Monday, April 30, 2018

grammar - Saying "try" in Japanese


There appear to be multiple ways in Japanese that would translate to "try" in English. These are:



Verb + te miru


Tamesu (verb)


Kokoromiru (verb)


Verb + to suru


What is the difference between these?




grammar - What is the role of あるいて?



駅からは歩いて十分ぐらいです。
It takes 10 minutes on foot from the station.




The confusing part is the 歩いて.
Is あるいて a noun? What is its role?



Answer



歩いて is the te-form of the verb 歩く, and means "on foot". Of course the te-form usually connects to another verb, but the te-form of some words (seem to) have idiomatic usage which can be used on its own. (As a native speaker I haven't learned Japanese grammar systematically, so I may be wrong...)



  • もって3日だ。 (Someone can bare/survive) for three days at most.
    (This もって is the te-form of 持つ or 保つ in this sense, and used idiomatically to mean "even if one hangs on")

  • まして let alone / not to mention

  • 従って therefore



In the case of 歩いて, I think you can also think 行くと or 行けば is omitted after 歩いて (i.e., 歩いて行くと10分です).


hebrew - Meaning of abbreviation tblch"t / tblch"a


What do these abbreviations stand for? I have seen them beside the names of righteous females. Does it mean that she should have long life? What is the equivalent for males?



Answer



See p. 322 of this Google book. The Hebrew abbrevaiation is יבדל"א for males and תבדל"א for females.


Loose transliteration - TiBadel/YiBadel Lecha'im Arukhim meaning "May s/he live long, on the contrary".


The alternate version you mentioned (tblch"t) stands for the same, except that Arukhim is switched with Tovim, meaning "good life."


The expression is used when referring to a living male or female in the context of mentioning a deceased person. For example, at a speech, one might say, "We recall Aunt Esther, aleha Hashalom (peace be upon her). And we are thrilled to see Grandma Royza, tibadel lechaim Arukhim with us, here, today."


tefilla - Recommended changes to the text of selichos when you say them at the "wrong" time


Some of the piyutim in selichos assume that you're saying them at the ideal time - before Amud Hashachar (for example, at the end of selicha #70 שחרנוך קדם עמוד השחר). Many people don't make it at that time, and there are minyanim from the very bedieved 10PM until as late as 9AM. I've heard that R' Ovadya even suggested saying them before mincha if no time in the morning works, though I've never seen a minyan that does that.


A similar issue comes up during Neilah, with the line היום יפנה השמש יבא ויפנה. The Taz, Mishna Berurah, and others just say you should make sure to say it before sunset, but the Mattei Efrayim and Kaf Hachayim recommend that if you say it too late you should change the text to היום פנה השמש בא ופנה.


Is there a list anywhere of recommended changes to the selichos when saying them at a non-optimal time? It's very hard to come up with these on the fly.


The ideal list would:




  • preserve the rhyme scheme, rhythm, acrostic, etc.

  • give different options for 10PM, 6AM, 9AM, 5PM, etc. where that's relevant. (For example at 6AM in many places you could reasonably say שחרנוך עם עמוד השחר, like I did this morning, but that doesn't work at 9.)


but even a list of lines where this problem is relevant would be helpful so that I'm not caught off guard.


For me personally a list based on Artscroll's version of Minhag Lita would be best, but lists for other minhagim are welcome.




everyday chemistry - How to dissolve candle wax (paraffin)?


Wikipedia states that waxes can be dissolved by non-polar organic solvents.


I failed to dissolve candle wax in both acetone and ethanol, which are the only organic solvents I have at home.


I have some clothes with wax stuck on them. How can I dissolve the wax and drive it away without damaging my clothing?



Answer



Ethanol and acetone are not non-polar organic solvents. Each one has a slight dipole moment; due to the difference of electronegativity between $\ce{H}$ and $\ce{O}$ in ethanol and between $\ce{C}$ and $\ce{O}$ in acetone. Wax is composed of heavy, long-chain alkanes. And as "Like dissolves like" try to dissolve your wax in toluene or in xylene.



equilibrium - Why is the Haber process carried out at such high temperatures?


On a large scale, ammonia is prepared via the Haber process:


$$\ce{N2(g) + 3H2(g)->2NH3(g)} \qquad \Delta _\mathrm{f}H^\circ = -46.1~\mathrm{kJ \cdot mol^{-1}}$$


The optimum conditions for the productions of ammonia are a pressure of $200~\mathrm{atm}$ and a temperature of about $700~\mathrm{K}$.


The process obviously is exothermic and $700~\mathrm{K}$ is, by no means, a low temperature. Shouldn't the temperature be much lower for optimum production of ammonia?



Answer



As others have pointed out, it is purely kinetics, but you may still wonder, why.


For a reaction to actually occur (in both directions) and thus for an equilibrium to be reached, you need to overcome the activation energy. In the case of the Haber-Bosch process, this involves breaking the highly stable $\ce{N#N}$ triple bond. Even with the catalysts used, the energy required to break apart $\ce{N2}$ is still enormous. Therefore, a lower temperature may give a better yield of ammonia theoretically (i.e. based on equilibrium and Le Châtelier considerations) but the reaction speed would be a lot slower.


Even if you consider a batch-wise process of generating ammonia (which, as orthocresol points out, isn’t the case), it is more efficient to run two batches in half the time for two sets of $15~\%$ than to run a single batch for twice the time to get an overall yield of maybe (note: This yield is a ballpark estimate) $25~\%$ — with a batch size where $1~\%$ yield is equivalent to $100~\mathrm{kg}~\ce{NH3}$, two runs at higher temperature give $3~\mathrm{t}\ \ce{NH3}$ and one run at lower temperature $2.5~\mathrm{t}\ \ce{NH3}$ in the same time frame.


parshanut torah comment - Why the Heel of the foot? (Parshas Ekev)


Parshas Ekev starts off



וְהָיָה עֵקֶב תִּשְׁמְעוּן אֵת הַמִּשְׁפָּטִים




Rashi says on this:



אם המצות הקלות שאדם דש בעקביו תשמעון:



What is the significance of the so called lite Mitzvos which people trample with there feet?



Answer



The Gemara in Avodah Zara(ב, ב) says that in the Future the gentiles will have a complaint to Hashem we would have accepted the Torah too for the Jews you held Har Sinai over their heads if you would have done it to us we would of also accepted. Hashem hears there complaint and Gives them one LITE Mitzvah the Mitzvah of Sukkah. Hashem takes out the sun and makes it extremely hot they go out and Kick the Sukkah and leave. Now we know why it is all dependant on Lite mitzvah which people trample with their feet as this is the test the gentiles will fail when Mosicach Comes and they have their complaint hence עֵקֶב תִּשְׁמְעוּן the Mitzvah people are דש בעקביו.


halacha - Gentile living with a Jewish flatmate


I've been talking with someone about possibly moving in to a room in her house later in the year. Her kitchen is kosher and her house is shomer Shabbos, but since I'm used to spending Shabbos in Jewish homes and also I mostly buy raw non-animal products to eat or cook with... it wouldn't really be an adjustment for me anyway. I'd just like an idea about what other issues might be relevant to ask about or think about. Obviously this question is practically relevant to me, but I'm only asking so I have a better idea about the topic. No doubt she will ask for the relevant information herself, and there are rabbis I can ask my own questions from. But do any of you have personal experience in this area? Or do you have any thoughts? I guess that some of the considerations will also be around holidays, like Pesach.


Thanks :)



Answer




I go to college and lived with a gentile roommate last semester, and I wish I had someone as considerate; but, let's get started. Obviously make sure to be considerate on Shabbat by leaving the bathroom light on and avoiding any sort of problem that must be solved by breaking one of the Shabbat rules. For example, don't leave something of importance that she might need on Shabbat outside the house if there is no eruv, because for her to bring something from outside back in would violate the prohibition of transferring in between domains. Another foreseeable scenario is if you lock the front door on Shabbat when she might leave it unlocked during Shabbat so that she doesn't need to carry a key. I'm not very creative with these sorts of scenarios, so make sure to ask your Jewish friend if you ever have a concern.


I'm assuming your friend is also shomer negiah and follows the rules of yichud so avoid bringing in male friends or at least ask for the house to yourself if you really need a male buddy to come on over; and, make sure your male friend (if the situation ever comes about) knows not to hug/touch your Jewish friend. I'm not saying you have to obey yichud or be shomer negiah, but having male guests can create a problem for your female friend. It's very awkward watching my roommate cop a feel from his girlfriend when I'm davening only a few feet from him. This isn't as much of a problem if your friend has a husband or male relative living in the house as well, but better safe than sorry.


As for pesach, avoid bringing in any leavened breads into the home, and if your friend abstains from kitniyot, then avoid bringing in those foods as well. Chametz must be removed from the home before Pesach and cannot be introduced into the room until after the holiday is over. As for kitniyot, there is no prohibition, as far as I understand it, of having it within the home; but, I don't know what your Jewish friend's preferences. It's better to ask or just play it safe.


