Tuesday, January 31, 2017

thermodynamics - Liquid water below freezing temperature


I got in my car this morning and the temperature read 13 F (that's around -10.5 C.) While driving down the road, I noticed a bottle of water in my cup holder was frozen solid as expected.


Another bottle of water (cheap, thin-walled, plastic disposable water bottle) contained liquid water! I shook the bottle, not a single crystal of ice!


Shortly thereafter, I noticed the water became slushy, so it had begun freezing quite quickly!



The interior of the bottle was hardly perfectly smooth given the quality of the bottle and the water was half drunk so it was probably not super pure.


What caused this? Was this supercooling?



Answer



You may have just experienced supercooling.


Ordinary crystallization upon reaching the freezing point of a liquid requires nucleation sites - places for crystals to form. In absence of nucleation sites, water can be cooled down to lower temperatures until crystal homogeneous nucleation occurs. In water, this can occur as low as $224.8\ \mathrm{K\ (-48.3\ ^\circ C,\ -55\ ^\circ F)}$.


Nucleation can also be induced by disrupting the system, which happened when you shook the bottle. Even so, the fact that it only became slush may attest to the presence of impurities. A $\mathrm{19\ ^\circ F,\ 10\ ^\circ C}$ freezing point depression is not unreasonable depending on the amount of saliva that might have ended up back in the bottle.


computer vision - Suggested Preprocessing methods for OCR on Circular Images


Hello this is my sample image I am going to do real time character detection on images like that.


I've tried SURF, SIFT, MSER and template matching on original image without any preprocessing. I can detect characters but when the image changes this feature detection methods does not work because there isn't a lot of interested points in the characters on the image. I am not exactly sure what kind of preprocessing I should do for higher accuracy.


so my question is what methods can you guys suggest me to do for character detection with higher accuracy.


thanks in advance.


enter image description here




Answer



Here is what I did for a client (What you are asking is the same).


Assuming that you have access to certain type of a pattern on the image (or the center of the hole), you could always detect the template to obtain the location of a possible unwarp:


Pattern matching


Note that in the transformed image, two region of interests are defined and the region within which we would like to read the characters is the torus lying between two circles. Using this information, we could warp this image using an inverse polar transform to obtain:


inverse_polar_transform


I also provide the MATLAB code for this transformation at this file-exchange post.


In the next step, thanks to the template matching, the characters to be read always lie in the local region defined in the image above. Now, if you have appropriate illumination the character segmentation is nothing but a trivial set of image processing operations:


character segmentation


The connected components obtained eventually are fed into a neural network or an SVM, first to train and then to classify. This part is composed only of a basic machine learning task, which I won't go into the details, here.



Don't forget to take good care of the illumination, as it is almost solving the problem half way.


halacha - Television on Shabbos


Let's take as a given that it is forbidden to turn a television on or off or otherwise use electricity on Shabbat. Let's also ignore the whole issue of watching TV in the first place. We can also assume that you are not allowed to (or wouldn't want to) leave the volume on.


May one turn a television on before Shabbat, mute the sound, and watch it on Shabbat? Sources or solid arguments only.




Why do we substract a background image and not divide it?



Subtracting a background image for background correction is the standard way of doing background correction to obtain the foreground.


I am wondering if there are situations, where it would make sense to divide with the background image instead.



  • For example, it seems that having a uniform image intensity after division could be beneficial in interpreting an image. E.g in microscopy images.

  • It also seems physically more intuitive to have uniform baseline intensity after background correction/division than to have zero baseline intensity due to subtraction.




halacha - Stealing from or causing damage to a third party to save life or limb


Suppose Fred is in danger of death or injury, and the most direct way to avoid that fate involves stealing or damaging property belonging to Ernie, an uninvolved person.


Examples:




  • Fred is being pursued by a would-be assailant on foot, and finds Ernie's bicycle unlocked. Fred can steal the bicycle to enable a quick escape from the pursuer.





  • Fred is in a car whose brakes stop working. The most direct way to avoid crashing into something hard is to intentionally crash into Ernie's fruit stand.




Questions:




  1. Is this action by Fred allowed?





  2. Does Fred have to compensate Ernie afterward?




  3. Does the likelihood or not of actual death to Fred if he doesn't steal or damage matter to 1 and 2? What if the worst possible consequence is just injury?




