halacha - Saying 100 Berachoth in a day

What is the source for the idea that one should say 100 Berachoth in a day, and how serious of an obligation is this? Is it mandatory, is it laudatory, or is it merely a nice idea?

Answer

From the Tur (Orach Chaim 46): It is from a braisa based on pesukim. According to Natronai gaon, David haMelech set it into halacha to stop the deaths of 100 Jews daily where the spiritual cause of there death was unknown until "he delved and understood with ruach hakodesh and fixed" the 100 brachos.

So, it an obligation and is brought so in the Shulchan Aruch (Orach Chaim 46:3). Many have shown how if one davens appropriately, with the exception of shabbos, your 100 are covered.

science - Time Travel and Judaism

Has time travel ever been discussed before in terms of Judaism? According to Judaism would (should) it be possible to travel through time?

midrash - Why miracle of no blood dripping on Pinchas, if Zimri and Kozbi were still still alive?

The Midrashim [Bamidbar] Rabbah and Tanchumah, and the Targum Yonasan Ben Uziel write that When Pinchas killed zimri and Kozbi many miracles took place.

Two of the miracles are listed as follows:

Bamidbar Rabbah

הַתְּשִׁיעִי, לֹא הִטִּיפוּ דָם, שֶׁלֹא יִטַּמָּא פִּינְחָס. הָעֲשִׂירִי, שֶׁשָּׁמַר הַקָּדוֹשׁ בָּרוּךְ הוּא רוּחוֹתֵיהֶן שֶׁלֹא יָמוּתוּ וְיִטַּמָּא

Medrash Tanchumah

הַתְּשִׁיעִי, לֹא הִטִּיפוּ דָּם, כְּדֵי שֶׁלֹּא יִטָּמֵא פִּנְחָס. הָעֲשִׂירִי, שָׁמַר הַקָּדוֹשׁ בָּרוּךְ הוּא רוּחָם שֶׁלֹּא יָמוּתוּ.

Targum Yonasan Ben Uziel

נֵס חַדְסְרָאֵי דְאִתְנַטְרוּ כַּד חַיָין עַד זְמַן דַהֲלִיךְ יַתְהוֹן בְּכָל מַשִׁרְיָיתָא מִן בִּגְלַל דְלָא יִסְתָּאָב כַּהֲנָא בְּאָהֳלֵי דְמִיתָא. נֵס תְּרֵיסְרָאֵי דְאִתְקַרִישׁ אַדְמֵיהוֹן וְלָא נָפִיל עִילַוֵיהּ

Translation: 1) Their blood did not drip on Pinchas as not to make him Tamei.

2) Their life was kept in them (as long as Pinchas was carrying them) so as to avoid Tumah.

Question: If they did not die until later, why would their blood make Pinchas Tamei, if it was blood that dripped while they were still alive?

Note: The Sifrei only brings the miracle of the blood not dripping out, but not the one of them not dying.

Answer

The Matnas Kehuna actually writes that the point of the medrash rabba so as not become impure, actually means so as not to become dirty.

שלא יטמא. כלומר שלא ילכלך ויטנף אותו.

Pirush Maharzo quotes this Matnas Kehuna but offers a different explanation. He suggests that considering how Kozbi was speared, the blood under discussion was actually blood from her makor, dam nida. Which is only impure on a rabbinic level by nonjews, but nonetheless, this miracle spared Pinchas from even that.

שהרי דם זה בא מן המקור שדקר אותה שם והוא טמא ומטמא עכ׳פ מדרבנן בעובדי כוכבים

Edit: If we take this idea of the Matnas Kehuna into consideration and assume that the miracle spared him from a rabbinic impurity, then we can suggest another idea based on a comment from @msh210.

There is something called Dam Tevusa. This is a blood which came out of a dying person which later mixed with blood that came out of him after he died. The details are subject to dispute in the linked mishna, and Rambam rules in accordance with Rabi Akiva there. But according to all opinions there is at least the possibility that the blood coming out of Zimri could theoretically combine with blood that came out of his body after he died and combine into a riviis to render Pinchas impure, at least on a rabbinic level.

This of course is a further step removed from the actual rabbinic impurity mentioned by Matnas Kehuna, as this blood is only a precursor to the blood from after death. However, it is something that could theoretically be impure, that a miracle would be appreciated to save him from.

halacha - How long does a Bracha last for if I'm moving around in a building?

I work in a school with quite a large building. I have my own office, but I spend a lot of time out of it, checking the building, going into classrooms etc. If I make a Bracha on food and then leave my office for a short while, do I have to make another Bracha when I come back in order to continue eating?

mitzvah - Is serving Hashem in order to receive reward in Olam Habah ideal?

משנה אבות פרק א משנה ג

אַל תִּהְיוּ כַעֲבָדִים הַמְשַׁמְּשִׁין אֶת הָרַב עַל מְנָת לְקַבֵּל פְּרָס, אֶלָּא הֱווּ כַעֲבָדִים הַמְשַׁמְּשִׁין אֶת הָרַב שֶׁלֹּא עַל מְנָת לְקַבֵּל פְּרָס, וִיהִי מוֹרָא שָׁמַיִם עֲלֵיכֶם:

Mishna Avos 1:3

Do not be as servants who are serving the master in order to receive a reward, rather be as servants who are serving the master not in order to receive a reward; and may the fear of Heaven be upon you

גמרא מסכת עבודה זרה דף יט עמוד א

במצותיו חפץ מאד אר"א במצותיו ולא בשכר מצותיו והיינו דתנן הוא היה אומר אל תהיו כעבדים המשמשין את הרב על מנת לקבל פרס אלא היו כעבדים המשמשין את הרב שלא על מנת לקבל פרס

Gemara Avoda Zara 10a

“He delights greatly in His mitzvot.” Rabbi Elazar says: The person delights in His mitzvot themselves and not in the reward for performing His mitzvot. And this is the same as we learned in a mishna (Avot 1:3): Antigonus of Sokho would say: Do not be like the servants who serve the master on the condition of receiving a reward; rather, be like the servants who serve the master not on the condition that they receive a reward.

ספרי, עקב מח יב:

לאהבה את ה' אלוקיכם, שמא תאמר הריני אלמד תורה בשביל שאקרא חכם, בשביל שאלמד בישיבה, בשביל שאאריך ימים לעולם הבא, תלמוד לומר לאהבה את ה' אלוקיכם, למוד מכל מקום, וסוף הכבוד לבוא".

Sifrei Ekev 48:12

"to love the L-rd your G-d": Lest you say: I will learn in order to sit in sessions; so that I merit eternal life in the world to come; it is, therefore, written "to love the L-rd your G-d" — Learn in any event; honor will come as a matter of course.

רמבם הלכות תשובה פרק י הלכה א

אַל יֹאמַר אָדָם הֲרֵינִי עוֹשֶׂה מִצְוֹת הַתּוֹרָה וְעוֹסֵק בְּחָכְמָתָהּ כְּדֵי שֶׁאֲקַבֵּל כָּל הַבְּרָכוֹת הַכְּתוּבוֹת בָּהּ אוֹ כְּדֵי שֶׁאֶזְכֶּה לְחַיֵּי הָעוֹלָם הַבָּא, :

Rambam Hilchos Teshuvah 10:1

Let no man say: "Behold, I perform the precepts of the Torah, and engage myself in its wisdom so that I will receive all the blessings described therein, or so that I will merit the life in the World to Come;

Question: How can we reconcile this with:

מסילת ישרים פרק א ------ Meslat Yesharim (path of the just) ch.1

יסוד החסידות ושרש העבודה התמימה הוא שיתברר ויתאמת אצל האדם מה חובתו בעולמו ולמה צריך שישים מבטו ומגמתו בכל אשר הוא עמל כל ימי חייו.

The foundation of piety and the root of perfect service [of G-d] is for a man to clarify and come to realize as truth what is his obligation in his world and to what he needs to direct his gaze and his aspiration in all that he toils all the days of his life... והנה מה שהורונו חכמינו זכרונם לברכה הוא, שהאדם לא נברא אלא להתענג על ה' ולהנות מזיו שכינתו ...ומקום העידון הזה באמת הוא העולם הבא, כי הוא הנברא בהכנה המצטרכת לדבר הזה.

...that man was created solely to delight in G-d and to derive pleasure in the radiance of the Shechina (divine presence). ... The place of this pleasure is, in truth, in Olam Haba (the World to Come).

This seems to be saying that"perfect service of Hashem" and the "gaze and aspiration in all that one toils all the days of his life" is solely for the purpose of reaching Olam Haba.

Is this not what the Mishna, The Gemara, The Sifrie, and the Rambam call serving the master in order to receive reward in Olam Habah?

