physical chemistry - Why weren't the electrons attracted to doubly charged Helium particles in the Rutherford experiment?

I have a chapter and in it there was a topic on the Rutherford experiment.

It is written that doubly charged helium particles or alpha particles were thrown towards a very thin gold foil and some of the alpha particles where bounced back because there were positive particles (protons) and positive and positive always repel each other.

If this was the reason for the bouncing back of the alpha particles, then why didn't the electrons, which are much smaller than protons, get attracted from alpha particles? Especially when the alpha particles are doubly charged.

Answer

The gold foil experiment conducted by Rutherford (or more appropriately by Geiger and Marsden under Rutherford's direction) involves a stream of $\alpha$ particles (which are helium nuclei) bombarding a thin gold foil.

Why didn't some electrons go with the alpha particles because of electrostatic attraction? Some probably did. The experiment was equipped with a fluorescent zinc sulfide screen to detect alpha particles ($\ce{He^{2+}}$ ions). This screen might have also detected $\ce{He+}$ ions (but not necessarily in a way that was different than the detection of alpha particles), but probably not free electrons or helium atoms. The experiment was only set up to detect alpha particles, and so that's all that Rutherford, Geiger, and Marsden observed. We'll never know how many (if any) alpha particles picked up electrons in their experiment. We could, however, repeat the experiment, replacing the fluorescent screen with a mass analyze to detect at least the difference between $\ce{He^{2+}}$ and $\ce{He+}$.

More importantly, we known that many alpha particles passed through (and some were deflected) unchanged. Why didn't these particles pick up electrons? The answer to this question is another question: What is holding those electrons in the gold foil?

Gold atoms have 79 protons holding down those electrons. The first ionization energy of gold is 890.1 kJ/mol and the second is 1980 kJ/mol. However, these values are for isolated gold atoms. Gold (like all metals) is held together by metallic bonds with delocalized electrons occupying a valence band. Each electron is not being held by just one gold nucleus. Once the first few electrons are ejected or snatched by the alpha particles, the gold foil will have a net positive charge. It will be much harder to remove negatively charged particles from the positively charged foil.

How to remove or filter the drift problem in measured Strain signal?

I have the strain signal of a lateral beam of a car measured at sampling rate 1,200Hz from data acquiring system. Even after using temperature compensation in strain gage, we are getting drift. So I wanted to remove drift in post processing of the strain signal. I have tried using High pass filter (HPF) of order 10th with cutoff freq = 200Hz, but I am losing peaks of the strain signal. So HPF is not useful.

Which filter is suitable to remove drift for strain signals? considering the fact that I want to retain peaks and what other methods I can use to remove the drifts?

Also, what are the exact factors to consider in choosing the cutoff frequency for HPF? and how to check it is correct?

I have attached the strain signal and HPF filtered signal of 10th order.

Answer

The usual first approach to this is to use a DC Blocker: $$ y[n] = \alpha y[n-1] + x[n] - x[n-1] $$ where $0 < \alpha < 1$, $y$ is the DC blocked signal and $x$ is your original signal.

If I simulate your signal and apply the DC Blocker to it, the results are in the figure below.

It should preserve the peaks well.

R code to implement it below.

How to choose $\alpha$ ?

This really depends on what you are going to use the data for later. If it's a control application, then phase is probably important to you.

More generally, you want to JUST remove the DC component and not much else. In that case, just look at the magnitude frequency response of the filter.

As you can see from the plots below, low values of $\alpha$ (less than $0.9$ tend to have a bigger impact on the lower frequencies. Hence, I tend to use values of $\alpha$ between $0.9$ and $1.0$.

---

R Code Below

#27468


T <- 1000
Npeaks <- 10

idx_peaks <- runif(Npeaks,1,T)

strain <- rnorm(T) + c(seq(1,2*T/3,1) ,seq(2*T/3+1,0,-2))/100

strain[idx_peaks] <- strain[idx_peaks] + 10

detrended <- 0*strain

alpha <- 0.9

for (k in 1:length(strain))
{
  if (k>1)
  {
    detrended[k] <- alpha*detrended[k-1] + strain[k] - strain[k-1]
  }
  else
  {

    detrended[k] <- 0
  }
}

par(mfrow=c(2,1))
plot(strain,col="blue", type="l")
plot(detrended,col="blue", type="l")

minhag - Hataf-patah instead of sh'va na‘ in Sephardic and Ashkenazic tikkunim

In my Yeshiva, we have Sephardic tikkunim called, ״איש מצליח,״ basically the Sephardic equivalent of סימנים. I own an Ashkenazi tikkun (not סימנים). In my tikkun, sometimes a hataf-patah will appear under letters other than אהח״ע, usually in a word from the root ברך, or in the case of double letters such as ויכננך and יסבבנהו. In Artscroll Ashkenazi siddurim, they always appear with a sh'va. In the Sephardic tikkun, they appear with a sh'va and at the bottom there's a footnote saying, for example, ״ויכננך [with a hataf-patah] למנהגנו, וכ״ה בקורן" ... according to our [the Sephardic] custom, and it's also like that in the Koren [Tanakh]. Sometimes it will leave out that last part because Koren has it with a sh'va and not a hataf-patah.

So my question is: When should I, an Ashkenazi, pronounce it with a hataf-patah, and when should I pronounce it with a sh'va na‘, keeping in mind that I don't bring my Askenazi tikkun to Yeshiva, that it's not the most accurate tikkun, and that my brother's Ashenazi tikkun and the Siddurim always say sh'va na‘?

convolution - Sampling Theorem and Dirac Comb

I am reading "The Scientist and Engineer's Guide to Digital Signal Processing" and trying to understand Figure 3.5 below which is about the sampling theorem and aliasing.

I do not understand the picture of the frequency domain. The signal can be represented as $$f(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}F(x)e^{ixt}dx$$ where $F(x)$ is the Fourier transform of $f$. This represents $f$ with the "frequencies" $e^{ixt}$ and these can have $x$ negative. How then am I suppose to understand Figure 3-5 which shows the frequency domain for only greater than zero and moreover real and not complex.

Also why does the frequency domain of the impulse train have the original frequency spectrum appear flipped half the time? My current understanding is that the repetition comes from something like $$\mathcal{F^{-1}} \{f(t)\Delta(t)\} = F(x)*\Delta(x)$$ where $\Delta$ is the dirac comb and probably some kind of constant like $2\pi$ is needed in there somewhere. How does the flipping half the time in the frequency domain arise from $F(x)*\Delta(x)$. The image I think for convolution is that $\Delta$ is flipped and as it is moved to the right by $s$ the "area" of $F(x)\Delta(s-x)$ is the value of the convolution at $s$. This would seem to replicate the original spectrum multiple times but without the flipping half the time as shown in Figure 3.5.

Answer

Let $X(f)$ denote the Fourier transform of $x(t)$ where $$\begin{align*} X(f) &= \int_{-\infty}^{\infty} x(t) \exp(-j2\pi ft) \mathrm dt\\ x(t) &= \int_{-\infty}^{\infty} X(f) \exp(+j2\pi ft) \mathrm df \end{align*}$$ which I will denote via $x(t) \leftrightarrow X(f)$. The following transform pairs will be needed in what follows. $$\begin{align*} \delta(t) &\leftrightarrow 1\\ \delta(t-t_0) &\leftrightarrow \exp(-j2\pi f \,t_0)\\ \sum_{n=-\infty}^{\infty}\delta(t-nT) &\leftrightarrow \frac{1}{T}\sum_{k=-\infty}^{\infty}\delta\left(f-\frac{k}{T}\right)\\ \end{align*}$$

Given a signal $x(t)$, its sampled pulse train (at intervals of $T$ seconds) is $$x(t) \sum_{n=-\infty}^{\infty}\delta(t-nT) = \sum_{n=-\infty}^{\infty} x(t)\delta(t-nT) = \sum_{n=-\infty}^{\infty} x(nT)\delta(t-nT).$$ Since multiplication in the time domain corresponds to convolution in the frequency domain, we have $$\begin{align*} x(t)\sum_{n=-\infty}^{\infty}\delta(t-nT) &\leftrightarrow X(f)\circledast\frac{1}{T}\sum_{k=-\infty}^{\infty}\delta\left(f-\frac{k}{T}\right)\\ &\leftrightarrow \frac{1}{T}\sum_{k=-\infty}^{\infty} X(f)\circledast\delta\left(f-\frac{k}{T}\right)\\ &\leftrightarrow \frac{1}{T}\sum_{k=-\infty}^{\infty} \int_{-\infty}^{\infty} X(f-w)\delta\left(w-\frac{k}{T}\right) \mathrm dw\\ x(t)\sum_{n=-\infty}^{\infty}\delta(t-nT) &\leftrightarrow \frac{1}{T}\sum_{k=-\infty}^{\infty} X\left(f-\frac{k}{T}\right) = \hat{X}(f) \end{align*}$$ Thus, the Fourier transform of the impulse train formed by sampling $x(t)$ at $T$ second intervals is $\hat{X}(f)$ which is obtained by repeating $X(f)$ along the $f$ axis at intervals of $T^{-1}$ Hz and summing the result. Furthermore, $\hat{X}(f)$ is a periodic function of the frequency variable $f$ with period $T^{-1}$ Hz. That is, for all $f$, $$\hat{X}\left(f + \frac{1}{T}\right) = \hat{X}(f).$$ Note that all of this holds regardless of what $X(f)$ is: $X(f)$ could be nonzero for all $f$, and the result would still be valid.

Now suppose that $X(f)$ is zero if $f < a$ or $f > b$. Then, $\hat{X}(f)$, obtained by repeating $X(f)$ periodically along the $f$ axis, is nonzero only in the intervals $$\ldots, \left[a-\frac{2}{T}, b-\frac{2}{T}\right], \left[a-\frac{1}{T}, b-\frac{1}{T}\right], [a, b] \left[a+\frac{1}{T}, b+\frac{1}{T}\right], \left[a+\frac{2}{T}, b+\frac{2}{T}\right], \ldots $$ and so if $$b -\frac{1}{T} < a \Rightarrow b-a < \frac{1}{T},$$ that is, the support $b-a$ of $X(f)$ is smaller than the repetition interval $T^{-1}$ Hz, then the repetitions of $X(f)$ do not overlap. Indeed as the OP's figures show, for a real-valued signal whose spectrum extends from $a = -f_0$ to $b = f_0$ (support of $X(f)$ is of length $2f_0$), sampling $x(t)$ at intervals of $T = (3f_0)^{-1}$ (and thus repeating $X(f)$ at intervals of $3f_0$ Hz on the frequency axis) leads to no overlap while sampling $x(t)$ at intervals of $T = (1.5f_0)^{-1}$ leads to overlap of the repetitions of $X(f)$.

