kanji - What kind of Japanese "dialect" is this?

In a Japanese translation of exerpts of the Lotus Sutra, there is kanji which is used that is to varying degrees still used today. Some of them are relatively common in normal speech or writing, whereas others seem to me to be more stilted or only used in formal writing (e.g. 無量 as muryō). Other times, there was kanji used that is still commonly seen in writing, but when one says it, there is a different name for it (e.g. 力 is used in the text and is written in katakana as "りき", but I believe that nowadays, its said, "ちから").

What is the name of this dialect (if there is one) and is it just a temporal difference that caused this contrast- similarly to how Shakespeare sounds weird to English speakers in the modern day. And lastly, is there a way to learn more about this type of Japanese?

Here is a link to a webpage that has the translation written in romaji. I couldn't find one that had just the Japanese and kanji on it, so I just have a sample photo below:

Answer

The origins of Buddhist sutra are compilicated, but they are generally based on the transliterated Sanskrit/Pali or their Chinese translations. See Lotus Satra on Wikipedia. Although they might have been more or less "Japanized" in terms of pronunciation, they are basically not Japanese. (Noticed all the characters in the page are read with on-yomi?) I believe no Japanese people talked in this way anywhere in the history. Some words such as 感無量 were "cherry-picked" into the ordinary Japanese vocabulary, though.

Today, all Japanese high school students learn basic 古文 (archaic Japanese), but they cannot understand the meaning of sutra because they look totally different. Personally, I can identify some words (三昧, 如来, 未曾有, ...) in the pasted page, but cannot get the meaning of the sentences at all.

If you want to seriously learn more about this language, perhaps you need to enter a university that has a Buddhism course. Or learning Chinese may help?

TL;DR: It's more like Latin rather than Shakespeare :)

fft - Auto-correlation function, an inverse problem

$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $

we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$

Its auto-correlation function $C[n]$ is uniquely defined as: $$ C[n]=\sum_{i=0}^{L-1} x[i+n]x^*[i] $$ $C[n]$ also has the periodic property: $$C[n+L]=C[n]\tag{1}$$

And ''conjugate-symmetry'' property: $C[-n]=C^*[n] \tag{2}$

---

Now my question is:

For given $C[n]$, which satisfies property (1) and (2):

Can we find the corresponding $x[n]$ ?

If yes, is it unique? and what is the method to find $x[n]$?

If no, what other constraint properties should we add to $C[n]$, in order to make it yes?

---

Answer

Let's look at the case $x[n] \in \mathbb{R}$, where $x[n]$ is real.

Autocorrelation is basically convolution of the signal with it's time inverse. This can be easily expressed in the frequency domain.

$$ \mathscr{F}\Big\{ r_{xx}[n] \Big\} = \mathscr{F}\Big\{ x[n] \Big\} \cdot \mathscr{F}\Big\{ x[-n] \Big\} $$

$$R_{xx}(\omega) = X(\omega)\cdot X^*(\omega) = \Big| X(\omega) \Big|^2 $$

So it's easy to see that the Fourier Transform of the auto correlation is simply the magnitude squared of the Fourier Transform of the input signal. That's sometimes referred to as the Power Spectrum.

It's also easy to see that information gets lost in the process. There are $N$ unique values going in but because of the symmetry properties of the auto correlation there are only $\frac{N}{2}$ unique (independent) values coming out. Looking in the frequency domain, we can see that the phase is lost.

If yes, is it unique? and what is the method to find $x[n]$?

No, it's not unique

Can we find the corresponding $x[n]$ ?

There is an infinite number of $x[n]$.

1. Take the Fourier Transform of the autocorrelation



2. Take the square root


3. Add an aribtiraty (but odd-symmetric) phase function


4. Do an inverse Fourier Transform

Any signal derived this way will have the same original auto correlation function.

if no, what other constraint properties should we add to $C[n]$, in order to make it yes?

You can't make it a yes, since it's not unique. No matter what auto correlation you choose, there will be infinite $x[n]$ that will have it as an autocorrelation.

matlab - Frequency shifting of a quadrature mixed signal

I've a quadrature mixed signal with 10 MHz as highest frequency available. I want to shift it to any frequency lesser than 10 MHz. I should get it by multiplying this signal by cosine of the required frequency. Right?

Answer

If you have a quadrature mixed signal, you have two outputs of the signal in 90 degree phase to each other. To complete a full complex frequency conversion (which would shift the frequency in one direction, as opposed to a real frequency conversion which would create two sidebands) you need to multiply one of the outputs by the cosine term of the required frequency shift and the other output by the sine of the required frequency shift. By swapping sine and cosine ports, you change the direction of the shift. The outputs after each multiplier are then summed in phase. See diagram and derivation using trig identities for the multiplication of sines and cosines below.

If you are comfortable with the idea of exponential frequencies (full complex frequency including positive and negative frequency etc) then I prefer the view point below to describe single sideband frequency translation. Comparing the two diagrams shows the value of converting "I" and "Q" signals as typically constructed in hardware to implement complex signals into one complex signal path for the purpose of analysis. Using cosines and sines instead of exp can be quite cumbersome especially as the complexity of the system increases.

For those less familiar with the notation, $Ke^{j\theta}$ is simply a complex value with magnitude K and angle $\theta$. Therefore $e^{j\omega t}$ is a signal whose magnitude is 1 and angle is increasing linearly with time at rate $\omega$; a spinning phasor counterclockwise on a complex IQ (polar) plot, representing a "positive" frequency. Similarly $e^{-j\omega t}$ spins clockwise and represents a "negative" frequency. With that, one should be well equipped to use the more compact and analytically simpler exponential notation.

Notice too how the two block diagrams that I included are related, with the second one taking the real of the product to make the outputs equivalent. To do frequency translation, we use complex conjugate multiplication (the conjugate assures we shift in the direction desired). Consider a full complex conjugate multiplication, as is done prior to the real operation:

$ e^{j\omega_ct} = I_1+jQ_1$ representing the carrier after the quadrature split

$ e^{-j\omega_st} = I_2-jQ_2$ representing the conjugate of the I and Q terms of your signal

$ e^{j\omega_ct}e^{-j\omega_st} = (I_1+jQ_1)(I_2-jQ_2) = (I_1I_2+Q_1Q_2)+j(I_2Q_1-I_1Q_2)$

The real portion is also called the dot product and the imaginary portion is called the cross product. Notice the dot product does match the implementation block diagram shown at the top of this answer.

Further details for the very interested to understand complex frequency translation:

The following additional figures and content were added to help answer the question on the subsequent down-conversion and to build a better understanding of the complex (positive and negative) frequency domain in describing frequency translation implementations.

First consider a generic quadrature mixed signal, it is at "baseband", meaning not modulated to a carrier for purpose of transmission, and centered about DC (0 Hz) with the positive and negative frequencies independent of each other. The way we implement such a signal in practice is with two real signals (we could choose the real signals to have one represent the real and the other the imaginary such as I and Q in I+jQ, or one represent the magnitude K and the other represent the phase $\theta$ such as $Ke^{j\theta}$. In any event, by observing the spectrum and noting that the positive and negative frequencies do not match, we know from that detail it is a complex signal and two real signal paths are required to represent this in implementation. For a real signal in contrast, the positive and negative frequencies would be conjugate symmetric, meaning identical in magnitude and opposite in phase.

Frequency spectrum of baseband quadrature modulated signal (this could be a single tone on one side, or multiple independent frequencies, point is the positive and negative frequencies are independent):

Now consider a carrier signal $cos(\omega_ct)$, this has an impulse in the frequency domain at the positive frequency $\omega_c$, and another at the negative frequency $-\omega_c$ (also shown as two complex frequencies using Euler's identity $2cos(\omega_ct) = e^{j.\omega_ct}+e^{-j\omega_ct}$):

If we split the carrier in quadrature (with a Hilbert transformer, or a 90° splitter, or just generate a sine and cosine component, but in the end have two tones with a 90° relationship to each other), then in implementation we have two real signals used to represent a single complex frequency $e^{j\omega_c}$ (you may start to see how it is so much easier doing all analysis with the e's and then do the implementation with the sines and cosines):

UPCONVERSION

To up-convert the baseband signal to the carrier frequency, we multiply the two signals in the time domain (which is convolution in the frequency domain; so for an impulse function such as our carrier it is a simple shift). First consider what would happen if we multiplied the baseband signal with the carrier $cos(\omega_ct)$ directly (eliminate the 90° splitter in my first figure, replacing $sin(\omega_ct)$ with $cos(\omega_ct)$). Notice the output would still be complex as the positive and negative frequencies are not the same- so we could not transmit this with a single antenna (2 real signals are required to represent a complex signal). If we proceeded to take the real portion, distortion of our signal would result as depicted in the figure, so we can't transmit that either.

Figure showing spectrum result with an INCORRECT upconversion approach:

This explains why we need to also take the Hilbert transform of the carrier (converting the cosine into sine and cosine components, and representing a complex version of the carrier that is a single spinning phasor $e^{j\omega_ct}$, or in the frequency domain a single impulse in the positive domain with no negative component) prior to multiplication. We take the real portion of the product and can then send an undistorted real waveform representing our baseband signal modulated up to the carrier frequency.