IMHO we cannot answer this by saying:

since the Mesilat Yesharim is written for gradual improvement, His statement about thinking about the World to Come is only the motivation for someone at a low level, whereas someone who is at the level of piety (חסידות) should serve only for God's honor with no thought of reward, similar to the different motivations he gives for different groups of people in chapter 4, which are focused on reward and punishment at worst, and self-improvement at best. Serving God for the sake of reward leads to serving him for its own sake, but such a person is still "far from perfection" (chapter 16), and that at the beginning of the book, the reader isn't expected to be at such a level

because the MY writes clearly in his opening statement, that he is teaching us במה צריך שישים מבטו ומגמתי בכל מה שהו עמל כל ימי חייות - to what he needs to direct his gaze and his aspiration in all that he toils all the days of his life" so this is obviously not just a beginners's entry level exercise, but rather the ultimate end toward which one toils and aspires all his life.

translation - What's meaning of 担当さん

なんと担当さんがその辺に落ちてた枝や石を使って実際に作ってくれました

I can't finish the translation due I can't understand the 担当さん. At first time, somebody said me that it's name. But it's not name, right? I was told that this occupation. But I'm not sure in it. And now I don't know how to translate it. Help me, please! And thanks for your help!

product recommendation - Academic abbreviations

Academic texts typically use acronyms to refer to books in Tana"ch, Talmud, and rabbinic literature. I am presently working on editing the citations given within a translation to bring them more in line with academic standards. However, I have only been able to find abbreviations for biblical books and sha"s. Is there any resource for academic abbreviations for other sefarim in Rabbinic literature?

minhag - Beracha on lighting yom tov candles : before or after?

There are two minhagim concerning the time the beracha should be said on lighting yom tov candles for a woman, before or after (like shabbos neros).

I've read arguments like these :

• before, because we don't receive yom tov with the beracha we can say it before the lighting


• after, to not differentiate with shabbos procedure

I would be glad to know a little more on the subject with sources and some poskim opinions

Is fruit sold in bulk at the store kosher?

At some supermarkets / stores, there is a "bulk fruit" section. I'm not talking about selecting fresh fruit off of the shelf or "fruit island" as is seen in some stores, like where they keep the apples etc..

I'm talking about where they keep bulk fruit in big plastic containers, and you use some kind of big spoon to pick them out and put into your plastic bag.. Here's a picture of what I'm talking about (except the kind I'm talking about have actual dried fruit instead of candy):

SO it's pretty reasonable to assume that the same containers which now have kosher fruit in them at one time contained dairy-coated snacks or or non-kosher items. So is the fruit taken from there still kosher, since it's safe to assume they reasonably cleaned the containers, or no?

Just BTW, one time someone gave me a bag of figs from one of those containers and I actually found a chocolate (probably most-definitely non kosher, milk chocolate) covered nut mixed in with the rest of them. IDK if this was a 1/10000 case and in general it's safe to assume that they are always cleaned, or no (?)

Answer

This dried fruit may or may not be kosher. The reason has nothing to do with the bins it is stored in, however. Room temperature solids are not halachaly able to render one another non-kosher, so a non-kosher chocolate in a fig bin, as per your example, will not render the dried figs non-kosher. (Below 110° F, but if it's above 110° F at your local supermarket, you've got bigger problems than whether or not the bulk dried fruit is kosher.)

The real kashrut issue is insect infestation- non kashrut-certified dried fruit should conform to FDA standards at least, but these are significantly more lenient than kashrut as pertains to bugs and bug parts. You should ask a rabbi what dried fruits are considered problematic in your area and those need to be checked prior to eating.

https://oukosher.org/publications/inspecting-dried-fruits-for-insects/

Interestingly, a Hidabroot article on Tu B'ishvat I am unable to link to states that "Kashrut of oil spread on fruit: dried fruit often has oil spread on it and you should make sure those oils are kosher". I have personally never heard of anything like that at all but it may be worth speaking to a Rav about.

Why Wavelet developed when we already had Short-time Fourier transform

If we already had Short-time Fourier transform for better analysis of a signal than Discrete Fourier Transform, then what was the need that leads to development of Wavelet Transform ?

Answer

The short-time Fourier transform doesn’t offer better analysis of data than the discrete Fourier transform, it offers a different kind of analysis. The DFT offers an exact decomposition of data to a frequency representation. The STFT offers an approximate decomposition to a time/frequency representation. Which is better depends on what you are after. The same holds true of the Wavelet transform. Wavelet transforms can be thought of as decomposition to a time/frequency representation, but wavelet transforms generalize the concept of decomposition. Different wavelet functions have been created so you can choose a decomposition that suits your needs.

word choice - What's the difference between the kanji forms for わかる?

The verb わかる can be written using either 分かる, 判る, or 解る - what's the semantic difference between these forms, if any?

Answer

The answer lies in the kanji. This data is from EDICT/Jim Breen's kanji lookup:

• 分: "...understand; know..."


• 解: "unravel...explanation; understanding; untie; undo; solve; answer...explain..."


• 判: "judgement; signature; stamp; seal"

分かる is clearly the most common - just to know or understand something:

私は日本語が分かります。 I know/understand Japanese.

解る implies understanding of a problem, not simple knowledge.

やっとあの数学の問題が解りました。 At last (I) figured out that math problem.

Which implies to me that you solved the problem. If I read the same sentence with 分かりました, I might not think twice -- but it could also mean that you didn't spend any time solving it at all; you already knew how to solve it (and therefore did so immediately).

判る is probably the least common use I've seen in the wild.

Because the word "judgement" is connected to it, ala 判断 (はんだん), so if a judgement was made that something WAS something, that might be 判る. A cursory Google search yielded this Yahoo! page which indicated the same.

現場で指紋が見つかったからには、犯人が判るのも時間の問題です。
Now that (we) found fingerprints at the scene, it's only a matter of time before (we) know/figure out who the criminal is.

DISCLAIMER: These sentences and translations are my own, and I'm no translator, nor a native speaker!

tefilla - Rabbi Nachman on connecting to Tzaddikim and Tefillah

Rabbi Nachman M'Breslov in Likutei Moharan (2:6) writes:

(Source from Sefaria.org)

(Partial Quote)

וְצָרִיךְ כָּל אֶחָד לְכַוֵּן בִּתְפִלָּתוֹ, שֶׁיְּקַשֵּׁר עַצְמוֹ לַצַּדִּיקִים שֶׁבַּדּוֹר, כִּי כָּל צַדִּיק שֶׁבַּדּוֹר הוּא בְּחִינַת מֹשֶׁה מָשִׁיחַ, כְּמוֹ שֶׁמָּצִינוּ שֶׁהַצַּדִּיקִים קוֹרִין זֶה לָזֶה מֹשֶׁה, כְּמוֹ: מֹשֶׁה שַׁפִּיר קָאֲמַרְתְּ

And everyone must aim in his prayer, that he should tie himself to the Tzaddikei Hador/righteous saints of the Age, because every Tzaddik Hador is an aspect of Moshe Mashiach (Moses-Messiah), as we have found, that the tzaddikim call each other "Moshe," as in [the saying of the sages]: "Moshe, you have said well."

What does it mean that one should aim his prayer so that he should attach himself to the Tzaddikim of the Generation? Shouldn't one try to attach himself to G-d?

Answer

Though having a different understanding of what a Tzaddik is the Noam Elimelech on Parshas Eikev provides an interesting insight on this concept.

(Source from Sefaria.org)

(Partial quote)

או יאמר "והיה עקב תשמעון כו'", "עקב" הוא רמז לאנשים כאלה שאין להם שכל ובינה להשיג גדולת הבורא ועבודתו שלימה לעבדו באמת ובשלימות, רק שהם מחברים עצמם אל אנשי צדק ואמת היודעים ומכירים גדולת הבורא ב"ה ועובדים באמת, אזי נחשב גם להם כאילו גם הם עשו עבודתם שלימה כהצדיקים השלימים

"And it will be (EIKEV) because of your listening etc." (Deut 7:12), "EIKEV" alludes to those who do not have the intelligence and understanding to perceive the greatness of the Creator and His complete task so as to serve him with honesty and perfection. Only because they attach themselves to righteous, truthful individuals who know and recognize the greatness of the Creator, blessed be He, and serve Him truthfully. It is then considered that they too have also done their service perfectly like the completely righteous.

Hope this is insightful for others also!

grammar - Usage (correctness) of だと after verbs

I've noticed だと showing up after verbs for a while now in various forms of media, such as blogs, anime, regular TV shows & also when speaking to Japanese people. However, I was originally told that this grammar is incorrect, as だと can only be used after nouns - so what is going on here?

An example from a manga/anime called Prince of Tennis: Character realises he is about to get beaten up by another character - in a bid to stop it happening he says: なんでもします! To which the other character replies (angrily) なんでもするだと！？

fourier transform - Conditions for symmetric and unimodal windows in both time and frequency domains

After a lecture on harmonic analysis and time/frequency methods, I reconsidered the Gaussian kernel, defined in continuous time.

It is unimodal and symmetric, and its continuous Fourier transform is another Gaussian, thus unimodal and symmetric (from Fourier transform of a Gaussian is not a Gaussian, but that's wrong!):

As a filter or a window, the Gaussian ensure a monotonic weight decay around its center. The interpretation in the frequency domain is similar: frequencies are monotonically attenuated away from a center frequency.

Such a property allows a straightforward interpretation in both the time and the frequency domain.

• For continuous kernels, are there generic characterizations (necessary or sufficient conditions) under which unimodal and symmetric windows also have a unimodal and symmetric amplitude spectrum?

Answer

This is only also partial answer. I translate unimodular into ripple-free, because ripples are essentially extremal points, and we just want to have a single one.

A ripple-free Fourier Transform translates (to my knowledge) to an infinitely often continuously differentiable time-domain function. Furthermore, to let the Fourier Transform be defined easily, the function should either decay very quickly or should have compact support. Hence, candidate functions would be from the Schwartz space of functions.