Finally, the OP asks about negative frequencies and the interpretation of the pictures which show positive frequencies only. For a real-valued signal, $X(f)$ has conjugate symmetry, meaning that $X(-f) = X^*(f)$, and so specifying $X(f)$ for positive values of $f$ suffices. In any case, the pictures he is looking at are of $|X(f)|$ and $|\hat{X}(f)|$ which are even functions of $f$, and so showing only the positive axis saves space, though it does make the pictures look a bit lopsided since only half the lobe is shown at low frequencies. For complex-valued signals, $X(f)$ does not have conjugate symmetry and $|X(f)|$ need not be an even function of $f$ and so the whole axis would need to be shown. But, the general development above is still applicable, and we still need to sample at rate exceeding $b-a$ Hz, and it helps to keep in mind that in this general case, each sample is actually two real numbers, not one, since we are sampling a complex-valued signal.

kashering kosherization - Can rags and oven mits become non-kosher or be kashered?

If kitchen rags or cloth oven mits have been used in a non-kosher kitchen, may they be used in a kosher kitchen after they are laundered? Or do they become non-kosher (for example, from contact with a hot non-kosher stove or hot non-kosher food) and require kashering? If so, how does one kasher cloth? Does it make a difference if the oven mits have some rubber or plastic on them, as opposed to being made solely of cloth?

Do non-redox reactions exist?

Redox reaction is a type of chemical reaction, and is the result of electron transfer between chemical species. But, all chemical reactions somehow involve electron transfer!

So, are there chemical reactions without electron transfer?

everyday chemistry - How does WD40 displace water?

How does WD-40 displace water? Or does it even displace water? WD40.com explains what WD-40 stands for:

WD-40® literally stands for Water Displacement, 40th formula. That's the name straight out of the lab book used by the chemist who developed the product back in 1953. The chemist, Norm Larsen, was attempting to concoct a formula to prevent corrosion—a task which is done by displacing water. Norm's persistence paid off when he perfected the formula on his 40th try.

If it displaces water then I always thought that that meant it was denser or heavier. I just tested to see: I sprayed a couple teaspoons into an empty glass then poured that into another glass half filled with water. The WD-40 floats! So what does it mean to say that it "displaces water"? Surely it doesn't mean that it's hydrophobic, all lubricants are hydrophobic.

chanuka - How do you get oil residue off of a menora?

When you light olive oil in a metal menora, some of the oil invariably finds its way into the cracks between parts of the menora. How do you remove this residue?

Answer

Put water and dishwashing detergent in a basin; let the entire menora soak in it.

inorganic chemistry - Why is CO2 not in the C∞v point group?

It seems to me that CO2, since it can be linearly rotated around the z-axis without change of shape, ought to be in the C∞v point group. However, in all the character tables I can find, it's listed as a D∞h. What's the difference between these two, and why does CO2 fall in the D∞h and not the C∞v?

Answer

Both are linear with a $C_{\infty}$ axis, but $D_{\infty h}$ has a center of inversion and $C_{\infty v}$ does not.

words - why is the reading of 瞬く and 瞬き not the same?

Out of sheer curiosity I was wondering why 瞬く is read as またたく but 瞬き is read as まばたき.

Answer

1. （A）まばたくー （B）まばたき


2. （A）またたくー （B）またたき

where (A) is a verb and (B) is a noun.

I think that the use of these words depends on the generation and the dialect very much, therefore what is written from now on is my personal opinion.

Generally group 1 is used to describe the blink of eyes, on the other hand group 2 is used to describe the fluctuation of emitted light from objects such as stars, fishing boat equipped with fishing lamps, candles, etc.

As the Japanese word for the set phrase "in a very short time", またたくまに is used but まばたくまに is not.

As for しばたく/しばたたく and しばたき/しばたたき which are described in broccoli forest's answer, I have rarely said or heard them said; a very little use frequency of them is also written in the follow-up survey in the answer.

The etymology

The verb matataku (瞬｛またた｝く) is made of ma and tataku (叩{たた}く) where ma means eye (目{め}) and tataku (叩{たた}く) means to strike, so matataku (瞬{またた}く) literally means to strike eyes (with eyelids), then matataku (瞬{またた}く) means to blink eyes. As for mabataku (瞬{まばた}く), ma means me (目{め}), and bataku is an euphonic change from hataku (叩{はた}く) which means strike. Therefore matataku (瞬{またた}く) and mabataku (瞬{まばた}く) have the almost same origin derived from the same motion of blinking eyes.

On the other hand, shibataku (しばたく) has different etymology; it is derived from shiba (しば) and tataku (叩{たた}く).　shiba (しば) is abbreviated from shibashiba (屡/屢{しばしば}) which is an adverb meaning often or many times. Hence the whole meaning of shibatataku (しばたたく) is to strike often. Originally shibatataku (しばたたく) was used as the phrase "me wo sibashiba tatataku (目{め}をしばしば叩{たた}く)" which means to strike eyes often (with eyelids).

So if we trace the word, we found out that the original phrase gradually turned to the present form as:
"me wo shibashiba tataku" → "shibashiba tataku" → "shiba tataku" → "shibataku" → (it becomes nearly an obsolete word now.)

---

I'll show you the intonations of the words in the following illustration. Before that the rules of accent or intonation of a Japanese word are like:

1) Accent is relative emphasis or prominence given to a certain syllable in a word.
2) Intonation is a pattern of rise and fall in the level/pitch of the voice.

3) Emphasis is produced through pitch alone, so it is called pitch accent.
4) Largely, words are divided into two groups whether there is an accent or not.
5) The accent given to the emphasized syllable is called an accent nucleus.
6) Pitch falls after the accent nucleus.
7) Unless the first syllable is an accent nucleus, there is a rise of pitch after the first syllable of a word.

I'll show you how the intonation lines written in red in the illustration are decided by the rules.
As for まばたく, we give an accent to た which is called an accent nucleus by the rule 5), so by the rule 6) the pitch becomes to fall from た to く, then the intonation around たく becomes like まば[たく]{HL}. And by the rule 7) the intonation around まば becomes like [まば]{LH}たく, so the whole intonation becomes [まばたく]{LHHL}. 　

As for accent nucleus, ば in まばたき and the second た in またたく become the accent nucleus of each word, and またたき has not it. And after applying the rule 6) and the rule 7) to these words, each intonation becomes like this respectively.
[まばたき]{LHLL}, [またたく]{LHHL} and [またたき]{LHHH}

halacha - Is it permissible to be mechalel Shabbos to save the life of an animal or pet?

Is it permissible to be mechalel Shabbos to save the life of an animal, such as a family pet? Could minchag, chumras, and/or purely Rabbinical prohibitions be relaxed in such a situation, and to what extent?

Please assume no Gentile is available to save the animal's life. However, if it would be permissible to relax certain rules in order to summon a Gentile for this purpose, please discuss.

Answer

From the Mishna Brurah 332:6 it is assur to violate a Torah or Rabbinic law to save an animals life but one can ask a אינו יהודי . However to heal it in a certain way see Mishna Brurah 332:5,9 .

organic chemistry - Why does NaBH4 reduce double bonds conjugated to carbonyl groups, while LiAlH4 does not?

I have been going through reduction of aldehydes using $\ce{LiAlH4}$ and $\ce{NaBH4}$. If there is a double bond conjugated with the carbonyl group, $\ce{LiAlH4}$ doesn't reduce it, leading to an allylic alcohol. However, using $\ce{NaBH4}$, some of the fully reduced alcohol will also be formed. Why is this so?

Answer

Neither $\ce{LiAlH_4}$ nor $\ce{NaBH4}$ are able to reduce an isolated $\ce{C=C}$ bond. But if you have an enal (a conjugated aldehyde) it can react (as an electrophile) either at the $\beta$-carbon or at the carbonyle group's carbon. According to the HSAB Principle the $\beta$-carbon is a "soft" center and would react preferably with "soft" nucleophiles while the carbonyle carbon is a "hard" center and prefers to react with "hard" nucleophiles. Now, $\ce{NaBH4}$ is a rather soft nucleophile and thus it reacts with an enal at the $\beta$ carbon. After this reaction the $\ce{C=C}$ bond is gone. But, if what is left behind is still a very reactive simple aldehyde that gets reduced to the alcohol by $\ce{NaBH4}$ in a second step. $\ce{LiAlH_4}$ on the other hand is a rather hard nucleophile and thus reacts with an enal at the carbonyle carbon. After this reaction there is just an isolated double bond left that can't be reduced by $\ce{LiAlH_4}$ in a second step.

usage - What's the difference between 悪 and 惡 ?

I'd like to know what the difference between 悪 and 惡 is. And also what usage you should do between both. I heard that they both mean "bad"

Answer

惡 is the traditional (pre-1946) form of the kanji, while 悪 is the new, simplified form. The simplification in this case may not seem much (just a single stroke has been removed), but it was probably made to make the form of the kanji more 'natural' and flowing.

definitions - Does "敬語" (keigo) just mean "politeness" or is it a technical term specifically relating to Japanese grammar?

What is the difference between the Japanese term "敬語" (keigo) and the English term "politeness" (Specifically regarding language)?

I assumed politeness is more general covering things like "please" and "thank you" and that "敬語" (keigo) specifically referred to those aspects of Japanese grammar that deal with politeness in a technical way that has no equivalent in English.

But upon reading a bit and using this site a bit I'm not sure anymore. What are the overlaps and differences in meanings?

(I considered asking this as a meta question concerning the keigo and politeness tags but I decided it's of much broader interest.)

what's the source for Bar Mitzvah being at 13?

How do we know that a person is not obligated in Mitzvos before the age of 13, and is obligated from that point forward?

thermodynamics - Estimating maximum size of magnetite particles in this Nile Red ferrofluid video?

In the Nile Red video Making ferrofluid from scratch a suspension of small magnetite ($\ce{Fe^{2+}Fe_2^{3+}O_4^{2−}}$) particles is produced from a combination of ferrous chloride and ferric chloride.

The nanoparticles are then given a coating of oleic acid ($\ce{CH3(CH2)7CH=CH(CH2)7COOH}$) to provide steric stabilization to prevent aggregation, then dissolved in kerosene.

After about 23:20:

…the magnetite isn’t truly dissolving, it’s going into suspension. This is because the nanoparticles aren’t soluble in the solvent, but they’re small enough that they can still easily get dispersed.

The oleic acid coating that helps with this, by preventing two particles from coming too close together, and by also allowing them to interact with the non-polar solvent. The result of this is a stable suspension known as a colloid, where it’s almost like the magnetite being dissolved.

As an exercise I'd like to estimate the maximum size of the oleic acid-coated magnetite particles that can be stable in this solution. Some considerations are:

1. 
   

   While the magnetite particles themselves have a high density (over 5 g/cm³), the oleic acid molecules might be arranged radially making the volume of the complete particle much larger than the magnetite core.

   
   


2. 
   

   While large magnetite particles would sink quickly to the bottom due to gravity, the thermal agitation (Brownian motion) at room temperature is sufficient to keep these in colloidal suspension if they are small enough. This suggest that there might be some ratio of $k_B T$ with some expression of gravitational potential energy.

   
   

Question: How would I go about estimating the maximum size of the magnetite nanoparticles that could remain in stable suspension in this case?