Figure showing spectrum result with a CORRECT upconversion approach:

DOWN-CONVERSION

With the details of the up-conversion process in mind, it will now be very easy to answer the question if a quadrature conversion of the received signal is required prior to multiplying by sine and cosine to recover the baseband signal. The answer is no, but there is an advantage to doing so in situations when an image frequency cannot be easily filtered.

Figure showing spectrum doing a downconversion with no Hilbert transform of the received signal. It is interesting to note if you swapped sine and cosine in the (real) multipliers, this would represent a single impulse in the positive frequency domain, shifting the negative frequency component of the received signal to baseband, causing the spectrum at baseband to be inverted:

Figure showing spectrum doing a downconversion with a Hilbert transform of the received signal prior to sine/cosine multiplication. Here you can see what would happen if you swapped an input to one of the (real) multipliers: The signal would be shifted to a higher frequency twice the carrier instead of to baseband.

Note I believe there would also be an SNR advantage up to 3dB in doing the receiver with a Hilbert transform prior to the multiplication. In the first case without the Hilbert transform, the signal energy is split and the upper portion filtered out while the noise is unchanged, while in the second case with the Hilbert transform all the signal energy is translated to baseband. I could be wrong here as I have not verified this point, so perhaps someone else can weigh in on that.

fourier transform - DFT of discrete signals, why do we only analyze frequency bins equal to number of input samples?

If we have a signal $x[n]$ such that we have $N$ samples i.e. $n=0, \ldots, N-1$, then when we analyze the DFT $X[k]$ we only analyze for $k=0,\dots,N-1$ as well.

• Why is the range of $k$ tied to the range of $n$?


• Why don't we analyze more, or less number of frequencies?

Answer

From the definition of a $N$-point DFT of a sequence $\left\{x[n]\right\}$, you have:

$$X[k]=\sum_{n=0}^{N-1} x[n]\exp\left(-j\frac{2\pi kn}{N}\right),\quad k=0, 1, \dots, N-1\tag{1}$$

• 
  
  

  Let's say for a fixed $N$ we go against equation $(1)$ and compute more values to let's say $N_2$ such that $N_2\gg N$. Looking at the exponential term, let's say: $$e_k = \exp\left(-j\frac{2\pi kn}{N}\right),\quad k=0, 1, \dots, N-1, N, N+1, \ldots, N_2-1$$

  
  

  It can be verified that for $m\in \mathbb Z$: $$e_{k+m N} = \exp \left[-j\left(\frac{2\pi kn}{N}+ 2\pi mn\right)\right]=\exp\left(-j\frac{2\pi kn}{N}\right)\cdot 1=e_k\tag{2}$$

  
  

  In other words, all the values you'll compute for $k \gt N-1$ you already computed them. Equation $(1)$ requires $N$ harmonically related exponentials determined by the index $k$, and that is sufficient for a $N$-point DFT. No extra/new info beyond that, all the signal's spectral information can be extracted to at most $k=N-1$. And this is regardless of the nature of $x[n]$, whether $x[n]$ is periodic or not periodic the DFT by its definition in equation $(1)$ does not make such an assumption. (@Matt. L puts it nicely in his answer and comments here regarding the confusion on the periodicity assumption).

  
  


• 
  

  Yes, we can analyze more than the range of $n$. Let's say $N_2$. Note that we are doing a $N_2$-point DFT, (i.e. the denominator in the exponential term is $N_2$) and $0\leq k \leq N_2-1$. The choice of $N$(here $N_2$) determines two things: the frequency spacing of the DFT samples and the computation time taken to compute those DFT samples. The corresponding frequency spacing $\Delta f$ in $\textrm{ Hz}$ between two consecutive DFT samples is: $$\Delta f=\frac{F_s}{N}$$ $$N_2>N \Longrightarrow \frac{F_s}{N_2} < \frac{F_s}{N} $$ So, this will increase the computation time as you'll have more DFT samples since you have more $k$'s; but the frequency spacing gets smaller (i.e. reduces the spectral separation of consecutive DFT samples), and this gives a high resolution in the frequency domain.

  
  


• 
  

  Yes, we can even analyze less than the range of $n$. Application-dependent like the Goertzel algorithm already mentioned is one example. Or depending on nature of the signal, like real signals for instance where the resulting redundancies in the DFT can be used to compute up to half of the values to have a full spectral characteristic instead of going up to $N$.

  
  

halacha - Walking In-front of Someone Davening Shemona Esrei

1. 
   

   I read somewhere that shtenders, chairs, tables and benches aren’t considered an interruption between the one davening and one passing before him unless the shtender is 10 טפחים tall by 4 טפחים wide. Where is the halachic source for this?

   
   


2. 
   

   I also read that even if there is an interposition of 10 טפחים and 4 טפחים wide one should be strict not to pass before someone davening. Where is the halachic source for this?

   
   

What's the grammar behind ヤカンのある部屋?

I tried to make a sentence saying that since I don't have the key I cannot go inside the room that has a kettle:

鍵がないからヤカンがある部屋に入れなかった

But I was told that it sounds better if I changed it for

鍵がないからヤカンのある部屋に入れなかった

What's the grammatical reason that explains this?

Thanks.

Answer

The grammar behind this is explained in this question, although you may already know this: How does the の work in 「日本人の知らない日本語」?

I personally think this sentence is perfectly fine and natural regardless of whether you use が or の. Someone might feel the sentence sounds slightly more "soft" or "sophisticated" with の, but this is very subjective. I think you can safely ignore the difference unless you're interested in aesthetic writing.

halacha theory - What were the "pieces" of Moses' transmission of the Oral Law?

BT Eruvin 54b presents the method of Moses' Torah study:

תנו רבנן: כיצד סדר משנה? משה למד מפי הגבורה. נכנס אהרן ושנה לו משה פירקו ... נכנסו בניו ושנה להן משה פירקן ... וכו'

The Sages taught: What was the order of teaching the Oral Law [in general, not THE Mishnah]? Moses learned directly from the mouth of the Almighty. Aaron entered ...and Moses taught him his lesson ... Aaron’s sons entered, and Moses taught them their lesson ...

What was that "פרק" - was it a Torah verse, a Mitzvah, a Mishnah?

hashkafah philosophy - How do we learn "Taamei HaMitzvos"?

The Rambam famously believed that sacrifices were given to ween people off idolatry.

Therefore, it can be assumed that when Mashiach comes, there won't be a need for sacrifices. Yet, the Rambam doesn't mention that in the Mishnah Torah.

There are many other places where "rationalistic" Taamei Torah (reasons behind Mitzvos) contradict Halacha.

How are these resolved?

torah reading - Is getting an aliyah and Bar-Mitzvah laining needed

Is it needed to get called up to the bimah and, also is it needed for you to lain from the torah on your Bar-Mitzvah?

Answer

Not really.

Jewish law treats a male as an adult as soon as they reach age 13 (assuming they've also had the onset of puberty). There is no official "bar mitzvah" ritual; you're an adult, you're an adult.

It's become normal to demonstrate to everyone that the young man is an adult by calling up the fellow for an aliyah (i.e. saying the brachas before and after the reading), and also usually for reading some or all of the Torah. Or giving him "maftir", so he makes the brachas on the end of the Torah reading, then makes the brachas on the Haftorah (then either he or someone else can read it).

Now it's usually not that hard to prepare for just saying the brachas, and traditional practice is worth a lot, and there is a special bracha that the father makes when his son has his first Aliyah. But again, a boy becomes bar mitzvah no matter what he does.

Rabbi Moshe Rosenberg, rabbi of Etz Chaim in Kew Gardens Hills, suggested in a recent journal article that some boys who aren't really into leining should probably just get an Aliyah, and maybe spend their other bar-mitzva-prep time doing a chessed project.

usage - 〜くて form of a verb

I ask here my question because I couldn't find anything on internet. My problem is about 〜くて form for a verb.

I asked a Japanese friend what for example "会いたくて" means. She told me that there is a complicated nuance behind that... It means

I want to meet you (but I can't)

I didn't have the opportunity to ask again so I ask here. Could someone explain to me the usage of 〜くて? I'm so confused (>_<). Especially with the form which expresses the desire like "食べたい" → "食べたくて".

stoichiometry - What exactly does the term "gram atoms" mean?

The Wikipedia article on the mole states:

 The term gram-atom (abbreviated gat.) has been used for a related but distinct concept, namely a quantity of a substance that contains Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of $\ce{MgB2}$ is 1 gram-molecule of $\ce{MgB2}$ but 3 gram-atoms of $\ce{MgB2}$.

Can anybody explain the difference between moles and gram atoms, and how is it that 1 mole of $\ce{MgB2}$ is 1 gram-molecule of $\ce{MgB2}$ but 3 gram-atoms of $\ce{MgB2}$?

Answer

$\ce{MgB2}$ is 1 gram-molecule of $\ce{MgB2}$ but 3 gram-atoms of $\ce{MgB2}$.