Cooking is also a very complicated question. I'm not sure if she double-wraps or if her home has separate ovens for meat and dairy, so ask her about cooking. Maybe she wants you to use your own kitchenware, maybe she wants you to use a specific sink to wash your kitchenware, maybe she wants you to use her kitchenware and be aware of which is for meat and which is for dairy. Either way, this is a very complicated question and all I can recommend is that you ask her about that. As for your question about your kitchenware un-koshering other kitchenware, I'll explain the problem (or lack thereof) and the solution. In halacha for kosher, at least for meat and dairy, taste is principle (Yoma 73b; Yoma 80a). You transfer the taste by washing and cooking the kitchenware to cook meat and dairy, but this can be more technically explained here. You can (according to law, not according to the rules of the household) use kosher kitchenware that the family uses as long as you do not prepare anything fit for a king's table (or anything else not kosher, of course). The reasoning for this is that if you prepare food that is bishul akum, then the utensils are now not kosher. That's why there's an advantage to you having your own kitchenware, but then there's a load of questions with whether or not you're using her oven, if you're cleaning in her sink, et cetera. I don't feel comfortable enough in this area to discuss it in detail, so ask her or a rabbi for more information on this subject.


Avoid playing music in the house during the Counting of the Omer and during certain holidays and periods of times (like the Three Weeks and the 9 Days). She might not even consider it a prohibition to listen to recorded music, but it's better to ask than assume. If you really need to listen to music, get a pair of headphones.


Besides that, you should be okay. Maybe there are some female oriented concerns for Jewish life that I'm not looking at, but I'm not very well versed in any of that. Be considerate, be nice, have a good relationship with your friend and reach an understanding between the two of you. I wish you the best of luck.


Detecting direction of sound using several microphones


First of all, I've seen a similar thread, however it's a bit different to what I'm trying to achieve. I am constructing a robot which will follow the person who calls it. My idea is to use 3 or 4 microphones - i.e. in the following arrangement in order to determine the from which direction the robot was called:


enter image description here


Where S is source, A, B and C are microphones. The idea is to calculate phase correlation of signals recorded from pairs AB, AC, BC and based on that construct a vector that will point at the source using a kind of triangulation. The system does not even have to work in real time because it will be voice activated - signals from all the microphones will be recorded simultaneously, voice will be sampled from only one microphone and if it fits the voice signature, phase correlation will be computed from the last fraction of second in order to compute the direction. I am aware that this might not work too well i.e. when the robot is called from another room or when there are multiple reflections.



This is just an idea I had, but I have never attempted anything like this and I have several questions before I construct the actual hardware that will do the job:



  1. Is this a typical way of doing this? (i.e. used in phones for noise cancellation?) What are other possible approaches?

  2. Can phase correlation be calculated between 3 sources simultaneously somehow? (i.e. in order to speed up the computation)

  3. Is 22khz sample rate and 12bit depth sufficient for this system? I am especially concerned about the bit depth.

  4. Should the microphones be placed in separate tubes in order to improve separation?



Answer



To extend Müller's answer,





  1. Should the microphones be placed in separate tubes in order to improve separation?




  1. No, you are trying to identify the direction of the source, adding tubes will only make the sound bounce inside the tube which is definitely not wanted.

    The best course of action would be to make them face straight up, this way they will all receive similar sound and the only thing that is unique about them are their physical placements which will directly affect the phase. A 6 kHz sine wave has a wavelength of $\frac{\text{speed of sound}}{\text{sound frequency}}=\frac{343\text{ m/s}}{6\text{ kHz}}=5.71\text{ mm}$. So if you want to uniquely identify the phases of sine waves up to 6 kHz, which are the typical frequencies for human talking, then you should space the microphones at most 5.71 mm apart. Here is one item that has a diameter that is less than 5.71 mm. Don't forget to add a low pass filter with a cut-off frequency at around 6-10 kHz.





Edit


I felt that this #2 question looked fun so I decided to try to solve it on my own.





  1. Can phase correlation be calculated between 3 sources simultaneously somehow? (i.e. in order to speed up the computation)



If you know your linear algebra, then you can imagine that you have placed the microphones in a triangle where each microphone is 4 mm away from each other making each interior angles $60°$.


So let's assume they are in this configuration:


       C
/ \
/ \

/ \
/ \
/ \
A - - - - - B

I will...



  • use the nomenclature $\overline{AB}$ which is a vector pointing from $A$ to $B$

  • call $A$ my origin

  • write all numbers in mm


  • use 3D math but end up with a 2D direction

  • set the vertical position of the microphones to their actual wave form. So these equations are based on a sound wave that looks something like this.

  • Calculate the cross product of these microphones based on their position and waveform, then ignore the height information from this cross product and use arctan to come up with the actual direction of the source.

  • call $a$ the output of the microphone at position $A$, call $b$ the output of the microphone at position $B$, call $c$ the output of the microphone at position $C$


So the following things are true:



  • $A=(0,0,a)$

  • $B=(4,0,b)$

  • $C=(2,\sqrt{4^2-2^2}=2\sqrt{3},c)$



This gives us:



  • $\overline{AB} = (4,0,a-b)$

  • $\overline{AC} = (2,2\sqrt{3},a-c)$


And the cross product is simply $\overline{AB}×\overline{AC}$


$$ \begin{align} \overline{AB}×\overline{AC}&= \begin{pmatrix} 4\\ 0\\ a-b\\ \end{pmatrix} × \begin{pmatrix} 2\\ 2\sqrt{3}\\ a-c\\ \end{pmatrix}\\\\ &=\begin{pmatrix} 0\cdot(a-c)-(a-b)\cdot2\sqrt{3}\\ (a-b)\cdot2-4\cdot(a-c)\\ 4\cdot2\sqrt{3}-0\cdot2\\ \end{pmatrix}\\\\ &=\begin{pmatrix} 2\sqrt{3}(b-a)\\ -2a-2b-4c\\ 8\sqrt{3}\\ \end{pmatrix} \end{align} $$


The Z information, $8\sqrt{3}$ is just junk, zero interest to us. As the input signals are changing, the cross vector will swing back and forth towards the source. So half of the time it will point straight to the source (ignoring reflections and other parasitics). And the other half of the time it will point 180 degrees away from the source.


What I'm talking about is the $\arctan(\frac{-2a-2b-4c}{2\sqrt{3}(b-a)})$ which can be simplified to $\arctan(\frac{a+b+2c}{\sqrt{3}(a-b)})$, and then turn the radians into degrees.



So what you end up with is the following equation:


$$\arctan\Biggl(\frac{a+b+2c}{\sqrt{3}(a-b)}\Biggr)\frac{180}{\pi}$$




But half the time the information is literally 100% wrong, so how.. should one.... make it right 100% of the time?


Well if $a$ is leading $b$, then the source can't be closer to B.


In other words, just make something simple like this:


source_direction=atan2(a+b+2c,\sqrt{3}*(a-b))*180/pi;
if(a>b){
if(b>c){//a>b>c
possible_center_direction=240; //A is closest, then B, last C

}else if(a>c){//a>c>b
possible_center_direction=180; //A is closest, then C last B
}else{//c>a>b
possible_center_direction=120; //C is closest, then A last B
}
}else{
if(c>b){//c>b>a
possible_center_direction=60; //C is closest, then B, last A
}else if(a>c){//b>a>c
possible_center_direction=300; //B is closest, then A, last C

}else{//b>c>a
possible_center_direction=0; //B is closest, then C, last A
}
}

//if the source is out of bounds, then rotate it by 180 degrees.
if((possible_center_direction+60) if(source_direction<(possible_center_direction-60)){
source_direction=(source_direction+180)%360;
}

}

And perhaps you only want to react if the sound source is coming from a specific vertical angle, if people talk above the microphones => 0 phase change => do nothing. People talk horizontally next to it => some phase change => react.


$$ \begin{align} |P| &= \sqrt{P_x^2+P_y^2}\\ &= \sqrt{3(a-b)^2+(a+b+2c)^2}\\ \end{align} $$


So you might want to set that threshold to something low, like 0.1 or 0.01. I'm not entirely sure, depends on the volume and frequency and parasitics, test it yourself.


Another reason for when to use the absolute value equation is for zero crossings, there might be a slight moment for when the direction will point in the wrong direction. Though it will only be for 1% of the time, if even that. So you might want to attach a first order LP filter to the direction.


true_true_direction = true_true_direction*0.9+source_direction*0.1;

And if you want to react to a specific volume, then just sum the 3 microphones together and compare that to some trigger value. The mean value of the microphones would be their sum divided by 3, but you don't need to divide by 3 if you increase the trigger value by a factor 3.





I'm having issues with marking the code as C/C#/C++ or JS or any other, so sadly the code will be black on white, against my wishes. Oh well, good luck on your venture. Sounds fun.


Also there is a 50/50 chance that the direction will be 180 away from the source 99% of the time. I'm a master at making such mistakes. A correction for this though would be to just invert the if statements for when 180 degrees should be added.


Sunday, April 29, 2018

Need minyan to answer Kaddish?


While you can't say Kaddish without 10 men present, it's possible that not all of the other men will make the appropriate responses (whether oblivious, ignorant or apathetic). Another case would be where two or more people are saying Kaddish at the same time and part of the audience is responding to one person and part to another.


What does it mean for the effectiveness/validity of the Kaddish if a minyan doesn't answer? If you are certain it will happen should you rather not say it?




Answer



Michael Sandler, you have 2 questions:



  1. Do 10 have to hear kadish? (No)

  2. Do 10 have to say Amen to kadish? (No)


(OK, maybe that progression should have been the other way around.)


A "davar shebekedusha" is a matter that requires a special presence of G-d (from the pasuk of Hashem nitzav ba'adas e-l we learn that this is 10 adult men). Once Hashem's special presence is assumed, the required kaddish may be said regardless of whether people are listening. The Aruch haShulchan (OC 55:12) uses the above idea to justify why one who can speak but not hear may be counted as one of the 10.