---

usage - Do you also say 「もしもし」 on Skype?

Is 「もしもし」 only used when you cannot see the person you're talking with (I once heard that it's somewhat akin to "Anyone there?", which wouldn't make much sense if you could see your conversation partner) or do you also use it when making video calls?

Answer

もしもし is like "Hello" and it's used in two kinds of situations:

1. As the very first word of the call ("Hello, this is Tanaka speaking.")


2. As the word to check if the other person can hear you, when the line is noisy or unstable ("Hello? Hello? Can you hear me?")

In video calls, you can still safely use もしもし in the second situation. In the first sense, and in a video call, I feel もしもし is probably not very common. Many people probably use other nonspecific greetings like おはようございます, どうも. But some people may use もしもし, and it's not that strange.

The tense of the て form of verbs

Just a quick question on the て form, as what I am about to say isn't really made clear by textbooks. Is the tense of a verb in て form dependent on what follows? for example if someone was to say 教えてあげた, would the 教えて become past tense (or completed, as at doesn't have to take place in the past)?

Thanks is advance.

transition metals - Magnetic susceptibility trend

So I was recently looking at this website.

http://www.fizika.si/magnetism/MagSusceptibilities.pdf

It lists the susceptibility values for inorganic compounds, and I've noticed that the trends don't appear to follow logic. The stronger the ligand OH, CN etc.., the larger the energy needed to reach the higher orbitals, and thus more paired electrons so a stronger diamagnetic effect, whilst the weaker ligands cause the pairing energy to be higher relative to the energy needed to go up to the higher shells, so less paired electrons so higher magnitude of magnetic susceptibility.

If one takes a look at CuI, CuBr, CuCl, and CuCN we can see that the negative susceptibility values become more positive (from -63, to -49, to -40, to -24) as ligand strength increases. Similarly, some compounds don't follow the trends of stronger ligands like $\ce{NiI2}$, to, $\ce{NiBr2}$, to $\ce{NiCl2}$. How can this be?

Also, I've tried plotting transition metal radius alongside their susceptibility values for bonding w/ Br for same oxidation states. I got a proportional relationship. Apparently, the atomic radius of the transition metal increases the susceptibility. Does this make a bit of sense? I mean, logically, larger radius essentially means larger diamagnetic and hence lower paramagnetic susceptibility values, right?

grammar - 「～たじゃない」 expression in spoken Japanese

I noticed in an anime I watched, one of the characters said something like below:

さっき食べたじゃない。

And what I think the meaning is: Didn't you just eat a few while ago?

From what I have learned in Japanese classes, 「じゃない」, which is the shortened form of 「ではない」, must follow a noun word/phrase/clause. But in the spoken sentence above the 「じゃない」 follows a 「～た」 form of a verb. Is that sentence grammatically correct? Is this one of the many examples where colloquial language may skip a few grammar rules here and there?

I think the sentence would be grammatically correct if there is　「ん」 in between the two phrases: 「さっき食べたんじゃない」. Did I actually mishear?

Answer

I do not know if さっき食べたじゃない is grammatically correct or not, but sentence + じゃない is a common colloquial construct whose meaning is similar to a tag question as Amanda wrote: “You ate it a little while ago, didn’t you?” It is a statement rather than a question, and the じゃない part indicates either that the speaker is surprised by the fact that he/she has to say it or that the speaker wants a confirmation.

An example of surprise:

A: 冷蔵庫に入れておいたケーキがない! (I cannot find the cake I put in the fridge!)
B: あんたさっき食べたじゃない。 (You ate it a little while ago, didn’t you.)

An example of wanting confirmation:

A: さっきケーキを食べたじゃない。あれじつは1週間前に賞味期限が切れていたの。 (We (or you or …) ate cake a little while ago, didn’t we? To tell the truth, that cake was best before a week ago.)

I think that さっき食べたんじゃない has a different meaning from さっき食べたじゃない. さっき食べたんじゃない has two meanings:

1. Without the raise of pitch at the end of the sentence, it is a negation of さっき食べた. “It is not true that I ate it a little while ago.” The usual negation of さっき食べた is さっき食べなかった (I did not eat it a little while ago), and they have different meanings, but I cannot explain it clearly.


2. With the raise of pitch at the end of the sentence (often denoted by a question mark: さっき食べたんじゃない?), it is a question “Didn’t you eat it a little while ago?” with indication that the speaker thinks that “you” probably ate it a little while ago.

grammar - How does the use of いかんによっては in this question determine one answer over another?

In my JLPT practise book, in a section explaining the use of いかんによっては, which roughly means "depending on", they have the following question:

学生{がくせい}：先生{せんせい}、台風{たいふう}が近{ちか}づいていますね。明日{あした}のゼミは休講{きゅうこう}ですか？

先生{せんせい}：そうですね。台風{たいふう}のコースいかんによっては______

A: 休{やす}みです。　B:　決{き}めましょう。

I chose the answer B, thinking it roughly meant, "We will decide depending on the course of the typhoon."

However, according to the book, the correct answer is A, which is translated as, "depending on the path it might be a holiday." (The English translations in this book are not so smooth.)

Both make logical sense to me, but, despite what the book says, I can't help but feel that B makes more sense because the path of the typhoon is uncertain, and therefor so is the decision about the seminar. Thus, "let's wait and decide."

Why is A the correct answer?

Answer

According to 新完全マスター　文法　N3:

によって：means to change state or behaviour depending on something or according to something. It expresses variety and is often used with さまざまだ　and かえる.

によっては：pinpoints one outcome from a range of possible outcomes

For the sentence:

そうですね。 台風{たいふう} のコースいかんによっては_________

A: 休{やす}みです。　B:　 決{き}めましょう。

A pinpoints one outcome, B does not.

Note on いかん／いかんによって

I've got to the correct answer using N3 grammar but I should not really ignore いかん. It　means "what" or "how" so in the above sentence I would say the expression equates to "depending on what [course]". The impact of adding は to いかんによって　is the same as if added によって.

An alternative way to look at this is to consider いかんによって as one expression, equivalent to いかんで, which approximates to "in accordance with/is contingent upon".

The impact of adding は is the same as the difference between いかんで　and いかんでは, which is perhaps easier to workout intuitively.

References: 新完全マスター文法N3, 日本語表現文型辞典

purim - How old was Mordechai in the Megillah?

I have been trying to calculate Mordechai's age, and according to my estimates he must have been around 100, if not older, when the Purim saga begins.

Are there any textual sources which provide the precise age of Mordechai during the Purim story?

signal analysis - understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into a sum of unit impulses. We have unit impulse function $\delta$:

$\delta[n] = 1\ if\ n = 0, 0\ if n \neq 0$

then $x[t]$ can be represented as:

$x[t] = \sum_{k = -\infty}^{+\infty}x[k]\delta[t-k]$

so the input signal at $t$, $x[t]$, can be represented this way because $\delta[t-k]$ is going to be 1 only if $t = k$, and 0 elsewhere. this makes great sense.

the confusion for me begins in Transparency 4.2 of above link. the left hand side makes perfect sense, but what does the right represent? how does one unit impulse generate a sequence of responses? what does $x[0]h[n]$ represent here? How do you go from this to Transparency 4.9 where $h$ is used instead of $\delta$?

put differently: can someone explain the intuition behind $h$ (the response of a an LTI system) being reflected and time shifted? in the above trick for representing simply the input signal $x[t]$, there's no time shifting really; $\delta[t-k]$ seems like just a mathematical trick for getting a $1$ in the right place and zero elsewhere; it's not intuitive for me to think of it as time shifted.

if we use the fact that in LTI, the response of a system to input $n$, $y[n]$, is just the superposition of the responses to unit impulses of input signal $x[n]$, why can't we write convolution this way instead?

$y[n] = \sum_{k=-\infty}^{+\infty}x[k]h[n]$

Answer

You know that $h(n)$ is the system's response to the input $x(n)=\delta(n)$. Because of time-invariance, the response to $x(n)=\delta(n-k)$ is given by $h(n-k)$. If you write the input signal as

$$x(n)=\sum_kx(k)\delta(n-k)\tag{1}$$

then, due to linearity, you can write the output signal as the sum of the responses to each individual term $x(k)\delta(n-k)$ in (1), which is $x(k)h(n-k)$. So you get the convolution sum

$$y(n)=\sum_k x(k)h(n-k)\tag{2}$$

To compute (2) for a given value of $n$ you need to multiply $x(k)$ with $h(n-k)$ for all relevant values of $k$. Since you have $h(n\color{red}{-k})$ in (2) (i.e. with a minus sign before $k$) you need to flip the impulse response (shifted by the current value of $n$), multiply it with $x(k)$ and compute the sum.

shabbat - Why is the Boro Park eiruv controversial?

I know I might be hitting a touchy subject, but I'm prefacing it with this so I can clarify right away: I don't want a Psak, or who holds what. That's for each person to figure out... I just want to know what all the issues are with respect to the Boro Park eiruv, and why someone would hold what he does.

Answer

A couple good places to start would be here and here, both from the Eruv Blog.

The second link, which itself contains many relevant and detailed links, addresses the technical issues of the geography, demographics, and (artificial) geology of Brooklyn that govern the permissibility/restrictions of an eruv. The first link addresses a non-legal complication in the case regarding the authenticity of influential documents.

Existence verbs in the Kansai Dialect

In this part of this Wikipedia article, it states

In other areas such as Hyogo and Mie, いる /iru/ is hardly used and おる /oru/ does not have the negative usage.

What I want to know is, does this statement mean that おる is used in nearly all of the instances いる would be used in Standard Japanese? Does おる also replace the duties of ある? How does おる work in Hyogo and Mie?

Answer

That statement basically only applies for おる as a simple existence verb. Non-humble おる is very common in Kansai. As a subsidiary verb, various forms including とる/ちょる/よる are commonly used instead of standard (～て)いる, but there are considerable regional variations even inside Kansai. See this discussion.

• 太郎はおる。
  There is Taro. / Taro is here. (≒太郎はいる)


• 太郎は来とる。
  
  [Chugoku/Shikoku] Taro has (already) arrived. (≒太郎は来ている)
  [Osaka/Kyoto] Taro is (now) coming. / Taro has (already) arrived. (≒太郎は来ている)


• 太郎は来よる。
  [Chugoku/Shikoku] Taro is (now) coming. (≒太郎は来ている)
  [Osaka/Kyoto] (Damn,) Taro will come! (≒太郎は来やがる)

おる does not replace ある for inanimate objects. 本がおる is incorrect. (The article says the opposite (先生がある) happens in parts of Wakayama, but I'm not familiar with that.)

isotope - Why atomic masses aren't integers?

Most of the elements have isotopes, so the atomic masses are calculated depending on the percentage of the existing isotopes. That is clear. However, what about elements that have only one isotope (monoisotopic) - like fluorine? Shouldn't the atomic mass for it be a whole number and not 18.9984?

Answer

The short answer is nuclear binding energy, which is the energy needed to disassemble an atom into its subatomic parts (or in some cases the energy released when this happens). The binding energy is a consequence of the strong and weak nuclear forces that hold atoms together.