Unimodality further reduces the number of candidates, with the Gaussian being a prominent example. Others are Hermite Polynomials, weighted with the Gaussian. With a clever linear combination of Hermite function, you can create a function that is unimodal, different from a gaussian and still has ripple-free and symmetric Fourier transform.

import scipy.special
%matplotlib inline

Fs = 100
t = np.arange(-10, 10, 1./Fs)

H = scipy.special.hermite
g = lambda t: (H(4)(t)+H(2)(t)+80*H(0)(t)) * np.exp(-t*t)
gauss = lambda t: np.exp(-t*t)
plt.subplot(1,2,1)
plt.plot(t, g(t))
plt.plot(t, 80*gauss(t))
plt.xlim(-4,4)

plt.subplot(1,2,2)
plt.plot(20*np.log10(abs(np.fft.fft(g(t), 7*len(t)))))

I believe the ripples in the frequency are due to finite windowing and numerics. Might need more analysis with analytic solutions, e.g. from Mathematica.

So, the answer might be: The window needs to be unimodular and stem from the Schwartz space of functions?

tzibur community - who says "baruch hu uvaruch sh'mo" before birkas hamazon

Ashk'nazi prayer books generally include the line

ברוך הוא וברוך שמו

after the zimun (invitation to say birkas hamazon and before the actual birkas hamazon. It generally (in my experience) is preceded by the instruction:

יחיד אינו אומר

yachid eno omer, which means "an individual does not say" or "someone alone does not say"; the word yachid is often used to refer to someone not part of a minyan.

Who should say this, and who should not — and why?

Ideas that come to mind are:

• Anyone included in a zimun should say it, but not someone saying birkas hamazon without a zimun.


• Anyone saying birkas hamazon with another says it, but not someone alone.


• Anyone included in a zimun of a minyan says it, but not someone saying birkas hamazon without a minyan.



• Anyone leading a zimun (the m'zamen) says it, but no one else.

I'd appreciate any argument or, especially, source. Naturally, for practical guidance, each person should rely on his rabbi rather than answers here.

Answer

Many thanks to Menachem who, in a comment on the question, gave references to some of the following, which led me also to the others:

• The Avudraham (Abudirham) says that only the leader of a zimun (the m'zamen) says it, and has a different nusach (wording): Baruch hu uvaruch zichro l'olme ad. (Many thanks to Menachem for finding this!)


• The Tur, OC 192 (and all citations below are to OC 192), mentions saying baruch hu uvaruch sh'mo. It seems to me from his language that he holds that it's only said when there's a zimun, and only by the leader (m'zamen). Others comment that it's not mentioned in the g'mara, Rosh, Rif, or Rambam, but that the L'vush and Rokeach (284) also mention it — but I haven't looked them up.
  
  
  
  • The Rama (in Darke Moshe :2) holds not to say it.
  
  
  
  • The Bach seems to hold (if I understand him correctly) that those answering to a zimun of a minyan say it, but no one in a smaller (or no) zimun.
  
  
  • The P'risha (:2) holds (if I understand him correctly) that only the leader (m'zamen) says it.
  
  
  
  


• The Shulchan Aruch and Rama (in the Mapa) make no mention of baruch hu uvaruch sh'mo. Nor does the Taz. The Magen Avraham and Baer Hetev comment that the Shulchan Aruch holds that we don't say it.
  
  
  
  • The Magen Avraham himself (:0), however, notes the common practice is to say it, and adds that one should not say it without a zimun.
  
  
  • And Baer Hetev himself (:3) says that the common practice is to say it when there's a zimun. He doesn't seem to say who should say it when there's a zimun, though I suspect that he'd follow the Tur and others cited above and hold that only the leader (m'zamen) says it.
  
  
  • The Shaare S'shuva says that no one but the leader of a zimun (the m'zamen) should say it.
  
  
  
  
  


• The Shulchan Aruch Harav (:2) notes that some have the practice of saying it, and adds in parentheses that no one but the leader of a zimun (the m'zamen) should say it.


• The Aruch Hashulchan (:5) says that it's appropriate to omit baruch hu uvaruch sh'mo and that that's the common practice.


• The Mishna B'rura (:4) says it's said only with a zimun, and only by the leader (m'zamen).
  
  
  
  • The Shaar Hatziyun (:3) says that the G'ra holds not to say it.
  
  
  
  

heterodox - What is mainstream Chabad's view on Elohists?

There is a small group of people who believe that the Lubvatcher Rebbe Menachem Mendel Schneerson zt"l is in fact God. For example, the front page of the website for a synagogue(?) in Mikwaukee reads, in part, "Yechi Eloheinu Moreinu V'Rabbeinu Melech HaMoshiach L'Olam Va'ed!"

Is there an official Chabad/Lubavitch position on the status of those people? Does mainstream Chabad consider them to be true Hasidim? Perhaps they are even considered to be non-Jews? If there is no official position, is there a general consensus among the community?

Answer

Of course, Chabad (or anyone else really, but they may use different language) would consider someone practicing Avodah Zarah in its most egregious form still Jewish, but Chabad, both the non-Meshichist side and the Meshichist side, reject this completely.

See here for some links to source letters. Note that the one from the Beis Din of Crown Heights is signed by Rabbi Marlow ע"ה, who was a supporter of the Meshichist side.

There was also a huge Mechoh made back in the times before the internet was in wide use of most of the Rabbonim who support the Meshichist side condemning this idea as completely against Torah. I don't know if a copy exists online.

There is no test of being a "true" Chosid. Such a statement can mean many things, from fitting into the normative practices of the Chassidic community, to a true dedication to the Rebbe's cause. The former is a much larger group than the latter, but there is no official litmus test.

number - Asara Umatayim?

Who knows two hundred ten?

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

• 
  

  Upvote all interesting answers.

  
  


• 
  

  Accept the best answer.

  
  



• 
  

  Go on to the next number.

  
  

Answer

210 are the years of shi'bud Mitzrayim. (Rash"i on B'reshis 15:13)

usage - How do you respond to thanks given?

How do you respond to ありがとうございます　and other ways of giving thanks? Are there any expressions similar to the English "You're welcome" or "No problem", or is it appropriate to not respond at all?

Answer

The simplest one is 「いいえ」, "not at all". The next one up is 「どういたしまして」, "would do the same". Another one you may come across is 「とんでもない」, "don't mention it", or one of its more polite variants (replacing 「ありません」 or 「ございません」 as appropriate). There are even more polite responses, but as a 外国人 you will not be expected to have to worry about them.

grammar - The difference between くらい and ほど in hyperbole

The following two sentences, I believe, are grammatically okay, however I'm not sure on how they differ in nuance.

もう歩けないほど疲れた！ (もうあるけないほどつかれた)
もう歩けないくらい疲れた！ (もうあるけないくらいつかれた)

Additionally, why is it that:

死ぬほど恥ずかしい (しぬほどはずかしい)

is grammatically okay but

死ぬくらい恥ずかしい (しぬくらいはずかしい)

is not?

(However 死にたいくらい恥ずかしい is okay.)

From looking at this, it seems くらい cannot show volition. Is there a logical reason for this that I'm not seeing?

Answer

OK, I think I've got something here. Essentially, the difference boils down to the following:

• ほど expresses an upper bound; it is often emphatic and therefore expresses surprise


• くらい expresses a lower bound; the level indicated may be exceeded

Let's look at 歩けない｛ほど／くらい｝疲れた. Diagrammed, it looks like this:

Both ほど and くらい express the level of tiredness marked by the red dot (not being able to walk at all). But ほど focuses on the left side of that dot, and it emphasizes the fact that the level of fatigue exceeds both the level where your legs get a little wobbly (first dot) and the level where you can't keep your balance well (second dot). But ほど does not exceed the red dot.

With くらい, on the other hand, the scale starts at the red dot, and may even go higher to the last dot (not even being able to stand up). The surprise expressed by ほど is mostly absent, and the sentence is more along the lines of a simple statement of fact.

Places where ほど can be used, but not くらい

This page has a section with some examples along these lines. Let's look at a few in light of the rules derived from the above diagram:

ヨットが買えるほどお金持ちではないよ。 He's not so rich that he can buy a yacht.

僕のお小遣いで買えないほど高くはなかった。 It wasn't so expensive that I couldn't buy it with my allowance.

どうしても結婚したいというほど愛してはいなかった。 She didn't love him so much that she wanted to marry him at all costs.

The common thread running through these sentences is that the level marked by ほど is not reached. (All of the sentences could be reordered to fit the pattern "B may be true, but not to the extent A.") In other words, the actual level lies to the left of the red dot on the above diagram. Because it's on the left side, only ほど can be used.

Places where くらい can be used, but not ほど

From the same page:

ここに入っちゃいけないぐらい知ってるでしょう？ You do at least know that you can't come in here, right?

入賞したぐらいで喜んではいけない。 You shouldn't be happy just over winning an award.

休みの日でも警備員をおくぐらいできるだろう。 We should be able to at least station some guards on days off.

In all of these sentences, くらい (sometimes ぐらい; the difference was covered in this question) marks a minimum level. So now we're dealing with the portion of the diagram to the right of the red dot. Thus, only くらい is allowed.

Effect on hyperbole

So based on what we've seen so far, why are these two different?

死ぬほどさびしい so lonely one could die (not really serious)

死ぬくらいさびしい so lonely one could die (serious, possibly suicidal)

In statements like these, ほど, because it covers the left end of the scale, implies that you haven't reached the red dot yet, but it feels like you're getting close. くらい is different. With くらい, you're at the red dot and are on the way to more extreme levels (toward the right end of the scale). 死ぬくらい thus conveys more immediacy and reality than 死ぬほど, which can be used "lightly" and without really meaning it.