Why is this so? Let us consider this problem in the familiar mole:

If we were asked how many moles of the substance (molecule) were in this, we would state 1 mole, if there were $\pu{45.3 g}$ of substance. However, if we were asked how many moles of atoms were in the substance, we would accordingly state 3. Thus, in one molecule, there are 3 atoms, so if we simply consider the number of atoms, there would be the necessity of counting the number. of atoms in a molecule, as a molecule is comprised of more than a single atom

* This is purely hypothetical. One would probably not consider $\ce{MgB2}$, as J. LS pointed out, it decomposes . However, the concept can be applied to other compounds

FFT on non-rectangular part of image

I need to do a FFT on an image for noise reduction, but the problem is that I do not need the complete image, but only a circle in the middle. The borders are a fixed rig, thus I am not interested in what it displays, but it has an impact on the result of the FFT.

Is there any way to just cut out a circular part and use that for the FFT? Note that if I use black background, the edge between background, and image data will have quite an impact.

Answer

Instead of having a hard edge between the image data of interest and the background, you could use a two-dimensional tapered window function, as is often done in spectral analysis. You might start by trying a Gaussian window, which for a two-dimensional case would look something like:

$$ w[x,y] = e^{-\frac{\left(x-\frac{N_x-1}{2}\right)^2}{2\left(\sigma_x \frac{N_x-1}{2}\right)^2}} e^{-\frac{\left(y-\frac{N_y-1}{2}\right)^2}{2\left(\sigma_y \frac{N_y-1}{2}\right)^2}} $$

$N_x$ and $N_y$ are the dimensions of the desired transform in the $x$ and $y$ directions, respectively, and $\sigma_x$ and $\sigma_y$ are parameters that allow you to control the shape of the window; for small $\sigma$ values, most of the energy in the window function will be concentrated toward the center, with that effect decreasing as you increase $\sigma$.

nuances - How to "shoo away" a sales clerk?

When I go window shopping, the sales clerk would usually come near me asking what I like. How should I politely shoo them away? Can I simply say

いいえ、けっこうです

or something like

自分で見る

I know I can just ignore them and they get the body language that I just want to look by my own. What is the common way to say it?

I usually feel awkward especially in electronic shops like yodobashi or yamada. For bookshops, they just leave you alone. I guess electronic shops' clerks are agressive.

By the way, as a side question. Is there a word for "shoo" in Japanese? I know Japanese are polite but do they have it?

Answer

When the clerk asks me if I'm looking for anything particular (何かお探しですか?), I usually say あ、だいじょうぶです。 or あ、もうちょっと見てから。.

When the clerk says at places like boutiques よかったらどうぞ試着してみてくださいね～(Please try them on) or 他のサイズ/お色もご用意してますのでね～(We have different sizes/colours too), I say quite shortly あ、はい or あ、ども.

"to shoo away" = [追]{お}い[払]{はら}う...?

halacha - Can one rely on Kol Nidrei?

In Kol Nidrei, one says

All vows, and prohibitions, and oaths, and consecrations, and konams and konasi and any synonymous terms, that we may vow, or swear, or consecrate, or prohibit upon ourselves, from the previous Day of Atonement until this Day of Atonement and ... from this Day of Atonement until the Day of Atonement that will come for our benefit. Regarding all of them, we repudiate them. All of them are undone, abandoned, cancelled, null and void, not in force, and not in effect. Our vows are no longer vows, and our prohibitions are no longer prohibitions, and our oaths are no longer oaths."

[Emphasis mine].

Does this mean that I am allowed to make a false (future, and not-interpersonal) oath nowadays?

---

The Wikipedia article says that many were opposed to this prayer for this reason. Yet, now that we do say it, why does one have to keep any not-interpersonal vow nowadays?

tefilla - Do Jews pray to deceased forefathers?

Shalom,

I would like to know if Jews consider it acceptable to pray to deceased ancestors, forefathers, or "saints" like some Christians in the Catholic tradition do. Deuteronomy 18:11 would seem to prohibit speaking with the dead or praying to them, and several pagan religions have "ancestor cults" where they pray to their predecessors. Therefore I would expect it to be explicitly forbidden in Judaism to pray to any of the dead, whether they were righteous or wicked.

However, I was reading in Sotah 34b and I noticed that it reads:

Raba said: It teaches that Caleb held aloof from the plan of the spies and went and prostrated himself upon the graves of the patriarchs, saying to them, 'My fathers, pray on my behalf that I may be delivered from the plan of the spies'. (As for Joshua, Moses had already prayed on his behalf; as it is said: And Moses called Hoshea the son of Nun Joshua,17 [meaning], May Jah save thee [yoshi'aka] from the plan of the spies.)

This seems like mere speculation on the Rabbi's part and is an interpretation that appears to conflict with Deuteronomy 18:11. Do Jews take Sotah 34b as an example of legitimate prayer to deceased ancestors? And if so is there any teaching in Judaism that the deceased can hear when someone calls to them?

If Judaism allows praying to ancestors then how would that be distinguished from the forbidden practice of necromancy, and the episode of King Saul consulting the sorceress at Endor to speak with the prophet Samuel?

Answer

For a long time there have been Jews who have indeed beseeched the dead. However, numerous sources state this is is prohibited Some state that it is permitted if the request is not directly from the dead, but just that the dead beseech God.

Forbidden when the request is directly of the deceased

Maharam Shikk writes in a responsum (OH 293) that such practices raise both the issue of doresh el hametim (Deut. 18:11) and of serving God through an intermediary (apparently the prohibition of avoda zara; idolatry). He concludes that if one relates one's problems to the dead hoping that they will intercede with God it is permissible, but if one wants help from them directly, it would be forbidden. He emphasises that even using them as intermediaries is forbidden according to many authorities.

Similarly, the Ben Ish Hai writes in a responsum (Rav P'alim Vol II YD 31) that it is forbidden to make requests of a dead person directly. Doing so constitutes doresh el hametim. One may only ask that the dead intercede with God. He writes this in explanation of the Zohar (Acharei Mot: 71) which is quoted by some as a source to permit praying to the dead:

נמצא לא הותר לאדם להתפלל על קברי הצדיקים, לשאול בקשתו מן הצדיקים עצמן, כי זה חשיב דורש אל המתים, אלא הוא מתפלל ושואל בקשתו מהקב"ה, ורק מבקש מנפש הצדיק שתתפלל עליו לפני הקדוש ברוך הוא, שישמע תפלתו ויעשה בקשתו

Always forbidden

Others, take an even harsher stance; that it forbidden even if the request from the deceased is just that it intercede with God. R. Moshe Tsuriel notes here that Rambam (Hilkhot Ta'aniyot 4:17) emphasises that prayers in a graveyard are not meant to be directed to the dead. In this, Rambam rules like Rabbi Levi Bar Hamma, in Ta'anit 16a against a contrary opinion recorded there. R. Tsuriel (there) is of the opinion that those who were accustomed to pray in various forms to the dead are following the contrary view in Ta'anit, but that halakha is not in accordance with that view.

The Sefer Hameorot (Ta'anit 16a) similarly explains that according to the latter Talmudic view (who he himself follows) addressing petitions to the dead is forbidden:

שאין לנו לבקש מן המתים שיבקשו רחמים על החיים, שהרי לא מצינו בכל המקרא בכמה צרות שאירעו לישראל, ליחידים או לרבים, שיבקשו מן המתים לבקש רחמים עליהם

Similarly, the Bach (YD 217:51) implies that prayer in a cemetery can only be permitted if it is addressed to God; not the dead. (although he cites views that even this would be prohibited, see there for more):

ודוקא להשתטח על קברי אבות ולהתפלל לפניו יתברך

Additionally, the Hokhmat Adam (Issur V'heter 89:7) writes negatively about people who discuss their problems with the dead:

ז איסור דורש אל המתים זה שמרעיב עצמו ולן בבית הקברות כדי שתשרה עליו רוח הטומאה (סימן קע"ט סעיף י"ג) ואותן נשים וכן עמי הארצות שהולכין על קברי מתים וכאילו מדברים עם המתים ואומרים להם צרותיהם קרוב הדבר שהם בכלל זה

And [regarding] those women and ignoramuses who go to graves and speak as though to the dead and tell them their woes, and it seems likely that they are included in this prohibition. (My translation of the bolded portion)

Maharam Shikk understands that he is saying that it is doresh el hametim.

Maharam Mintz (Responsa:79) similarly cites the opinion that making requests of the dead; even just that they intercede with God is forbidden as doresh el hametim:

כי בלאו הכי יש גדולים קראו תגר ע"ד זה וקראו ודורש אל המתים, דרוב עמי הארץ ונשים עבידי מליצים בינם ובין קונם ב"ה.

The Minhagei Maharil (Hilkhot Ta'anit 18), quoted by the Elya Rabba (581), Ba'er Hetev (OH 581:17), and the Mishna Berurah (581:27) similarly writes that one shouldn't address the dead at all:

והמשתטח על קברי הצדיקים ומתפלל אל ישים מגמתו נגד המתים השוכבים שם, אך יבקש מאת השם יתברך שיתן אליו רחמים בזכות הצדיקים שוכני עפ

That is, one mustn't address the dead or even pay attention to them, but only address God.