Where does this energy come from? It comes from the mass of the nucleons! What? It is true; most atoms have less mass than the sum of their parts, and that mass defect is converted into the energy that holds them together. If you do not believe me, let us look at one atom of carbon-12, which is used as the definition of the atomic mass unit:

$$\mathrm{1\ u}=\dfrac{1}{12}\text{ of the mass of one }\ce{^12C}\text{ atom}$$

Thus, the atomic mass of an atom of $\ce{^12C}$ is by definition $\mathrm{12\ u}$. The atom is constructed from 6 protons, 6 neutrons, and 6 electrons, and the masses of those particles are:

particle   mass                     number    total mass
p          1.00727646681290     u   6         6.0436588008774    u
n          1.0086649160043      u   6         6.0519894960258    u
e          5.485799094622×10^−4 u   6         0.0032914794567732 u
                                     TOTAL:  12.0989397763600    u

The sum of the parts of the $\ce{^12C}$ atom are more than the mass of the atom! This mass defect, $\mathrm{0.0989397763600\ u}$ in this case, is the value of the nuclear binding energy when converted to energy using $E=mc^2$.

This handy graph from the Wikipedia article linked above shows that the binding energy per nucleon is not the same for all nuclei.

If it were, then we would have integer values for monoisotopic nominal masses. However, the consequences of this change in reality could be as drastic as the heavier elements (like iron) not having enough energy to hold themselves together. An additional consequence is that there would be no productive nuclear reactions (fission, fusion, or radioactivity). All nuclear transmutations are driven by conversion of nuclei with lower binding energy per nucleon to nuclei with higher binding energy per nucleon, resulting in a net conversion of mass to energy. Without a difference in binding energy per nucleon, we would not have nuclear bombs (and probably we would be better off as a civilization), but we would also not have nuclear power and radioisotopes for compound labeling, cancer therapy, and medical diagnostics. We would also not have a ready supply of deuterium for NMR solvents, and we might not be able to use variations in isotopic distributions of $\ce{H}$, $\ce{C}$, and $\ce{O}$ to determine all sorts of things like did that "locally grown" food from that restaurant you like actually come for your geographic region?

tefilla - Why is it a sheva na in ha-leviyim?

Before the Psalm for the day at the end of Shacharis each day, we say a sentence, "Today is the Xth day of the week..." In that sentence is a word for Levites, and that word in Hebrew has a sheva under the lamed. Why is that sheva a sheva na? (All six siddurim I have checked show it as a sheva na: Artscroll, Koren, Metsuda, NeHalel, and the two reported here https://judaism.stackexchange.com/a/82836?noredirect=1.)

What rule is being followed that tells us that it is a sheva na?

Update: Two sefardic siddurim I checked showed this sheva as a sheva nach. Perhaps the sheva na pronunciation is only in ashkenaz siddurim.

purim torah in jest - Can I Have a Chumra Please?

I'm looking to take on a really, really, really enourmous chumra which will greatly affect my life to show how dedicated I am to Hashem. Does anyone have any suggestions?

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General rules for final kana in names ending with consonant?

I'm starting to study Japanese — and of course, it seems one of the first things one is taught in any language is how to introduce oneself. So, according to some (admittedly sketchy looking) online transliterators...

リック です。

But I wonder: The name I go by in English (Rick) ends with a consonant, so why 「ク」 and not any of the other k-series kana? Is it something to do with this name in particular, e.g. it's a masculine name? Simply because of the tendency (which I don't fully understand just yet) of final ~u to become devoiced? Something else entirely?

More generally, are there general rules for transliteration that lead to this result? I'm afraid I'm too new to the language to know what to search for in that department (at least, my tries so far have come up empty).

Answer

There are at least general tendencies, if not necessarily hard-and-fast rules regarding the matter.

Just off the top of my head ---

Japanese vowel assigned vs. Ending consonant of English name

ウ: b, f, g, sh, k, l, m, p, s, v, z　（ボブ、ジェフ、グレッグ、ジョッシュ、リック、カール、トム、etc.）

オ: d, t （トッド、マット, etc.）

イ: ch （リッチ、ミッチ）

When an English name ends with "r", our usual practice is to elongate the preceding vowel and ignore the "r". （Oscar ==> オスカー）

Not even sure if that covers all the possible name-ending consonants in English. Feel free to edit.

Please remember that we are ONLY discussing the transliteration of English names, not of names from other European languages. I mention this because, for instance, even though "Oscar" as an English name is 「オスカー」 as I stated above, "Oscar" as a French name is written 「オスカル」.　Likewise, "Charles" as an English name is 「チャールズ」, but it is 「シャルル」 for the French.

organic chemistry - Which ring expansion in cyclobutyl(cyclopropyl)methanol is favourable?

Predict major product:

In this question first I've protonated the OH group and then water is removed to form a carbocation. Now I have to expand the ring, but I'm confused which ring to choose: 3-membered ring or 4-membered ring?

Note: I can make an alkene (which would be the final product of the reaction) by removing an alpha hydrogen if it is known which ring to expand.

Answer

It is clear to me that no matter which ring you open the first, you'd get the same product as A. Michael Lautman gave the correct product , first opening the cyclopropyl ring. Michael's mechanism is fair, but I'm reluctant to say it is the most preferable path because it gives you bicyclobutyl $2^\circ$ carbocation as an intermediate, which needed extra 1,2-hydride shift to get stabilized as $3^\circ$ carbocation (total of 5 steps). However, if you have opened the cyclobutyl ring first, you'd get the same final product A, through a relatively low energy cyclopropylcyclopentane carbocation (total of 5 steps) even though it is also needed a 1,2-hydride shift (in relatively more stable cyclopentyl $2^\circ$ carbocation when compared to $2^\circ$ carbocation in cyclobytyl ring in Michael's mechanism) to get stabilized as $3^\circ$ carbocation. Complete mechanism is depicted below:

This mechanism is supported by following reference:

• G. K. Surya Prakash, V. Prakash Reddy, G. Rasul, J. Casanova, G. A. Olah, “The Search for Persistent Cyclobutylmethyl Cations in Superacidic Media and Observation of the Cyclobutyldicyclopropylmethyl Cation,” J. Am. Chem. Soc. 1998, 120(51), 13362–13365 (https://doi.org/10.1021/ja9828962).

shevatim 12 tribes - Yaakov's sons kvarim

When Yosef died in Mitzraim, he was interred in Mitzraim until Moshe exhumed his remains which were eventually brought to Israel and reinterred. However, when Reuven, Judah, ... (the 11 brothers) died, there is no mention of their burial nor exhumation. We assumed they were buried in Mitzraim where they remain ad hayom hazeh. A few question are raised (1) has anyone seen any information about the whereabouts of their kvarim? And related, (2) why was their burial so low profile (these were the founders of the shvatim, quite an important role in Jewish history)?

町｛ちょう｝、町｛まち｝、街｛がい｝、街｛まち｝ - how to pick the correct pronunciation?

I've grown accustomed to enunciating both 町 and 街 as まち in my head but it turns out this may have been totally incorrect, as 三省堂｛さんせいど｝ lists two possible pronunciations for 町 and only one (がい) for 街 - even though IME returns まち as a 街 next to 町. It's clear-cut in constructs like 町並み｛まちなみ｝ or 街道｛かいどう｝ (consult a dictionary - problem solved), but what about meeting these Kanji by themselves?

This came to head as I tried speaking through this sentence:

わたしたちの住んでいる街、冬木市｛ふゆきし｝は大きくわけて二つの町で構成｛こうせい｝される街だ。

There is no further context to see what the narrator meant by these things, except that she goes on to describe the two 町 that 冬木市｛ふゆきし｝ is divided into. Please help!

よろしくお願いします

Answer

The entry for 街【がい】 you linked to is:

(尾) まちなみ． ▼繁華～

If you take a look at the explanation for the dictionary, we find what (尾) means:

　(尾)　接尾語

Ie, it is used at the end of words, and not in isolation. Other dictionaries say

がい【街】

　(造)

...

(造) means almost the same: used only to form words, but not in isolation. 「街灯」「商店街」「オフィス街」「地下街」「繁華街」「街路」

For 町, the same applies. 町【ちょう】 is used mostly within words. 「町会」「町議会」「町人」. [A chō is also a unit for an area (~99.2m²) or for a distance (~109m).]

街【まち】 or 町【まち】^※ is a word that can be used on its own.

Also, some dictionaries do list 街【まち】, ie. the デジタル大辞泉.

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But hold on, there's one more important class of words where you will encounter these kanji.

For place, names, there is no rule. You cannot know, unless you do know.

Names could potentially be anything. There is common sense, there is a tendency. And there are exceptions. Lots of them.

I ran some statistics on a database of Japanese place names (based upon ZIP codes); and analyzed each place name whether the part before 町 consisted of on or kun readings. This was done by a script, so there are some erros, but it should give you the general idea. But note that

• Names classified as mix should often be split: 豊田町中村 → 豊田町 + 中村.



• Names classified as unknown often use non-standard kun readings or variations: 「富村【とびむら】」「馬喰町【ばくろうまち】」「小深町【こぶけちょう】」「轟町【とどろきちょう】」

ちょう: 15348 (69%)

• kun: 7257 (47%) 「月見町【つきみちょう】」「萩原町【はぎわらちょう】」


• on: 1594 (10%)　「愛光町【あいこうちょう】」「水明町【すいめいちょう】」


• mix: 5348 (35%)　「瓦師町【かわらしちょう】」「嵯峨朝日町【さがあさひちょう】」


• unknown 1149 (7%)　「尾上町【おのえちょう】」「西愛宕町【にしあたごちょう】」

まち: 7002 (31%)

• kun: 3123 (45%)　「笹目町【ささめまち】」「暁町【あかつきまち】」


• on: 578 (8%)　「和歌町【わかまち】」「海隣寺町【かいりんじまち】」


• mix: 2854 (41%)　「宇津貫町【うつぬきまち】」「栄恵町【さかえまち】」


• unknown: 447 (6%)　「廿里町【とどりまち】」「[下タ町]{したまち}」

other: 1

• 半町 (大阪府【おおさかふ】 箕面市【みのおし】半町【はんじょ】)

ちょう is more common overall. kun readings are more likely for place names ending on 町, regardless of whether 町 is read まちor ちょう. There are many exceptions.

And here's まち vs. ちょう by geographical location:

(zoomed-in: 1, 2, 3, 4)

There's a slight preference for one pronunciation in certain parts of Japan, and there are some smaller local aggregations.

---

Not exactly common in place names.

がい

• on: 4 (　南街【なんがい】　,　 銀南街【ぎんなんがい】　,　 中央街【ちゅうおうがい】　,　 新市街【しんしがい】　)


• mix: 6 (　中久著呂市街【なかくちょろしがい】　,　 虹別市街【にじべつしがい】　,　 磯分内市街【いそぶんないしがい】　,　 長島町又木市街【ながしまちょうまたぎしがい】　,　 長島町西外面市街【ながしまちょうにしどもしがい】　,　博多駅中央街【はかたえきちゅうおうがい】　)

まち

• mix: 2 (　河芸町杜【かわげちょうもり】の街【まち】　,　 二見町光【ふたみちょうひかり】の街【まち】　)

こうじ

Apparently, this reading exists as well.