In contrast, the Shulchan Aruch (OC 124:4) states that by the leader's repetition of tefila, if 9 are not paying attention, the brachos are almost as if in vain. I would guess this is because kaddish is a requirement even for 1 person, but there is a technicality that it can only be said among 10 (see end of Aruch haShulchan 55:9). The repetition of tefila is created only through having 10 people, so ten congregants have an equal obligation to say the repetition, a requirement fulfilled by the appointed leader- the shatz.


Note that the Shuchan Aruch's requirement by the repetition (124:4) just says they have to pay attention. Saying amen in not a requirement of the congregation, but a personal requirement that when we hear a bracha we should say amen (see Aruch haShulchan 124:11). Even if one is fulfilling his obligation through the bracha and the amen becomes more pertinent, we say shomea k'oneh (listening is like answering).



messiah - What is the connection between Moshiach and Tisha B'Av?


I often see the following from Yerushalmi Berachot cited as a source that Moshiach will be born on Tisha B'Av:



עובדא הוה בחד יהודאי דהוה קאים רדי געת תורתיה קומוי עבר חד ערביי ושמע קלה א"ל בר יודאי בר יודאי שרי תורך ושרי קנקנך דהא חריב בית מוקדשא געת זמן תניינות א"ל בר יודאי בר יודאי קטור תוריך וקטור קנקניך דהא יליד מלכא משיחא




What is the nature of the connection between Tisha B'Av and Moshiach? Are there other sources that discuss this relationship?




halacha - Can a non-Jewish person participate in a bris?


My best friend is Jewish, and I have been involved in most of the most important events in his life. I was the best man at his wedding, I celebrated Hanukkah with his family, and I am the "godfather" of his son (although this last item is purely honorary, and if my friend and his now-ex-wife died, I'm sure he would be adopted by one or the other set of grandparents).


I was asked if I wanted to attend the bris, and even to participate in the ceremony, but I just couldn't bring myself to do it - I'm not especially squeamish, but I think seeing the circumcision taking place would have been too much for me to handle. I politely excused myself from the event.


I'm not sure if it is generally accepted for a non-Jewish person to take part in a bris. My friend is almost totally non-observant (not only does he cover himself in tattoos and eat whatever he wants regardless of kosher laws, he even celebrates Xmas), so I am wondering if his invitation was possible only because he doesn't care about the accepted practice among observant Jews.


Is it acceptable for a non-Jewish person to participate in a bris?



Answer



See this article regarding the ceremony itself. Near the beginning of the article, it states that non-Jews may attend a brit. As a matter of fact, I invited the CEO of my company, a non-Jew to my 1st son's brit. (It was well-worth the gift that he gave, afterwards, but that wasn't my incentive ;-)


As for participating, IIRC, my rav mentioned that there is no problem with a non-Jew being the Kvater - the one who presents the baby coming into the room. (See details on the ceremony). Sometimes this is given to the grandparents, and there have been many cases where the grandparents are not Jewish, but the parents are. The rav could not find any problem with this honor.


I'm not sure if the sandek must be Jewish. Refer to this reference (I'll try to edit in relevant parts from it, later.) Then, again, being a sandek would bring you about as close to the baby as the mohel, and if your squeamish, you're definitely not going to want to be a sandek.



word choice - Is there a rule for when to use くらい vs ぐらい?


I see phrases like 200人ぐらい, 半々ぐらい, and 何分くらい, which seem to indicate that くらい and ぐらい are synonymous, if not interchangeable. Is there any kind of rule for deciding which to use, or is it a stylistic preference?



Answer



This page at the goo.ne.jp Q&A site quotes the NHKことばのハンドブック, which states that while there were at one time rules for when to use くらい and when to use ぐらい, modern-day Japanese has no such distinction. I agree with Tsuyoshi that ぐらい "feels" colloquial, but more often than not I think it's a matter of which rolls off the tongue with the most ease.


vocabulary - Are there names like ワンコイン for the other coins?


So ワンコイン refers to a 500円 coin, but is there other names for the other coins?


Also in conversation does ワンコイン refer to any specific currency or only to 500 yen (as in the sense of being a default).



Answer




I'm not sure how SE works and why there are only comments with answers and no actual answers...


However, ワンコイン, as mentioned by Dave and others in the comments, is not a term for any particular coin, but just a sales practice by any shop. Whenever they sell items where you can pay using just one coin, then it's a sales point they'll put on signs.


It could apply to any of the coins. So if a shop had everything for 100 yen, or 10 yen, 5 yen, or 1 yen, then they could say ワンコイン.


I have never heard the term used in conversation, at least not in reference to currency. It would only be used when talking about a shop or sale.


etymology - Where does 「えっと」 come from?


I wanted to describe that 「えっと」 was similar to "Ummm" in English when someone is trying to think about what they are going to say, but I wasn't even sure if that was correct. Is that just a generalization? What does 「えっと」actually come from? Can it be considered to be a word or phrase?




molecules - How to find out oxidation state when compound has multiple electronegativities


How do I solve for oxidation state in something like CH3-O-F? The fluorine is more electronegative than the oxygen which is more electronegative than the carbon which is more electronegative than the hydrogen. In this case would everything except the fluorine be oxidized?




halacha - How far may one go with doing an aveira (violating a negative mitzva) if it means performing a positive mitzva?


I cannot remember where, but somewhere in gemara it mentions that when confronted with doing a positive mitzva or keeping a negative mitzva, one should do a positive mitzva. How far does this go though? What are some negative mitzvot that one cannot do (outside of those three cardinal sins) that one may break in order to do a positive mitzva?



Answer



The rule is עשה דוחה לא תעשה - a positive commandment pushes away a negative commandment. Basically this is in fact quite limited, but in theory if something is simply forbidden by a negative commandment but a Mitzvah comes along that requires violating it in order to fulfill it, then we go ahead and do the Mitzvah if there is no way to avoid the negative commandment. (If it could have been avoided previously but can't be right now when it is time to do it is a subject of dispute).


Not all negative commandments are included in this dispensation however, and sometimes Chazal forbid it (as the case of a Yibbum where there is a negative commandment involved in the relationship).


Examples of excluded negative commandments include theft, things which are forbidden by a positive as well as a negative commandment, as well as possibly including things which have a death penalty associated with them, where there are two negative commandments involved simultaneously, and other such exceptions.


avot patriarch fathers - How did Avraham discover that God exists?


How did Avraham discover that God exists? Was because of logic or tradition since Adam? If was by logic, why do we call him Ivri (from Ever, his grandfather). Please bring sources.



Answer



There is a midrash in Bereshit Rabbah 39 where Avraham deduces the existence of God who created the world, and only then did God call out to Avraham lech l'cha. A summary of the midrash from my notes after a class:



Mashal: One day a man was traveling and he saw a tower (birah) "on fire" (doleket). He said, this tower has no owner? A man peeked out and said "I am the owner". Nimshal: The traveler is Avraham Avinu, who said: this world has no owner? And Ha-Kadosh Baruch Hu peeked out at him, saying: I am the ruler of this world.


(My notes from the class:) According to this midrash, God didn't reveal himself to Avraham until Avraham reasoned that the world must have a creator/ruler and went looking. Avraham was a seeker; God didn't just speak to him out of the blue and say "lech l'cha".




So according to this midrash, Avraham was inquisitive enough to deduce the existence of, and then seek out, the Master of the Universe.


Another midrash (B'reishit Rabbah 42) offers a few different explanations for the name Ivri (h/t Menachem). One of these, attributed to R. Nechemiah, is that it comes from Eber, from whom Avraham learned the monotheistic tradition (passed down from Shem). That interpretation contradicts the midrash above. The other two explanations there are not related to this. R. Yehudah says that it is because Avraham worshiped one God unlike those around him, and others understand it geographically, because Avraham "crossed over" and wasn't a native.


slang - What is the meaning of all those "w"s in email and SNSs?


You see a lot of w and ww and even www in Twitter and casual chat. What does it mean? I've always thought it was わいわい but never found out. How is it pronounced?


Here's an example from Twitter



なんでじゃろうねwwとりあえず電車なうだから間に合いそう笑




Answer




They derive from 笑う(わらう). They're the Japanese equivalent of "LOL".


grammar - Can 「食べも飲みもしない」 be rewritten as 「食べなくも飲まな くもある」?


I'd like to see if I understand a couple grammar points correctly. I'd like to rewrite this sentence:



 1. 食べも飲みもしない



As either one of these:




 2a. 食べなくも  飲まなくもある
 2b. 食べなくもあり飲まなくもある



I think both 2a and 2b are grammatical with the same meaning as 1. But I'm not sure I've done this correctly, and I'm particularly unsure about whether the あり is necessary in the first half.




The following is my reasoning. (I've tried to express it as clearly as I can, but it's probably too long and confusing--my apologies!)


I'm working off Hiroshi Aoyagi's idea that -i is a suppletive form of -ku ar-(r)u, so the end of the sentence looks like this:


  *飲みも   しなくある    → 飲みも   しない
*nom(i)-mo si-na-ku ar-u → nom(i)-mo si-nai


Here, the stem si appears because the suffix -(a)na-ku needs to have something to attach to, and it can't attach directly to the verb stem nom- because -mo is in the way.


I'm moving -(a)na-ku before -mo and attaching it directly to both verb stems, so si is no longer necessary and it disappears. But the tense morpheme -(r)u still needs to appear at the end of the sentence, so I have to insert the dummy verb ar- for it to attach to:


  飲まなくも    ある
  nom-(a)na-ku-mo ar-u

Since -mo appears between -ku and ar-(r)u, it can't take the usual form of -i.