This contrast between くらい's immediacy and reality and ほど's figurativeness appears in sentences like this:

死ぬくらいならなんでもする。 If I were at the point of death, I would do anything.

ほど doesn't work nearly as well here, because the setting for this sentence is that the speaker has a life-and-death choice and is literally staring death in the face. This is solidly on the right end of the scale, so くらい is the best option.

From this we can also explain the unnatural feeling from your example fragment:

死ぬほど恥ずかしい so embarrassed one could die (playful exaggeration)

死ぬくらい恥ずかしい so embarrassed one could die (weird)

The second sounds weird because, unlike loneliness, which can and does lead to suicide, embarrassment is an unusual reason for dying. But as you correctly pointed out, 死にたいくらい is fine here. This is because feeling like one wants to die after being embarrassed is common and quite different from actually carrying out that feeling.

halacha - Can you learn portions of Avot D'Rav Nattan on Tish'a B'Av?

This M.Y. answer provides a list of permissible learning items on Tish'a B'Av. All these items are somehow related to the themes of mourning, the Temple destruction, etc.

Avot D'Rav Natan has several Mishnayot that seem to relate to the theme of Tish'a B'Av related to the setruction of Jerusalem. Examples:

Avot D'Rav Natan 4:4 and 4:5 Rav Yohanan ben Zakkai's request from Vespasian for Yavneh

Avot D'Rav Natan 6:3 Near the end of Mishnah; story of Kalba Savu'a who had enough food to feed everyone in Jerusalem for 22 years. Yet, the Zealots destroyed his storehouses

Would it be appropriate to learn these? Why weren't these included in the list?

Answer

Tanna v'sheeyer - Anything fitting the mood of the day is acceptable (at least without iyun [in-depth analysis]; see also sources cited by @WFB in comments below which are lenient even with regard to iyun). It would be impossible to have a comprehensive list since Torah SheBaal Peh (the oral Torah) is constantly expanding. (My assumption is that these specific passages were also not included in the list because they are relatively short.) See also, e.g., the Aruch HaShulchan (554:5) who permits reading the sad passages in Neviim left unmentioned by the Brayta:

ויראה לי דכן דברים הרעים שבשארי נביאים – מותר לקרות. ומה שהש"ס חשיב רק ירמיה – משום דבירמיה יש הרבה דברים רעים.

It seems to me that, so too, one is allowed to read the sad passages [lit: bad things] in the other Prophets and the reason the Talmud only mentioned Jeremiah is because there are many sad passages in Jeremiah.

(This inclusive understanding, by the way, is the basis why later codes and commentaries [e.g. Levush cited by Mishna Berura] added to the original Talmudic list.)

shemos sacred names - Would most Jews deem a tattoo containing the tetragrammaton offensive?

I understand that this question involves a measure of subjectivity, but I am curious to hear people's opinions. I understand that getting a (real) tattoo is forbidden by Jewish law. I also know that the name of G-d/Hashem is very holy and not spoken. When I was younger, far less concerned about offending others, and not a follower of any religion, I tattooed קֹ֖דֶשׁ לַֽיהוה on my left hand as a wedding band. I am now in the process of getting this tattoo removed (my marriage is still going strong, in case you were wondering).

I am curious, however, if this would actually be deemed offensive to most Jews or not. Also, if there are any sources where this has been dealt with in the past I would love to hear them. Either way, I am still getting it removed.

I ask because I intend to soon attend Hebrew school as a Gentile observer, but I am debating whether or not I should conceal my tattoo.

Answer

The Talmud (in Masekhet Shabbat 120b) directly discusses this issue:

דתניא: הרי שהיה שם כתוב לו על בשרו - הרי זה לא ירחוץ ולא יסוך ולא יעמוד במקום הטינופת. נזדמנה לו טבילה של מצוה - כורך עליה גמי ויורד וטובל. רבי יוסי אומר: לעולם יורד וטובל כדרכו, ובלבד שלא ישפשף

As it was taught in a baraita: If one had a sacred name of God written on his skin he may neither wash it in water lest it be erased, nor may he smear it with oil, nor may he stand in a place of filth because it is disrespectful of God's name. If an immersion of mitzvah happened to present itself, he wraps a reed over God's name and then descends and immerses. Rabbi Yosei says: Actually, he descends and immerses in his usual manner, even if it is not an immersion of mitzva, provided that he does not rub the spot and erase the name. Apparently, Rabbi Yosei's opinion is more lenient than that of the Sages with regard to indirectly causing a prohibited outcome. (Koren Talmud Bavli Steinsaltz translation - bolded words are the translated Hebrew text).

The law, as the Rambam in Yesodei HaTorah 6:6 records, is according to the Sages: that the person must wrap a reed around the name because one may not be naked before God's name.

Since you are asking about personal opinions, I would find it offensive to see a tattoo of God's name regardless if the person was Jewish or not. There is a visceral reaction, probably because Judaism treats the name (i.e., how it is written out, how it is not pronounced, etc.) with such reverence. I could further question the underpinnings of such emotions, but I think it is fair to say that many observant Jews would feel uncomfortable seeing such a tattoo

So out of respect to others, I would find it more appropriate to conceal the tattoo when visiting a Hebrew school.

meaning - How can I tell if a Japanese person's given name is male or female?

I am hoping that there may be some particular kanji and/or sounds used in determining if a persons given name is male or female.

Answer

There are a number of common suffixes you can use to try to guess. Here is an incomplete list of common suffixes which are a pretty safe bet:

Female

• ko 子


• mi 美


• ka 花・華


• e 江・恵


• na 奈・菜


• no 乃


• ri 里

Male

• rō 郎


• ta 太


• suke 介・助・祐


• o 男・夫・雄・生


• ya 哉・也


• kichi 吉


• hiko 彦


• nobu 信

Also, "girly" kanji—like 愛 "love", 幸 "happiness", 華 "flower", 美 "beauty" etc.—or hiragana will usually indicate a girl's name.

Similarly, "boyish" kanji—like 正 "righteous", 健 "health/strength", 勝 "win", 信 "honesty", etc., will usually indicate a boy's name.

translation - How would you express the sentiment of "Happy New Era"

Something like 良いお時代を。? Or would you specifically say 令和?

If not that, what would be a literal English translation?

Answer

Good afternoon, I was curious as well as what would be better to say so I looked online to see what Japanese people were saying about the new era. No one really said congratulations or happy new era, but I found one blog where the writer said something like "Congratulations for the new Era, 令和!"
She wrote:

令和、[新]{あたら}しい[時代]{じだい}の[幕開]{まくあ}けおめでとうございます！

Here is a link to the posters blog where I found this sentence.

Hope it helps.

organic chemistry - Why is CF3COOH exceptionally acidic?

The pKa values of almost all carboxylic acids lie much above 0. But this is violated by trifluoroacetic acid(-0.25). How can this be justified?

Answer

Try drawing the structure of the conjugate base $\ce{CF_3COO^-}$. In general, the more stabilized the negative charge of the conjugate base is, the more the equilibrium favors that form, thus the more the acid dissociates, thus the "stronger" the acid is.

So for a stronger acid (lower $\ce{pK_a}$), the negative charge must be more stabilized. When comparing $\ce{CF_3COOH}$ (TFA) to $\ce{CH_3COOH}$ (we'll use acetic acid to represent a "typical" carboxylic acid), TFA is stronger than acetic acid because its conjugate base can better stabilize the negative charge. If we draw the structures of the conjugate bases (I encourage you to do so), we will see that they both can stabilize the negative charge via resonance in the carboxylate functional group. However, TFA also has three highly electronegative fluorine atoms which withdraw electron density "through the single bonds" via induction.

As stated above, the $\ce{-CF_3}$ moiety is an electron withdrawing group, by the inductive effect. So our negative charge (rather, the electron density it represents) will be slightly drawn through the bonds toward the fluorines, thus it is further delocalized and thus more stable.

Note that we do not have convenient structural diagrams to show induction like we do resonance, but you should be able to imagine the electrons "sloshing" more towards one side of a bond/functional group. It's the same concept as a good old polar bond like $\ce{H-Cl}$; we say Cl "hogs" the electron density and pulls it away from H. In the same way $\ce{-CF_3}$ will draw electron density toward itself.

So to summarise, in general:

Stronger acid ~ more stable conjugate base. Whenever you want to qualitatively rationalize the relative strengths of two acids, draw their conjugate bases and determine which is more stable. (If your acid was neutral, its conjugate will be negative, and it will be easier to use this method than for a positive acid/neutral conjugate.) Stabilizing factors are size and electronegativity of the atom bearing the charge, resonance delocalization of the charge, hybridization of the orbital holding the charge, induction delocalization of the charge, and hyperconjugation which donates electron density and may destabilized a negative charge. SERHIH, roughly in that order of significance.

In this example, TFA and acetic acid are tied at size & electronegativity because both place the charge on an oxygen atom, tied at resonance because both may use the carboxylate functionality, tied at hybridization because the atoms in a carboxylate are necessarily $\mathrm{sp^2}$, but now induction is present in TFA and not acetic acid, so we expect TFA will be a stronger acid.

halacha - Why does earthly punishment start at 13 and divine punishment at 20?

Inspired by this question.

The age when one is obligated to keep Mitzvos is 13 (for a male and 12 for a female). (See Avot 5:21 and Bartenura)

After that age, Beit Din may punish them if they transgress the law.