• kun: 5 (　桜街【さくらこうじ】　,　 吸川街【すいかわこうじ】　,　 下大槻街【しもおおつきこうじ】　,　 広街【ひろこうじ】　,　 上大槻街【かみおおつきこうじ】　)


• on: 1 (　十軒街【じゅっけんこうじ】　)

むら

• kun: 105 「赤石村【あかいしむら】」「水橋中村【みずはしなかむら】」


• on: 16　「福村【ふくむら】」「多伎町久村【たきちょうくむら】」


• mix: 108　「栗沢町宮村【くりさわちょうみやむら】」「初瀬本村【はつせほんむら】」



• unknown: 11　「散布村【ちりっぷむら】」「炊村【かしきむら】」

そん

• on: 2 (本村【わきのさわほんそん】, 兵村【へいそん】, 南兵村【みなみへいそん】)

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※ For the usage of the kanji, see for example 文化庁＝＝「異字同訓」の漢字の使い分け

まち

【町】行政区画の一つ。人家が多く集まった地域。

　　　町と村。町役場。町ぐるみの歓迎。下町。町へ買物に行く。町外れ。

【街】商店が並んだにぎやかな通り・地域。

　　　街を吹く風。学生の街。街の明かりが恋しい。街の声。街角に立つ。

halacha - Using a plata on Shabbat

I have a plata--an electric warming tray that does not have knobs or adjustments. I can leave it plugged in throughout Shabbat. I want to use it correctly when I have guests and to up my observance.

Can I use it to reheat solid food from the refrigerator on Shabbat? Do I need to put an empty cooking tray between the plata and the food container? I can move the food to the plata on Shabbat morning, right?

Any other issues with using the plata? Should I not stir the food while on the plata or does that issue not apply?

I can't reheat soup or other liquids on the plata, right?

organic chemistry - Why is only one lone pair in imidazole delocalised?

I was wondering why only one of the nitrogen lone pairs in imidazole is involved in the delocalized π-system. Specifically, I was wondering why it is that lone pair B in particular is delocalized, instead of lone pair A:

Here is my conjecture about why B's lone pair is delocalized while A's lone pair cannot be.

1. 
   

   If we delocalize A, we'd get extreme ring strain; we'd make the geometry around that nitrogen $\ce{sp}$. This implies a $120^\circ$ bond angle. That's problematic.

   
   



2. 
   

   Effective $\unicode[Times]{x3C0}$-orbital overlap (conjugation) only occurs when the p-lobes are planar — i.e. parallel with each other. If the nitrogen with the B lone pair kept its B lone pair, then that nitrogen would be tetrahedral and that would distort the planarity of the molecule; everything else in the molecule appears to be $\ce{sp^2}$ hybridized.

   
   


3. 
   

   We also run into formal charge issues; we get a positive formal charge on the "A" nitrogen and a negative formal charge on the B nitrogen. While this isn't a dealbreaker, it's not preferable, as there is separation of like formal charges.

   
   


4. 
   

   Anything I miss? Any points I mangled?

   
   

Answer

The correct answer to this question is more direct, and not listed in your items. The non-bonding electron pair in nitrogen 3 is in an orbital perpendicular to the π-bonding p orbitals of all other atoms in the imidazole ring. Thus, it does not have the appropriate geometry to overlap with other orbitals forming π-bonds, and does not participate in any resonance effects.

This effect of orbital geometry is often invoked to explain the difference in basicity between pyridine and pyrrole. In the former, the nitrogen lone pair is of type 3 and does not participate in resonance, and so it has a basicity comparable to regular amines and imines. However, in the latter, the lone pair is of type 1 and does participate in the aromaticity of the ring. Protonation of the nitrogen atom would require localization of the electron pair on the nitrogen, breaking most of the resonance effect. This is energetically unfavourable, so pyrrole displays a much lower basicity than expected for amines or imines.

This section on pyridine has a little more information on why the type A lone pair does not delocalize, including a helpful picture. Notice that the lone pair is in an $\mathrm{sp^2}$ orbital parallel to the plane of the ring, while the π-bonded system is perpendicular.

I can make the following observations on your conjectures:

1) I don't think this applies, actually. The fact that orbital overlap is disallowed in the first place precludes the possibility of even thinking what would happen to the geometry of the molecule if the electron pair in nitrogen 3 formed a π-bond; it just doesn't.

However, if the molecule had a boron atom instead of carbon in position 2 (with an empty $\mathrm{sp^2}$ orbital pointing in the same direction as the full $\mathrm{sp^2}$ orbital in nitrogen 3), then I'm not sure what would happen. A more simple example of this type of structure would be 1,2-azaborine (of which only the 1,2-dihydro derivative seems to have been isolated as of yet).

I could imagine canonical structures in which the electron pair on nitrogen links with the boron atom, forming an additional bond (analogous to benzyne, which is isoelectronic with 1,2-azaborine). However, to form an extra N–B π-bond, then either the bond will be a $\pi(\mathrm{sp^2}\text{–}\mathrm{sp^2})$ bond (which is unusual as far as I know), or both the nitrogen and boron atoms would have to partially rehybridize into a mix of $\mathrm{sp^2}$ and $\mathrm{sp}$ configurations to allow a $\pi(\text{p–p})$ bond, which would likely imply an increase in bond angle and a huge increase in ring strain. Neither option seems particularly good, so I suspect such canonical structures would contribute little to the actual bonding picture in the boron-substituted ring.

2) The nature of the nitrogen atom which participates in resonance is actually something between $\mathrm{sp^2}$ and $\mathrm{sp^3}$. The concept of hybridization isn't very adept at explaining resonance naturally.

I'm also not happy with how much my arguments rely on hybridization, but I don't know other effective means to explain what's going on.

synagogue - when is shushing in a shul permited, when forbiden and when obligated

In my shul there is someone who shushes people that talk. He believes that he is obligated to do this. I understand that there is a prohibition against embarrassing people publicly and that sometimes you are obligated to protest publicly on a violation.

My question is (please give sources so that he will respect the answer more): In this shul people usually talk (there is no minhag not to talk) and the people that are talking are not davining. When can one attempt to quieten the talkers and when is it forbidden?

1. There is no minyan (<10) and the chazan started to davin (befor yishtabach)


2. There is a minyan but the minyan is holding before baruch sheamar


3. The minyan is holding before shma


4. The minyan is holding in shma


5. The minyan is holding in shmona esrai


6. The minyan is holding in chazoras hashatz


7. The minyan is holding before krias hatorah


8. The minyan is holding during krias hatorah


9. Between aliyos


10. After krias hatorah

thank you very much

rashi - Limud for Levi not being part of the spies

Devarim 1:23 reads:

וַיִּיטַב בְּעֵינַי הַדָּבָר וָאֶקַּח מִכֶּם שְׁנֵים עָשָׂר אֲנָשִׁים אִישׁ אֶחָד לַשָּׁבֶט׃

And the matter pleased me; so I took twelve men from you, one man for each tribe.

Rashi:

שנים עשר אנשים איש אחד לשבט: מגיד שלא היה שבט לוי עמהם׃

twelve men… one man for each tribe: [This] tells [us] that the tribe of Levi was not with them. (Sifrei).

My question is:

What is Rashi explaining/clarifying here and why do we need a special limud (exegesis) for this?

In Parshat Shelach (Bamidbar 13:4-15) all the the spies are named one-by-one and clearly there is no mention of a representative from the tribe of Levi!

halacha - When should one cut his nails for Shabbos when Friday is Rosh Chodesh

In the answer to Rules for Cutting Nails it quotes the Mishna Berura 260:6 that one should not cut their nails on Thursday. Mishna Berura explains that by cutting them on Thursday they will begin to grow on Shabbos. It also mentions the Be'er Hataiv 260:2 based on Rabbi Yehuda HaChasid not to cut one's nails on Rosh Chodesh. If Friday is Rosh Chodesh is there an exception to this rule? Or do you make an exception and cut them rather on Thursday? Perhaps it is done on Wednesday? (sources)

Answer

The website/sefer Halachically Speaking Vol.3 here says:

The poskim say one should not cut his nails or hair even when Rosh Chodesh falls out on Friday and wants to do so for kovod (for the honor of) Shabbos¹.

Although some say one can be lenient², the custom is like the first opinion quoted³, and one should cut them on Thursday instead⁴.

(Earlier he brought in the footnotes: Some say if one normally cuts his nails every Friday you can do so even on Friday Rosh Chodesh (Maharam Brisk 2:99, Orchos Chaim (Spinka) 260, see Shivim Temarim 56-57).

---

1. 
   

   Refer to Magen Avraham 260, Shulchan Aruch Harav 260:1, Moreh B’etzbah 136:page 42, Yesod V’shoresh Hu’avodah 8:1:page 382, Chasam Sofer 158, Kitzur Shulchan Aruch 72:14, Lekutei Maharich 2:page 5 (old), Shulchan Hatohar 260:4, Darchei Chaim V’sholom 353, Aruch Ha’shulchan 6, Shemiras Shabbos K’hilchoso 42:49, Rivevos Ephraim 4:97:37, Shraga Hameir 8:74, Divrei Shalom 4:57, Natei Gavriel (Pesach 3) page 221, Chai Ha’Levi 5:47, Yisroel V’hazemanim 1:22:page 319.

   
   


2. 
   

   Knesses Hagedolah 260:page 131, Yosef Ometz 37:4, Tehilla L’Dovid 260:1, Lekutei Maharich seder erev Shabbos 2:page 306 (new), Aruch Ha’shulchan 260:6, Shemiras Shabbos K’hilchoso 42:footnote 174 in depth, Rivevos Ephraim 4:97:35, 37. The Nishmas Shabbos 1:160 says if one forgot to cut them on Thursday he may cut them on Friday (meaning Thursday night) during ben hashmoshes.

   
   


3. 
   

   Horav Yisroel Belsky Shlita, see Chut Shuni Shabbos 4:page 319 quoting this as the opinion of Horav Korelitz Shlita, Doleh U’mashka page 173.

   
   



4. 
   

   Shivim Temarim ibid, Darchei Chaim V’sholom 353, Kaf Ha’chaim 260:12, Taamei Haminhagim page 122, Nishmas Shabbos 1:159, Divrei Shalom 3:65. Some have the custom to cut the hair and nails in this situation on Wednesday (Chai Ha’Levi 5:47).

   
   

organic chemistry - Which proton in cyclohexene is the most acidic?

I know that $\mathrm{H^b}$ is most acidic due to conjugation (resonance).

But I am confused as to how to compare $\mathrm{H^a}$ and $\mathrm{H^c}$. I think $\mathrm{H^a}$ should be more acidic than $\mathrm{H^c}$ due to hyperconjugation.

tefilla - Praying on an airplane

Often times on flights to/from Eretz Yisroel there are people who put together a Minyan at the back of the plane. I for one always pray at my seat as I feel it can easily come to a Chillul Hashem. Is that correct?