Since the tense morpheme -(r)u only has to appear once at the end of the sentence, I don't think I need to add the dummy verb ar- to the first half. But if I do, I think it ends up in "infinitive" form (あり):


  食べなくも         飲まなくも    ある
  tabe-na-ku-mo nom-(a)na-ku-mo ar-u


  食べなくも   あり   飲まなくも    ある
  tabe-na-ku-mo ar-(i) nom-(a)na-ku-mo ar-u

So based on this, I suspect that both 2a and 2b are equivalent to 1. Am I correct or mistaken?




tefilla - Non-Jews praying with the Jewish community


I read a comment made on another question that regardless of how they are worded, blessings that are made in communal prayer can only be prayed by someone who is obligated to them.


The idea that non-Jews shouldn't make blessings for things that were commanded only to the Jewish people, or say lines referring to things like 'our ancestors', makes sense to me. These are important. But I've never come across the thought that gentiles can't pray more or less beside the community in the synagogue or in Jewish homes.


Are there any opinions or sources about this perspective? Even individual perspectives about what is gained or lost in either case would be meaningful to hear.




Saturday, April 28, 2018

brit milah - If I wanted to convert to Judaism, would I need to have my circumcision repeated?


I was baptized in the Catholic Church, raised in the Methodist Church, and became an atheist when I was about 14 years old. My grandmother on my father's side was a non-observant Jew, but my father has always been Methodist. I was circumcised as a baby, although I have no idea how long after birth it was done; I assume it was performed by a doctor, but my mother says he was Italian, and probably Catholic, not Jewish. It certainly wasn't a bris, and the doctor obviously wasn't a moyle (excuse me if I misspelled the words).


I'm not planning to convert, but I am curious as to how my circumcision would be handled if I did convert. Would the procedure need to be repeated by a moyle?




Answer



Normally the circumcision preformed by a physician is sufficient to meet the physical requirements of "milah" (circumcision), nevertheless a process known as "hatafas dam bris" (הטפת דם ברית) is necessary (Shulchan Aruch, Yoreh Deah 268:1). In this process the Mohel draws a ritual drop of blood from the place of circumcision for the sake of the covenant. It is, or at least can be, painless. Insofar as most contemporary mohelim are unacquainted with adult circumcision, it is often the case that an uncircumcised convert will have the procedure preformed by a physician and subsequently have it "kashered" through hatafas dam bris.


midrash - Does p'shat explain everything?


Ways of reading Chumash are commonly divided into four headings: p'shat, simple readings; d'rash, exegeses; remez, hints; and sod, secrets. The g'mara and midr'she halacha are full of d'rash: they engage in diyuk, nitpicking, paying careful attention to each word, asking why each word appears where it does. It is commonly said about that that there are no extraneous words in chumash; for example, because Biblical Hebrew sometimes omits "es", the accusative-case marker, a tana derived something from every single es in Chumash. But that's all at the level of d'rash. My question is, what about p'shat? That is, is it true that there is a p'shat-level explanation for every nuanced wording change, for every diyuk? (For example, can every presence or absence of "es" be explained in terms of cadence, unambiguity, or other p'shat-level concerns?) Or does P'shat (my made-up personification of p'shat) sometimes (perhaps often) simply throw up her hands and say "it just is that way, I don't have to have a reason; try asking D'rash"?



Sourced answers strongly preferred.




kanji - What is the proper way of writing the first stroke of 言?



I am wondering why is it that 言 looks different in different fonts. In Gothic, the topmost part is just a horizontal line while in Google Search, it is a drop. I am really confused about what is really the proper way of writing this kanji.




halacha - Can pants ever be considered modest?


What are the sources that would support the position that pants can be modest if: a) they are very loose almost resembling a skirt or b) by wearing a top that is long enough that it covers all the way down to the split in the legs.



enter image description here





word choice - What's the difference between じき and すぐ?


すぐ, and especially 今すぐ, is my habitual way to express "soon", or "right after this".


I know that じき means more or less the same thing, and when I hear it or see it written, I get the general meaning of the sentence.


However, I don't feel comfortable saying it myself because I'm unclear on how they differ and what the nuances are.


What are the conditions in which to choose one over the other, and do they differ in meaning?



Answer



じき means temporally farther than すぐ. I don't know if the meaning of じき overlaps with the English soon. If it does, then soon has a broader meaning than すぐ. じき can instead be translated as 'sooner or later', or 'eventually'.



halacha - Is there a Mitzvah to love parents?


Is there a special mitzvah to love one's parents?


If so, does it require the parent's awareness of that love?



Answer



Considering the fact that the Torah only writes of one's relationship to one's parents in terms of fear and respect, it would seem that the answer is no (as this Rabbi's asserts rather emphatically).


The Chayei Adam, however, writes in the beginning of the Laws of Honoring Parents:



פשיטא שצריך לאהוב אותם כגופו שהרי הוא בכלל ואהבת לרעך כמוך אלא שבאביו ואמו הוקש אהבתם לאהבת המקום כדאית׳ בזוהר פ׳ תצא



Based on a Zohar, a person should have the perspective that honoring his parents is similar to honoring God. Therefore, aside from the general mitzvah of loving one's fellow Jew, just as a person has a special mitzvah to love God, there is, by extension, a special mitzvah in loving one's parents.



In addition, loving one's parents makes sense in light of the obligation to respect them, because loving them makes doing the necessary services for them much easier. Anything that helps one do mitzvos is a good thing [citation needed].


product recommendation - English translation of Reshit Chochmah


Is there an English translation of the book Reshit Chochmah By Rabbi Eliyahu DaVidas?





halacha - Is Dina D'Malchusa a din in Gavra or in Cheftza?


Let's say that Reuvain owes Shimon money in American law, and Dina Demalchusa applies, does that mean:



  1. Reuvein has a halachic monetary obligation to Shimon which is as strong as any other obligation, and Shimon can take him to Beis Din over it, or merely

  2. Reuvein has a law between him and Hashem that he must pay Shimon?


Also, assuming that Reuven and Shimon both pass away, with Reuven "owing" Shimon money, and his inheritors are in another country who don't follow that "rule" entitling Shimon with that money:




  1. Must Reuven's yorshim pay Shimon's yorshim (inheritors), as it became a classic hischayvus (monetary obligation), or

  2. Is he free, as the obligation was on Reuven and not on his money (somewhat similar to the case of a knas (fine))?



Answer



I haven't had time to go through the whole sugya, but this article by Dov Daniel (published in Daf Kesher vol 922, Parshat Pinchas 5763) seems to say that it is a din on the gavra and not the cheftza:




דברי ר' יונה:


"לא הוזכר דינא דמלכותא אלא בהפקעה שהנכסים מופקעים מבעליהם בדיני המלך וכענין הפקר בית דין הפקר ומי שיורד בהם במצות המלך זוכה בחזקה אבל כל זמן שלא החזיק בהם לא זכה בהם"

([Commentary to] :ב"ב נד)



מכאן שאין המלכות יכולה ליצור חיובים אלא להפקיע בעלות ואפילו אז, ההפקעה רק מאפשרת לתפוס אך אין היא חלה עד שייעשה מעשה קניין. כלומר, "דינא דמלכותא דינא" היא קביעה שמתייחסת ל"גברא" - התורה מכירה בזכות המלכות לעשות מה שרואה לנכון אפילו בדיני ממונות אך רק במידה שהיא יכולה להתיר מעשים של השתלטות ולא במידה שיכולה לקבוע קביעות שיתפשו בעולם של חושן משפט, כלומר אין המלכות יכולה לפעול ישירות על מעמד ה"חפצא".



In short, it would seem that the goverment has the halachic standing to confiscate Reuvein's money, but not to directly assign it to Shimon. Shimon must go and be koneh the money in order to acquire it. Much the same as when Beis Din is mafkir someone's property.


I'm going to keep looking into this.


halacha - Bein hashmashot and bris


If a baby is born "bein hashmashot" how do we count the days till the 8th for the bris? For example, if it's bein hashmashot Sunday evening, will the bris be the following Sunday or following Monday because you could say that since it's after shkiya that it's the following day?





fft - Applying Image Filtering (Circular Convolution) in Frequency Domain


To filter an image we can:



  1. Use a 3x3, 5x5, 7x7, etc. filter, that is convolve the image and the filter in the space domain.

  2. Use a FFT on both the image and the filter, multiply them together in the frequency domain, and then perform an IFFT on the image to get the filtered result.



These two approaches should produce equivalent result.


Questions:



  1. Are there any conditions placed on the filter so that the results are equal?

  2. Will there be any information loss in the second approach or will the images be exactly equal (neglecting floating point precision error)?

  3. As the kernel size increases, will the second approach start outperforming the first?



Answer



In my StackExchange Signal Processing Q38542 GitHub Repository you will be able to see a code which implements 2D Circular Convolution both in Spatial and Frequency Domain.



Pay attention to the function CircularExtension2D().
This function align the axis origin between the image and the kernel before working in the Frequency Domain.
Remember that for Discrete Signals the implicit assumption on signals, In frequency Domain analysis, is being periodic (Circular).


In the discrete case one could indeed apply Circular Convolution by element wise multiplication in the Frequency Domain.


With proper padding one could apply linear convolution using circular convolution hence Linear Convolution can also be achieved using multiplication in the Frequency Domain.


See:


enter image description here


In depth description can be found in FFT Based 2D Cyclic Convolution.


Regarding your questions:




  1. The filter is just an array of numbers. As long as you are after 2D Circular Convolution there is no constraints on the Filter. If it is valid for 2D Spatial Circular Convolution it is valid for Frequency Domain Circular Convolution.

