speaking, who abides by this custom? For instance, some (e.g. Satmar) clearly do adhere to this practice whilst others (e.g. Sepharadim) clearly do not. My understanding had been that this was an exclusively hasidic minhag. Is this truly so? Are there non-Hasidim/Misnagdim who hold this way? If so, who? Conversely, are there Hasidim who don't practice this? If so, who, and why?




halacha - Do surgically removed body parts require Kevurah?


If one has surgery (may it never be necessary) that requires the removal of an organ of the body (e.g. a gallbladder or appendix), is burial required? Or can the body part simply be discarded?




korban - Where did Hevel get the idea to offer an animal?


We know (Bereishit 4) that Hevel kept flocks (not for eating yet, but perhaps for wool and/or milk?), and on that fateful day he offered one to God which Rashi says God consumed in fire. Where did he get the idea to offer an animal in the first place? Or if Adam and Chava offered animals and he learned from them, where did they get the idea?


Nowhere in the text does God call for such offerings and it doesn't seem like an obvious idea. Did they reason somehow that this would be desired by God? Is there midrash in which God does call for korbanot?


(This related question asks how killing an animal was ok before people could eat meat.)




parshanut torah comment - What happened to the bechorim (first-borns)?


In the begining of sefer bamidbar, the males between 20 and 60 are counted and it says that there are over 600,000 of them. Theoretically each, or most, of these people should have had a first-born child and half of these children should be males. But two prakim later, the first-born males one month old and up are counted and instead of there being about 300,000, there are only about 22,000. Why are there so few?


I checked several mefarshim and none of them seemed to have an answer.



Answer



Some portion of the 600k males were not married, and some of the married ones had no children at all.


Of those that were, only 22k families had first-borns which needed to be redeemed by a Levite or 5 shekalim. Not all firstborns need redemption, in fact, a Pidyon heBen ceremony is relatively rare.



  1. As you already noted, the child must be male.

  2. If the child was preceded by a non-viable child, it is exempt.


  3. The child must have born naturally (i.e. males born via C-section are exempt).

  4. Neither the father nor the mother may be a member of the tribe of Levi.

  5. Some percentage of the remainder were no longer alive.

  6. The son must have been born first for certain - if there were twins and it isn't certain which arrived first, there is no redemption. (Recall that Jewish mothers gave birth on their own, to 6 at a time, in the fields, sometimes abandoning their children. It is likely that many were unsure which was the first born).


Sunday, January 28, 2018

halacha - Is it a sin to joke about sinning?


For instance, to joke about committing suicide or something less extreme like eating non-kosher.


My inclination is towards saying that it is forbidden since it might desensitize one to the idea itself, even if only by a small amount. However, I have no sources on the matter, which is why I ask.


Edit: To clarify, I'm strictly talking about a spoken joke, not a practical one.




Slang for "funny", うくれ?


A friend of mine told me that he heard うくれ or 受けれ was slang for funny (He said it was suppose to be "we accept"). I don't really know much more that that so I'm having trouble finding it online-does anyone have ideas what it could have been?




infinite impulse response - How does this "simple filter" work?


I'm new to DSP, and I'm using this basic "1-pole LPF" Param Smooth filter which "smooth" param when I change it. The code is pretty simple:


class CParamSmooth
{
public:
double a, b, z;

CParamSmooth() {
a = 0.8;
b = 1. - a;

z = 0.;
}

double Process(double in) {
z = (in * b) + (z * a);
return z;
}
};

If I try some values with "strong" a coefficients, I can see that it starts heavy on increment, then becomes smooth till "rounding" happen, setting z = in:



0 | 0.16
1 | 0.288
2 | 0.3904
3 | 0.47232
4 | 0.537856
5 | 0.590285
6 | 0.632228
7 | 0.665782
8 | 0.692626
9 | 0.714101

10 | 0.731281
11 | 0.745024
12 | 0.75602
13 | 0.764816
14 | 0.771853
15 | 0.777482
16 | 0.781986
17 | 0.785588
18 | 0.788471
19 | 0.790777

20 | 0.792621
21 | 0.794097
22 | 0.795278
23 | 0.796222
24 | 0.796978
25 | 0.797582
26 | 0.798066
27 | 0.798453
28 | 0.798762
29 | 0.79901

30 | 0.799208
31 | 0.799366
32 | 0.799493
33 | 0.799594
34 | 0.799675
35 | 0.79974
36 | 0.799792
37 | 0.799834
38 | 0.799867
39 | 0.799894

40 | 0.799915
41 | 0.799932
42 | 0.799946
43 | 0.799956
44 | 0.799965
45 | 0.799972
46 | 0.799978
47 | 0.799982
48 | 0.799986
49 | 0.799989

50 | 0.799991
51 | 0.799993
52 | 0.799994
53 | 0.799995
54 | 0.799996
55 | 0.799997
56 | 0.799998
57 | 0.799998
58 | 0.799998
59 | 0.799999

60 | 0.799999
61 | 0.799999
62 | 0.799999
63 | 0.799999
64 | 0.8
65 | 0.8
66 | 0.8
...