Answer

Indeed, some say to pray in one's seat, for precisely the concern you mentioned, of Chillul Hashem.

According to this VosIzNeias article, an unnamed Manchester rabbi "told a meeting that it is better to pray in your seat rather than risk a disruption by standing in the aisle", and his motivation was concerned "about the impression made on potential passengers, especially if Jews simply got up and tried to pray in a minyan". Commenters on that article cite other rabbinic figures saying similarly.

According to another VosIzNeias article Rabbi Yehuda Leib Steinman also ruled that it is preferable to say Shemoneh Esrei on a plane sitting down.

This is all rather one-sided, in that I've presented rabbis who agree with your reasoning and conclusion. That is not to say that there might (in theory) be other rabbis who would disagree.

adjectives - What is ~げに suffix actually?

Today, while looking up random words in WWWJDIC, I stumbled upon an example sentence for the word いとしい as below:

少女は人形をいとしげに抱き締めた。 The girl squeezed her doll affectionately.

The sentence uses ~げに adjective suffix that I have never seen before. Based from the above translation, it seems to convert the adjective into adverb, just like what ~く does. Also, a quick check with Google showed that can also follow a noun, e.g. 自慢げに.

What is this suffix actually and how is it different from ~く form? As I mentioned in previous paragraph this is the first time I've seen it so I am not even sure is it standard Japanese or a slang or whatnot.

Answer

The most important thing about げ is that it describes an observed quality. That is, you cannot use げ to refer to yourself:

○ 毎週楽しく聴かせていただいています。 I enjoy listening every week.

× 毎週楽しげに聴かせていただいています。 (incorrect)

The reason for this is that げ (which in kanji would be 気, but it's never written in kanji) is defined as そうだ or らしいようす, according to Daijisen. (Daijirin also lists 気配 as a definition, and you can see my answer to this question about 気配 to get a sense for that word.) Since そう is for describing something based on observation, it would be odd to use it to describe something about yourself. But you can easily use it to describe someone else:

○ 少女はうれしげにプレゼントをあけた。 The girl happily opened the present.

○ 少女はうれしそうにプレゼントをあけた。 (equivalent)

Why not just use the normal adverbial form of うれしい (うれしく) here? Because うれしく would presume that you have accurate knowledge of someone else's emotional state, which you don't (unless you're writing a book and talking about one of your characters). All you have are observations, and so you have to show that your judgment of うれしい comes from observation by using either そう or げ.

Although you could technically use げ with any word fit for describing behavior, not every such construction is common. For instance:

○ みんなはケーキをおいしそうに食べている。 Everyone looks like they're enjoying the cake.

？みんなはケーキをおいしげに食べている。 (same meaning, but far less common)

When you can freely substitute げ for そう (as with the うれしい example above), I don't personally feel any difference in emphasis, but a native speaker or someone with a solid reference on this may weigh in with a different opinion.

gezel stealing - "Cheating" on a test

Here's the case: It is possible to acquire a test given by a teacher the previous year. Said teacher gave the test back to the students, and a student passed it along to someone in the year below. It is known that this teacher never makes up new tests, and it is almost definite that this will be the same test.

Is it muttar to look at this test? Or would be asur, and considered cheating?

halacha - What are the standards for bathroom design?

Starting from scratch in building a multiple occupancy bathroom, what standards should be maintained in its design and construction?

There are plenty of relevant halachos regarding modesty and proper activity inside the room, but how do they feed back into ground-up design?

Some concerns that come to mind are:

• Height of walls between stalls



• Placement of the sink


• Presence of a mirror


• Presence of upright toilets


• Separators on 3 vs. 4 sides


• Placement and orientation with respect to the rest of the building

halacha - Reading Mi Yodeya in the bathroom

Is it ok to open Mi Yodeya in the bathroom and skim through the questions trying to find ones that aren't really included in limud ha'torah in order to read them? Or is the opening of the app and the skimming the questions in the bathroom already included in degradation of words of Torah?

molecular structure - Why is water a dipole?

Water ($\ce{H2O}$) is a dipole. The reason why is simply because it is not symmetrical, there are more electrons on the oxygen side than on the hydrogen side, and the electronegativity of oxygen.

But why isn't $\ce{H2O}$ symmetrical like $\ce{CO2}$? Why isn't $\ce{H2O}$ non-polar like $\ce{CO2}$? Does it have anything to do with the orbitals?

Answer

Yep, it has to do with the orbitals.

$\ce{CO2}$ is linear, so even though the $\ce{C-O}$ bonds have individual dipole moments, the overall dipole moment is zero as these cancel out (they point in opposite directions, as shown in the diagram below).

On the other hand, $\ce{H2O}$ is "bent", which means that the individual dipole moments of the bond are at an angle to each other. They add up to give a net dipole moment (shown with grey in the diagram).

The colors indicate electron density, red is more dense/blue is less dense. Dipole moment is from low density to high density.

OK, so why do these molecules have differing shapes? This is where orbitals come in. I'll try to explain as much as I can without going into orbitals.

Carbon has an outer shell electronic configuration as $2s^22p^2$. Out of these four electrons, two are used in $\pi$ bonds, and two in $\sigma$ bonds. If you don't know what those are, just look at it like this for now: A set of bonds between two atoms will have one and only one $\sigma$ bond, with the rest of them $\pi$ bonds. So, any single bond is made up of just a $\sigma$ bond, a double bond is made up of one $\sigma$ and one $\pi$, and a triple bond is made up of one $\sigma$ and two $\pi$ bonds. What these types of bonds actually are can be explained if you know what an orbital is.

Now, what VSEPR says is that the geometry of the molecule is only decided by the $\sigma$ bonds and lone pairs on the central atom. You count up the $\sigma$ bonds and lone pairs (lets say they add up to $x$), and decide the geometry based on that. The geometry is the most stable configuration of $x$ hybrid orbitals. In simple terms, if we took $x$ balloons and tied them together, the directions the balloons point in help us correspond to where the bonds and lone pairs lie:

In $\ce{CO2}$, we have two $\sigma$ bonds and two $\pi$ bonds (as each double bond has one of each type). Each bond takes up one electron from carbon, so we have no leftover electrons for forming any lone pair. Since we have two $\sigma$ bonds and 0 lone pairs, $x=2$, giving us the structure given by the first set of balloons, which is linear. And $\ce{CO2}$ is indeed linear:

Now let's take water. The central atom (Oxygen) has a valence configuration of $2s^22p^4$, that is, 6 electrons. In water, since we have two single bonds, we have one $\sigma$ bond each (and no $\pi$ bonds). So we have total two $\sigma$ bonds.

But this leaves us with $6-2=4$ unpaired valence electrons. These form two "lone pairs" (pairs of electrons which do not bond). With two lone pairs and two $\sigma$ bonds, $x=4$. This gives us a tetrahedral structure (third in the balloon diagram). Two of the four points in the tetrahedron are occupied by the lone pairs, and two by bonds:

(Note that the angle 104.5 is not the same as the angle in perfect tetrahedra, 109.25--this is due to the lone pairs repelling each other)

So finally, we have the following "bent" structure for water:

From the structure, as shown above, it is very easy to check if the molecule has a dipole moment.

matlab - Detecting and isolating part of an image

I'm working with cross-sectional CT scans of the leg using matlab's image processing toolbox. Part of what I'm attempting to do is to automatically isolate the leg in any image, which requires removing any extraneous objects that are present in the image. So far my code is able to take out most objects, which works for the majority of my images. However, some of the images have an object that is flush with the leg, which my code isn't able to remove.

Here's an example of the problem: The first image shows the original image, and the second one shows the "filtered" image, after it has gotten rid of extraneous objects. But as you can see, there is still something outside of the leg cross-section that I would like to get rid of.

I've thought of using something to detect ellipses, but unfortunately some of my images are not very good homogenous shapes (like the one below).

And here's the current code I have:

% Read input file
inputfile = dlmread(filename,';');

% Normalise input file (0 to 1) & show original image
I_original = mat2gray(inputfile,[min(inputfile(:)) max(inputfile(:))]);
figure; imshow(I_original)

% Detect leg
BW1 = im2bw(I_original,.2);
BW2 = imfill(BW1,'holes');


% Remove misc. objects around leg (i.e., stray objects <5000 pixels)
BW_final = bwareaopen(BW2,5000);

% Generate filtered image
I_filtered = I_original;
I_filtered(imcomplement(BW_final)) = NaN;
figure; imshow(I_filtered)

Any suggestions on how to fix this would be appreciated! Thanks!

halacha - Giving charity to someone about whom the giver knows nothing?

I often pass by a Jewish store where a person is standing outside asking for tzedaka/charity. Call me cynical but I have no way of knowing A)if the person is really poor, B) if the person is Jewish and C) what he will do with the money (possibly drugs or something else harmful).

Is there any halachic obligation (under the rubric of tzedaka or any other mitzvah) to give him money?

marriage - How does the kohein gadol's substitute wife work?

The first mishna of Yoma¹ explains that before Yom Kippur, a substitute wife is prepared for the kohein gadol lest his wife die -- because the torah says he makes atonement for himself and "his house", and "his house" means his wife. But he has to be married to exactly one woman on that day because it says "house", not "houses".

The g'mara on 13a-b describes a system of conditional gittim (bills of divorce), but I'm having trouble understanding how this actually works. Do I understand correctly that he takes an additional wife before Yom Kippur, with gittim written such that he will be married to exactly one woman when he performs the avodah? If so, does it have to be a different wife each year because of the laws of divorce and kohanim?

Since he could (in an unfortunate turn of events) end up married to the substitute, it seems like everyone involved would want to take as much care with this match as with any other. Yet, finding a good (and different) shidduch every year seems challenging, perhaps burdensome, especially as each must be a betulah. Is that just part of the cost of being kohein gadol, or am I misunderstanding this g'mara?

¹ in the Bavli. The Yerushalmi understands this as a conditional marriage to the second woman rather than a conditional divorce (h/t Fred), which would reduce but not eliminate the problem.

Tetrahedral microphone array beamforming

I have a microphone array of 4 channels taken as channels [6,10,22,26] from Eigenmike spherical microphone array. I wish to do 3D beamforming and create $8\times 4$ beams, 4-elevations with 8 wavefronts per elevation equally distributed.

I can't seem to work out the math as to the delays between the microphones. I also can't find an "off the shelf" code for that. This is my first beamformer so I am not even sure I am not missing anything. Is delay and sum process all I need?

What are the equations for determining the delays between the channels per beam? Do I need any other equations to create a beamformer?

Specifically, I am trying to create beams in direction from all possible combinations of $\varphi_s \in \{-\frac{3\pi}{8},-\frac{\pi}{8},\frac{\pi}{8},\frac{3\pi}{8}\}$ and $\theta_s\in\{-\frac{7\pi}{8},-\frac{5\pi}{8},-\frac{3\pi}{8},-\frac{\pi}{8},\frac{\pi}{8},\frac{3\pi}{8},\frac{5\pi}{8},\frac{7\pi}{8}\}$.