  4. Does it matter how Fred got into the dangerous situation, e.g. through pure accident, his own negligence, someone else's negligence, or someone else's malice?





(Inspired by this question and this challenge.)




coordination compounds - Why do transition metals form particularly stable complexes?


The pre-transition metal ions can form complexes but the ligands are weakly bound unless they are multidentate and thus benefit from the chelate effect. For example, crown ethers and cryptands.


However, transition metal ions can form a vast array of stable of stable complexes with monodentate and multidentate ligands. Why is there such a difference between the pre transition elements and the transition metals in this respect.


My initial thoughts are that the transition metal ions will have a higher charge and smaller radius so the electrostatic attraction is larger. I also thought about the d-orbitals but the pre transition elements have d orbitals available, they're just not filled. As a result, is increased stability related to exchange energy or perhaps the lower energy d orbitals? Are there any more factors? Are my suggestions valid?




parshanut torah comment - Why mention the ger in Lev 19:10, 23:22?


Vayikra 23:22:



וּבְקֻצְרְכֶם אֶת קְצִיר אַרְצְכֶם לֹא תְכַלֶּה פְּאַת שָׂדְךָ בְּקֻצְרֶךָ וְלֶקֶט קְצִירְךָ לֹא תְלַקֵּט לֶעָנִי וְלַגֵּר תַּעֲזֹב אֹתָם



When you reap the harvest of your Land, you shall not completely remove the corner of your field during your harvesting, and you shall not gather up the gleanings of your harvest. [Rather,] you shall leave these for the poor person and for the stranger



Vayikra 19:10:



וְכַרְמְךָ לֹא תְעוֹלֵל וּפֶרֶט כַּרְמְךָ לֹא תְלַקֵּט לֶעָנִי וְלַגֵּר תַּעֲזֹב אֹתָם


And you shall not glean your vineyard, nor shall you collect the [fallen] individual grapes of your vineyard; you shall leave them for the poor and the stranger



( Chabad.org translations )


I always read these verses as saying that we should give פאה (a corner of the field designated for the poor to take) and לקט (forgotten stalks, left for the poor to take) and other מתנות עניים (gifts to the poor) like פרט ועוללות (grapes that fall off the vine by harvest, and funny-looking clusters of grapes [פאה ד:ג-ד]) to the poor and to the גר, because the גר is, generally speaking, in a disadvantaged position.


However, a friend of mine just raised the point that ממה נפשך -- if the גר is poor, then he is an עני (pauper); if he isn't poor, then (presumably) he doesn't take לקט and פאה.

So why should these verses specify גר?


The גר here is the גר צדק, the convert, as codified by Rambam (Rambam, Hilchot Matnot Aniyiim 1:9), who adds that we do not withhold charity from non-Jews, מפני דרכי שלום in order to keep the peace.




nuances - How to Pronounce 化学 "Chemistry"?


A Japanese teacher on Twitter posted that 化学 is pronounced かがく and means "chemistry". I double-checked it on tangorin.com and it lists that pronunciation but says that it's pronounced ばけがく to avoid confusion with 科学 ("science").


I can't find any more info on the net about this... could somebody confirm this?


In particular, for my Anki vocabulary deck, which pronunciation should I learn? Or should I shoehorn both into my deck somehow?



Answer



I think the basic word is かがく, but the other reading is possible. Here's what 明鏡国語辞典 says at the bottom of its entry for 化学{かがく}:




►「科学」と区別して「ばけがく」ともいう。



If you pronounce it this way, you're deliberately using the other reading of the first kanji to make sure the person you're talking to knows which word you mean. I would definitely learn the reading かがく, though.


halacha - Newspaper Delivery on Shabbos



Is getting a paper delivered on Shabbos allowed?


If not, what may be done with it upon delivery?



Answer



This source seems to disagree: http://www.ottmall.com/mj_ht_arch/v38/mj_v38i41.html#COA


It Seems to be quite complex.


Monday, January 30, 2017

halacha - Praying whilst breastfeeding



If a woman is suitably dressed in a modest manner and is covered to the greatest degree possible, would she be permitted to pray whilst breastfeeding?


If yes, would this be reserved for sha'at hadchak or can she do this lechatchila?




thermodynamics - What is the difference between enthalpy (H) and heat (q)?