  2. Up to Floating Point Quantization errors both are mathematically equivalent (See Convolution Theorem).

  3. If the Convolution Kernel is similar in its size to the image and both are large enough Frequency Domain Convolution becomes more efficient than Spatial Domain.


Friday, April 27, 2018

organic chemistry - IUPAC rules on omission of locants in carboxylic acid



I have been lately in debate with my teacher as to why did the IUPAC name the compound with the current official IUPAC name of 2-methylpropanoic acid. (CN: isobutyric acid)


My argument is that:




  • You can't attach a methyl in carbon 1 (because the bonds in carbon 1 will exceed 4)




  • You can't attach a methyl in carbon 3 (because it will become butanoic acid)



  • Placing the locant in a substituent with no other constitutional isomers will be useless when to be interpreted, will be a few more characters longer, and will be less pleasant for the eyes end ears (I mean, methylpropanoic acid a bit more pleasant to see and hear than 2-methylpropanoic acid, right?)



To verify my initial assumption, is the name of such compound 2-methylpropanoic acid? If it is, then we may proceed to the real question in the next paragraph.


So, where in the 2013 Blue Book or any updated IUPAC nomenclature guidelines with less complicated wordings in organic chemistry books (this has seniority over the former) can I see that you must not omit the locant in these cases (and why).


Additionally, how can I request to the Union to alter this notion to make it methylpropanoic acid because of the stated reasons? (It's a bit like ethan-1-ol and ethanol.)



Answer



According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the preferred IUPAC name is 2-methylpropanoic acid. The trivial name ‘isobutyric acid’ is no longer recommended (see Subsection P-65.1.1.2.4).


2-methylpropanoic acid


Concerning your objection



You can't attach a methyl in carbon 3 (because it will become butanoic acid)




IUPAC nomenclature doesn’t work like that. Generally, the complete information about a structure is explicitly given by the name and does not rely on any implied information or hidden logic involving other structures.


The given parent structure is propanoic acid. It includes two kinds of substitutable hydrogen. Therefore, the locant cannot be omitted in substituted propanoic acid, e.g. 2-chloropropanoic acid or 3-chloropropanoic acid.


2-chloropropanoic acid and 3-chloropropanoic acid


This principle applies to any substituent. The special situation that replacing the chloro substituent in 3-chloropropanoic acid with a methyl substituent would actually lead to the name butanoic acid instead of 3-methylpropanoic acid does not change the preferred name for 2-methylpropanoic acid.


2-methylpropanoic acid and butanoic acid


Nevertheless, there are a few exceptional cases where locants are omitted, but only when there is no ambiguity. For preferred IUPAC names, the nomenclature rules explicitly stipulate when locants are omitted. Most of these rules apply to the omission of the locant ‘1’. One case is the example given in the question:



(It's a bit like ethan-1-ol and ethanol.)




Homogeneous chains consisting of only two identical atoms such as ethane only have one kind of substitutable hydrogen. Therefore, the current IUPAC recommendations include a rule (in Subsection P-14.3.4.2) that the locant ‘1’ is omitted in monosubstituted ethane; i.e. ethanol (not ethan-1-ol) is the preferred IUPAC name. However, if any locants are essential for defining the structure, then all locants must be cited for the structure, e.g. 2-chloroethan-1-ol (not 2-chloroethanol; see Subsection P-14.3.3).


2-chloroethan-1-ol


Coming back to carboxylic acids, acetic acid also has only one kind of substitutable hydrogen, i.e. all substitutable hydrogen atoms have the same locant. Therefore, explicitly according to Subsection P-14.3.4.6, this locant is omitted, e.g. chloroacetic acid (not 2-chloroacetic acid).


chloroacetic acid


tefilla - Why did the Rabbis make a decree for Yovel?


Rambam (Hilchos Tefila 2:8) says that



בד"א ביום צום של כל שנה ושנה אבל ביום צום של שנת היובל מתפלל תפלת המוספים תשע ברכות כמו שהתפלל במוסף ראש השנה והם אותן הברכות עצמן לא פחות ולא יותר ואין מתפללין אותן אלא בזמן שהיובל נוהג: ‏




He says that the Rabbis decreed 9 blessings on Mussaf Yom Kippur on a Yovel year when Yovel is practiced.


Yovel is only practiced when all Jews live in Israel on their ancestral portion (See Rambam Hilchos Shmitta and Yovel 10:10). That stopped during the First Temple period with the exile of the northern ten tribes (a bit more than a hundred years before thee First Temple's destruction).


But the prayers were instituted by the "Men of the Great Assembly", who were active during the destruction of the Beis Hamikdash and the Babylonian exile. So they instituted a prayer on an event which (as of then) hasn't happened for over a hundred years and won't happen again until Moshiach comes.


Why institute a prayer to be said only when Moshiach will be here (sort of Hilchasa LeMeshicha)?




medicine - Pharmaceuticals and Kashrut


To what degree does medicine need to be kosher (not regarding pesach)? Most medicines are a random series of active ingredients with little meaning to the non medical professional - but what about "chocolate flavored" etc tablets or liquids?



I know that here in Australia there exists a kosher book for regular food, but not one for medicine. On the other hand i recall hearing that Strepsil lozenges (sore throat) that used to be kosher are not any more.


So, points of interest are:



  • flavouring

  • degree of importance (heart medicine / sleep pills / stimulants / sore throat lozenges)

  • age?




organic chemistry - IUPAC name for 1,2,3-trichlorocyclopropane?


What is the IUPAC name for the two isomers of 1,2,3-trichlorocyclopropane? Similarly what is the name for isomers of 1,2,3,4-tetrachlorocyclobutane, 1,2,3,4,5-pentachlorocyclopentane, etc?


1,2,3-trichlorocyclopropane has two isomers, one of them with all the chlorine atoms facing in one direction and the other with one chlorine facing the opposite direction of the other two. In CIP rule, if two substituents on an atom differ only in their absolute configuration, R takes priority over S. However I have difficulty applying the rule here: two of the substituents are exactly the same. Nevertheless the two molecules are clearly distinct.


In practice the problem could be circumvented by using trans- and cis- prefix. But it does not address the key problem and fails on longer chains --- 1,2,3,4-tetrachlorocyclobutane has 4 possible arrangements, though not necessarily all of them have the problem.





Here are the isomers of cyclobutane and their mirror images. I use + and - to denote a chlorine atom above or below the plane. The number in the parenthesis is the number of distinct molecules.


+ + | - -    (1)
+ + | - -

+ - | - + (1)
+ + | + +

+ - | - + (1)
+ - | - +


+ - | - + (1)
- + | + -


tamei tahor ritual purity - Why didn't women complain about not being able to bring the Pesach?


During the first year in the desert, some men were tamei and complained that they couldn't bring the Pesach. This resulted in the mitzvah of Pesach Sheni.


Men and women are equally obligated to bring the Pesach. And a significant fraction of the women must have been niddos at the time. Why didn't they complain as well?


(Women are not obligated in Pesach Sheni, but they're allowed to bring it if they want to. In any case, they couldn't have known this then because they didn't even know Pesach Sheni existed!)


DoubleAA points out that anyone who was a niddah for Pesach Rishon is likely to be a niddah again for Pesach Sheni. Even if you argue that they would have complained but these men were quicker and got in first, they should still have complained again, because the mitzvah of Pesach Sheni didn't address their needs.




maaser tithes - Meiruach through a side door


There is a concept that ma’aser is only required once Meiruach (literally, “smoothing”) is performed on the crop (Peah 1:6 et. al.), at which point the crop is complete and eligible for taking Ma’aser and Terumah (Yachin ad. loc.).


I have heard that if the produce was brought into the storehouses through a side door and not through the main entrance that Meiruach is not considered to have been performed, and therefore such produce is not eligible to Ma’aser. Is this correct, and if so, where is the source?



Answer



You are confusing Meiruach (or more generally, Gemar Melakha -- finishing the labor) and Keva' (establishment).


When one picks produce owned by a Jew in Israel, he is allowed to snack on it (אכילת עראי) even before tithing it until he finishes his work on the harvest (גמר מלאכה, such as your example of smoothing the piles) if he is planning on selling the crop. If he intends to keep it, then there are 6 ways the produce is established to be tithed (נקבע למעשר) after the harvest is done: bringing it into his house, separating Terumah from it, selling it, cooking it, pickling it, or trying to eat it on Shabbat. After one of those things happens, he can't even snack on the food before tithing it. (Rambam Maaserot 3:1-3)



The rule of "bringing it into your house" only applies if you bring it through a main doorway, not if you pass it in through the window. So if you wanted to avoid tithing, you could bring your produce into your house in a non-standard way and then only snack on it raw. The Gemara in Gittin (81a) praises the early generations who brought their produce home the normal way in order to establish it to be tithed, unlike the lowly later generations who would bring their produce home via the roof in order to skip out on tithing.


physical chemistry - Do catalysts shift equilibrium constant towards 1?


I want to be able to understand shifts in equilibrium from the maxwell boltzmann distribution. One thing I cannot get my head around is the effect of catalysts on the equilibrium position - supposedly it's none at all.


But consider these diagrams of the M.B distribution of both reactants and products of a reversible reaction. enter image description here


The top diagram shows the distribution of the products of the reaction which equilibrium favours. It has a bigger concentration of particles. The line dividing the shaded region on these diagrams represents activation energy and the $dE$ represents the shift in activation energy due to the catalyst. We can see that the shaded regions, $A_1=A_2$ because forward and backward rates are the same at eqm. But clearly, the rate of the top reaction increases more as a greater fraction of particles have above activation energy. So adding a catalyst should shift equilibrium to the middle?