So, basically, each iteration is a sum of 0.16 + prev z * 0.8. And here is where I don't understand: why 0.16 + prev z * 0.8 can't go "over" 0.8?



In fact, this become stable when z = in. Without rounding, z will always be < in. Why it can't go > in?


It's a sum on each iteration... who limits it?



Answer



In more standard DSP terms, you have the following filter:


$$ y[n] = (1-a) x[n] + a y[n-1] $$


where $x[n]$ and $y[n]$ are the input and output signals at time $n$ respectively.


The transfer function (which you didn't ask for) is:


$$ H(z) = \frac{1-a}{1 - az^{-1}} $$


so here is your single pole, at $z=a$ in the complex plane. This filter is also known as exponential smoothing, exponential moving average (EMA), or exponentially weighted moving average (EWMA).


The infinite impulse response is $h[n] = (1-a) u[n] a^n$. In layman terms, when the input signal is 0 except for $x[0]=1$, the output signal is an exponential $(1-a) \times a^n$ starting at $n=0$.



What you want is the step response (i.e. what happens if the input signal is a constant $K$ starting at time $n=0$).


In this case, the output signal is the convolution $h \star Ku$ of the impulse response and the step signal. This is (for time $n \ge 0$):


$$ y[n] = \sum_{k=0}^{k=n} K \times h[k] = K(1-a) \sum_{k=0}^{k=n} a^k = K(1-a)\frac{1-a^{n+1}}{1-a} = K (1-a^{n+1}) $$


As the time $n$ grows, $a^{n+1}$ vanishes, and the step response grows monotonically to its limit value $y = K$, which is the value of the input signal.


This is what you get in your simulation.


jewish books - Jacob Neusner's talmud bavli and yerushalmi


How does Jacob Neusner's translations of the talmud bavli and yerushalmi compare to artscroll's, koren's, and soncino's?



I have never seen Neusner's in a shul or bais midrash unlike the other three mentioned; is there a reason for that? Is it an accurate translation?




meaning - Why is ば in this sentence?



そんなトコで何ばしよる。




I'm reading a manga and from the context of the pictures I think this sentence reads, "What are you doing up there," but I have no idea what part ば plays. The character speaks in a dialect so my confusion could be a result of that, but any help would be much appreciated.enter image description here



Answer



is the accusative particle used in wide area of (northern, as I remember) Kyushu as much as を in Standard Japanese. Etymologically it's from を + は contracted but no longer has share the は sense in Standard Japanese, as we can see that it's able to mark the question word (thanks to @user4092).



そんなトコで何ばしよる。



means



そんなとこで何をしてる(んだ)。




or a bit more textbook-friendly,



そんなところで何をしている(のだ)。



organic chemistry - HCH bond angle in cyclopropane and cyclobutane


I understand why the $\ce{CCC}$ bond angles in cyclobutane and cyclopropane are less than ideal $109.5^\circ$ due to the geometric restrictions they encounter in a cyclic structure. However, it is not clear to me how the $\ce{HCH}$ angles (which turn out to be greater than ideal) are affected by this constraint.




usage - What does ただいま actually mean?


I was wondering what the literal translation really means. I've seen it translated as I'm home but I've also seen it in a few situations where the person wasn't arriving home.



Answer



The [ただいま]{LHHH} that you say when you arrive home is a contraction of ただ今帰りました.
(ただ = たった/just, 今 = now, 帰りました = (I) came back / came home / returned)


I think one other situation you're talking about might be where you say 「ただいま」, 'Certainly, sir' / 'Yes sir, I'll do that right away' / 'Yes, I'll be right with you', etc., when someone tells you to do something or calls you, and probably rushes you. I think this [ただいま]{LHLL} (with a stress on だ and a falling tone on いま) literally means 'right now' 'right away', like 「(はい、)たった今(行きます/参ります。」 or 「(はい、)今すぐに(します/やります)。」


onomatopoeia - What does バタバタ mean?


What does バタバタ mean?



コラム書かなきゃ。映像チェックしなきゃ。アレも書かなきゃ。アレも考えなきゃ。バタバタバタ子さん(´・_・`)



Everything make sense to me except for the last part.