It seems that in some cases it's the same (that is, $\Delta Q_p=\Delta H$) yet in others they differ. For example, \begin{align} \ce{2H2(g) + O2(g) &->2H2O(l)} & \Delta H &= -572~\mathrm{kJ} \end{align}



The answer for one mole of $\ce{H2O}$ produced is $\mathrm{-572\times 0.5~kJ}$. Is this under the assumption of constant pressure? Therefore it's $\Delta Q_p=\Delta H$?




usage - 「そうなの?!」、「マジで?!」、「本当に?!」


For the most part (contextually) these phrases seem to be interchangeable, like "really?!", "for real?!", "seriously?!" etc.


Are there cases/scenarios when only one would be applicable?



Answer



Well, for starters let's say that you probably don't want to say マジで?! to your boss. :)


Maybe native speakers can be more specific but as far as I know the main difference is in politeness level, the meaning is the same.



So in a formal situation you would want to use 本当ですか, while if you are talking with a close friend you can say “マジで?” that is way more casual (and similarly for そうなの).


At this link you can actually even see that マジ is listed as a common mistake people sometimes make in formal situations where 本当ですか should be used.


Ps. let me make clear that hence also 本当に? is actually quite casual (I think less than マジで though) and so when in doubt is always better to use 本当ですか instead. Here is another related link.


history - What happened to Siman 168?


If you look in the Tur Yoreh Deah Siman 168 (so too the Shulchan Aruch), you'll notice that there's nothing there.


Was it lost sometime in history? It looks like the Shulchan Aruch also didn't have anything there, so it should have been lost not long after publication (they lived around two hundred years apart).



Answer



In the footnote of the Machon Yerushalayim edition of the Tur, he explains that various editions of the Tur with different commentaries divided up the sections differently - one missing a siman (not 168), another dividing up a siman into 2 or more simanim. So in order to line up the Tur with all its major commentaries it was decided in more recent editions to skip/merge siman 168.


What is the source and meaning of the word מהול?


I am trying to get to the bottom of what the word מהול means in the context of being circumcised.


I can't find it used in Mishna or Talmud, but by the Rishonim and Medrashim it is commonly used to mean someone who was circumcised. I did not search gaonic works.


My question is twofold. If there is a dikduk reason, and this is simply a version of מילה, I'm curious what the rule is and why the word was seemingly never used by chazzal.


Possibly the word implies something else. Here are a couple of suggestions.



In Nach the word is found in Yeshaya 1 22 where Rashi comments:



מהול מעורב ואין לו דמיון במקרא ומ''א פותר לשחוק אמרתי מהולל ( קהלת ב' ב' ) מעורבב :



Which would work as far as the person with the mila is now mixed into society.


In maseches דמאי the phrase מחל ושותה is used which Bartenura in one explenation ties back to that verse in Yeshaya and says מיחל is the same as מיהל and it means מוזג. I guess that is similar enough to Rashi.


This is all just a suggestion. My question stands as what is the source and meaning to the usage of this word in this context.




words - What is the meaning of the phrase לצאת ולבוא?


What is the meaning of the oft-repeated phrase לצאת ולבוא as in Deuteronomy 31:2 ? I realize it means "to conduct business" or "to lead", but I was hoping for more of a deep dive (does it come from a shepherding metaphor?)




Answer



R' Samson Raphael Hirsch, in his commentary on Deuteronomy 31:2, calls "לצאת ולבוא" "the general term used for the public efficient activity of national leadership," and points us to his full workup of the term in his commentary on Numbers 37:17, where Moses uses similar terminology in asking God to appoint his successor:



אֲשֶׁר־יֵצֵ֣א לִפְנֵיהֶ֗ם וַאֲשֶׁ֤ר יָבֹא֙ לִפְנֵיהֶ֔ם וַאֲשֶׁ֥ר יוֹצִיאֵ֖ם וַאֲשֶׁ֣ר יְבִיאֵ֑ם וְלֹ֤א תִהְיֶה֙ עֲדַ֣ת יְהוָ֔ה כַּצֹּ֕אן אֲשֶׁ֥ר אֵין־לָהֶ֖ם רֹעֶֽה׃


who shall go out before them and come in before them, and who shall take them out and bring them in, so that the LORD’s community may not be like sheep that have no shepherd.”