The Hayei Adam (138:5), and Kitsur (128:13) paraphrase the Maharil and add that addressing the dead directly would seem to violate doresh el hametim:

ויעשה הקדוש ברוך בו חסד בזכות הצדיקים אבל אל ישים מגמתו נגד המתים השוכנים שם, כי קרוב הדבר שיהיה בכלל ודורש אל המתים

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Do Jews take Sotah 34b as an example of legitimate prayer to deceased ancestors

As mentioned, like non-Jews, many Jews throughout the ages have beseeched the dead. Some invoked this story in Sotah as justification. However, those authorities who prohibit such activities clarify that the passage is not a proof. For example, R. Hayim Paltiel of Magdeburg cited by the Bach (ibid), writes that the passage in Sota refers to praying to God, and merely using the grave-site as a holy location which at which it is advantageous to pray:

דלא מצינו רק גבי כלב שנשתטח על קברי אבות- היינו שמתפללים לה', ומקום קדוש גורם שתהא תפילתם נשמעת

[It is not clear to me exactly how he read the passage in Sotah; perhaps he had a variant text.]

Most sources saying it is forbidden do not mention the passage. Perhaps this is because it is aggadic and does not carry the same authority as halakhic passages. Additionally, even were the passage in Ta'anit halakhic, not every halakhic position in the Talmud is accepted. In this matter, for example, we have already noted commentators who understand the matter of addressing prayers to the dead to be the subject of a Talmudic dispute. Accordingly, the passage in Sotah could be aligned with the view in Ta'anit that permits, while the aforementioned authorities could nevertheless rule against it, in accordance with the other view in Ta'anit.

And if so is there any teaching in Judaism that the deceased can hear when someone calls to them

Although you are only asking for sources that the deceased can hear one praying according to those who invoke the passage in Sotah as a source to beseech the dead, in reality, the question exists in a vacuum; that is, even if it is forbidden to beseech the dead, they may still be able to hear the living.

An aggadic passage in Berakhot 18b indicates that the dead are aware of the goings on in the world, and can hear people talking to them. However, others are of the opinion that the dead are not aware of what is happening in their vicinity. (See R. Qafih's explanation of Rambam's Hilkhot Evel (14:13). One verse that indicates the contrary is Ecclesiastes (9:5) which states:

הַחַיִּים יוֹדְעִים, שֶׁיָּמֻתוּ; וְהַמֵּתִים אֵינָם יוֹדְעִים מְאוּמָה

The living know they will die; but the dead don't know a thing.

In a similar vein, R. Yehuda ibn Bil'am writes in his commentary to Isaiah (8:19):

הנפש אין לה שום ידיעה אחר פרידתה מן הגוף

The soul has no knowledge after its separation from the body.

Radak similarly implies that he understands the verse in Ecclesiastes simply, and that for this reason, any prayers to or through the dead, are absurd in his commentary to Isaiah (8:19):

אבל זה שאתם אומרים לנו שנדרוש אל האובות והידעונים זהו דבר שאין הדעת סובלתו כי הם מתים, ואיך נדרוש בעד החיים אל המתים, כי המתים אינם יודעים מאומה

But this that you say to us, that we should seek out the ovot and yidonim, this is something that the intellect does not accommodate, for they are dead! And how can we beseech the dead on behalf of the living, for the dead don't know anything.

If Judaism allows praying to ancestors then how would that be distinguished from the forbidden practice of necromancy

At this point I will mention some of the opinions of those who permit such practices. R. Eliezer of Metz writes in his Sefer Yereim (334-335) that the prohibition of doresh el hametim only includes involvement with the body of the deceased; involvement with the spirit of the deceased, however, would be permitted. This is one of the sources cited in justification of the practice to distinguish it from forbidden practices.

organic chemistry - What is the purpose of ammonium chloride in anti hydrogenation of alkynes?

In my organic chemistry textbook, lithium is used to create a free radical of the alkynes, to then allow the anti addition of hydrogen to get an alkene.

"The Dissolving Metal Reduction of Alkynes" is a reaction that then uses $\ce{NH4Cl}$. Why put $\ce{NH4Cl}$?

Answer

Products from reaction step (1) are the trans-alkene and 2 equivalents of the amide $\ce{LiNHEt}$, a strong base. Step (2) is the workup of the reaction mixture with aqueous $\ce{NH4Cl}$ solution, which serves several purposes. First, it quenches the lithium amide and unreacted lithium metal.

$$\ce{LiNHEt + NH4Cl ->~ EtNH2 + NH3 + LiCl}$$ $$\ce{Li + H2O ->~ LiOH (aq) + \frac{1}{2} H2\uparrow}$$

Secondly, the trans-alkene is usually less water-soluble than ethyl amine and the lithium and ammonium salts, and can be separated from the workup mixture by precipitation or extraction with an organic solvent.

hybridization - Hybrid orbitals forming molecular orbitals

My teacher showed me this diagram on how the hybrid orbitals of two atoms combine to form molecular orbitals. I was confused by this because I thought that VB and MO theories were two separate theories. In VB theory, atoms form hybrid orbitals that overlap, and the electrons are located in the overlap.

In MO theory, molecular orbitals are formed from the superposition of regular atomic orbitals (not hybrid orbitals), so most MO diagrams I see are drawn like this:

So are molecular orbitals formed from regular (s,p,d, etc.) atomic orbitals, or are they also formed from the hybrid orbitals? And if hybrid orbitals do combine to form molecular orbitals, are the electrons still in between the two bonded atoms or are they delocalized like in the MO theory?

Answer

It is still LCAO-MO theory, but just dumbed down a lot. The difference is that, instead of feeding the "pure" atomic orbitals into the LCAO mechanism, you carry out an additional mathematical step in order to get orbitals that have nice directional properties, and you feed those into the LCAO mechanism instead.

Let's talk about a simple example, methane. You could hybridise the $\mathrm{2s}$ and $\mathrm{2p}$ orbitals on carbon to obtain a set of four $\mathrm{sp^3}$ hybrids. If you now try to derive the symmetry of these $\mathrm{sp^3}$ hybrids, you will realise they transform as $A_1 + T_2$. And if you didn't bother doing the hybridisation step, guess what are the symmetries of the $\mathrm{2s}$ and $\mathrm{2p}$ orbitals? The $\mathrm{2s}$ orbital transforms as $A_1$ and the $\mathrm{2p}$ orbitals transform as $T_2$. In the end, you get roughly the same picture through MOT regardless of whether you use hybridised orbitals or not. (Note that the $4\mathrm{sp^3}$ in the second diagram does not indicate a principal quantum number of $4$, but rather that there are four such orbitals. I should have changed it, but I was lazy.)

There is a difference between this and conventional VB theory. Conventional VB theory tells us that each of the $\mathrm{sp^3}$ orbitals overlaps with one of the hydrogen $\mathrm{1s}$ orbitals to form four identical bonds. Once you draw a MO diagram, complete with symmetries, you are entering the realm of MO theory.

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However, part of the reason why that example worked so well is that methane has a central atom. When you come to larger molecules, and have to piece together different fragments of the molecule, there is a difference between LCAO using the hybridised and unhybridised orbitals. The best example is the very first MO diagram that you drew - I cannot tell what it is, but I think it is that of an alkene. So let's consider ethene, $\ce{C2H4}$.

In fact, the diagram is "wrong". There are 8 electrons in total in the constituent AOs, but the MOs only have 4 electrons. This is not because of any elementary mistake by your teacher. It is because two of the $\mathrm{sp^2}$ orbitals on each carbon do not point towards each other; they point towards the hydrogens instead. Therefore, they are assumed to be involved only in C-H bonding and not in C-C bonding. Strictly speaking, they should therefore not be shown on the MO diagram. Nevertheless, it is this assumption that gives us some insight into the difference between this "hybridisation-LCAO" treatment and normal LCAO treatment using the pure AOs.

We'll first look at the "real" MOs of ethene (image taken from Fleming, Molecular Orbitals and Organic Chemical Reactions):

$\hspace{15 mm}$

We can try and draw some parallels between your "simplistic" MO diagram and this "proper" MO diagram here. In the simplistic diagram, the C-C $\sigma$ bonding arises from overlap of the two $\mathrm{sp^2}$ hybrid orbitals. So, this is likely to somewhat correspond to the $\pi_x$ MO above, which kind of looks like what you would expect from constructive overlap of $\mathrm{p}$ orbitals on carbon pointing towards each other. However, there's likely to be a bit of the $\sigma_s$ MO mixed into it, because you are using $\mathrm{sp^2}$ hybrid orbitals which also have the $\mathrm{s}$ orbital mixed in. The other filled MOs are not likely to contribute since they are antibonding with respect to the two carbons. In fact, they are mostly there to provide the additional C-H bonding required to make the molecule stable, which is exactly what is neglected in the simplistic diagram.

However, the $\pi$ bonding orbital in your simplistic diagram is a resounding success. It's exactly the same as the $\pi_z$ MO in the real diagram! And the $\pi^*$ antibonding orbital in the simplistic diagram is also exactly the same as the $\pi_z^*$ orbital in the real diagram! This leads us to the main point: we can do this much simpler MO treatment using hybrid orbitals and get a sufficiently accurate MO picture, without having to go through a bunch of symmetry arguments to determine which AOs overlap and which AOs don't. Furthermore, guess which are the most important MOs that control the reactivity of ethene? Exactly; it's the two $\pi$ orbitals.

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Now that I've gotten that out of the way, I can proceed to answer your specific questions:

I was confused by this because I thought that VB and MO theories were two separate theories.