Answer



バタバタ is an onomatopoeia expressing busyness. Usually, a Japanese onomatopoeia repeats a two-mora part (like バタ) twice, four morae in total, but here, it is repeated thrice.


Saturday, January 27, 2018

halacha - What to do with the Cross on the Chess King?


Many (perhaps most) Chess sets come with a King piece that has a cross on the top of it. Is there any problem with owning or using such a chess set? Should one break off the cross?




Is there a negative connotation around converting to Judaism?



Is there any text in the Torah or Mishnah that sees a convert as some kind of "imitation" Jew or someone who isn't as good as a real-deal matrilineal Jew?



Answer



A ger tzedek is a very great thing and there's nothing negative about it. One of the greatest Jewish scholars, Onkelos, was a convert. His translation of the Torah into Aramaic is printed in most chumashim.


It's a very negative thing if someone converts insincerely or for ulterior motives, marriage is a very common reason. As Shalom answered " The Talmud does say that "converts are as troublesome for mainstream Jews as a skin disease." " I recall this gemara, although I'm not so sure if it said skin disease, or something else similar. An example of this is Shlomo Hamelech's wives, who converted insincerely and cause a lot of trouble.


avodath hashem - Is one allowed to say God's name twice in a row?


I remember hearing that one should not say the name of God twice in row, because some might conclude there are two gods. (The only exceptions would be direct Torah quotes, such as "Hashem, Hashem, kel rachum vechanun…", because the context makes it clear there is only one God.)


Is this true and what is the source?




usage - What's the difference between [V-ながら][V2] and [V-ている]間 [V2]?


What's the difference between [V-ながら][V2] and [V-ている]間[V2] ?


For example, is there any difference in nuance between these 2 sentences:




  1. トムはテレビを見てる間勉強していた





  2. トムはテレビを見ながら勉強していた





Answer




田中さんは、AをしながらBをします



means that Mr Tanaka primarily does A. Incidentally, he also does B.



田中さんは、友達と飲みながら通常会話を学びます。 Mr Tanaka learns casual conversation skills while drinking with his friends.




The main action is drinking, it's the whole context. Incidentally, it's also the unrelated opportunity to practice conversation.


Some grammar books would tell you that "ながら" is similar to "のに", to show that it's linking two different actions, and does not concern time (even though they are simultaneous):



テレビを見ながら、宿題に集中する



is almost "even though I'm watching the telly, I'm concentrating on my homework." It's a kind of opposition showing that the two actions are not logically connected.


noble gases - Why can't helium nuclei (alpha particles) react with fluorine?


Alpha particles are basically just helium nuclei, so it will accept an electron pair to become stable.


Will fluorine, being highly electronegative, not just donate an electron pair but form a bond with helium?



Answer



Why, many atoms would readily create a bond with helium, when it comes in a form of alpha particle (just cooled down enough to chemically interact with). There is comparatively stable $\ce{HeH}^+$ and other similar particles, too. But a positive particle is not a compound yet. And when you try to form a compound out of it, that is, to balance it with some negative ions - well, that's where the problem arises. It would violently react with absolutely anything else, form some compound, and happily release the neutral helium atom.


Friday, January 26, 2018

halacha - Does braille go to sheimos?


Do things that, when written in print, require placement in sheimos (such as shem Hashem and divrei Torah), need to be placed in sheimos when written in Braille? Would we say that since most people can't read it, it doesn't need to be put into sheimos; or, would we say that since a large portion of the population can read it, that it would require placement in sheimos?



Answer



Rav Zilberstein writes in Veha'arev Na (page 441), that sheimos written in Braille require placement in sheimos, as they are read by a wide audience of blind people.



Challenge: May divrei Torah written in braille be thrown in the garbage, or do they require genizah like divrei Torah written in normal script?


Solution: Since braille is a written language read by a wide audience of blind people, it has the same status as any other written script. Therefore, divrei Torah written in braille must be placed in genizah.



colloquial language - Is 行ってみい a dialect form of 行ってみよ?


The following dialogue is from Final Fantasy XII:




さて……王宮に忍びこむ方法じゃがな。
まず5番倉庫に行ってみい
あそこに扉が2つあるじゃろう?



I bolded 行ってみい. I'm not sure what this is, and there's no dictionary entry for みい. My guess is that it's a dialect form of 行ってみよ with the last vowel dropped. I think that without the /o/ at the end, /miy/ becomes /miː/. Does this make any sense?