There, R' Hirsch also explains that "לצאת ולבוא" refers to leadership activities in general, and not [only] to military leadership. He brings two other Biblical usages of this construct as evidence:




  • In I Kings 3:6-9, when Solomon requests that God grant him wisdom, particularly to be able to judge the people (v. 9), he points out (v. 7)




    וְאָֽנֹכִי֙ נַ֣עַר קָטֹ֔ן לֹ֥א אֵדַ֖ע צֵ֥את וָבֹֽא׃ ...


    ... but I am a young lad, with no experience in leadership.





  • In Joshua 14:11, Caleb explicitly treats "לצאת ולבוא" as separate from military endeavors:



    עוֹדֶ֨נִּי הַיּ֜וֹם חָזָ֗ק כַּֽאֲשֶׁר֙ בְּי֨וֹם שְׁלֹ֤חַ אוֹתִי֙ מֹשֶׁ֔ה כְּכֹ֥חִי אָ֖ז וּכְכֹ֣חִי עָ֑תָּה לַמִּלְחָמָ֖ה וְלָצֵ֥את וְלָבֽוֹא׃


    I am still as strong today as on the day that Moses sent me; my strength is the same now as it was then, for battle and for activity.






Finally R' Hirsch interprets the "going out" and "coming in," respectively, as setting a good example in the public and the private spheres, thereby influencing people to "faithfully fulfill all public and private duties."


Kosher flavored beer without certification on the bottle?


I've always heard that the rule in the United States is that domestic non-microbrewery/craft unflavored beer needs no certification as kosher, as all such beers are kosher, but that any other beer (viz, foreign, microbrewery/craft, or flavored) needs certification. Apparently, that's almost correct: The Star-K's "Star-K Liquor List", March 2014 edition, reads in part:




Beer, UNFLAVORED: Acceptable WITHOUT Certification EXCLUDING when brewed in a craft, pub or home brewery that may bottle non-kosher flavored beers (Oyster, Bacon etc.) EXCLUDING English Milk Stouts


Beer, FLAVORED: Requires Certification



And yet I've recently been in the homes of two different religious families, who served two different brands of flavored beer (I forget which) without certification on the label. So I'm wondering whether they simply erred, or whether there's more to it:



  • Are there accepted authorities who dissent from the Star-K and maintain that flavored beer doesn't need certification (perhaps only for certain flavors or something)?

  • Are there brands of flavored beer known to be under certification without its being printed on the bottles?

  • Or is there perhaps some other justification?





food - falling asleep on the left side to aid digestion


Kitzur Shulchan Aruch 71:5 reads, in part (translation my own):



And it's good that he'll lie at the start of his sleep on the left side and at the end on the right side, as this is good for the health of the body, for the liver rests in the right side and the stomach on the left side, so that when he leans on the left side then the liver will be over the stomach and will warm it with its warmth; thus, the food will digest quickly. After the food is digested, it's seemly for him that he'll lean on the right side, so that the stomach will rest and the food waste will descend.




As always, for practical advice, CYLOR.


A few questions:



  1. Does modern science agree with these facts about digestion?

  2. Does he mean to imply that if someone falls asleep on his left side, then his body will shift during the night and he'll wind up on his right?

    1. If so, does modern science agree? (This is independent of the above question, which is about digestion. This one has nothing to do with digestion. Rather, it's asking whether modern science grants that someone who falls asleep on his left side will wind up on his right side assuming he sleeps awhile and assuming he winds up anywhere for an extended time (i.e., does not toss and turn a lot).)

    2. If not, then how does he expect us to lie on the right after our food digests?




  3. Do other modern halachic decisors agree with this? (I don't see it in Mishna B'rura, for example, though that doesn't, of course, mean it's not there.)


Sources, where possible, please.



Answer



Per the following health websites - sleeping on the left side avoids heartburn


http://www.ehow.com/way_5206251_sleeping-positions-better-digestion.html


http://www.livestrong.com/article/69972-sleeping-positions-better-digestion/


The Rambam in Hilchos Deios Perek 4 Halacha 5 also mentions to start off sleeping on the left and then switch over to the right.


Organisation in Periodic table



Why do we find big spaces in the periods of the Periodic Table between $\ce{H}$ and $\ce{He}$, $\ce{Be}$ and $\ce{B}$, and $\ce{Mg}$ and $\ce{Al}$?


What is the logic of such organization of the periods?




Sunday, January 29, 2017

grammar - What does 遅れに遅れて mean?