What I wrote above mostly applies to this confusion. The crux of the matter is, hybridisation can be applied to VB theory and it is actually in this context that you first meet hybridisation, but it is not exclusive to VB theory. You can do a little mix-and-match in order to simplify your life, without sacrificing too much accuracy.

Are molecular orbitals formed from regular (s,p,d, etc.) atomic orbitals, or are they also formed from the hybrid orbitals?

It is your choice. One leads to a more accurate picture, but it becomes extremely tedious as the molecule becomes more complex.

And if hybrid orbitals do combine to form molecular orbitals, are the electrons still in between the two bonded atoms or are they delocalized like in the MO theory?

The electrons are localised. This is most obvious from the difference in the $\sigma$ orbitals shown above. Full delocalisation a la "proper" MO theory would imply that there are MOs which lead to bonding over the whole molecule, i.e. the $\sigma_s$ orbital.

Then why do you still call it MO theory if the electrons are localised?!??!!??!

You didn't ask this question, but I anticipated you might wonder about it, since I've been going on and on about MOT only to end up saying that the electrons are localised. It's still LCAO-MO theory, just that the basis set of orbitals chosen is different, which leads to a different form of the wavefunction which happens to be localised between two nuclei. In terms of the electron density distribution, it is the same qualitative picture that is painted by VB theory. But, remember that VB theory has no idea what an antibonding orbital is, or that it even exists. So, what you have done is: you have actually arrived at the same result (localised electron density) by another means (MOT).

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^{Disclaimer: There are people who will debate exactly what "VB" and "MO" theories are. Wavefunctions exist in VB theory as well, except that they are constructed differently, and one might very well say that the simplistic MO theory above is, in fact, VB theory. Nevertheless, I am sticking to the introductory, qualitative notions of VB and MO theory here.}

hashkafah philosophy - Should a Jew who doesn't believe in G-d observe the commandments?

In an earlier question, I asked if it was a commandment to believe in G-d. As with so many areas, there were differing opinions. Some of the respondents claimed that there would be no point in being Jewish if one did not believe. While I disagree with that view, surely we all recognize that there are Jews who do not believe who, nonetheless, have varying levels of observance. Irrespective of whether or not one sees a point to doing so, should a non-believing Jew observe (the other) commandments?

Answer

In a word, yes. The Midrash (Eichah Rabbah, intro. 2), paraphrasing Jer. 9:12, states:

הלואי אותי עזבו ותורתי שמרו, מתוך שהיו מתעסקין בה, המאור שבה היה מחזירן למוטב

"Would that, even if the Jewish people abandoned Me, they had kept My Torah! By being involved with it, the illumination in it would bring them back to the right path."

Or as the Talmud (Sotah 47a, et al) puts it:

לעולם יעסוק אדם בתורה ובמצות, ואף על פי שלא לשמה, שמתוך שלא לשמה בא לשמה

"A person should always be occupied with Torah and good deeds, even if not for the right reasons, because from doing it for the wrong reasons he will come to doing it for the right ones"

- and goes on to illustrate this with the case of Balak, the Moabite king who offered numerous sacrifices with the improper intention of convincing G-d to allow the Jewish people to be cursed, yet who ended up being the ancestor of Ruth (and, through her, of King David and eventually of Moshiach).

fft - Using fourier coefficients to reconstruct data in matlab

When doing a discrete fourier transform on some data using matlab's fft function, its output is a set of fourier coefficients but I was wondering how do I go about converting these into an and bn so I can reconstruct the signal using sines and cosines.

E.g. I'd have a for loop that continually adds up a_i cos(ix) + b_isin(ix), where i = 1:N

grammar - I don't understand what のも means in this sentence

Here's the sentence in question:

生まれたのも育ったのも京都なんですよ

I thought using の in a sentence signified possession (ie. 私の本 [My book]). If I interpret the sentence as such, it doesn't make any sense.

Then I came to the conclusion that I should include the も from the sentence and read it as のも, but doing that made the sentence even more confusing.

Please help!

Answer

Cleft sentences

In linguistics, there's something called a cleft sentence. The basic idea is that you split a sentence into two parts in order to focus something:

　１ａ. I met her that day.　　　 　 　　　(original sentence)　
　１ｂ. It was her that [I met that day].　　(clefted sentence)

In this example, we split the sentence into "I met __ that day" and "her". Because we've neatly divided the sentence in two, we call this a "cleft" sentence. It expresses the same basic information, but it puts the focus on "her", the element we pulled out.

We could just as easily focus a different element instead:

　２ａ. I met her that day.　　　 　 　　　(original sentence)　
　２ｂ. It was that day that [I met her].　　(clefted sentence)

All of these sentences express the same basic information, but their focus is a little bit different. We could think of our first cleft as answering the question "Who did I meet that day?" and our second cleft as answering the question "When did I meet her?"

With that in mind, let's look at our examples again:

　1ｂ. It was her that [I met that day].

    non-focused element: I met (𝑥) that day

        focused element: (𝑥) = "her"

　２ｂ. It was that day that [I met her].

    non-focused element: I met her (𝑥)
        focused element: (𝑥) = "that day"

The non-focused element introduces a variable 𝑥, and the focused element tells us the value of 𝑥.

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Cleft sentences in Japanese

Japanese has cleft sentences that work like this, too! You've probably seen them before, although you might not have known the technical term. The most basic type of cleft looks like ＡのはＢだ in Japanese, where Ａ introduces a variable 𝑥, and Ｂ tells us the value of that variable.

Let's use a simplified version of your sentence as an example:

　３ａ. [京都]{﹅・﹅}で生まれた。 　　　'[I] was born in Kyōto.'

This is a basic sentence. We want to turn it into a cleft sentence, so let's split it into two parts!

　３ｂ. 生まれたのは[京都]{﹅・﹅}だ。 　'It's [in] Kyōto that [I] was born.'

    non-focused element: (𝑥) 生まれた
        focused element: 京都で = (𝑥)

We want to focus [京都]{﹅・﹅}で, which goes at the end of the sentence before だ (dropping the case marker で). Then we add the nominalizer の to the non-focused portion, 生まれた, so we can make it into the topic of the sentence.

Now we have a statement containing a variable ("[I] was born 𝑥") and we also have the value of that variable (𝑥 = "[in] Kyōto"). Note that the final sentence is missing the case particle で, so we have to understand the relationship between the two halves from context.

By the way, sometimes it's natural to use a cleft in Japanese when we'd use a non-cleft in English. So don't get too hung up on the English translations here―they're designed to show you the meaning of the Japanese sentences, not to give you the most natural way to communicate in English.

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Putting it all together

As it happens, your sentence is a little more complicated! To come up with your sentence, we'll need to put two of these things together, and of course when we do so we'll naturally need to use も instead of は. Let's start with these sentences:

　４ａ. 生まれたのは[京都]{﹅・﹅}だ。 　'It's [in] Kyōto that [I] was born.'
　４ｂ. 　育ったのは[京都]{﹅・﹅}だ。 　'It's [in] Kyōto that [I] was raised.'

And combine them into this:

　４ｃ. 生まれたのも育ったのも[京都]{﹅・﹅}だ。 'It's [in] Kyōto that [I] was born and raised.'

Finally, to get your sentence we have to make a few more changes. We'll add のだ, contract の to the informal ん, replace だ with the polite です, and add the assertive final particle よ:

　４ｄ. 生まれたのも育ったのも[京都]{﹅・﹅}なのだ。
　４ｅ. 生まれたのも育ったのも[京都]{﹅・﹅}なんだ。
　４ｆ. 生まれたのも育ったのも[京都]{﹅・﹅}なんです。
　４ｇ. 生まれたのも育ったのも[京都]{﹅・﹅}なんですよ。

Since the exact meaning of のだ depends on context, I've provided no explanation here―that could, of course, be the subject of another question.

And that's it! For more explanation of cleft sentences, see Martin's 1975 Reference Grammar of Japanese, p.863-869. For more explanation of English clefts, see Huddleston & Pullum's 2002 Cambridge Grammar of the English Language, p.1414-1427.

Why do digital filters work?

So I just started reading on FIR and IIR filters and am amazed by how "simple" the theory seems, so far.

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  But what confuses me is, why does filtering work by creating a weighted sum of previous samples?

  
  


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  What intuition makes one think this can produce desired filtering effects?

  
  
  


• It seems a bit unintuitive to me eventhough anyone can verify that summing delayed signals together does produce comb filtering. But desirable filtering? Why?

inorganic chemistry - de-yellowing lego

I have a huge lot of yellowed Lego's, I want to try to de-yellow them. I have searched around the internet and this method seems the most promising:

http://www.retr0bright.com/

I have a few questions about this : - What is happening at the surface of the ABS plastic ? - My knowledge on this subject is very limited, but would the process go faster when you perform the process in a ultrasonic bath ?

A bit of unrelated question : - Is it possible to combine the de-yellowing with filling any scratches gaps in the bricks ? It seems not to me because you have to have some filler in the solvent or break the bonds in the lattice, i guess ?

any help, information is welcome, I'm like to learn new stuff !! I can only understand it a little bit from a nanotech point of view.

Answer

According to the retrobright website the process involves the use of activated hydrogen peroxide and possible UV light. This won't work as well in an ultrasonic bath as the bath will keep out most of the light.