Punishment from heaven starts at 20 years old (Shabbat 89B).

Why is the age when one may be punished by Beit Din 13 years old, and the age of punishment from heaven 20 years old?

Answer

The Chacham Tzvi (Paragraph 49) gives 4 answers about whether punishment starts at 13 or 20 years old (brought in the Pardes Yosef here):

1. 
   

   It was only before the giving of the Torah that punishment started at 20, after the giving of the Torah it starts at 13. (I believe this only answers why we say Sarah was free from sin at 100 as when she was 20. It does not address the Gemara or any others who say that Heavenly punishment starts at 20)

   
   


2. 
   

   The Heavenly Court doesn't always punish for crimes committed under 20, and that's part of Yitzchok's "deal" with G-d, to ignore any sin committed before 20.

   
   


3. 
   
   

   The Heavenly Court doesn't punish people in this world for doing something wrong when they are under 20. Once they go up to heaven, however, they are judged for everything done after 13 years old.

   
   


4. 
   

   The Heavenly Court waits until one is 20 to see if they do Teshuva. Once the person reaches 20 without doing Teshuva, the person is punished for the sin he committed when younger.

   
   

The Pardes Yosef on Parshat Chayai Sarah (Chapter 23) gathers many different opinions about what it means "The Heavenly Court does not punish someone under 20 years old". It appears he includes most (if not all) of the opinions brought here (and more), as well as giving one of his own.

The Pardes Yosef himself (I think) points out that heavenly punishment is stricter than earthly punishment, as is brought in Baba Kamma (55B-56A). The Gemara there brings cases where the earthly Beit Din would not punish for actions (since they are too inconsequential), but the Heavenly Court will still extract punishment. When it comes to time, however, the Heavenly Court is more lenient, waiting until 20 to punish.

This is because due to the public nature of the punishment. When the earthly Beit Din punishes someone, it is for their own benefit, since they will learn not to do it again. Even when he is killed by Beit Din, other people learn from this, and refrain from sinning themselves. This is good for others, and good for the punished as well, since this merit helps his atonement process.

On the other hand, when a person is punished by the hands of G-d, it is too late for him to learn from his punishment, and therefore G-d waits till the person is 20 before holding him liable for his actions.

Furthermore, the Pardes Yosef continues, it says in Sefarim that when a person sins he causes a blemish on his soul, and Heavenly punishment wipes away these blemishes. A person under 20 has not yet achieved full intellectual maturity, and therefore the blemishes are not so great and do not yet require cleansing. (He brings a proof from our Sages that a person does not reached full intellectual maturity until 20, but I am unfamiliar with the statement and he does not bring a source, so I can't look it up.)

Here Rabbi Zweig brings a different explanation in a similar vein.

etymology - Are the names Akiva and Ya'akov related?

Are the names Akiva and Ya'akov related?

halacha - Blessing on Grace After Meals

Why is a birkat mitsvah not recited upon performing the mitsvah of the recitation of birkat hamazon? This would perhaps be akin to the blessing upon Bitkat Kohanim as noted by @danno.

Answer

This is discussed in the Sefer ליקוטי שושנים on page 13.

Essentially he answers:

Since we bless Hashem during the Birkat Hamazon (Grace After Meals), there's no need to first bless Him before doing the Mitzva.

There's no need to make a Bracha on a Bracha, since the point of making the Bracha is taken care of as we say the actual Bracha.

Similarly we don't have a Bracha upon reciting Kriat Shma, since Shma is all about accepting the yoke of heaven, making the pre-blessing redundant.

terminology - Quick and simple explanation of molar mass, molecular mass and atomic mass

As a physics student, I hardly deal with such quantities and when I do, I blunder through. I think it’s a good time to be given a good explanation for these since I’m in a class of Nuclear physics. I have tried googling but it seems that some sources are ‘misleading’ and most have more than 1 terminology for the same thing! Horrifying but real.

Please tell me what is the difference between molar mass, molecular mass and atomic mass and what are their associated twin terminology.

minhag - What is the Heter for the prevalent Clothing among Women?

The Eida HaChareidis¹ paskened (and R' Wosner agreed) in accordance with the Mishna Berura², who requires women to go in public places only when wearing redid (a head-covering wrapping the entire body like men wear a talis³) concealing the triangular space between head and shoulders, and the split between arms and torso. This applies even today.⁴

According to R' Moshe Feinstein⁵ a woman may select any posek she wants, even if her husband is a posek. Indeed, no wife of any of these poskim followed their husband's psak. It is also the prevalent custom not to follow this, although some do.⁶

Which poskim would they be following?⁷

---

<sup>1. Written kol koreh by R' Weiss with R' Fisher, R' Rabinowitz, R' Halberstam, R' Bernsdorfer, and R' Ulman.
2. Biur Halacha on Siman 75: Veda shekol ze (...) le kula alma (...) overes al das yehudis...
3. Rambam Hilchos Ishus Perek 13 & 24, Shulchan Oruch Even HaEzer Siman 73.
4. Diyuk in Rambam ibid. shenohagu bnos yisroel and not shenohagin i.e. it doesn't change according to current custom.
5. Written by R' Leib Tropper in the name of R' Feinstein's son.
6. At least in Bet Shemesh, Jerusalem, Kiryas Joel, London, Monsey, and Montreal. E.g. one of the two Shomer Emunim Rebbetzins, and R' Shlomo Brevda's daughter-in-law.
7. It would seem that they would be either later than the Mishna Berura, or that he did not know (or consider) them.</sup>

fft - DFT-like transform using triangle waves instead of sin waves

We know that DFT (discrete Fourier transform) breaks down a signal into multiple frequencies of sine waves. Does there exist a transform that does the same thing, but for triangle waves?

For my purposes, im only talking about 1-d signals (like voltages, etc). I'm studying historical stock market data, and I just want to look at reversals in certain stocks. In other words, I want to perform a "low-pass" on the stock price using this transform.

Edit: If yes, how can I do it?

safety - Why is use of calcium carbide as an artificial fruit ripening agent banned?

Fruits like mangoes can be ripened using agents like ethylene, acetylene or calcium carbide. Of these, the latter is dangerous and is banned in most countries. Wikipedia says it is because calcium carbide has traces of arsenic and phosphorus. Is there any other reason?

Will it still be unsafe if pure calcium carbide is used?

Answer

Calcium carbide is typically used by traders who can't afford a proper infrastructure for fruit ripening (sealed storage locations and gas generators). Carbide stones are put in permeable packets (typically paper bags) and hanged above the fruit boxes, where they absorb water from the air to produce acetylene gas.

This leads to two issues:

• the concentration of acetylene is uncontrolled, and given enough moisture can reach explosive levels


• permeable bags release fine particles of reaction byproducts which land on the fruits

Of course, pure calcium carbide would be safe, at least from the nutrition perspective. You'd still have the risk of explosion though, and because carbide cannot be used safely for fruit ripening, nobody is producing it in food grade in the first place.

particle も - Combination of verb + ことも

In the following sentence:

知りたい こと も、後で ちゃんと 教えてあげる…

The first part: 知りたい こと, I understand as: what (you) want to know, because of -tai and koto combination.

The second part: 後で ちゃんと 教えてあげる…, means I think: (I) will properly inform (you) later.

The above seems to make sense when put together, but I think I'm not capturing the meaning of も. The first part seems like a noun and with a single も in the sentence my guess would be too/also.

Considering this, could the sentence be translated as: (It is) what (I) want to know too, (I) will properly inform (you) later.? Am I at least close?

Answer

As soon as I read your last sentence, I knew that you were overthinking. The sentence in question is much simpler than you seem to think both in structure and meaning.

「知{し}りたい こと も、後{あと}で ちゃんと 教{おし}えてあげる。」

The 「も」 simply suggests that there are other things (besides what the listener wants to know) that the speaker will be explaining/teaching for the listener later on.

In other words, 「も」 modifies 「教えてあげる」.

Your guess of 「も」 being "too/also" is correct, but the important thing is to know "what too", "also what", etc.

Unless this sentence appeared in a context/situation so unusual that I could not even have imagined, it would mean:

"I will surely teach (or "explain to") you the thing(s) you want(ed) to know and stuff (or "other things")."

theoretical chemistry - Bonding in diatomic C2, a carbon-carbon quadruple bond?

Carbon is well known to form single, double, and triple $\ce{C-C}$ bonds in compounds. There is a recent report (2012) that carbon forms a quadruple bond in diatomic carbon, $\ce{C2}$. The excerpt below is taken from that report. The fourth bond seems pretty odd to me.

$\ce{C2}$ and its isoelectronic molecules $\ce{CN+}$, BN and $\ce{CB-}$ (each having eight valence electrons) are bound by a quadruple bond. The bonding comprises not only one σ- and two π-bonds, but also one weak ‘inverted’ bond, which can be characterized by the interaction of electrons in two outwardly pointing sp hybrid orbitals.

According to Shaik, the existence of the fourth bond in $\ce{C2}$ suggests that it is not really diradical...
If $\ce{C2}$ were a diradical it would immediately form higher clusters. I think the fact that you can isolate $\ce{C2}$ tells you it has a barrier, small as it may be, to prevent that.