I'm pretty sure ~れに~れて is a grammar form that I have studied in my JLPT textbooks, but I came across it again in a text and I can't for the life of me find it again in my grammar dictionaries. I also looked on JGram, but couldn't find it there.


The particular case I came across was:



人間{にんげん}は昔{むかし}、遅{おく}れに遅{おく}れて自{みずか}らの年{とし}を自覚{じかく}する。



Without knowing what 遅{おく}れに遅{おく}れて is doing, I feel I'm missing an important nuance.


I think it's something like, "From long ago, people have been slow to be conscious of their own age." But how is the above sentence different from this one:




人間{にんげん}は昔{むかし}、遅{おそ}くて自{みずか}らの年{とし}を自覚{じかく}する。



...?



Answer



An attempt to answer your question about how the two sentences are different:


遅くて means something like "because it's late" and doesn't make much sense in the sentence.


遅く might make more sense semantically, but doesn't seem to put enough emphasis on the being late "Long ago, humans become conscious of their age late". The "late" doesn't quite know what it wants (Sorry, can't explain this much better).


遅れに遅れて tries to capture the sense of "finally" or "after much delay" and therefore implies that man should have become conscious about his age earlier. "Long ago, humans finally become conscious of their age".


It would be easier to be certain if I had more context for your sentence.


halacha - Is there any issue with using aerosols on Shabbos?


I've heard from many people that you shouldn't use aerosols (such as air fresheners, disinfectants or deodorants) on shabbos, usually citing some vague reason of changing the form from liquid to gas, or some such. This always seemed rather insubstantial as the mist that issues from an aerosol can is actually just small liquid droplets.


So, is there any truth to this? Is it indeed forbidden for this, or any other, reason? Is there any truth to this concern?



Answer



The Shulchan Aruch Harav writes (based on a Yerushalmi) that if one who spits into the wind, and the wind spreads it out, he violated the Shabbos prohibition of Zora (winnowing). He adds that it may be only a Rabbinic prohibition, as it is a Melacha Sheina Tzricha Legufa.


However, in Hilchos Pesach he writes that in order for one to violate Zora one must do it in a way of Borer. In other words, it must be similar to classical winnowing where the wind separates the chadd from the wheat.


However, the Ktzos Hashulchan writes that even according to the lenient opinion in the Shulchan Aruch Harav in Hilchos Pesach, there is still a Rabbinic prohibition to spit into the wind (or to destroy Chametz on Pesach by crumbing it and throwing it into the wind) as it appears to winnowing.



However, the Mishna Brura rules leniently for two reasons.


The first is a Tshuva of R' Akiva Eiger where he was asked if one is permited to throw water out of a window where the wind will scatter the droplets. R' Akiva permitted it for two reasons:




  1. The Yerushalmi isn't mentioned in the early poskim and the Halacha is like the Bavli that Zora requires Borer (a separation of good from bad) and




  2. Even if there is a concept of Zora where there is no Borer, it's possible that it applies only to things that grow from the ground (as winnowing is similar to threshing and gathering which are only prohibited to be done to items which grow from the ground). As R' Akiva Eiger says that spit is considered something that grows from the ground, the Yerushalmi prohibits spitting into the wind. However, water (which) isn't something which grows from the ground and would be permitted to scatter.





  3. One doesn't care if the water is scattered, and according to some opinions a Psik Reisha whose result isn't needed is allowed.




The second reason is the Alfei Menashe which says that the Yerushalmi isn't prohibiting spitting into the wind because of Zora but because of carrying in a public domain. Therefore, everyone (including the Yerushalmi) would agree that Zora requires Borer.


So it appears from the Shulchan Aruch Harav that there is (at least) a Rabbinical decree against scattering objects (the Shulchan Aruch Harav includes bread in the prohibition, and the Ktzos Hashulchan includes paper).


According to the Mishna Brura, it would appear to be permitted.


However, according to Rabbi Yosef Yitzchak Zalmanov, one would be permitted to apply spray deodorant on Shabbos. Presumably, it's because there's no wind involved in spraying deodorant.


korban - Why is it our responsibility to bring a Chatas for the Moon's sin?