Here's a picture from the game:


Screen shot of Final Fantasy XII



Answer



「わしは~」「~じゃ。」「~(じゃ)ろう。」「~(じゃ)のう。」「~てみい。」 etc. are not regional dialect but フィクションにおける老人語 (Wikipedia):




この老人語は江戸時代以来、セリフの約束ごととして、老人や知識人を表現するための役割語として演劇・小説・漫画等に定着したものという。
これらの言葉は現代の広島弁に近いが、広島弁が直接的に老人語とされたわけではない。江戸時代、江戸在住の知識人は京都や大坂など西日本の出身者が多く、西日本出身でなくても知識人はそれに合わせた話し方をしていたとされる(当時「じゃ」は近畿地方を含む西日本各地で使用されており、現在の「や」に移行するのは江戸幕末期以降である)。当時「物知り」と云われる人は年配者であり、また当時の文化の中心は近畿地方であったことから、「老人」と「西日本出身」のイメージが結びつき、それらの人の言葉が定着したのではないかという。



老人語・・・ [行ってみい]{LLHHL} (老人語 is spoken with the intonation of standard Japanese)


関西弁・・・ [行ってみい]{HHHLH} (We have a different intonation pattern in Kansai)




Yes, the みい is from みよ. According to Wikipedia 近畿方言・命令:



五段・カ変動詞の命令形は共通語と変わりないが、サ変・一段動詞の命令形には文語命令形「・・・よ」の転「・・・い」を用い(例:見よ→見い)・・・




grammar - The uses & etymology of で


In Japanese, the particle で seems to have multiple uses:



  1. Instrumental: 車{くるま}大阪{おおさか}に行{い}った。 "I went to Osaka by car."

  2. Locative: 図書館{としょかん}数学{すうがく}を勉強{べんきょう}している。 "I'm studying math in the library."

  3. て-form of copula: 水{みず}はきれい静{しず}かだ。 "The water is pretty and calm."

  4. て-form of copula (sentence conjunction): 彼{かれ}は来{く}るの、大丈夫{だいじょうぶ}だ。 "He's coming, so it'll be fine."

  5. 連用形{れんようけい} of copula: そうはない。 "That's not how it is."



(It may be possible to analyze #4 as a 連用形, in the 中止形{ちゅうしけい} sense, but I don't think that's what is in modern usage, since there is an implication of temporal order.)


What is the origin of these uses? Do all these でs historically come from one thing?


(I've heard that "で came from にて", but that doesn't really explain much for me in terms of how all these forms came about and if they are really all from the same original thing.)



Answer




What is the origin of these uses?




  1. Instrumental: contraction of case particle -ni and particle -te. In many cases (*), you can interpret this as ni + verb + -te. In your example, it could be 車に乗って大阪に行った.

  2. Locative: contraction of case particle -ni and particle -te. In many (*) cases, you can interpret this ni + verb + -te. In your example, it would be 図書館「に来て」数学を勉強している.


  3. Te-form of copula: contraction of 連用形 of copula -nari (-ni) + the particle -te. More precisely, -nari itself is a contraction case particle -ni + verb ar-, so while not direct, the etymology is essentially the same as #1 and #2.

  4. Reason: This is not the te-form of the copula. Rather, it expresses reason. It is a contraction of case particle -ni and particle -te.

  5. 連用形 of copula: Same as #3.


Note (*): I have not done a survey of this, nor am I aware of any such studies. So I will refrain from saying 'always'. But it is a tendancy that I have noted numerous times over the years.



Do all these でs historically come from one thing?



You would be safe to split them into two groups: (#1, #2, #4) and (#3 and #5). Though as I wrote, an argument could be made that they are all ultimately of the same etymology.


There is another de that you are missing. As in a conversation a person can say "de? (dou natta? nani ga atta?)" to help continue the topic. This is an abbreviation of "soko de" or "sore de".



There is also de found in various Kansai dialects. "iku de", "koute kita de". This is thought to be a variation of "ze" (~zo).


Both of these would be in their own etymology groups as well.


grammar - How to express two of the same object, but different colors?


For example, I would like to say, "Please wash the white and blue plates." Meaning that there are white plates and blue plates to be washed. (Not plates that contain both the colors blue and white)


I know you could say 白い皿と青い皿, but is there a way to express the same idea without having to repeat the noun (in this case 皿) and not sound unnatural?


I wasn't sure if 白い皿と青い皿 could be expressed to something like 白いと青い皿。(Which doesn't look right to me)



My attempt:白いか青い皿を洗いなさい。(This still sounds kinda strange to me)


And to my understanding,


白い青い皿=Plates that are colored both white and blue


白くて青い皿=Same as above? Plates that are colored both white and blue? (I'm not sure if the くて gives a different meaning. I looked at this, but I'm still a little unsure.