Basically, catalysts work better on reactants with higher concentration. So shouldn't the side with the lower concentration be favoured?



Answer




TL;DR Your Maxwell–Boltzmann diagram up there is not sufficient to describe the variation of rate with $E_\mathrm{a}$. Simply evaluating the shaded area alone does not reproduce the exponential part of the rate constant correctly, and therefore the shaded area should not be taken as a quantitative measure of the rate (only a qualitative one).



There is a subtle issue with the way you've presented your drawing. However, we'll come to that slightly later. First, let's establish that the "proportion of molecules with sufficient energy to react" is given by



$$P(\varepsilon) = \exp \left(-\frac{\varepsilon}{kT}\right) \tag{1}$$


Therefore, for a reaction $\ce{X <=> Y}$ with uncatalysed forward activation energy $E_\mathrm{f}$ and uncatalysed backward activation energy $E_\mathrm{b}$, the rates are given by


$$k_\mathrm{f,uncat} = A_\mathrm{f} \exp \left(-\frac{E_\mathrm{f}}{kT}\right) \tag{2} $$


$$k_\mathrm{b,uncat} = A_\mathrm{b} \exp \left(-\frac{E_\mathrm{b}}{kT}\right) \tag{3} $$


The equilibrium constant of this reaction is given by


$$K_\mathrm{uncat} = \frac{k_\mathrm{f,uncat}}{k_\mathrm{b,uncat}} = \frac{A_\mathrm{f}\exp(-E_\mathrm{f}/kT)}{A_\mathrm{b}\exp(-E_\mathrm{b}/kT)} \tag{4}$$


As you have noted, the change in activation energy due to the catalyst is the same. I would be a bit careful with using "$\mathrm{d}E$" as the notation for this, since $\mathrm{d}$ implies an infinitesimal change, and if the change is infinitesimal, your catalyst isn't much of a catalyst. So, I'm going to use $\Delta E$. We then have


$$k_\mathrm{f,cat} = A_\mathrm{f} \exp \left(-\frac{E_\mathrm{f} - \Delta E}{kT}\right) \tag{5} $$


$$k_\mathrm{b,cat} = A_\mathrm{b} \exp \left(-\frac{E_\mathrm{b} - \Delta E}{kT}\right) \tag{6} $$


and the new equilibrium constant is



$$\begin{align} K_\mathrm{cat} = \frac{k_\mathrm{f,cat}}{k_\mathrm{b,cat}} &= \frac{A_\mathrm{f}\exp[-(E_\mathrm{f} - \Delta E)/kT]}{A_\mathrm{b}\exp[-(E_\mathrm{b} - \Delta E)/kT]} \tag{7} \\[0.2cm] &= \frac{A_\mathrm{f}\exp(-E_\mathrm{f}/kT)}{A_\mathrm{b}\exp(-E_\mathrm{b}/kT)} \frac{\exp(\Delta E/kT)}{\exp(\Delta E/kT)} \tag{8} \\[0.2cm] &= \frac{A_\mathrm{f}\exp(-E_\mathrm{f}/kT)}{A_\mathrm{b}\exp(-E_\mathrm{b}/kT)} \tag{9} \end{align}$$


Equations $(9)$ and $(4)$ are the same, so there is no change in the equilibrium constant.




The question then arises as to how eq. $(1)$ is obtained. The simplest way is to invoke a Boltzmann distribution, which almost by definition gives the desired form. However, since you have a Maxwell–Boltzmann curve, I guess I should talk about it a bit more. The fraction of molecules with energy $E_\mathrm{a}$ or greater is simply the shaded area under the curve, i.e. one can obtain it by integrating the curve over the desired range.


$$P(\varepsilon) = \int_{E_\mathrm{a}}^\infty f(\varepsilon)\,\mathrm{d}\varepsilon \tag{10}$$


where the Maxwell–Boltzmann distribution of energies is given by (see Wikipedia)


$$f(\varepsilon) = \frac{2}{\sqrt{\pi}}\left(\frac{1}{kT}\right)^{3/2} \sqrt{\varepsilon} \exp\left(-\frac{\varepsilon}{kT}\right) \tag{11}$$


At first glance, we would expect this to be directly proportional to the exponential part of the rate constant, i.e. $\exp(-E_\mathrm{a}/kT)$. Alas, it is not that simple. If you try to work out the integral


$$\int_{E_\mathrm{a}}^{\infty} \frac{2}{\sqrt{\pi}}\left(\frac{1}{kT}\right)^{3/2} \sqrt{\varepsilon} \exp\left(-\frac{\varepsilon}{kT}\right) \,\mathrm{d}\varepsilon \tag{12}$$


you don't get anything close to the form of $\exp(-E_\mathrm{a}/kT)$. Instead, you get some "error function" rubbish, and some nasty square roots and exponentials. (You can use WolframAlpha to verify this.)



Why is this so? Well, it turns out that there are other terms that also depend on $\varepsilon$ and therefore need to go inside that integral (they aren't constants and can't be taken out).


The simplest example is that faster molecules tend to collide more often, so even though the right-hand tail of the diagram seems to contribute very little to the "proportion of molecules with sufficient energy", it actually contributes more significantly to the overall rate because these molecules collide more often. In collision theory this is described using the "relative velocity" of the particles $v_\mathrm{rel}$.


There is also another complication, in that the Maxwell–Boltzmann distribution, the direction of the particles is not accounted for. (For more insight please refer to Levine Physical Chemistry 6th ed., p 467.) Therefore, there has to be yet another term that takes into account the direction of movement of the particles. The idea is that a head-on collision between two molecules is more likely to overcome the activation barrier than is a $90^\circ$ collision. The term that compensates for this is the "collision cross-section" $\sigma$.


If you go through the maths (and I don't really intend to type it out here, it's rather long, but I will give some references) then you will find that at the end you will recover the form $\exp(-\varepsilon/kT)$. Once you have arrived at this, it's very straightforward to see that the increases in rate of both the forward and backward reaction cancel each other out.


Now, as for the promised references, Pilling and Seakins's Reaction Kinetics pp 61-2 have a short outline of the proof. Atkins's Physical Chemistry 10th ed. has a slightly longer proof on pp 883-4.


halacha - Mitzvah of living in Eretz Yisrael


What halachic sources exist affirming the post-destruction mitzvah of individuals to live in Eretz Yisrael, and what is the nature (obligatory, meritorious) of the mitzvah? This question does not relate to sources denying the present-day mitzvah, such as Va-yoel Mosheh.


This is a fork of What justifications are there for not moving to Eretz Yisrael?


I found Eim ha-Banim Semeichah available online, to get us started: http://www.tsel.org/torah/emhabanim-eng/



Answer




The first place to start is the shita of the Ramban, who writes in parshas Masei (33:53) that it is a mitzvas aseh. He also asks why the Rambam does not count this as one of the 613, which is something that the acharonim debate.


The Megillas Esther holds that according to the Rambam there is no mitzvah bizman hazeh, while The Avner Nezer says that there is according to the Rambam, but it is subsumed within the mitzvah of destroying the seven nations.


There are obviously other acharonim who discuss it, but these are probably the most well known. IIRC I remember reading that Rav Ovadiah says that the shita of the ME was "pushed away with both hands" by the acharonim.


The Rambam himself says in Yad that "A person should always live in Israel" - but he also says that it is permissible to live in other countries.


There is a very good piece by Rav Schachter here.


physical chemistry - Are there any free electrons in metal vapor?


Metals contain free moving electrons, in both the solid and liquid state. Does this happen when it is in vapor form?




particle に - understanding the grammar of "XをYに"



兄さんをエサにホムンクルスを引っ張り出します




Is there an implied verb after に, or not? Is this sentence more along the lines of the situation when you have two verbs connected with the ~て form, or is it more along the lines of "兄さんをエサに" being an element of the verb 引っ張り出す in the same way that ホムンクルスを is?


Could you replace に with として here? If so, how would it compare with the sentence using に? If not, why not?


I know I asked a lot of questions; just address whichever ones make the most sense.


niisan wo esa ni



Answer



You are on the right track about the missing verb. The missing verb can be して. But you do not need to change the particle. Just add the missing verb: 兄さんをエサにして. Using here is unnatural. I think として can be used as "as if", implying that it is not actually it. In 兄さんをエサにして...を引っ張り出す, the brother is actually treated as bait, so should be used. In 兄さんをエサとして扱う or 兄さんをエサとみなす, there is implication that the brother is not actually bait, so is used.


Thursday, April 26, 2018

hashkafah philosophy - Bereishit vs. science


How does Judaism deal with the differences between scientific evidence of the beginning of the world and the account(s) in Bereishit?




algorithms - Books/resources for implementing various mathematical functions in fixed point arithmetic for DSP purposes


I'm looking for books or resources that cover the following in detail:





  • implementing mathematical functions (e.g., logarithm, exponential, sine, cosine, inverse) in fixed point arithmetic for DSP purposes.




  • techniques like using lookup tables, Taylor series, etc.




I am fairly familiar with C programming and am more interested in the algorithms on how to go about implementing various mathematical functions in an efficient manner.