Molecular orbital theory for dicarbon, on the other hand, predicts a C-C double bond in $\ce{C2}$ with 2 pairs of electrons in $\pi$ bonding orbitals and a bond order of two. "The bond dissociation energies (BDE) of $\ce{B2, C2}$, and $\ce{N2}$ show increasing BDE consistent with single, double, and triple bonds." (Ref) So this model of the $\ce{C2}$ molecule seems quite reasonable.

My questions, since this is most definitely not my area of expertise:

• Is dicarbon found naturally in any quantity and how stable is it? Is it easy to make in the lab? (The Wikipedia article reports it in stellar atmospheres, electric arcs, etc.)


• Is there good evidence for the presence of a quadruple bond in $\ce{C2}$ that wouldn't be equally well explained by double bonding?

Answer

Okay, this is not so much of an answer as it is a summary of my own progress on this topic after giving it some thought. I don't think it's a settled debate in the community yet, so I don't feel so much ashamed about it :)

A few of the things worthy of note are:

• 
  
  

  The bond energy found by the authors for this fourth bond is 13.2 kcal/mol, i.e. about 55 kJ/mol. This is very weak for a covalent bond. You can compare it to other values here, or to the energies of the first three bonds in triple-bonded carbon, which are respectively 348, 266 and 225 kJ/mol. This fourth bond is actually even weaker than the strongest of hydrogen bonds ($\ce{F\bond{...}H–F}$, at 160 kJ/mol). Another point of view on this article could thus be: “valence bond necessarily predicts a quadruple bond, and it was now precisely calculated and found to be quite weak”.

  
  


• 
  

  The findings of this article are consistent with earlier calculations using other quantum chemistry methods (e.g. the DFT calculations in ref. 48 of the Nature Chemistry paper) which have found a bond order between 3 and 4 for molecular dicarbon.

  
  


• 
  

  However, the existence of this quadruple bonds is somewhat at odds with the cohesive energy of gas-phase dicarbon, which according to Wikipedia is 6.32 eV, i.e. 609 kJ/mol. This latter value is much more in line with typical double bonds, reported at an average of 614 kJ/mol. This is still a bit of a mistery to me…

  
  

nevua prophecy - Why was Mesha king of Moav successful?

King Mesha of Moab fought against the kings of Yisrael, Yehuda and Edom (2 Melachim chapter 3). The navi Elisha prophecies, under oath, that the Jews will be successful. However at the end of the chapter Mesha sacrifices his son (or perhaps the son of the king of Edom) which somehow causes a reversal of fortune with Mesha and Moav remaining undefeated.

This story is puzzling. What has Mesha achieved in killing his son? He was not commanded to do so by God, in fact it violates one of the 7 noachide laws. This is equally true if he killed the son of the Edomite king. Why then would God turn things in his favor as a result of this act? Furthermore the navi already said there would be victory. We have a principle that a positive prophecy will not be revoked.

How do we understand these turn of events?

fft - Why do I have frequency leakage in DFT after zero padding if frequency resolution is fine?

Let's consider this example:

Fs=1000; 
Ns=500;
t=0:1/Fs:(Ns-1)*1/Fs;
f1=10;
f2=400;
x=5+5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t);

X=fft(x);

In this scenario, frequency resolution is 2, and all frequency components are captured correctly. However, if I do this:

  X=fft(x,1000);

frequency resolution is 1, but there is a spectral leakage. Similar effect is seen here. It seems to me, that Fourier transforms of both windows (one with length 500, and one with length 1000) have zeros at the frequencies that are presented in the signal, so I don't see why leakage will happen?

Answer

This phenomenon has nothing to do with spectral leakage. What you are observing is the effect of zero padding. Given a number of samples $N$, there is a maximum possible frequency resolution $\Delta f$ that can be achieved:

$$\Delta f=\frac{f_s}{N} $$

In your case $\Delta f$ is exactly $2\;\mathrm{Hz}$. If you zero-pad your signal, there is no extra information to retrieve - you will only decrease the frequency spacing.

In the example above, when you increase $N$ to $1000$, you get a frequency spacing of $1\;\mathrm{Hz}$. All extra observed samples are merely an interpolation, done by the window function ($\mathrm{sinc}$ in your case). You will start observing side-lobes of the window spectrum. Since you implicitly multiplied your signal by a rectangular window, this will result in the convolution of the spectrum of your signal (two Dirac's + DC) with the $\mathrm{sinc}$ function.

---

Another way to look at it is to imagine that DFT is basically a filter bank, consisting of shifted $\mathrm{sinc}$ functions. Those are aligned in such a way, that peak of one is where zeroes of all the remaining ones are present. If you start looking in between those zeros, you will start taking those samples. Here is an example plot of such $\mathrm{sinc}$ filter bank.

Let's imagine that frequency corresponding to the blue filter is present. That will yield the amplitude in a corresponding bin. All the remaining frequencies are not present (orange and yellow), thus you multiply those $\mathrm{sinc}$'s by $0$ and get nothing in the bins. In the case of zero padding, that will be no longer the case. Samples of that blue $\mathrm{sinc}$ will fall in the intermediate bins and will be sinc-interpolated.

---

Here is what happens for $N=1000$ and $N=10000$:

And a zoomed part:

Things to notice:

• 
  

  For $N=500$, there is no leakage whatsoever. There are perfect spikes, representing each of your frequencies and DC offset.

  
  


• 
  

  We can also observe the FFT noise at the very bottom.

  
  


• 
  

  For $N=10000$ the shape of $\mathrm{sinc}$ function is clearly visible.

  
  
  

---

And obviously the code to reproduce the results:

Fs=1000; 
Ns=500;
Ns2=1000;
Ns3=10000;
t=0:1/Fs:(Ns-1)*1/Fs;
f1=10;

f2=400;
x=5+5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t);

X1 = abs(fft(x))/length(x);
X2 = abs(fft(x, Ns2))/Ns;
X3 = abs(fft(x, Ns3))/Ns;

F1 = 0:Fs/Ns:Fs-Fs/Ns;
F2 = 0:Fs/Ns2:Fs-Fs/Ns2;
F3 = 0:Fs/Ns3:Fs-Fs/Ns3;


plot(F1, 20*log10(X1))
hold on
plot(F2, 20*log10(X2))
plot(F3, 20*log10(X3))
xlim([0, Fs/2])
grid on
legend({'N=500', 'N=1000', 'N=10000'})

dft - Digital filter selection for sensor

I am having a LM35 sensor which gives $10\textrm{ mV}$ signal per degree rise of temperature. Now I have one question, which digital filter will be the best for this ?

This sensor will be use in very noisy industrial environment. Also digital filter have some cutoff frequency what should be the cutoff frequency set for this filter ? As signal coming from sensor is an analog signal but not a periodic frequency signal.

One I know is FIR Moving average filer. This takes the mean of previous samples. This I do not want to use as I have used it before, $$ \frac 1N\sum_{n=0}^{N-1}x[k-n] $$

If I am right then DFT is not required as I am not interested in the spectrum analysis of the signal coming from LM35 sensor.

Is there any other DSP digital filter which I can use ?

torah study - Proper Way of Learning Jewish Mysticism

I have been very much interested in learning the core teachings of mysticism since I was a young boy. I didn't know that it was called Jewish mysticism but nonetheless I was attracted to its beliefs with the books and symbols I have been acquainted with from some folks who, I believe, were deeply associated with it.

Please tell me, how and where should I start? Am I even allowed to study it? If I am, am I allowed to pursue this knowledge on my own do I have to to have a "guide" with me?

solubility - Is there any substance that is liquid at room temperature and pressure that doesn't contain H as one it's constituents apart from mercury?

I want to know if there's any substance that is liquid at room temperature and atmospheric pressure that doesn't contain HYDROGEN atom(s) in its make up. Any substance dissolved in water or any substance that contains HYDROGEN is not required

product recommendation - Do Tefilin need to be painted with "special" ink?

When painting tefillin, are there any requirements regarding the ink (other than the need to be black)? Or is any ink okay to use?

Like in the comments to this answer, shoe polish is recommended. Is that indeed correct?

Answer

Keset HaSofer 21:14 rules that you can't put ground ivory into the tefillin paint as it is not from a kosher animal (an elephant). Accordingly, it would seem that one would need to make sure to use paint that has a certification ensuring that all ingredients are from kosher species.

everyday chemistry - Why does hot oil fry things, but hot water does not?

When a slice of potato is dropped into hot oil, it gets fried but the same in hot water, gets ‘cooked’. What is it about oil that gives the slice of potato the crispy feature while water only makes it soft?

Answer

Oil can get hotter than the b.p. of water, 373 K.

The browning (decomposition) of starches proceeds very slowly (perhaps years for a noticeable change) at 373 K. In addition, the water in the potato will not evaporate away, since the potato is in water (not the water vapor above the liquid, which can be hotter than 373 K). Since the cooking oil is hotter (e.g. 440 K), starch decomposes (caramelizes) in a few minutes, and dehydration makes the chip crunchy. Bon appétit!

halacha - When asking for personal requests in Shemoneh Esrei, how should one phrase them?

The Shulchan Aruch (OC 119:1) rules that one may add to a middle Brachah (i.e. from Atah Chonein to Shema Koleinu, inclusive) of Shemoneh Esrei a personal request on the topic; for instance, if one wishes to daven for a sick person, he may include it at the end of Refa’einu. In Shema Koleinu, one may add any requests he has. The Rema holds that one may only add to the end of a Bracha. The Shulchan Aruch quotes Rabbeinu Yonah that one who davens for many people should phrase his request in the plural, and one who davens for an individual should phrase his request in the singular, though if one adds to Shema Koleinu or the end of Shemoneh Esrei, he can phrase it however he wishes.