My microphone array contains 4 microphones $m_i=(r_i,\theta_i,\varphi_i)$, at the following positions: \begin{pmatrix} 0.042 & \frac{\pi}{4} & \frac{7\pi}{36} \\ 0.042 & -\frac{\pi}{4} & -\frac{7\pi}{36} \\ 0.042 & \frac{3\pi}{4} & -\frac{7\pi}{36} \\ 0.042 & -\frac{3\pi}{4} & \frac{7\pi}{36} \end{pmatrix}

$r_i$ is in meters. $\varphi_i, \theta_i$ are azimuth and elevation respectively, according to the microphone's documentation, given herein radians.

A quick sketch of the configuration from two views. Note that the distance of all mics is 42mm from the origin:

$(x,y,z)$ values in this system is extracted in the following manner to my understanding: $$x=r\cdot \cos(\varphi)\cdot \cos(\theta)$$ $$y=r\cdot \cos(\varphi)\cdot \sin(\theta)$$ $$z=r\cdot \sin(\varphi)$$

Answer

I don't know what the fuss is about. This is a simple vector problem.

"Well, if it is that easy please elaborate. I have 4 microphones on the following locations (0.042,45,35),(0.042,-45,-35),(0.042,135,-35),(0.042,-1355,35). These are coordinates for the microphones with m1=(ri,θi,φi), where −π≤θ≤π and −π2≤φ≤π2. create a beam towards a sourse at (θs,φs)=(22.5,67.5). – havakok"

You need to define five vectors in Cartesian coordinates, one for each mic and one for the beam. The beam vector should be normalized to a length of one.

If the sound source is sufficiently far away, the assumption that the wavefront is coming in as a planar wave is a fairly accurate approximation. Therefore, you simply have to find the projection of each mic location onto the line defined by the beam vector. The projection for each mic is found by dotting the mic vector with the normalized beam vector. The value you get is the distance along the line (where one is the beam vector length). Use the speed of sound to convert this distance to a time shift. Use your sampling rate to convert the time shift to a sample shift. Shift and add. The last mic to receive the signal is not delayed, and the previous mics are delayed relative to their projection's distance to the last mic's projection.

It should be obvious that you only get one beam direction at a time. Don't be oversold on the "beam" notion either.

Ced

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Two Answers:

1) Rounding to the nearest sample should be negligible.

Some ball park figures to consider: Suppose you have a 1000Hz tone. Sound travels at roughly 1130 feet per second. Thus one cycle of the tone is roughly 1.130 feet long, or about 13 and 1/2 inches. At CD quality sampling, about 44 samples. So each sample is about 3/10 of an inch (this is frequency independent). Compared to the length of the cycle, this isn't a lot. However, if you are concerned about frequencies above 10k, this may matter. In that case, a simple linear interpolation in your delay should do the trick.

2) The beam effect is formed by "coordinated interference effects", i.e. signals coming from other directions will be added together in an out of phase manner (only the signals in the desired direction are in phase), thus you are relying on interference to destructively interfere. This is frequency dependent. Also, signals coming in nearly at the beam angle won't be affected much, so perhaps "cone forming" is more accurate.

You didn't mention whether these were omnidirectional mics or not. No bearing on the math, but may influence your results.

halacha - Niddah and Counting 7 Clean Days - What are its Origins?

The following comment is made in the wikipedia entry on Niddah:

In the days of the Amoraim, because of possible confusion in determining when menstruation began and ended and hence whether blood was normal menstrual (niddah) or abnormal (zavah) blood, it became the accepted practice and practical halacha, that all women treat any emission as a continued abnormal flow (zavah gedolah—זבה גדולה) which requires counting seven abnormal-discharge-free days from the end of menstruation.

My question is exactly how did this become the accepted practice? Was it an enactment of the Sanhedrin or a general practice that became universal on its own? What was the extent of the original practice and what were the specific reasons behind it ( beyond the simple explanation given above )?

EDIT

I ran across the following from Rav Mordichai Eliyahu's book דרכי טהרה:

בנות ישראל החמירו על עצמן שעל כל טיפת דם קטנה כחרדל יושבות הן ז' נקיים כמו זבה גדולה. וסיבות רבות לחומרה זאת, והחשובה בהן היא כדי שתהיה לכל הנשים ספירה אחידה, ולא תצטרך כל אחת ואחת לחשב לעצמה חשבונות מסובכים שלא כולן בקיאות בהם. דין זה, אע"פ שהוא חומרה, נקבה בהלכה שאין עליה עוררין וכשהגמ' מדגימה "הלכה פסוקה", לגבי הנאמר במשנה "אין עומדין להתפלל אלא מתוך הלכה פסוקה", מביאה הגמ' הלכה זאת.‏

The above gives the following sources:

• רמב"ם ה' אסורי ביאה פי"א ה"ג וה"ד


• נדה סו. רמב"ם הל' אסורי ביאה פי"א ה"ד


• ב"י ס' קפ"ג


• ברכות לא ע"א

I found the following in Rambam's Mishne Torah, הלכות אסורי ביאה יא"ד

ד ועוד החמירו בנות ישראל על עצמן חומרה יתרה על זו, ונהגו כולם בכל מקום שיש ישראל: שכל בת ישראל שתראה דם--אפילו לא ראת אלא טיפה כחרדל בלבד ופסק הדם--סופרת לה שבעת ימי נקיים, ואפילו ראת בעת נידתה. בין שראת יום אחד, או שניים, או השבעה כולן, או יתר--משיפסוק הדם, סופרת שבעת ימי נקיים כזבה גדולה. וטובלת בליל שמיני, אף על פי שהיא ספק זבה, או ביום שמיני אם היה שם דוחק, כמו שאמרנו--ואחר כך תהיה מותרת לבעלה.‏

My original question still stands. How and why did this go from being a widespread personal chumra to being codified halacha?

This question is separate from the issue of the Rabbinic decree ( Gezirah ) during Talmudic times to treat all flows of blood as suspected Zav emissions ( ספק דם זיבות ).

הלכות אסורי ביאה יא"ג

Answer

Here is the second part of the answer: The first part with background information is here

Finally we get to the main question. In Niddah 66a ( נידה פרק י דף סו,א ) we have:

אמר רב יוסף אמר רב יהודה אמר רב התקין רבי בשדות ראתה יום אחד תשב ששה והוא שנים תשב ששה והן שלשה תשב שבעה נקיים אמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טפת דם כחרדל יושבות עליה שבעה נקיים אדבריה רבא לרב שמואל ודרש קשתה שני ימים ולשלישי הפילה תשב שבעה נקיים קסבר אין קשוי לנפלים ואי אפשר לפתיחת הקבר בלא דם א"ל רב פפא לרבא מאי אריא קשתה שני ימים אפילו משהו בעלמא דהא א"ר זירא בנות ישראל החמירו על עצמן שאפילו רואות טפת דם כחרדל יושבות עליה שבעה נקיים א"ל אמינא לך איסורא ואת אמרת מנהגא היכא דאחמור אחמור היכא דלא אחמור לא אחמור

R. Joseph citing Rab Judah who had it from Rab stated: Rabbi ordained at Sadoth [lit. in the fields], If a woman observed a discharge on one day she must wait six days in addition to it. If she observed discharges on two days she must wait six days in addition to these. If she observed a discharge on three days she must wait seven clean days. R. Zera stated: The daughters of Israel have imposed upon themselves the restriction that even if they observe a drop of blood of the size of a mustard seed they wait on account of it seven clean days. Raba took R. Samuel out for a walk when he discoursed as follows: If a woman was in protracted labour for two days and on the third she miscarried she must wait seven clean days; he being of the opinion that the law relating to protracted labour does not apply to miscarriages and that it is impossible for the uterus to open without bleeding. Said R. Papa to Raba: What is the point in speaking of one who was in protracted labour for two days seeing that the same applies even where there was the minutest discharge, since R. Zera stated, The daughters of Israel have imposed upon themselves the restriction that even where they observe only a drop of blood of the size of a mustard seed they wait on account of it seven clean days? — The other replied: I am speaking to you of a prohibition, and you talk of a custom which applies only where the restriction has been adopted. [lit. where they are stringent they are stringent where they aren’t stringent they aren’t stringent.]

There are two separate issues here; one is the enactment of Rabbi ( Yehuda HaNassi ) and the other is our subject here, what is variously called the Stringency of R. Zera, or the Stringency of the Daughters of Israel. None of the reasons behind either one are discussed in the Talmud, however later authorities provide various reasons why they might have came about. It’s not clear if these later explanations are part of an oral tradition or are simply educated guesses.

The enactment of Rabbi ( mentioned only this one time in the Talmud Bavli ), while not the subject here, deserves a little attention, if only for completeness’ sake. First off, the Soncino translation of the word בשדות may be a bit confusing, as they transliterate it as “at Sadoth”. בשדות literally means, “in the fields” and figuratively can be understood as rural areas or areas far from the centers of learning. In fact, the Soncino edition does bring this understanding in a footnote where it gives Rashi’s understanding of this enactment in his commentary to the above:

בשדות - מקום שאין בו בני תורה ואינן יודעות למנות פתח נידות מתי הן ימי נדה מתי הן ימי זוב

A place that was inhabited by unlettered people who were incapable of calculating the dates of the menstrual, and the zibah periods. ( Soncino above, footnote 32 )

When Rambam talks in הלכות אסורי ביאה יא,ג of a Rabbinic enactment to treat all of a woman’s days as Zivah days and all bleeding as suspected Zavah blood, it seems to me that he is almost certainly talking about this enactment. ( I would love to hear if someone has a better source. ) His seeming treatment of this as a general prohibition only makes sense when considered in light of his unique view that the seven niddah days and eleven zivah days strictly alternate and that the nature of women’s menstrual cycles had fundamentally changed ( וְנִתְקַלְקְלוּ הַוְּסָתוֹת ). In such a case virtually no one would be capable of keeping track of a womans niddah / zavah days, not even a learned individual, and the prohibition would in practice apply everywhere. However, if you accept the understanding of all the other Rishonim as put forward by the Sefer HaChinuch then the above enactment would seem to apply only to places populated by illiterate people and lacking Torah scholars to instruct the women in how to count.

Returning to our subject, the Stringency of R. Zera is mentioned three more times, once in the Bavli in Megillah 28b pg. 111 ( מגילה פרק ד דף כח,ב ), and another time in both the Bavli and Yerushalmi in parallel discussions in Berachoth. An interesting side note is that while the Bavli brings the stringency in the name of R. Zera, who was born in Babylon, emigrated to Israel and fasted 100 days to forget what he had learned in Babylon, the Yerushalmi mentions it only once in the name of R. Huna, R. Zera’s original teacher from Babylon. The reference from Megilla doesn’t seem directly relevant to this discussion.