Answer



the general polynomial form is:



$$\begin{align} f(u) &= \sum\limits_{n=0}^{N} \ a_n \ u^n \\ \\ &= a_{\small{0}} + \Bigg(a_{\small{1}} + \bigg(a_{\small{2}} + \Big(a_{\small{3}} + \,... \big(a_{\small{N-2}} + (a_{\small{N-1}} + a_{\small{N}} \,u \,)u \, \big)u \ ...\Big)u \, \bigg)u \, \Bigg)u\\ \end{align}$$


the latter form is using Horner's method, which is highly recommended, especially if you're doing this in single-precision floating point.


then for a few specific functions:


square root:


$$ \begin{align} f(x-1) & \approx \sqrt{x} \quad \quad 1 \le x \le 2 \quad \quad N=4\\ a_0 & = 1.0 \\ a_1 & = 0.49959804148061 \\ a_2 & = -0.12047308243453 \\ a_3 & = 0.04585425015501 \\ a_4 & = -0.01076564682800 \\ \end{align} $$


if $2 \le x \le 4$, use the above to evaluate $\sqrt{\tfrac{x}{2}}$ and multiply that result with $\sqrt{2}$ to get $\sqrt{x}$. as with $\log_2(x)$, apply power of $2$ scaling to scale the argument to the necessary range.


base 2 logarithm:


$$ \begin{align} x\cdot f(x-1) & \approx \log_2(x) \quad \quad 1 \le x \le 2 \quad \quad N=5\\ a_0 & = 1.44254494359510 \\ a_1 & = -0.7181452567504 \\ a_2 & = 0.45754919692582 \\ a_3 & = -0.27790534462866 \\ a_4 & = 0.121797910687826 \\ a_5 & = -0.02584144982967 \\ \end{align} $$


base 2 exponential:


$$ \begin{align} f(x) & \approx 2^x \quad \quad 0 \le x \le 1 \quad \quad N=4\\ a_0 & = 1.0 \\ a_1 & = 0.69303212081966 \\ a_2 & = 0.24137976293709 \\ a_3 & = 0.05203236900844 \\ a_4 & = 0.01355574723481 \\ \end{align} $$



sine:


$$ \begin{align} x\cdot f(x^2) & \approx \sin\left(\tfrac{\pi}{2} x \right) \quad \quad -1 \le x \le 1 \quad \quad N=4 \\ a_0 & = 1.57079632679490 \\ a_1 & = -0.64596406188166 \\ a_2 & = 0.07969158490912 \\ a_3 & = -0.00467687997706 \\ a_4 & = 0.00015303015470 \\ \end{align} $$


cosine (use sine):


$$ \cos(\pi x) = 1 \, - \, 2 \, \sin^2 \left(\tfrac{\pi}{2} x \right) $$


tangent:


$$ \tan(x) = \frac{\sin(x)}{\cos(x)} $$


inverse tangent:


$$ \begin{align} \frac{x}{f(x^2)} & \approx \arctan(x) \quad \quad -1 \le x \le 1 \quad \quad N=4 \\ a_0 & = 1.0 \\ a_1 & = 0.33288950512027 \\ a_2 & = -0.08467922817644 \\ a_3 & = 0.03252232640125 \\ a_4 & = -0.00749305860992 \\ \end{align} $$


$$ \arctan(x) = \tfrac{\pi}{2} - \arctan\left( \tfrac{1}{x} \right) \quad \quad 1 \le x $$


$$ \arctan(x) = -\tfrac{\pi}{2} - \arctan\left( \tfrac{1}{x} \right) \quad \quad x \le -1 $$



inverse sine:


$$ \arcsin(x) = \arctan\left( \frac{x}{\sqrt{1-x^2}} \right)$$


inverse cosine:


$$\begin{align} \arccos(x) &= \frac{\pi}{2} - \arcsin(x) \\ &= \frac{\pi}{2} - \arctan\left( \frac{x}{\sqrt{1-x^2}} \right)\\ \end{align}$$


history - Why do some of the Ten Commandments include Noahide Laws?


Of the Seven Noahide Laws, at least three are identical to one of the Ten Commandments. To be specific I am referring to



  • Do not murder

  • Do not steal

  • Do not deny God

  • Do not blaspheme


I understand that the Noahide Laws were in practice long before the Ten Commandments, so I assume the Israelites were already keeping these before the episode at Sinai.


My question is, why did some of these commandments need to be reincluded? Do the ten commandments override the Noahide laws?





translation - Have a trouble with まで



私がびくびく怯えて過ごしてるせいで、彼まで過敏になってる気がする




This まで confusing me. In this case it's translating like "even", right?



Answer



Here, まで is an intensifier and "even" is a valid translation.


[彼]{かれ}まで[過敏]{かびん}になってる = 彼さえ過敏になってる


Wednesday, April 25, 2018

particle と - だろうと how can I translate it?


I am reading The Little Prince in Japanese and I am not sure about how to translate だろうと in the following sentence:




大人たちにそう言われてから、今度はわかってくれるだろうとウワバミの中身を描いて見ました。



I don't know how to literally translate it, even if I understand the meaning of the sentence...



Answer



This と is the quotative-と. volition/inference + と can be used without any explicit following verb, and it means "thinking ...", "trying ...", "hoping ..." or such. だろう is part of the "quote."



今度はわかってくれるだろうと
=「今度はわかってくれるだろう」と思って
= ..., thinking/hoping (adults) will understand (the picture) this time, ...




Similar questions:



grammar - How do you ask for ordinality (order in a sequence)?


What phrase do you use to ask for the n-th position of an object? Is there a straightforward and general way to do so?




e.g. order of childbirth, place did the runner finish



Since you can use 3人目 for third, can you use 何人目 or 第何子 to ask, perhaps?


(This especially hard to ask since English has problems conveying this.)



Answer



Yes, you can say 何人目【なんにんめ】. You can add 目 to a counter regardless of whether it's attached to a specific number like 3 or a question word like 何, so you can say things like 何人目 or 何代目. Here's an example of the latter from ALC:



「クリントンはアメリカの何代目の大統領ですか?」「第42代大統領です」
"Where was Clinton in the chronological order of Presidents?" "He was the 42nd president."




More generally, you can say 何番目, which means "what number [in a sequence]". Amusingly, ALC includes almost the exact same example for 何番目:



「クリントンはアメリカの何番目の大統領ですか?」「第42代大統領です」
"Where was Clinton in the chronological order of Presidents?" "He was the 42nd president."



As you note, this is difficult to express in English, so you might use this sort of expression in Japanese when we'd normally talk about cardinal numbers in English. Take a look at the following example from Kenkyūsha's New Japanese-English Dictionary:



あなたの本当の病名を言い当てたのは何人目の医者でしたか。
How many doctors did you see before one guessed the name of your illness?




Note that the Japanese asks about ordinality (what position in the list of doctors), while the corresponding English translation asks about cardinality (the total number of doctors).


organic chemistry - How does toluene react at higher temperatures and why?




Reaction of toluene at high temperatures gives us (o-m)toluene; whereas at normal conditions of electrophilic attack, it gives us (o-p) directing.



Why does this happen at high temp although as methyl group is activating and o-p directing?




reaction mechanism - Why is it necessary to avoid even traces of moisture from a Grignard reagent?


This fact was written in my text book. I wonder why that should be so.



Answer



Grignard reagents are highly reactive and react with any source of proton to give hydrocarbons. Even water, alcohols, amines are sufficiently acidic to convert them to corresponding hydrocarbons.



$\ce{RMgX + H2O -> RH + Mg(OH)X}$


Where, $\ce{R}$ is a hydrocarbon.


sampling - FIXED POINT conversion Problem (DSP)


Actually after reading the data from ADC is an $Q15$ format (ie. ADC supports 0-3.3v, ADC is an unipolar type). then the $Q15$ data is converted to $q31$ format ($Q31$ value = $q15_{data}$ <<16). this $Q31$ value is fed in to FIR filter (FIR filter is an $Q31$ format) then filter output is fed in to the fftr(real fft).



Iam facing the problem like if my input is more than 600mv the value of the $Q31$ (after filter stage) is exceeding the $2^{31}$($q31$) limit. Kindly give some suggestion how to solve this problem.


My ADC output is 16bit (ADC MAX vge is 0-3v unipolar type). then this value i am converting to $Q31$ as follows uint_16 ADC_value;\ADC value $Q31$ value = (Q31) ((q15) (ADC_value-offset))<<16; \ here offset is (unipolar to bipolar conversion ie. AVG of ADC_value )16 bit to $Q15$ conversion


if my input voltage is more than 600mv $Q31$ value is not correct.


Kindly suggest me how to convert $Q15$ to $Q31$




acid base - How much can the pH change through dilution?


Consider an acidic solution with Hydrogen ion concentration, $\ce{[H+]}$ of $10^{-5}\:\mathrm{M}$. Since $\:\mathrm{pH} = -\log \ce{[H+]}$ the $\:\mathrm{pH}$ of solution is $5$. Suppose we dilute solution 10 times with water. Now, $\ce{[H+]}$ is $10^{-6}\:\mathrm{M}$ and $\:\mathrm{pH}$ is $6$. Further dilution should increase $\:\mathrm{pH}$ from $6$ to $7$ and then from $7$ to $8$ and so on. Can this go in for ever? Does this not imply that an acidic solution can be made basic/alkaline simply by adding water? But that doesn't happen? What prevents it?


Is there anyone already found answer for this problem or it is just an unsolved basic problem of chemistry?



Answer



Water undergoes autoionization, i.e., it reacts as follows:


$$ \ce{H2O + H2O <=> H3O+ + OH-} $$


The equilibrium constant for this reaction at standard conditions is $K_w = [\ce{H3O+}][\ce{OH-}] \approx 1.0 \cdot 10^{-14}$. In pure water, $[\ce{H3O+}] = [\ce{OH-}]$, hence $[\ce{H3O+}] = \sqrt{K_w} \approx 1.0 \cdot 10^{-7}\ \textrm{M}$.