Other than those brief statements there (which is all the Shulchan Aruch quotes on the topic), how should one phrase it? If one is davening in Hebrew, should he add his requests in Hebrew as well? If one is davening for himself, should he just refer to himself in the first person, or should he use his full name (ben/bas mother’s name)? Does it even matter?

Answer

You can pray in the language which is easiest for you and do not need the full name of the person.

R Heshy Kleinman in Praying with fire (p. 209) writes

All of these [personal prayer] requests can even be made in the person's own language if he has difficulty reciting them in Hebrew.

He then quotes the Chaye Adam (quoted by Mishna Brura 122:8) on the importance of adding personal requests to Elokai Netzor

It is appropriate and worthwhile for every person to pray each day specifically for his own financial needs, and other practical part of life, and that his children should be Torah scholars and that all his descendants should be God fearing people... And if he cannot phrase these thoughts in the Hebrew language of prayer, let him say his thoughts in his own language as long as they come from the depths of his heart.

See also SA OC 101:4.

---

I saw in another sefer (but couldn't find it now) that a prayer should be phrased starting with "May it be Your will that". I found a proof to that in the prayer composed by the Chazon Ish (Kovetz Igrot Chazon Ish 1:74) for the success of a child in Torah study

May it be Your will, our God and the God of our fathers, that you have mercy on my child (name and the mother's name) and turn his heart to love and fear Your Name and to dedicate himself to the study of our Holy Torah; and remove all the factors which prevent him from Torah study, and prepare all the factors which will bring him closer to learning your holy Torah.

In that same sefer, it said one can pray for himself by saying "May it be your will that you help me etc." without using one's full name. This is similar to how one can pray in presence of a sick person without using his full name.

control systems - Iterative Blind Sinus Signal Suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has unknown $A$ and $p$, but they are constant in the time of observation (for simplicity only, actually they aren't). The second signal is under control. We only have it's difference $x(t) = s_1(t)-s_2(t)$. Some iterative algorithm is needed to minimize power of $x(t)$. So $x(t)$ is available input and $A_2(t)$, $p_2(t)$ are parameters under control.

The question is: is it some robust and rapid algorithm for jointly control both amplitude and phase to minimize power of $x(t)$? My idea was to implement complex gradient method: phase and amplitude at each step are represented as a complex number $C(t)$. Signal $s_2(t)$ can be set as $Re[C(t) exp(iwt)]$. But I can't understand how to define cost function and gradient in this case and also this approach seems to be computationally redundant. Any ideas?

Thanks in advance!

Answer

I assume you do everything in discrete time. If I understood correctly then the observed signal is

$$x(n)=s(n)-A\sin(\omega_0n+\phi)$$

where $s(n)$ is a sinusoidal signal with frequency $\omega_0$ and unknown amplitude and phase. The parameters $A$ and $\phi$ are to be optimized such that the power of $x(n)$ is minimized. In a real-time algorithm you can define the cost function as the sum of $x^2(n)$ over a fixed length $N$:

$$F(A,\phi,n)=\sum_{k=n-N+1}^{n}x^2(k)$$

where $n$ is the current sample. For a steepest descent algorithm you need the gradient:

$$\frac{\partial F}{\partial A}=-2\sum_{k=n-N+1}^{n}x(k)\sin(\omega_0k+\phi)\\ \frac{\partial F}{\partial \phi}=-2A\sum_{k=n-N+1}^{n}x(k)\cos(\omega_0k+\phi)$$

The parameters are now updated in the following way:

$$A_n=A_{n-1}-\mu\frac{\partial F_{n-1}}{\partial A}\\ \phi_n=\phi_{n-1}-\mu\frac{\partial F_{n-1}}{\partial \phi}$$

where $\mu$ is the step size. Note that in every iteration you need to recompute the gradients with the current values of $A$ and $\phi$.

The figure below is a simulation of this gradient algorithm with the unknown signal $s(n)=2\sin(\pi n/3+\pi/2)$, $N=50$, $\mu=0.01$, and with zero initialization of both amplitude and phase (amplitude $A$ in blue, phase $\phi$ in green).

inorganic chemistry - How did hypophosphoric acid get its name?

Why does hypophosphoric acid has a strange name? My knowledge of inorganic nomenclature tells me that the prefix "per-" should be used with "-ic" acids and the prefix "hypo-" goes with "-ous" acids, which isn't the case here. Why is this so?

Just as part of an additional observation, two other things which I find strange about $\ce{H4P2O6}$ are:

• I think this is the only oxy-acid of phosphorus having a $\ce{P-P}$ bond.


• It has phosphorus in $+4$ oxidation state.

Answer

You are most of the way to the reason yourself:

$$\begin{array}{|c|c|c|}\hline \text{name} & \text{formula} & \text{oxidation number of P}\\ \hline \text{phosphoric} & \ce{H3PO4} & +5\\ \text{phosphorous} & \ce{H3PO3} & +3\\ \text{hypophosphorous} & \ce{H3PO2} & +1\\ \hline \end{array}$$

The "hypo-" prefix means "beneath" or "less than". Hypophosphoric acid, $\ce{H4P2O6}$, has oxidation number of phosphorous as +4, which is in between phosphoric acid and phosphorous acid. Thus, "hypophosphoric" refers to "beneath" phosphoric (but above phosphorous) acid.

fourier transform - redundancy of sin and cos waves with real data

I have the following question. Isn't it true that when applying a fourier transform to a real function (i.e. computing a characteristic function for a density), we only ever need one of the two waves: sin or cosin, to capture it's behavior.

I did a numerical exercise of moving back and forth between a probability density and a characteristic function, and every time it seems like either of the two waves is enough. Here are the waves: Here are the original real data histogram (yellow), estimated smooth density (red) and the same density reconstructed separately from the sin (green) and cosine (blue) waves of it's own characteristic function.

Maybe for the complex input, the two waves are really necessary, but there is clearly some redundancy when the input is real.

Has anyone seen this before?

halacha - Saying kaddish when davening in a minyan that isn't your nusach

I have been to many minyanim where people are saying kaddish of a variety of nuschaot. What should one do with regards to this?

Some examples: In a sephardi minyan, should an ashkenazi person remain silent for those parts of kaddish that a sephardi person would say? Conversely should a sephardi person assert his nusach of kaddish by quickly adding the additional parts that he would say if he is in an ashkenazi minyan?

Does it make a difference that it is 'easier' for an ashkenazi person to remain silent for parts of kaddish in a sephardi minyan in comparison with a sephardi person adding extra words within an ashkenazi kaddish?

Additionally, if you are in a non-nusach-specific minyan, what is the ideal way to say kaddish with other people who are saying it with a different nusach to you?

Why is fluoroantimonic acid so strong?

I learned that all strong acids have a 100% degree of ionization and that there are no degrees of strength in acids; however, I also read that fluoroantimonic acid is 20 quintillion times stronger than 100% sulfuric acid !!

Can you please explain the chemistry behind this?

Answer

For many common purposes we say there's weak acids and strong acids, and define strong acids to be ones that dissociate completely in water. This is because if the acid dissociates completely in water, then every proton dissociated will just protonate water, and turn it into $\ce{H_3O^+}$ (hydronium ion). The hydronium ion is the strongest acid that can exist in water as far as I understand, and hence why strong acids are simply strong acids in some contexts.

What you're describing is a super acid, that is not used in aqueous solution Take HCl for example. This is a classic strong acid, that will protonate a wide range of structures. But if we take something that is a VERY, VERY poor base (something that really does not want a proton), such as an alkane, HCl can't protonate it. The proton will rather stay with chlorine than protonate the alkane. That is one of the things you can do with the acid you mentioned.

The strength of an acid depends on many different factors, but it all comes down to how strongly the $\ce{H^+}$ is bound to the acid structure. If it is very loosely bound, the structure is high in energy, and the proton would like to find a more stable structure to partake in. In this case protonating an alkane to form a carbocation and molecular hydrogen is low enough in energy, that the acid can protonate it.

But remember that protonation is an equilibrium. If we achieve a vastly lower energy state by having the acid protonate another structure, then the protonation will be complete. If it is the same energy, half of the acid will have protonated (assuming equal concentrations of acid and base).

wedding - Why does the bride circle the groom in a counter-clockwise direction?

At a wedding, the groom is facing the audience. When the bride comes to the chuppah she begins to circle to her right as he is facing the groom, and circles first behind the groom proceeding in a counter-clockwise direction (beginning the circling leftward.)

This is what I've seen at every wedding. I assume that there is some halachic principle that the bride should start to her right, when she is facing the groom. But, I don't know its source, or if this is a halacha or minhag.

If a wedding is in Australia, does she circle in the opposite direction?

Answer

The idea of circling counter-clockwise, which is moving to the right, follows the avodah of the Kohanim in the Temple.Like is found in Mishnah Torah, Hilchot Beit HaBechirah 7:3.