Answer



白いと青い皿 is ungrammatical.


You can use くて to join two i-adjectives, and 白くて青い皿 means something like "a white blue plates", which is perhaps grammatical but a bit confusing. Anyway, it never means "blue plates and white plates" if you joined two i-adjectives like this.


白いか青い皿 is ungrammatical, but it's likely to be taken as the same as 白い、または青い皿 ("plates which are either blue or white").


I would suggest you say 白と青の皿 using the nouns to refer to colors. This is still ambiguous between "white-and-blue plates" and "white plates and blue plates", but at least can safely refer to the latter.




白と青の皿を洗って。赤いのはいいから。
Wash white and blue plates. Forget red ones.



halacha - Following minhagim when praying in a different community?


Say you go to a minyan of a different community than your own, how should you behave?



  1. When being hazan do you use their pronunciation or yours?


  2. Do you pray your nusach or theirs?





  3. Do you put on talit before marriage if the community does not?




  4. Etc.




To rephrase, do you adopt the customs of the community, or stick with your own or stick with your own in some cases and adopt the community's customs in others?



Answer



The rule of thumb Rabbi Moshe Feinstein applies is to not be disruptive.



In communities where it is clearly the standard practice that all men wear tallitot, I would think that doing otherwise would be disruptive and/or disrespectful. (And what's the downside, really?)


As for what text you yourself use, as long as you're not too loud, generally people aren't bothered by what words you're whispering. (It gets trickier with regards to the parts recited out-loud by the congregation, e.g. kadosh kadosh and the like; with Rabbi Feinstein of the opinion that you should follow the congregation's text for the entire kedusha.) If you want to use their text instead that's generally your option too. Rabbi Feinstein davened nusach ashkenaz but, as a boy, there was a point when his father took him to the local Hassidic synagogue, and instructed him to follow their text completely, with the exception of reciting the Mishnaic BaMeh Madlikin rather than the Kabbalistic KeGavna on Friday nights. (This is clearly a later addition, not even a prayer per se.)


The hazan's job description is shliach tzibur, he is the proxy of the congregation. As such he is expected to abide by their customs and standards. Now in your average American OU synagogue today it's not uncommon that several forms of Hebrew pronunciation are all acceptable. However if you were to go to say, a German or Yemenite synagogue that has very clear, homogeneous standards of pronunciation, then to not use those would be disruptive. Leaving pronunciation aside, if you are hazan and your personal text differs from the community's, obviously you'd use the community's for the out-loud repetition of the amida. Rabbi Feinstein's opinion is that you should even use their text for your own personal, silent amida if you are hazan, as the enactment was that the hazan should use this time to prepare for his out-loud recitation. On this last point I'm told that Rabbi Ovadiah Yosef shlit"a differs, allowing the hazan to use his personal text for the silent amida.


Rabbi Feinstein discusses the debate regarding Selichot prayers which seem to be addressing angels, rather than G-d; he writes that the Chasam Sofer (OC166) would skip the quietly-recited machnisei rachamim prayer, as this disrupted no one; but would recite the out-loud ones with the rest of congregation. (Even when not the chazzan.)


minhag - Origin of Chabad tefillin



I have wondered for some time about certain elements of Chabad minhagim re. tefillin, so here goes:



  • What is the origin of their kesher shel yad? (asked elsewhere)

  • When was it decided that they should be huge (4x4cm or larger)

  • Why must they be mikshah (made of one piece)?

  • Why is their ש different from both the Arizal ש and the written form of the Alter Rebbe ש? What is the source for this?


I'm sure there are other concerns which I have missed, but these are the main factors which make them unique, in my opinion.




filters - What should be considered when selecting a windowing function when smoothing a time series?


If one wants to smooth a time series using a window function such as Hanning, Hamming, Blackman etc., what are the considerations for favouring any one window over another?



Answer



The two primary factors that describe a window function are:



  1. Width of the main lobe (i.e., at what frequency bin is the power half that of the maximum response)

  2. Attenuation of the side lobes (i.e., how far away down are the side lobes from the mainlobe). This tells you about the spectral leakage in the window.



Another not so frequently considered factor is the rate of attenuation of the sidelobes, i.e., how fast do the sidelobes die down.


Here's a quick comparison for four well known window functions: Rectangular, Blackman, Blackman-Harris and Hamming. The curves below are 2048-point FFTs of 64-point windows.


enter image description here


You can see that the rectangular function has a very narrow main lobe, but the side lobes are quite high, at ~13 dB. Other filters have significantly fatter main lobes, but fare much better in the side lobe suppression. In the end, it's all a trade-off. You can't have both, you have to pick one.