Suppose we dilute a solution with some initial concentration of $[\ce{H3O+}]_i = \frac{n_i}{V_i}$, where $n_i$ is the initial number of moles of $\ce{H3O+}$ and $V_i$ is the initial volume. If I now add a volume $\Delta V$ of pure water (which would contain $(1.0 \cdot 10^{-7}) \cdot \Delta V$ moles of $\ce{H3O+}$) the resulting final concentration can be crudely approximated as:



$$ [\ce{H3O+}]_f \approx \frac{n_i + (1.0 \cdot 10^{-7}) \cdot \Delta V}{V_i + \Delta V} $$


We can see what value this expression approaches as we make the solution more and more dilute by taking the limit as $\Delta V \to \infty$:


$$ \lim_{\Delta V \to \infty} \frac{n_i + (1.0 \cdot 10^{-7}) \cdot \Delta V}{V_i + \Delta V} = 1.0 \cdot 10^{-7} $$


Therefore, $[\ce{H3O+}]$ tends towards $1.0 \cdot 10^{-7}$ with further dilution, so $pH$ will approach a value of $7.0$.


inorganic chemistry - How are alkalide ions synthesized?


How are alkalide molecules synthesized, for example, I have read in a paper that the reaction $$\ce{2Na -> Na+ + Na-}$$ is exothermic with a $\Delta H = \pu{-438 kJ/mol}$.



I have also read that in the presence of a certain type of crown ether, under specific conditions, $\ce{Na+}$ crystallizes at around $\pu{-20 ^\circ C}$.


Can someone walk me through the mechanism through which sodide, or any alkalide, in general, is actually synthesized?



Answer



The reaction energetics


Using the method of the superposition of configurations, the electron affinity of $\ce {Na}$ was theoretically determined to be $\ce {+0.54 eV}$ $\ce {^1}$, that is, around $\ce {-52.1 kJ/mol}$. The gas-phase process


$\ce {2Na (g) -> Na^+ (g) + Na^- (g)}$


has been determined to be endothermic by $\ce {4.54 eV}$ $\ce {^2}$ while the solid-state process


$\ce {2Na (s) -> Na^+ .Na^- (s)}$


has also been estimated to be endothermic by $\ce {0.8 eV}$ $\ce {^2}$.Thus, your assertion regarding the large exothermicity of the reaction is questionable. However, it is worthy to note that the $\ce { \Delta H_f}$ and $\ce {\Delta G_f}$ for $\ce {Na^+.Cry Na^-}$, where $\ce {Cry}$ = [2.2.2] cryptand, are $\ce {-10 kJ/mol}$ and $\ce {+28 kJ/mol}$ respectively $\ce {^3}$. Your large exothermic enthalpy may likely refer to the lattice energy, i.e. for the process


$\ce {M^+.Cry (g) + M^- (g) -> M^+.Cry M^- (s)}$.



For $\ce {M = Na}$, the $\ce {\Delta H}$ and $\ce {\Delta G}$ for the above process are $\ce {-323 kJ/mol}$ and $\ce {-258 kJ/mol}$ respectively $\ce {^3}$.


Preparation of the alkalide


$\ce {Na^-}$, $\ce {K^-}$, $\ce {Rb^-}$, and $\ce {Cs^-}$ anions are stable both in suitable solvents and in crystalline solids$\ce {^3}$. The latter can be prepared either by cooling a saturated solution $\ce {^4}$ or by rapid solvent evaporation.


The principal difficulty in preparation of crystalline salts containing alkalide ions by the method of cooling a saturated solution is the low solubility of these alkali metals in the amine and ether solutions $\ce {^3}$. Without a sufficiently large concentration of the metal dissolved in solution, precipitation of the solid upon cooling would be insignificant. This difficulty was resolved by the use of crown-ether and cryptand complexes, such as those of [18]crown-6 and [2.2.2] cryptand] $\ce {^3}$. The complexating agent complexes with $\ce {M^+}$ , shifting the equilibrium (1) far to the right, significantly increasing the concentrations of the dissolved metal ions.


(1) $\ce { 2M (s) -> M^+ (sol) + M^- (sol)}$


(2) $\ce { M^+ (sol) + Cry (sol) -> M^+.Cry}$


This technique of using complexating agents was also what Dye et al. used in their synthesis in 1973 $\ce {^4}$. As reported by Dye et al., a sufficiently concentrated solution of sodium metal (in excess) dissolved in ethylamine with [2.2.2] cryptand was first prepared. The solution is then cooled to dry ice temperatures, giving a gold-coloured crystalline solid precipitate. Through thorough analysis, this precipitate was then determined to be $\ce {Na^+.Cry Na^- (s)}$ with $\ce {Cry}$ being the [2.2.2] cryptand.


References





  1. Weiss, A. W. Theoretical Electron Affinities for Some of the Alkali and Alkaline-Earth Elements. Phys. Rev., 1968, 166 (1), 70-74




  2. Tehan, F. J.; Barnett, B. L.; Dye, J. L. Alkali anions. Preparation and Crystal Structure of a Compound which contains the Cryptated Sodium Cation and the Sodium Anion. J. Am. Chem. Soc., 1974, 96 (23), 7203–7208




  3. Dye, J. L. Compounds of Alkali Metal Anions. Angew. Chem., 1979, 18 (8), 587-598




  4. Dye, J. L.; Ceraso, J. M.; Lok, M. T.; Barnett, B. L.; Tehan, F. J. A Crystalline Salt of the Sodium Anion (Na-). J. Am. Chem. Soc., 1974, 96 (2), 608-609





halacha - Giving to the poor of your city first - home or workplace?


The poor of one's household take precedence over the poor of one's city, and the poor of one's city take precedence over the poor of another city, as implied by [Deuteronomy 15:11]: "[Open your hand generously] to your poor and destitute brother in your land."


What would be the ruling for someone who for example worked a whole day in one city but lived in another city ? Is "your city" determined by where you sleep or does where you spend your day (and if you are a business owner - where you pay taxes and share in the cities ordinances) have any weight in terms of Tzedakah preferences.


** The person who I was discussing this with seemed to recall something from the achronim in the laws of Kimcha D'Pischa that says you need to give in the city where you work as well. Didn't make sense to me so I thought I would ask the MY community.



Answer



According to R' Herschel Schachter, the designation of "your city" for this purpose is based on association, rather than geography. In an interview on the topic with Jewish Action magazine, he said:




However, aniyei ircha does not refer to the poor people of your city literally. I live in Manhattan. Are all the poor people in New York considered my aniyei ircha? I don’t think so. Years ago, the cities were small and aniyei ircha were the people you knew. Today, aniyei ircha are the people with whom you associate, with whom you have a kesher. There are so many shuls in New York, but I don’t daven in all of them. There are so many mikvaot in this city, but my family only uses one. The shuls and mikvah from which my family benefits are considered aniyei ircha. The yeshivot where I, my children and my grandchildren learned, even in distant cities or countries, are considered aniyei ircha. The institutions with which I have a connection are aniyei ircha, and those with which I have no link are aniyei ir acheret [the poor of another city].



Based on this principle, it would seem that institutions or poor people that you associate with in your place of business count as "your city" just as much as those that you associate with in your place of residence, and more than those that you don't associate with who happen to be located in your place of residence.


acid base - Why do diacidic and triacidic alkalis dissociate in one step?



My book states that dibasic and tribasic acids dissociate in water in two and three steps respectively but for diacidic and triacidic bases it states that they dissociate in one step. I do not know why.


For example:


$\ce{H2SO4}$ dissociates in water in two steps as follows: $$\ce{H2SO4(aq) <=> HSO4^{-} + H+}$$ $$\ce{HSO4^{-}(aq) <=> SO4^{2-} + H+}$$


but


$\ce{Cu(OH)2}$ dissociates in water in one step as follows:


$$\ce{Cu(OH)2(aq) <=> Cu^{2+} + 2OH-}$$


Why is this so. Why does not $\ce{Cu(OH)2}$ dissociate in two steps to form $\ce{CuOH+}$ in the first step and $\ce{Cu^{2+}}$ in the second step?




halacha - When do Sefardim start mourning in a year that Tisha B'av is postponed until Sunday?


As mentioned here, Sefardim observe the mourning period known to Ashkenazim as "The Nine Days" only during the week that Tisha B'av occurs.


Tisha B'av falls out on Shabbat this year (5772), and the fast is postponed until Sunday.


Do Sefardim observe the mourning period during the week the 9th day of Av occurs, or the week that the fast occurs?


In other words, do they end up having no days of mourning this year, or does the mourning period start from sunday, the 3rd of Av?




Answer



The Shulchan Aruch (551:4) rules regarding both the case of Tisha b'Av on Saturday and Tisha b'Av on Sunday that there is no mourning period and some say (Yesh Omrim) that there is mourning the entire preceding week. Generally when the Shulchan Aruch quotes two opinions and only the latter is prefaced by 'some say', the halacha follows the former opinion (Yad Malachai Klalei HaShulchan Aruch 17).


The Kaf haChaim (sk 78) rules as such, but notes that it is proper to be stringent only regarding haircuts for either the entire preceding week or at least just the Friday before in order to not enter Tisha b'Av looking too nice.


periodic trends - Comparing radii in lithium, beryllium, magnesium, aluminium and sodium ions

Apparently the of last four, $\ce{Mg^2+}$ is closest in radius to $\ce{Li+}$. Is this true, and if so, why would a whole larger shell ($\ce{...