Yellowing is thought to be caused by some degradation reaction of some of the additives in the ABS plastic (probably brominated flame retardants, though it could be something else). What is probably happening is that the yellow products of that degradation are being destroyed by activated peroxide. The UV light probably helps this reaction along a little faster, possibly by activating the degradation products (a yellow colour is often a sign that there is a strong absorption of light from the molecules in the near UV).

If you follow one of the recipes on their site (with their safety precautions) it looks as though it should work for Lego.

Filling scratches, though, will probably not be easy as this is not a chemical problem but a physical one. The only effective way would probably involve remelting the ABS and recasting it which seems like overkill (especially since you would need original Lego moulds). Any chemical that will dissolve the ABS is more likely to destroy it than to selectively reshape the surface.

experimental chemistry - Determination of hardness of water using EDTA

Finding hardness of water by using EDTA. For determining permanent hardness we take the sample of about $\pu{50 mL}$ and then add Eriochrome Black T (EBT) indicator that results in wine red color due to calcium complex made by and also ammonia buffer. Then titrating it with ethylene diamine tetra acetic acid (EDTA) where change in color (i.e. sky blue) marks the end point of titration.

While carrying out experiment we add EBT as an indicator. Is there any criteria to add so in a fixed particular amount?

Answer

There really is no need to add EBT in a fixed amount. Calcium EDTA complex is far more stable at $\mathrm{pH} \approx 10$ (ammonia buffer) and will be the dominant Ca-compound in the solution even if there is a huge excess of EBT.

However, the amount of EBT is important to track the color change. If there is too much EBT, the color will be too dark, and one can easily miss the red-blue transition. If there are only trace amounts of EBT, the colors will be pale and again the transition is going to be barely visible.

The amounts of EBT given in the lab manuals are typically approximate and are estimated for the convenience of the personnel and to reduce the error in determining equivalence point due to unclear reading of the solution's color.

physical chemistry - Chemical Equilibrium - Why does changing the temperature shift the equilibrium?

I know that raising the temperature in a reversible chemical reaction causes the equilibrium to shift to the endothermic side.

I know that $\Delta G = \Delta H − T\Delta S $ but I don't know how to put them together to show why the equilibrium would shift.

To summarise, I already know what happens when, and I'm interested in why.

Answer

I think the best way to think of equilibria intuitively is in terms of rates of reaction. At equilibrium, the forward and the reverse reactions are happening at the same rate.

If you increase the temperature, what happens to the rates of the forward and reverse reactions?

Using the Arrhenius equation

$$k = Ae^{-E_\mathrm{a}/(RT)}$$

you can see that as temperature increases, the rate will increase. The amount it increases depends on the activation energy ($E_\mathrm{a}$).

The activation energy on the endothermic side of the reaction will always be larger than the exothermic side. This is because the transition state is always higher in energy than either of the reactants/products, and the reactants for the endothermic reaction are by definition lower in energy than the products! This means that the endothermic reaction will be sped up more than the exothermic reaction. This means the reaction is now out of equilibrium and the endothermic reaction will happen until the reaction is back in equilibrium again.

halacha - Could a Torah Scroll Be Writtin in Ktav Ivri (Paleo Hebrew)?

The Talmud (ibid) brings different opinions about the origin of the two in regards to how was the Torah initially written.

It is agreed by all that the language has remained the same, Hebrew – as we know it today, It is similarly agreed that today we use only the Ktav Ashuri and the Ktav Ivri contains no sanctity. (Yadaim 4, 5; Megilah 8b; Rashi ibid)

Source: http://www.yeshiva.co/ask/?id=2626

It is brought down that we now use Ktav Ashuri and all of our Torah scrolls, tefillin, and mezuzot, and that this was instituted by Ezra. But if a sofer were to write a Torah in Paleo Hebrew (like as found in the Dead Sea Scrolls), what would the status of such a scroll be? Would the scroll be permitted for use? Would it have kedusha?

physical chemistry - Calculating pH in titration of monoprotic weak acid with strong base

$25.0\:\mathrm{ml}$ of $0.10\:\mathrm{M}$ $\ce{CH3COOH}$ is titrated with $0.10\:\mathrm{M}$ $\ce{NaOH}$. What is the $\mathrm{pH}$ after the addition of $30.0\:\mathrm{ml}$ $\ce{NaOH}$?

In broad strokes, as I understand it, the sodium hydroxide in this case would completely consume the acetic acid, leaving a solution of acetate ions, $\ce{Na+}$ and $\ce{OH-}$.

What makes sense to me then is to figure that the $\mathrm{pH}$ is now dominated by the concentration of hydroxide ions, so the $\mathrm{pH}$ would be given by

$\mathrm{pH} = 14-(-\log([\ce{OH-}])= 11.96$

where $[\ce{OH-}] = \frac{[(30.0 - 25.0) \times 10^{-4}]\:\mathrm{mol}}{(30.0+25.0) \times 10^{-3}\:\mathrm{l}}$

i.e., the remaining moles of hydroxide ($0.0005$) per liter of total volume ($55\:\mathrm{ml}$)

but is this correct? Do I need to take into account the conjugate base’s contribution to deprotonation of water? If so, how is that done?

I’d like to be clever and use the lack of $K_\mathrm{a}$ or related constants in the problem to indicate that I’m on the right track, but that would be giving too much credit to my professor’s design of these questions (and the prior question in this series does give $\mathrm{p}K_\mathrm{a}$ for acetic acid)

Answer

Your calculation is right. Regarding your question to take into account the conjugate base's contribution to deprotonation of water, I'd say:

If you calculate the equilibrium constant of the neutralization reaction $$\ce{CH3COOH + OH- <=> CH3COO- + H2O}$$ $$K= \frac{K_a}{K_w}=\frac{10^{-4.75}}{10^{-14}}= 10^{13.25}$$

Now, if you write of reaction of acetate ion with water:$$\ce{CH3COO- + H2O <=> CH3COOH + OH-}$$ It's the opposite of the neutralization reaction. Its equilibrium constant is $10^{-13.25}$.

You can see clearly that the neutralization reaction is the "predominant reaction". So, the pH is determined by this reaction as if it's the only one happening in the aqueous solution. So, you can neglect the reaction of of acetate ion with water.

blessing - Polyphasic Sleep and Halacha

I recently read an article on polyphasic sleep and I'm quite interested in experimenting with it. The article advises the Uberman approach which advocates 20-30 minute naps every four hours, meaning that you sleep about 2-3 hours per 24 hour period. I'm also interested in trying the Dymaxion approach which advocates 30 minute naps every 6 hours. The interesting thing is that eventually, you reach the point at which you get a full REM cycle every time you take a nap. It seems that from mouths of the people who do this and establish polyphasic sleep patterns, they have more energy and higher alertness.

The first and foremost question is whether one is allowed to do this out of the possibility of self-harm. For this and for the other questions, I'll be consulting my Rav.

Next comes the halachic aspects of berachos and the like. Since I'll only be sleeping 20 to 30 minutes each time, here's where the questions come in.

1. If I'm only sleeping for 20 to 30 minutes, do I wash my hands when I wake?
   
   
   
   • I remember there being something about the minimum length of sleep required in order to wash, and I'm not really sure what that minimum is.
   
   
   
   
   


2. When it comes to only sleeping for two or three (depending on sleep schedule) short periods in the night, when should I make my birchos hashachar and birchos hatorah?
   
   
   
   • I'll probably be studying Torah and doing other Torah-related things during the night, possibly before and possibly after chatzos. Let's give an example of this for clarity:
   
   
   
   


3. Do I just say Krias Shema Al Hamita only the first time I go to bed during the night?

Nap Schedule

  Nap Start Time | Nap End Time 
-----------------|---------------
| 7:40pm         | 8:00pm       |
| 11:40pm        | 12:00am      |
| 3:40am         | 4:00am       |
| 7:40am         | 8:00am       |

Zmanim Schedule

  Zman Name     | Zman Time     

----------------|----------------
| Nightfall     | 8:00pm        |
| Midnight      | 12:00am       |
| Dawn (Alos)   | 4:00am        |

Of course, the contrived example above is overly simplified and isn't necessarily real, but it should help to serve as an example. Can one give an answer on my three questions above given the above example? I'd like to be able to try this, but I need to be clear on what the halacha is so that in my sleeplessness, I don't transgress.

Answer

• 
  

  You wash your hands before davenings and with a bracha only before the shacharit one (assuming you have gone to the bathroom since davening maariv which seems highly likely)

  
  
  


• 
  

  You never say Birkot Hatorah as you never really take a break. Ideally you can have someone be motzi you in them after olot hashachar.

  
  


• 
  

  You can say Birkot HaShachar starting from chatzot except Hanotein Lesechvi Vina which should only be said after olot hashachar.

  
  


• 
  

  You will never need to say Kriat Shema al HaMitta.

  
  

This is all assuming that you sleeps are under 30 minutes.

If they are more than 30 minutes:

• 
  

  You will wash your hands each time, but only say a bracha on the one closest to davening shacharit.

  
  


• 
  

  You can say Birkot Hashachar after the last sleep that occurs before olot hashachar.

  
  



• 
  

  You say Hamappil before the first sleep that is after tzeit hakochavim.

  
  


• 
  

  You say Birkot HaTorah after each sleep.