So that said, your choice of window function is highly dependent on your specific needs. For instance, if you're trying to separate/identify two signals that are fairly close in frequency, but similar in strength, then you should choose the rectangular, because it will give you the best resolution.


On the other hand, if you're trying to do the same with two different strength signals with differing frequencies, you can easily see how energy from one can leak in through the high sidelobes. In this case, you wouldn't mind one of the fatter main lobes and would trade a slight loss in resolution to be able to estimate their powers more accurately.


In seismic and geophysics, it is common to use Slepian windows (or discrete prolate spheroidal wavefunctions, which are the eigenfunctions of a sinc kernel) to maximize the energy concentrated in the main lobe.


kinetics - Comparing rate of reaction of acetic acid and sodium bicarbonate at different temperatures


Given the reaction between $\ce{CH_{3}COOH {(l)}}$ and $\ce{NaHCO_3 {(s)}}$, which happens at the same pressure but at different temperatures, is there any way to mathematically compare the rate of reactions?


I thought using the rate equations of order 2, but I use the same concentration of materials. Suppose I could have found the connection between temperature of he material and its concentration, I would be able to find my required rate-indicators.


How to find the connection between temperature and concentration, or how to describe the rate of the reaction more exactly?



Answer



Yes, there is, it has been done by others. Typical acid-base reactions that occur in solution are diffusion controlled reactions. Such reactions do not follow second order kinetics because at virtually every encounter of the acid and base, rapid proton transfer occurs and the reaction is complete. The reaction rate is limited only by how fast the acid and base can diffuse and encounter each other. It is usually easy to identify diffusion controlled reactions because they are extremely dependent upon the rate of stirring or mixing. They are also very sensitive to the solution viscosity. Rate constants for these reactions are typically $>\pu{10^11 sec^-1}$. Here is a link to a full paper that provides considerable experimental detail on one way to measure the rate of diffusion controlled acid-base reactions.


noise - Approximating the frequency response of a median filter


A median filter is a non-linear and lossy process, so it doesn't have a closed form frequency response as would a FIR filter (say a box filter of the same length) in an LTI system.



  • But how closely can something similar to a frequency response of a median filter be approximated?

  • How would this scale with the length of a median filter?

  • Under what conditions or for what class of signals might this approximation be ballpark "close"?

  • For what class of signals might this approximation be very inaccurate?

  • What kinds of frequency domain distortion or additive noise does a median filter produce?




Answer



For a start, any non-linear system will not have an easily-identifiable frequency response. So, it's really a nonsensical question. I intend no offense; nonsensical questions are often the most enlightening!


However one way to try to answer your question is to assume that the LTI filter involved is the mean (rather than the median) of the windowed data.


Then your question:



Under what conditions or for what class of signals might this approximation be ballpark "close"?



becomes:



Under what conditions or for what class of signals might the mean be ballpark "close" to the median.




In that case, for a purely stochastic signal, the mean and median are similar when the probability density function (PDF) of the signal is symmetric about the mean.



For what class of signals might this approximation be very inaccurate?



When the signal's PDF is "very" asymmetric.


kitniyos semigrain legume - Does cooking kitniyot in a pot render it non-kosher-for-Passover for Ashkenazic Jews? If so, why?


I've heard of cases where a Sephardic family, for whom rice is totally kosher for Passover (assuming it's checked and contains no additives etc.), cooked rice in a pot. The next day, they invite their Ashkenazic neighbors over and cook completely kitniyot-free, but their Ashkenazic neighbors say it's a problem as even potatoes cooked in that "kitniyot" pot is a problem.


Am I getting this correct so far?


If so, is there any halachic basis to this, or is it "just one of those Passover customs"?


This should, in theory, be far better than a case of a non-kosher pot; by some quick back-of-envelope math, for any normal pot I can think of, the ratio of volume-of-the-pot-material-itself against volume-contained-within-the-pot should be far less than 50%.



Answer



Those that cited OC 453 are correct: the Mishna Berura in Se'if Katan 8 states clearly that if rice was found in soup, just throw out the rice, and you may eat the soup. The same applies for a pot that was used to cook kitnios for a child that must have kitnios on Pesach. Whether lechatchila you may use the pot is debatable. The Feinsteins hold that one should not use the pot lechatchila, but if it has been used, one may eat the food lechatchila.