In Parshas Pinchos (Bamidbor 28:15), in the obligation to bring a Korban Chatas (sin offering) on Rosh Chodesh, Rashi brings two explanations:


1) It is to atone for "טומאת מקדש וקדשיו" (defiling temple vessels) without knowledge, and Rashi says: "ללמדך שמכפר על שאין בו ידיעה לא בתחילה ולא בסוף, שאין מכיר בחטא אלא הקב"ה בלבד" - which makes senses because a Chatas is appropriate for a sin done b'shogeig (unintentionally).


2) According to a Midrash Aggada, it is to atone for the fact that HKBH reduced the moon (different opinions on what exactly the punishment was, but probably reducing its glow, rather than its size, and also waxing/waning): - "ומדרשו באגדה אמר הקב"ה, הביאו כפרה עלי על שמעטתי את הירח". (Incidentally, Rashi's loshon is a bit strange because it doesn't actually mention the Moon sinning?)



According to the second opinion, why should the Bnei Yisroel be responsible for making up for the Moon's sin? And as this is an aggada, and presumably the moon didn't actually "sin", its pretty hard to understand this as a reason to bring a chatas.


Also, why is the second answer needed? Is there something deficient in the first answer?


TIA



Answer



Why both ideas?


We can address your final question - why did Rashi cite both of these explanations - on a simple, structural level by looking at the Talmud passage Rashi got them from. In Shevu'ot 9a, the Talmud deals with an apparent tension between these two concepts, each of whose transmitters derive them from the same textual point - the fact that this korban chatat, unlike all others, is described by the Torah as "לַיהוָ֑ה" - "for God." The Talmud resolves this tension by concluding that the particular phrasing of this "extra" word is special in two ways, permitting both of these concepts to be derived simultaneously. As the Talmud's conclusion is that both ideas reside in this verse, it makes sense that Rashi echoes that position.


Korban for the moon?


To address your more fundamental question - what's going on with this strange-sounding idea of a sin offering for the moon - we need to delve deeper, with the help of some later commentaries. The Maharal addresses this idea at length in his Gur Aryeh supercommentary on this comment1 of Rashi, and R' Samson Raphael Hirsch explains this idea as well in his commentary on this verse2. They each come at it from different angles, but their explanations complement each other.


Maharal


The Maharal says that to understand this point in the Talmud, we need to understand that some of the terms used there and in the Torah have different meanings than people typically assign them:




  • Kapara here doesn't mean "atonement for wrongdoing," but "removal" or "cleansing." (As seen in Rashi's comment on Genesis 32:21.).

  • Korban is not an "offering" or "sacrifice" to appease or pay back, but a "means of getting close." (Note that its root, קרב, means "close.")

  • Chatat here doesn't mean "sin" so much as "deficiency." (See Genesis 39:31, where אנכי אחטנה means "I will make good the loss.")


So, chatat here doesn't refer to the moon's sin or, as if it could be said, to God's, but rather, to the moon's diminishment. From the point of view of the moon, it had as much right to being the supreme luminary in the sky as the sun does. However, from the point of view of the natural order, it simply didn't make sense to have two co-equal rulers. As described in a story in the Talmud on Chulin 60b, God therefore demoted the moon to secondary status, and it "took one for the team."


As the moon is diminished (chatat) from its "rightful" status, there is an opportunity to draw closer (korban) to God in an act of cleansing for (kapara) that deficiency. In general, the opportunity to draw closer to God comes specifically when one diminishes one's sense of self rather than puffing it up.3 Also in general, the קרבן חטאת is not "paying back for a sin," but "re-connecting with God in light of the deficiency created by sin."


This monthly chatat is therefore the Jewish nation's way to collectively respond to the moon's relative deficiency by recalling self-diminishment as an opportunity to come closer to God.


R' Hirsch


R' Hirsch also talks about the korban chatat as a response to a deficiency. He says that one is included in the offerings for each of the holidays to respond to the inadequacy of reality, compared to the lofty ideals of total dedication expressed by the holidays' korbenot 'ola. On Rosh Chodesh, when the theme is renewal after back-sliding, this concept is especially pertinent.



The diminishment of the moon, according to R' Hirsch, is symbolic of the very concept of imperfection in the world. He points out something striking: "Sins which human beings do are after all, in truth, the only bad things in God's world." If there's deficiency, it's thanks to our own choices.


But why, people ask all the time, does God let people make evil choices? Because without the freedom to choose sin or virtue, we'd be animals or angels, but not people, and we would not have our reason for being: to dedicate ourselves to God through free-willed good choices. So, like the moon's dimunition, the presence of evil in the world is a necessary part of the scheme of things, sub-ideal though it might look.