  
  

Sources: SA OC 4:15 47:13 92:5 and MB 4:30 47:25 47:23 and BH 4:13 and probably some other stuff that I can't find inside right now :)

halacha - Maaser Sheni Coin Value

I've been reading about redeeming maaser sheni and I've noticed people mentioning redeeming maaser on a coin of value significantly less than the value of the maaser:

"For example, a cRc company which purchased 30,000 pounds of Israeli watermelon seeds had 2,700 pounds of ma’aser sheini seeds, which is worth tens of thousands of perutos. They were able to transfer that kedushah onto an American nickel or dime and had no need for a perutah chamurah." (http://www.crcweb.org/Sappirim/Sappirim%2025%20%28Jul%202012%29.pdf)

"A coin is designated for the redemption of Maaser Sheini. This coin must be worth at least a shoveh pruta. At the time of writing, a nickel is sufficient." [There is no mention of a maximum amount to put on the coin, nor of higher value coins being needed for more maaser.] (How can one eat non-certified kosher Israeli produce?)

And yet there is also mention of "filling up" coins used to redeem maaser: "Once the coin has some ma’aser sheini on it additional kedushah can be added up to the full value of the coin."(http://www.crcweb.org/Sappirim/Sappirim%2025%20%28Jul%202012%29.pdf)

So my question is: does the value of the coin used to redeem maaser sheni have to correlate with the value of the maaser, and if so how? And if not, why?

Answer

The Gemara (Erkhin 29a) records:

הקדש שוה מנה שחיללו על שוה פרוטה מחולל אימר דאמר שמואל שחיללו לכתחלה מי אמר הני מילי בזמן שבית המקדש קיים דאיכא פסידא אבל בזמן הזה אפילו לכתחלה
[Shmuel said:] "Hekdesh worth 1 Maneh which was redeemed onto a Perutah is redeemed." He said "if it was redeemed", but who said you could do that from the outset? His words were when the Temple was standing and there would be a loss of value, but nowadays even from the outset you can do that [since there's no loss to Hekdesh since no one is using the money anyway]. (my translation)

See Rambam Erkhin 8:10, Shulchan Arukh YD 294:6

So originally you would redeem your Maaser Sheni onto a number of coins equal to the market value of the produce. But now that no one is actually using the coins to buy food in Jerusalem, you can redeem any amount of Maaser Sheni onto just 1 Perutah. A coin that is worth X Perutot can be used to redeem Maaser Sheni X times. Then you can redeem all X Perutot onto 1 Perutah of a different coin. Etc. Eventually you destroy the coin.

halacha - The Effect of an 18- or 6-Hour Day

Since the 18th century, Jews have been settling in Sweden without the requirement of conversion (source). As such, there are now a number of Swedish Jewish communities, the largest of which is in Stockholm. In mid-Summer, Stockholm can get over eighteen hours of sunlight a day, and in the middle of winter might receive as few as six. Looking at this chart, I see that in July the sun rises at 3:40am and doesn't set until 10:00pm, while in January it won't rise until it's almost 9:00am, and will set only a couple of hours into the afternoon.

Since the times at which various things can be done depend largely upon sunrise and sundown, how might a Jew in Stockholm conduct his day?

If the sun has risen before one could reasonably have awoken, and will remain in the sky until after one has gone to bed, what might be the earliest and latest times at which a person could recite the Shema in the morning and the evening? Are there similar concerns when it comes to davening shacharit or maariv? Or to determining the length of a fast day?

If the sun has descended below the horizon only shortly after lunchtime, such that it's no longer possible to recognise things from a short distance, would the obligation of wearing tzitzit be affected? Would such an afternoon be considered "nighttime" in every respect, such as to prevent one from reciting qorbanot, or delivering judgment in the Bet Din?

Answer

As long as we stay well (Stockholm is 7°/800 km/500 mi) south* of the polar circle, there will always be a sh'kia and a netz . Therefore, all zmanim can be calculated. Even a tzeis and an alos can be calculated by relying on the opinion that they occur a fixed number of minutes* (e.g. 72) after shkia and before tzeis.

Let's take some practical examples:

On shabbos korach, sunrise is at 3:31 and sunset at 10:08. This gives us until 7:34 to say Sh'ma, and sh'mone esrei has to be before 9:43. There is of course plenty of time for mincha, and ma'ariv could be said after p'lag, at 8:12, and then one could go to bed. The only real difficulty is waking up to repeat sh'ma after 11:21. Havdallah can be said then, or Sunday morning before breakfast, as havdallah over a cup of wine is only necessary before eating or drinking.

On shivah asar b'tammuz sunrise is at 3:57 and sunset at 9:50. One may of course begin fasting the night before, or take a mid-night snack. The usually lenient opinions actually come out later than 72 minutes, so eating can certainly be resumed at 11:02. Obviously, one may go to sleep in the evening, and eat in the middle of the night or the next morning.

For shabbos mikeitz, candles for chanukah and shabbos have to be lit before 2:30. Some choose to study before the meal, which also serves to push it off to a more normal hour. Shacharis can in fact be scheduled for a normal 8 o'clock the whole year, as neitz is 8:43. That shabbes is over at 4 o'clock should not pose any problems, but it is a good idea to limit the morning meal so that shalos seudos can be eaten in time. This gives an excellent opportunity to make melave malka something extra special!

The winter weekdays pose special problems, as many have to begin work before the earliest chance for shacharis. Being that the situation is temporary, one can be lenient and pray between misheyakir and neitz. Relying on opinions that specify alos by the sun's angle under the horizon, shacharis can be over around 7 o'clock. Otherwise, one would have to take a "tea" break in the morning, just as is universally done for mincha in the afternoon.

There are even more northern congregations, like Fairbanks in Alaska and Arkhangelsk in Russia, but their halachic times do not differ substantially. To my knowledge, the only permanent polar community is that of Murmansk, and I hope to add some information when I get a response from the local Chabad sh'liach.

Since we keep both opinions about tzitzis, this mitzva is not affected. Actual halachic processes in batei din are probably rare in these locations, but there are plenty of daylight hours available.

Source: Experience – this is where I come from.

---

^{* Everything here assumes that one chooses definitions so that (tzeis – sh'kia) + (netz – alos) > (netz – tzeis). E.g. if tzeis is 60 minuttes after sh'kia and alos is 72 minuttes before netz, then there must be at least 132 minutes between sh'kia and netz. This is the case for all locations well south of the polar circle.}

theoretical chemistry - Hybridization in PH3

Does $\ce{PH3}$ exhibit $\ce{sp^3}$ hybridization?

Arguments against hybridization:

1. 
   

   $\ce{PH3}$ is less basic than $\ce{NH3}$.

   
   



2. 
   

   This jibes with the supposition that $\ce{PH3}$ keeps its lone pair in what is essentially an unhybridized $\ce{s}$-orbital.

   
   


3. 
   

   $\ce{s}$-orbitals are symmetrical and therefore do not concentrate electron density anywhere.

   
   


4. 
   

   This lack of concentrated electron density as opposed to $\ce{NH3}$ which is $\ce{sp^3}$ hybridized makes $\ce{PH3}$ a poorer base.

   
   

However, my professor writes in his book that it can be argued that $\ce{PH3}$ exhibits $\ce{sp^3}$ hybridization.

Another professor told me that the wave function "blows up" when putting an electron pair in an s-orbital. What does that mean?

Answer

Pre: My views may be clashing with some people. I express them as far as I know.

---

To start with, hybridization is a hypothetical concept$^{*1}$ just to explain all facts and make our work easier, otherwise we would have to take into account every single interaction of electron-proton and also other phenomenons; many theories developed which explained all the major/important facts at a macro-level. And what I have been saying to take into account was all micro-level analysis. Attributing hybridization is purely personal choice because neither does it account all facts (for some molecules) nor it can be dropped altogether (for its $\cdots$), if then we would look for another theory$^{*2}$ to explain observed phenomenon. Parallels similarity between this and the situation of Ideal-Gas equation, in general no perfect theory has been developed, but the most easy, practical and useful are the hybridization$^{*3}$ and van-der-Waals equation.

As we move downwards in the periodic table the hybridization concept fails at many places due to overpowering of other factors. I wonder you didn't mentioned the bond angle$^{*4}$ ($93.5^\circ$) for a $\ce{sp^3}$ hybridized (ideally $109.5^\circ$).

In general atom/molecule doesn't seek to follow a theory, it does what it is best comfortable with, it is us, who mould the theory to the observations.

As a general rule, for sake of convenience, assume all molecules show hybridisation and the tendency to hybridise decreases down the group.

In conclusion, I would say it depends on the need of the situation and such dubious statements such as "Does $\ce{PH3}$ exhibit $\ce{sp^3}$ hybridization?" should be replaced with "Does hybridization explain all (actually not all) properties of $\ce{PH3}$"

Also there are weights in $\ce{sp^\alpha}$ where $\alpha$ ranges from 1 to 3(even upto 4$^{*5}$ and maybe beyond) and is in between these for $\ce{PH3}$ and some may continue to treat it has a hybridised molecule with suitable weights.