I would hesitate to cite Sfardic poskim on this issue. Some denigrate the Ashkenazic minhag of kitniyos and therefore rely on mattirim that we would not necessarily consider.



product recommendation - English-speaking yeshivoth for beginners


Can someone recommend a postsecondary yeshiva for English-speaking beginners in the US, Europe or Israel?


By "beginners" I mean people without good skills in gemara. For example, I studied Jewish law in an university in France but, in the religious world, my level would still be considered as low.




halacha - Swallowing fingernails


Although it is permitted to bite ones nails, and is not considered uncouth as is stated in Moed Koton (18a):




אמר רב שמן בר אבא הוה קאימנא קמיה דר' יוחנן בי מדרשא בחולו של מועד ושקלינהו לטופריה בשיניה וזרקינהו שמע מינה תלת שמע מינה מותר ליטול צפרנים בחולו של מועד ושמע מינה אין בהן משום מיאוס ושמע מינה מותר לזורקן



However, some people have a (IMO very disgusting) habit to swallow the nails after they bit them. Is this permitted? Is it considered as if you are consuming human flesh which is forbidden as stated in the Rambam (Maachlos Assuros 2:3):



והאוכל מבשר האדם או מחלבו בין מן החי בין מן המת אינו לוקה. אבל אסור הוא בעשה



Furthermore, the nature of biting nails is also that inevitably some parts of the skin around the nails is pulled off with the nail and that is consumed together with the nail.


Are there any poskim that discuss this?




halacha - Speaking lashon hara about someone who does not mind


Is it permitted to say negative things about someone when the person spoken about says that he does not mind and does not care if people speak negatively about him?




orthography - 皆さんはどんな字を書いていますか? / How do Japanese speakers write kana or kanji by hand?



この頃メタの方で「手書きの文字をチェックしてください」という質問は受け付けるべきかという話題がありました。個人的には受け付けてもよいと考えているのですが、何人もの学習者がわけもわからず同じような質問を繰り返すのでは生産性がない、という意見があり、これはその通りだと思いました。学習者は教科書などから字の書き方を学ぶと思いますが、初学者用の教科書体といえども、毛筆の運筆を残していたり、規範的すぎて普段自然にみる文字とはかけ離れた部分があると思います。



enter image description here enter image description here


また、今まで漢字・仮名のような独特の書き方の文字に接してこなかった人にとっては、教科書を見るだけでは、何に気をつけて書けばいいかわからないこともあると思います。


そこで、学習者にまず日本で行われている普通の手書き文字はどんななのか一定の認識を示し、そのうえで疑問点を明確にして質問を投稿してもらえるように、日本語の手書き文字のサンプルを集めたいなと考えています。



  • 自分はこういう字を書いている

  • こういう字が一般的だと思う

  • こういう書き方もアリだと思う


など、皆さんのご意見を募りたいと思います。よろしくお願いします。


(これはメインに置くべきかメタに置くべきか正直わかりません。移動すべきであればフラグを立ててください)




Recently we have a topic on meta about whether asking for checking handwriting is on-topic or not. I personally think those questions are not necessary to be ruled out, though I have to agree with an opinion that it's not productive to allow many learners to submit similar questions totally cluelessly. Who'd learn to write Japanese would refer textbooks or other resources, on which might be printed 教科書体 characters for novice writers, which is still somehow detached from what we see in the outside world by being too prim, prescriptive, or carrying over brushstroke style.


enter image description here enter image description here


Moreover, those who haven't ever come into contact with peculiar writing systems such as kana and kanji would have difficulties grasping the gist however they stared at the textbook.


So I'd like to accumulate living samples of ordinary handwritten Japanese so that we can provide a certain reference point to possible questioners to help them know well what they're going to ask. Any suggestions e.g.:



  • I write Japanese this way

  • I think this is a typical example

  • ... or an edge case



are appreciated.


Thank you for your cooperation!


(I'm not sure if this belongs on main or meta. If you think it should go meta, please flag it.)




Thursday, January 25, 2018

Why keep Kashrut?


Is there a known reason for keeping kashrut or is it a set of guidelines proposed by sages who we respect and don't question the logic behind?


Is there anything in the Torah that suggests kashrut?



Answer



These prohibitions come from the Torah, Leviticus 11. The sages added boundaries and stringencies but the source is from the Torah.


There are explanations given behind Kashrut, although the Torah does not explain them, nor are they dependent on the explanations.



For one explanation, Rabbi S. R. Hirsch, in Horeb (Chukim ch. 68 paragraph 464) says that the laws of Kashrut are because "you are what you eat," i.e. imbibing something symbolizes and in a certain respect creates an internalization of that thing. Therefore, vicious animals are prohibited to ingest because it internalizes viciousness. Rather, kosher animals are gentle - split hooves cannot be used as predatory, and chewing cud gives a certain nature of contentment with very little. Similar ideas are explained for all the types of non-Kosher (fish, creepy crawly things, etc.).