וְכָל הַנִּכְנָסִין לְהַר הַבַּיִת נִכְנָסִין דֶּרֶךְ יָמִין וּמַקִּיפִין וְיוֹצְאִין דֶּרֶךְ שְׂמֹאל חוּץ מִמִּי שֶׁאֵרְעוֹ דָּבָר שֶׁהוּא מַקִּיף עַל הַשְּׂמֹאל. לְפִיכָךְ הָיוּ שׁוֹאֲלִין לוֹ מַה לְּךָ מַקִּיף עַל הַשְּׂמֹאל. שֶׁאֲנִי אָבֵל. הַשּׁוֹכֵן בַּבַּיִת הַזֶּה יְנַחֶמְךָ. שֶׁאֲנִי מְנֻדֶּה. הַשּׁוֹכֵן בַּבַּיִת הַזֶּה יִתֵּן בִּלְבָבְךָ וְתִשְׁמַע לְדִבְרֵי חֲבֵרֶיךָ וִיקָרְבוּךָ:

This is a general practice which is seen in many different cases, like for example when one is called to the Torah reading like is found in Shulchan Aruch, Orach Chaim 141:7.

הָעוֹלֶה לְמִגְדָּל, עוֹלֶה בְּפֶתַח שֶׁהוּא לוֹ בְּדֶרֶךְ קְצָרָה מִמְּקוֹמוֹ וְיֵרֵד מֵהַמִּגְדָּל בְּדֶרֶךְ אַחֵר, שֶׁהוּא לוֹ בְּדֶרֶךְ אֲרֻכָּה עַד מְקוֹמוֹ; וְאִם ב' הַדְּרָכִים שָׁוִים, עוֹלֶה בַּפֶּתַח שֶׁהוּא לוֹ בְּדֶרֶךְ יָמִין, וְיוֹרֵד בַּפֶּתַח שֶׁכְּנֶגְדּוֹ.

And the comment of the Mishnah Berurah there, note 24:

(כד) עולה בפתח וכו' - כדאמרינן בעלמא כל פינות שאתה פונה לא יהא אלא דרך ימין:

When one is called, one approaches from the right, it is a sign of joy and kindness like is mentioned at the end of the Why paragraph at this link from Chabad. If one approached clockwise, meaning from the left, it is a sign of mourning and judgement.

The same principle applies with the circling of the bride under the Chuppah.

Regarding your final question pertaining to Australia, no, you do not approach from the left in the southern hemisphere.

Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It strikes me that this should be a text book example of a simple linear Kalman filter, but I can't seem to find any online links which discuss this. I can think of various ways of doing this, but rather than researching it from scratch, perhaps someone here can point me in the right direction:

1. Does anyone know the best way of setting up this system? For example, given the recent history of position observations, what's the best way of predicting the next point in the Kalman filter state space? What are the advantages and disadvantages of including acceleration in the state space? If all measurements are position, then if speed and acceleration are in the state space can the system become unstable? Etc ...


2. Alternatively, does anyone know of a good reference for this application of Kalman filters?

Thanks

Answer

This is the best one that I know of

Full derivation with explanation

Kalman

This is a good resource for learning about the Kalman filter. If you are more concerned with getting the smartphone app working I would suggest looking for a pre-existing implementation of the Kalman filter. Why reinvent the wheel? For example if you are developing for android, openCV has an implementation of the Kalman filter. See Android OpenCV

Bradski and Kaehler is a good resource on image processing in general and includes a section on the Kalman filter including code examples.

halacha - How is one allowed to live in Israel?

When Yehoshua came to Israel, he conquered it and divided it among the Jews. This land belongs to them and their descendants.

When the Jews were exiled many years later and came back (by the 2nd Beis Hamikdash), how were they allowed to live in any part of Israel? Land isn't stealable, and the land still "belonged" to the original owner.

Moreover, even if there was some kind of takana then (as there was a full Sanhedrin, prophets, etc.) how would Jews be allowed to move to Israel later on (say in the time of the Rishonim until now)? It could have had owners in the past?

Even if one can say that "Hamotzei Mechaveiro Alav Haraya", it still doesn't answer how can one lechatchila live in a place which he knows is definitely not his.

How does buying my house from the state (or JNF, or whoever owns the "unused land") affect acquisition from its original owners?

Plain form as imperative

Is the plain form ever used to give a command? What does "sugu ni tatsu" mean?

Answer

Yes, 終止形 can be used as a command like in this manga. Translation: "Then stand up right away!"

It sounds like parents or school teachers ordering their kids to do something right away. It's weaker/friendlier than 「立て」 but stronger than 「立って下さい」.

I believe such use of 終止形 is not usually heard in military organizations, so the right person sounds rather friendly than dignified as a supervisor.

Negative form is also possible. Example: 「(教室で先生が)そこ、喋らない！」「ごちゃごちゃ反論しない！」）

nomenclature - What does β stand for in β-potassium zirconate?

What do the Greek letters (α, β, γ...) convey when they are prefixed to a crystalline substance?

For example: β-potassium zirconate

halacha - Have women accepted Zachor on themselves?

Women are exempt from hearing shofar, but some hold they've accepted it upon themselves and are, for that reason, now required to hear it.

There is a dispute whether women are required to read/hear parashas Zachor, but the common practice nowadays is that they do so. I wonder whether anyone has argued that they have accepted it upon themselves and are for that reason now required to do so. Any authoritative source to that effect would be valuable, as would any authoritative source that specifically debunks the notion.

word choice - When is it appropriate to refer to yourself by これ?

I have occasionally heard and read instances, where a person has referred to themselves as これ. My Japanese dictionary also lists "Me, I." as a definition of これ.

Now, this obviously isn't used as frequently as 私, 僕, etc., so it makes me wonder: When can it be used to refer to one's self? and Does it have any extra or particular meaning as such?

Thanks! :)

Answer

To add a little bit more to what YOU said in his answer: in some Classical Japanese texts これ was indeed used as a first (and also second) person pronoun. It's not the most common first person pronoun in Classical Japanese (that would probably be われ), but it's a possible use, so maybe that's where your dictionary got that from.

The quote from 枕草子 (The Pillow Book) YOU referred to is probably the one which shows up in Daijirin:

殿上人なども「なほこれ一人は」などのたまふを

Don't ask me to translate that though. :)

inorganic chemistry - Reaction of borax with NaOH

How does borax react with NaOH? My textbook says that sodium peroxoborate is formed. I couldn't find the reaction anywhere else. Can anyone verify as well as explain it?

Answer

The following reaction schemes are adapted from [1, pp. 76–77]. Amorphous borax $\ce{Na2B4O7}$ forms tetrahydroxoborate in concentrated sodium hydroxide solution:

$$\ce{Na2B4O7 + 7 H2O + 2 NaOH → 4 Na[B(OH)4]}$$

Upon fusion sodium metaborate is formed:

$$\ce{Na2B4O7 + 2 NaOH →[\pu{700-750 °C}] 4 NaBO2 + H2O}$$

In order to form peroxoborate, a peroxide should be introduced in the first place, e.g. by using hydrogen peroxide (see also Preparation of Sodium Peroxoborate):

$$\ce{Na2B4O7 + 2 NaOH + 4 H2O2 + 11 H2O → 2 Na2[B2(O2)2(OH)4] * 6H2O}$$

References

1. R. A. Lidin, V. A. Molochko, and L. L. Andreeva, Reactivity of Inorganic Substances, 3rd ed.; Khimia: Moscow, 2000. (in Russian)

fft - Why do we say that "zero-padding doesn't really increase frequency resolution"

Here is a sinusoid of frequency f = 236.4 Hz (it is 10 milliseconds long; it has N=441 points at sampling rate fs=44100Hz) and its DFT, without zero-padding :

The only conclusion we can give by looking at the DFT is: "The frequency is approximatively 200Hz".

Here is the signal and its DFT, with a large zero-padding :

Now we can give a much more precise conclusion : "By looking carefully at the maximum of the spectrum, I can estimate the frequency 236Hz" (I zoomed and found the maximum is near 236).

My question is : why do we say that "zero-padding doesn't increase resolution" ? (I have seen this sentence very often, then they say "it only adds interpolation")

=> With my example, zero-padding helped me to find the right frequency with a more precise resolution !

Answer

Resolution has a very specific definition in this context. It refers to your ability to resolve two separate tones at nearby frequencies. You have increased the sample rate of your spectrum estimate, but you haven't gained any ability to discriminate between two tones that might be at, for instance, 236 Hz and 237 Hz. Instead, they will "melt together" into a single blob, no matter how much zero-padding you apply.

The solution to increasing resolution is to observe the signal for a longer time period, then use a larger DFT. This will result in main lobes whose width are inversely proportional to the DFT size, so if you observe for long enough, you can actually resolve the frequencies of multiple tones that are nearby one another.

--

To see how this plays out, here's a plot of the zoomed-in FFT of the addition of two signals: your original sinusoid, and one that differs in frequency from it by 0 to 100 Hz.

It's only towards the 100Hz difference end of the plot (left-hand side here) that you can distinguish (resolve) the two.

Scilab code for generating the plot below.

f = 236.4;
d = 10;
N=441;
fs=44100;
extra_padding = 10000; 


t=[0:1/fs:(d/1000-1/fs)]
ff = [0:(N+extra_padding-1)]*fs/(N+extra_padding);

x = sin(2*%pi*f*t);

XX = [];

for delta_f = [0:100];
    y = sin(2*%pi*(f+delta_f)*t);
    FFTX = abs(fft([x+y zeros(1,extra_padding)]));

    XX = [XX; FFTX];
end

mtlb_axis([0 1300 0 500])

figure(1);
clf
[XXX,YYY] = meshgrid(ff,0:100);
mesh(XXX(1:100,[50:90]),YYY(1:100,[50:90]),XX(1:100,[50:90]))