---

$^{*1}$(as far as I know)
$^{*2}$(probably the MOT)
$^{*3}$(many may argue for other theories which is genuine, but in context this follows)
$^{*4}$(One may argue as we move down the group electronegativity decreases and atomic size increases. In case of $\ce{NH3}$ due to higher bond pair bond pair repulsion (since electronegativity of $\ce{N}$ atom is very high hence it attracts bonded electrons of $\ce{N-H}$ bond towards itself) bond pair moves away from each other and hence shows greater bond angle. This may be considered one of the major factors for less hybridization.)
$^{*5}$[$\ce{O}$ in $\ce{H2O}$ which means that they have 20% s character and 80% p character, but does not imply that they are formed from one s and four p orbitals]

midrash - Why was Akeidas Yitzchok a bigger test (Nisayon) for Avraham than for Yitzchok?

Akeidas Yitzchok was the hardest test that Hashem gave to Avraham. Yet Yitzchok knew and also agreed to go along with it. Then why is it considered a bigger test for Avraham than for Yitzchok?

Answer

This is discussed by Abarbanel (Bereshis 22). He explains previous commentators as understanding that Avraham's pain in killing his own son, although less than Yitzchak's pain of actually being killed, would last throughout the rest of his life, and thus would have been much worse than Yitzchak's pain. In his words:

ואם כן יצחק שמסר עצמו לשחיטה עם היות צער המות שלו יותר גדול מצער אביו שישחטהו הנה צערו לא היה מתמיד כי מיד שישחט לא ירגיש כלום ולא יצטער עוד. אבל הזקן ההורג את בנו יהיה צערו מתמיד ומרת נפשו קודם השחיטה ובעת השחיטה ואחריה כל ימי חייו יום ולילה לא ישבות. ולכן היה ראוי ליחס פלא המעשה הזה לאברחם ולא ליצחק

Yitzchak, who gave himself up for slaughter, even though his pain of death would be greater than that of his father's who would slaughter him, his pain would not be constant and continuing, since after he is killed he will not feel anything; his pain will be over. But the father who kills his son, his pain will continue, and his bitterness before, during, and after the act of slaughter will never rest. Therefore, it is appropriate to attribute the marvel and wonderment of this event to Avraham rather than to Yitzchak.

[I myself, however, disagree with the assumption that Avraham's pain would have been less than Yitzchak's at all. It makes more sense to me, as @zaq wrote in the comments, that it is harder to kill one's "only" son than to be killed himself.]

Abarbanel, however, feels that although the above may be true, Yitzchak should have at least been given some credit while we don't really find that he is given much at all. Therefore, he disagrees with your basic assumption: Yet Yitzchok knew and also agreed to go along with it. He believes, rather, that Yitzchak was unaware that he was going to be offered as a sacrifice until his father actually tied him onto the mizbeach. Thus, he doesn't really deserve as much credit, since he did not actually go through with the plan willingly.

colloquial language - Use of 悪ィ over 悪い

それが良{い}いのか悪{わり}ィのか正{ただ}しいことなのか、少し考{かんが}える。

I interpret this clause from 僕のヒーローアカデミア as "As to whether that is a good thing or a bad thing or something correct, I will think about it a little."

Why is 悪{わり}ィ used instead of 悪{わる}い (i.e. why the り syllable after わ rather than the る syllable)? Also, why is the い at the end written in 小さいカタカナ rather than ひらがな?

Answer

As you can see in @Earthliŋ's answer that I linked above, this kind of sound change occurs quite often in colloquial speech.

/ui/ → /ii/
あつい → あちい・あちぃ・あちー

わるい → わりい・わりぃ・わりー
だるい → だりい・だりぃ・だりー

This is informal, and usually sounds masculine.

why is the い at the end written in 小さいカタカナ rather than ひらがな?

Katakana often look slangy, so I think they wanted to make it look more slangy.

Edit: As commented by @Sjiveru, the Kanatana ィ is also working as a cue for the slang pronunciation; 悪ィ with no furigana would still probably be read as わりい.

Is my translation correct?

Here is the excerpt,

学校というのは、とにかく「みんな仲良く」で、「いつも心が触れ合って、みんなで一つだ」という、まさにここで私は「幻想」という言葉を使ってみたいのですが、「一年生になったら」という歌に象徴されるような「友達幻想」というものが強調される場所のような気がします

Here is my try at it,

学校というのは、とにかく「みんな仲良く」で、「いつも心が触れ合って、みんなで一つだ」という、

It is said that school is a place where "everyone are getting along with each other, mutual touching and together as one". (Assumption: I've never heard this song)

まさにここで私は「幻想」という言葉を使ってみたいのですが

I want to try to use the word "idealised image" right here,

「一年生になったら」という歌に象徴されるような「友達幻想」というものが強調される場所のような気がします

I feel like it was emphasized by thing called "a fantasy friend" that was symbolized by a song, "become first grader"

---

I am not quite sure of the last part. Also from where should I start to translate? From the last word? And I'm confused about two ような and 受け身 here.

Answer

The basic structure:

学校というのは、 (very long modifier here) 場所のような気がします。
I feel that school is (such-and-such) a place.

場所 is modified by a relative clause, 「友達幻想」というものが強調される:

学校というのは、「友達幻想」というものが強調される場所のような気がします。
I feel that school is a place where something called "friend fantasy" is emphasized.

友達幻想 is further modified by 「一年生になったら」という歌に象徴されるような:

学校というのは、「一年生になったら」という歌に象徴されるような「友達幻想」というものが強調される場所のような気がします。
I feel that school is a place where something called "friend fantasy", as symbolized by a song named "When I Have Become a First Grader", is emphasized.

The song 「一年生になったら」 is further modified by とにかく「みんな仲良く」で「いつも心が触れ合って、みんなで一つだ」という:

学校というのは、とにかく「みんな仲良く」で、「いつも心が触れ合って、みんなで一つだ」という、「一年生になったら」という歌に象徴されるような「友達幻想」というものが強調される場所のような気がします。
I feel that school is a place where something called "friend fantasy", as symbolized by a song named "When I Have Become a First Grader", which says "Everyone should get along, touching one another's heart, together as one", is emphasized.

Finally, まさにここで私は「幻想」という言葉を使ってみたいのですが is a parenthetical phrase that introduces an aside information (perhaps this could be the most tricky part in this sentence):

学校というのは、とにかく「みんな仲良く」で、「いつも心が触れ合って、みんなで一つだ」という、まさにここで私は「幻想」という言葉を使ってみたいのですが、「一年生になったら」という歌に象徴されるような「友達幻想」というものが強調される場所のような気がします。
I feel that school is a place where something called "friend fantasy" (yes I want to use the word "fantasy" here), as symbolized by a song named "When I Have Become a First Grader", which says "Everyone should get along, touching one another's heart, together as one", is emphasized.

number - Echad Veshiv'im Umatayim?

Who knows two hundred seventy-one?

Please cite/link your sources, if possible.

At some undetermined point in the future, at least a day from now, I will:

• 
  

  Vote up all interesting, relevant answers.

  
  


• 
  

  Accept what I consider the "best" answer.

  
  


• 
  

  Move on to the next number.

  
  

Answer

271 is the days of pregnancy.

רות: ד. יג. ויקח בעז את רות ותהי לו לאשה ויבא אליה ויתן יהוה לה הריון ותלד בן

הריון = 271

Niddah 38a-b

Is there a word or phrase for "run around"?

I'd like to know if there is a phrase similar to the English phrase of "running around". To explain more clearly, it should mean to be able to go out freely and do whatever one like's without being restricted.

For example:

If you're going to own a dog, they need some space to run around and exercise.

Have you been running around with those hooligans again?

My wife makes me run around downtown doing all her errands.

It doesn't necessarily mean "to run" all the time though it may. Just wondering if there is any phrase that resembles this. The only thing I can think of is 遊び回る and that may only apply to children, games, and such.

halacha - Is block evasion a sin?

Let's say your account on Facebook or Wikipedia has been blocked by site administration. Is it a sin, according to Judaism, to create new account in order to evade the block?

halacha - Halakha book for modern working place

Is there a halakha book providing the guidance rules for proper behavior at a modern working place? I mean not only relatively obvious "halakhot yekhud" or "kashrut" but taking into consideration intricacies of modern cubicle world. For example:

• Halakhic view on criticizing manager or other employees at meeting?


• Is it good to report the failures of the manager to the manager above him?


• Is it possible to give unrealistic schedules if my job security is in danger in case I say the truth?


• Is it good to hire people while company is trouble...

etc...

physical chemistry - Aurora borealis - less favored energy transitions higher in atmosphere?

This question describes how some energy transitions become more prominent as you higher in the atmosphere. Short summary: Some electron transitions are "forbidden" by quantum mechanical selection rules, and so have a larger time delay from time of excitation until time of photon emission. Thus, low in the atmosphere (high pressure), it's more likely that the species loses the excitation energy by collision than emission.

However, as you go higher in the atmosphere, you see red (due to energy transition in atomic oxygen). The characteristic green line (also due to atomic oxygen, but different transition) disappears.

Why don't you see a mix of the two colours? After all, from the collision rate argument you would expect fast transitions (like the green of atomic oxygen) to become even more prominent.

Why is it that some transitions are less likely as you increase in height?

(I have a feeling that the answer to this question will also explain why nitrogen does not play a more central role in the colour of the aurora.)