始まる->始まり Is there a rule of making nouns from verbs (besides nominalization)?


Lately my ears started catching words ending in り that seem like nouns created from verbs. I'm sorry I don't have any other examples besides the one from the title 始まる (to start) -> 始まり (the start). Is it just a small number of word pairs like that or there is some magic grammar formula to produce such nouns? ありがとうございます!



Answer



As a rule, a verb's 連用形 (conjunctive/continuative form) can become a noun (名詞化). I think that technically it doesn't matter what word it is. All can take that form and become nouns. In regular use, though, I think you'll find that words that are used this way are relatively limited. So we have common words like 始まり、綴り、しゃべり、 etc. It may be useful to think of these as distinct words that happen to follow this rule of nominalization, because there are quite a lot of words that you wouldn't normally use this way (though I don't think that means you can't). It's just a matter of what's most natural. For example, you wouldn't say 彼の言いを聞いてください. Rather you'd say 彼の言うことを聞いてください, or something along those lines that uses other forms of nominalization.


In my experience, outside of the 'usual' words that you can use, compound verbs seem to be the most common targets of this form, like 話し合い or 打ち合わせ or もの探し. You can also use these verb stems as suffixes. For example you can add ~作り to the end of something to refer to the act of making something (ケーキ作り, or making cake).


There are some words that take on unique meanings in this construction, though, so be wary. Like 見合い, which refers to arranged marriage rather than the literal act of looking at each other.


What are the differences/characteristics between katakana, kanji and hiragana?



I know that romaji is the conversion from those to the roman alphabet, but what are the differences or characteristics between katakana, kanji, and hiragana?


Are they used on a different context? Is one of them more formal than the others? Do they have something in common?



Answer



I think the Wikipedia article on the Japanese writing system explains it pretty well, but to summarize:



  • Hiragana and katakana (collectively referred to as kana) are syllabic writing, that is, each character represents a syllable such as "ta" or "o". They're purely phonetic so they don't have direct connotations as kanji do, and both have the same set of syllables. In modern writing:

    • Hiragana is generally used for Japanese words when they're not written in kanji, and for all the grammatical "glue" such as conjugations and particles.

    • Katakana is usually used for loanwords and onomatopoeia. There's no strict rule though, so you will see katakana used for other purposes as well, such as emphasis.




  • Kanji is ideographic writing, that is, each character represents a concept or an idea. For example, 水 means "water" while 朝 means "morning". Each character also has one or more readings, and the correct one depends on which word the kanji is part of. Many kanji (such as my two examples) can also act as stand-alone words.


quotes - Use of past tense in quoting others


In my textbook, it says the translation of "Roberto said it was interesting" to be



Robert-さんはおもしろかったといっていました.



Since we quote the person in the same tense they used, does this imply that Robert thought it was interesting, and that it is no longer interesting?


If Robert still thinks it's interesting, would this make more sense?




Robert-さんはおもしろいといっていました.




Answer



I think this is a bit tricky. In short: you are getting it right, but in this particular example he doesn't necessarily think it is no longer interesting: his comment was probably made on something that had finished earlier.


There's no tense agreement in Japanese, so we can think of these two pairs



Robert さんはおもしろいといっています。 -> Robert さんはおもしろいといっていました。


Robert さんはおもしろかったといっています。 -> Robert さんはおもしろかったといっていました。




and your observations are justified. ("Robertさんはケーキを[食]{た}べたかったといっていました" means he said he had wanted to eat cake [before the time of his remark], and "ケーキを食べたいといっていました" means he said he wanted.)


However, the expression "おもしろかった" rarely means that '[sb] thought it was interesting but no longer'. Rather, the phrase is more like [sb] enjoyed it being interesting/funny/entertaining. Like, after finishing a book, we'll exclaim "ああ、おもしろかった!". So if what "it" in the example refers to took place earlier, we can safely interpret おもしろかった as "he enjoyed it".


Let's add some context. Let's pretend our Robert is a student, and he commented about some lectures.



Robert さんはその[授業]{じゅぎょう}がおもしろかったといっていました



He enjoyed the class, and said it had been interesting after it's finished.



Robert さんはその授業がおもしろいといっていました




His comment was most likely made during the class or mid-term.


digital communications - Understanding the Matched Filter

I have a question about matched filtering. Does the matched filter maximise the SNR at the moment of decision only? As far as I understand, ...