In Berachoth 31a pg. 114 ( ברכות פרק ה דף לא,א ) it says:

ת"ר אין עומדין להתפלל לא מתוך דין ולא מתוך דבר הלכה אלא מתוך הלכה פסוקה והיכי דמי הלכה פסוקה אמר אביי כי הא דר' זירא דאמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טיפת דם כחרדל יושבת עליה שבעה נקיים רבא אמר כי הא דרב הושעיא דאמר רב הושעיא מערים אדם על תבואתו ומכניסה במוץ שלה כדי שתהא בהמתו אוכלת ופטורה מן המעשר

Our Rabbis taught: A man should not stand up to say Tefillah either immediately after trying a case or immediately after a [discussion on a point of] halachah; but he may do so after a halachic decision which admits of no discussion. What is an example of a halachic decision which admits of no discussion? — Abaye said: Such a one as the following of R. Zera; for R. Zera said: The daughters of Israel have undertaken to be so strict with themselves that if they see a drop of blood no bigger than a mustard seed they wait seven [clean] days after it. Raba said: A man may resort to a device with his produce and bring it into the house while still in its chaff so that his animal may eat of it without its being liable to tithe.

What we have here in Niddah and Berachoth is two occurrences of Raba giving his opinion that said stringency does not qualify as a formal legal prohibition, but is only a local custom held in some places and not in others. In the first case he disputes with R. Papa, who was a student of his and of Abaye. In the second case he disputes with Abaye himself by giving a counterexample.

There is a principle that in any dispute between Raba and Abaye the halacha follows Raba except in six specific instances. The case under discussion is not one of those instances.

There is also an issue regarding the meaning of the phrase הלכה פסוקה. The phrase can also refer to the clarity of the matter, not necessarily it’s legal status. For example Rashi says:

הלכה פסוקה. שאינה צריכה עיון שלא יהא מהרהר בה בתפלתו

[ A matter ] that requires no discussion [ deep study ] that will not disturb him during his prayer.

In fact halacha is a very generic word and can simply mean that something is a part of Jewish tradition, for example even aggadot ( matters of Jewish folklore in the Talmud ) are called halacha in the Talmud, but they are clearly not formal rabbinic legislation. In addition, late post Talmudic customs such as Kitniyot are called halacha, although they are clearly distinct from Talmudic rabbinic legislation.

However, as mentioned at the beginning there are many authorities on both sides of this issue. Looking at some Rishonim on the side of seeing the Stringency as formally codified law:

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  HaMeiri ( ברכות דף לא ) - The sages received it from them [ the women ], and practiced what they said, and made it into an obligatory practice. ( קבלוה חכמים מהם וקיימו את דבריהם ועשאוה הלכה פסוקה )

  
  


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  Ramban ( הלכות נידה לרמב”ן פרק א ) - This stringency which was a custom among the daughters of Israel was ratified in the eyes of our sages and they made it into an obligatory practice in every place. ( חומרא זו שנהגו בנות ישראל הוכשרה בעיני החכמים ועשו אותה כהלכה פסוקה בכל מקום )

  
  


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  Rif ( שבועות דף ג עמוד ב ) - He calls it הלכה פסוקה and quotes from the above Berachot and it seems clear that he intends the phrase to mean obligatory practice.

  
  

In the middle we have the Ra’avad, who on the one hand clearly refers to it as a custom ( מנהגא מילתא היא ), but immediately afterwards calls it הלכה פסוקה. It seems from the context that his intention is not to say that the custom was formally ratified, but that in the issue he discusses the law is indeterminate and thus follows the custom.

Rashi seems to see it as only a custom - והן החמירו על עצמן - and they made a stringency upon themselves. This seems to be the case considering the above and his opinion of the meaning of the phrase הלכה פסוקה and the fact that he doesn’t seem to indicate otherwise anywhere.

Rambam is fairly straight forward, he calls it חומרה יתרה an excessive stringency and quotes החמירו על עצמן - they made a stringency upon themselves, without making any indication anywhere that it was formally codified. He says ואין לסור ממנה לעולם - and one shouldn’t deviate from this ever, however this just seems to be reminding people of the binding nature of custom, not indicating any formal codification.

Among later authorities who consider it to be a custom are Rav Dovid Ben Moshe from Novhardok, who says ( שו”ת גליא מסכת, עמ’ 180 ):

דעיקר מימרא דרבי זירא האמורה דאף טיפות דם כחרדל צריכה ז’ נקיים לא הוה מתקנות חכמים אלא בנות ישראל המה החמירו על עצמן חומרא זו מעצמן

From the essence of what Rabbi Zera said that even a drop like a mustard seed needs seven clean days, it is not a Rabbinic law, instead they the daughters of Israel made this stringency upon themselves by themselves…

Rav Kook says ( שו”ת דעת כהן סימן פד ):

ואולי עוד קלוש משאר איסורי דרבנן, שהרי הוא באמת רק מנהג שנהגו בנות ישראל, וידוע שמנהג הוא לא חמור כדרבנן ממש.

And maybe it is even weaker than other Rabbinic prohibitions, since really it is only a custom that the daughters of Israel practiced, and it is known that a custom is not as strict as a real Rabbinic prohibition.

Rav Yisroel Zev Gustman says in ( קונטרסי שיעורים, מסכת קידושין עמ’ 306 - 310 ):

ומעתה אסורה נא לעיין בענין חומרא דר’ זירא אשר מבואר דלא נעשה בתקנות חכמים אלא שבנות ישראל החמירו מעצמן בזה ולא נעשה זאת מתקנות ועד חז”ל

And now I will deviate if I may to address this issue of Rabbi Zera’s stringency as it was expounded it was not made into a Rabbinic enactment instead the daughters of Israel made this stringency by themselves in this matter and it was not made a formal enactment by the Council of our Sages.

The list could go on, but it is clear that there are respected opinions on both sides of this issue.

The last thing to address is why this stringency came about. As I mentioned before, there is no direct explanation in the Talmud of how or why this stringency came about. It is not clear if the reasons given by later authorities are based on some oral tradition or if they are just educated guesses.

These explanations fall into a few main categories more or less:

• The inability to distinguish between pure and impure bleeding


• inability to keep track of niddah days vs. zavah days


• that all women should have the same count of days


• that the physical reality relating to women’s periods had changed

I mentioned earlier that it seems Chaza”l had a method for distinguishing between pure blood that originated outside the uterus, and impure blood that originated from within the uterus, but that method became lost ( נידה כ ):

אמר רבי זירא: טבעא דבבל גרמא לי דלא חזאי דמא

The nature of Babylon caused me to be unable to distinguish between the bloods

It may be that the stringency started in Babylon due to a loss of their ability to distinguish between uterine blood and other blood, but that the land of Israel, where they apparently still had this ability, did not accept this stringency during R. Zera’s lifetime.

There are many more references to this loss of ability in the Talmud. As a result of this Rav Yaakov ben HaRo”sh posits the following problem and explanation ( ארבעה טורים, יורה דעה, קפג ):

משרבו הגלויות ותכפו הצרות ונתמעטו הלבבות, חשו שמא יבואו לטעות באיסור כרת, שמא תראה אישה בימי נידתה ששה ימים ויהיה הכל דם טוהר וביום השביעי שמא תראה דם טמא וסבורה לטבול בליל שמיני וצריכה עוד שבעה ימים - החמירו לטמא כל מראה דם אדום, וכדי שלא יבואו לידי טעות בין ימי נידה לימי זיבה הוסיפו חומרה אחר חומרה, עד שאמרו שאפילו אם לא תראה אלא טיפת דם כחרדל תשב עליה שבעה נקיים כזבה גדולה.

Due to the many expulsions, and frequent sorrows, and the shrinking of their hearts, they feared they would violate a prohibition of karet, that a woman would see during her Niddah days six days and it would be all pure blood, and on the seventh day would see impure blood and would think to immerse on the eighth night, when she really needs seven more days - due to this they declared all red blood impure, and in order that they should not make a mistake between NIddah days and Zavah days they added stringency after stringency, until they said that even if they saw a drop of blood the size of a mustard seed they will sit seven clean days like a major Zavah.

This is a good summary of the first two points above. In addition, Rav Mordchai Eliyahu mentions in his book, “The Ways of Purity”, that an additional reason was so that all women would count in the same manner:

וסיבות רבות לחומרה זאת, והחשובות בהן היא כדי שתהיה לכל הנשים ספירה אחידה, ולא תצטרך כל אחת ואחת לחשב לעצמה חשבונות מסובכים שלא כולן בקיאות בהם.

And there are many reasons given for this stringency, and the most important among them is in order that all women will have a unified way of counting, and each woman and woman won’t need to calculate for herself all kinds of complicated calculations that not everyone is versed in.

Another type of reason is given by Rambam ( הלכות אסורי ביאה יא,ג ):

וְנִתְקַלְקְלוּ הַוְּסָתוֹת - and their menstrual cycles became irregular

This would make sense in certain contexts, as it’s known that extreme mental and physical stresses, including things like malnutrition and starvation can cause women’s cycles to become extremely irregular. It may also indicate some kind of hishtane hateva argument - according to his method, how could women have ever tracked their niddah vs. zavah days unless prior to Talmudic times they had perfect 19 day menstrual cycles?

Lastly, there is an interesting hypothesis as to the origins of the Stringency attributed to Rabbi Yaakov Elman chair of Talmudic studies at Yeshiva University and his former student Dr. Shai Secunda:

As to the non-elitist Babylonian Jews, we have a report regarding the ordinary Babylonian Jewish women. Rabbi Zera reports that the “daughters of Israel had undertaken to be so strict with themselves as to wait for seven [clean] days [after the appearance] of a drop of blood the size of a mustard seed [although biblically they are required only to separate for seven days from the onset of menstruation]” (Berakhot, fol. 31a; Megillah, fol. 28b; Niddah, fol. 66a). It is clear from Niddah (fol. 66a) that this stringency was a popular practice and not a rabbinic prohibition, probably in response to a “holier than thou” attitude perceived by the populace as emanating from their Persian neighbors. It seems that Babylonian Jewish women had internalized their Zoroastrian neighbors’ critique of Rabbinic Judaism’s relatively “easy-going” ways in this regard; Jewish women did not have to remain isolated on spare rations in a windowless hut for up to nine days, as was prescribed in Pahlavi Vendidād (Elman, 2004a, p. 34; but see Secunda, 2007a, pp. 144-89).

Basically, the Jewish women didn’t want to be “outfrummed” by their Zoroastrian neighbors, as one blogger put it.

In conclusion, it seems clear from the vast majority of the sources that the stringency started as a personal stringency that women took upon themselves, then evolved into a widespread custom practiced in some communities and not in others, and then at some point after that, and it’s not at all clear when that point was, became a universal custom. The Talmud itself seems to give no real indication as to when this occurred. Much later post-Talmudic sources debate whether this custom was formally ratified or not by the Sages, and there are respected authorities on both sides of the issue. There are no reasons given for this practice in the Talmud itself, and it is not clear if the reasons given by much later Post-Talmudic sources are part of an oral tradition or are educated guesses.