This special korban chatat of Rosh Chodesh, then, is not atoning for any particular sin. It's atoning for the fact that sin has to exist - that the moon can't just light the sky all night like the sun does the day. It's also reframing that apparent negative as a positive, acknowledging the great gift of free will, and dedicating it to God.


R' Hirsch also relates these ideas to the Talmud's first explanation of this korban - that it's for those who became tamei without realizing it and then contaminated the holy places. In general, R' Hirsch sees being tamei as living under the illusion that physical forces are all there is, with no room for free will.4 Those contemplated by this korban are in particular danger, in that they are trapped in that illusion without even knowing it. Along comes this general chatat each month to jerk us all out of our unconscious spiritual depression and restore our sense of free will.


R' Hirsch concludes that the two ideas in the Talmud are really two sides of the same coin - dealing with the fact that we are necessarily imperfect and subject to physical forces by bringing us back to realizing the sublime free will that our imperfections enable.


Synthesis


I'm not sure how literally we're supposed to take the Maharal's understanding of the moon's deficiency and our cleansing for it, but the symbolic point is at least also there: When we contemplate our own limitations, we are at the point where we have the best opportunity to draw closer to God. It seems to me that this concept fits well with R' Hirsch's idea of the chatat - turning contemplation of our own [potential for] evil deeds into a celebration and rededication of our free will. For both of them, we bring the special Rosh Chodesh chatat to come closer to God over the very concept of deficiency, which the poor darkened moon, perforce embodies.




1. Pertinent points are summarized in English in this torah.org lesson by R' Yitzchok Adlerstein.
2. This link is to AlHatorah's online presentation of a Hebrew translation of this commentary. English translations are available in book form.

3. For an additional moon-related image to support this idea, I suggest watching this video about the journey that Israel's Beresheet spacecraft will take (starting in three days!) to the moon. When the craft falls the lowest in its orbit, that's the best time to make a push to improve and then go even higher.
4. I discussed this concept with respect to contact with death and with respect to childbirth in previous answers.


grammar - Difference between Noun+な and Noun+だという


I came across this sentence:




四月だというのに、結構寒いね。 "It is April, but it is rather cold isn't it?"



Recalling what I learned about the のに conjunction, I can also make the sentence:



四月のに、結構寒いね。



(Question) What is the difference?



Answer



In this case, there is very little difference, except in flavor. You shouldn't look at it as という vs. な because they can't be compared. The な here simply allows you to use のに with the noun 四月.



という, in my mind, is like putting air quotes on something. という gives the former example more flavor, I think. Source --> Opinions, one Japanese and one American. I asked the Japanese lady next to me and she agreed.


四月だというのに、結構寒いね。>> Even though it's April, it's quite cold, huh? Flavor: This super coldness doesn't feel like "April," you know?


四月なのに、結構寒いね。>> Even though it's April, it's quite cold huh? Flavor: I'm stating a fact about the weather this April.


というのに is used a lot, so keep an ear out for it.


physical chemistry - Is there a simple way to get the circular dichroism of a molecule from its structure?



Are there any heuristics to get the relative absorbtion of left and right circularly polarized light by a molecule from its molecular structure? Is it even possible to predict which polarization is selectively absorbed?



Answer




Is there a simple way to get the circular dichroism of a molecule from it's structure?



Short Answer: Yes, for many molecules if you know the molecule's structure, then you can predict the shape of the optical rotary dispersion (ORD) or circular dichroism (CD) curve. Conversely, and perhaps more importantly, if you know the shape of the ORD or CD curve, then you can predict the molecule's structure, in particular, the absolute configuration at chiral centers in the molecule. There are many empirical techniques, such as the "Octant" rule. These methods are based on numerous experimental observations that have been codified into sets of rules for different classes of compounds. These empirical rules can be used to determine the absolute configuration of cyclic ketones, conjugated dienes, alpha, beta-unsaturated ketones, twisted biphenyls as well as other systems.


Long Answer: When polarized light is passed through a chiral sample and the light is absorbed, there are two physical phenomenon that can be measured. One is called the circular birefringence and it measures the difference in the refractive indices ($\ce{n_{R}, n_{L}}$) of the sample when a beam of right and left circularly polarized light is passed through the sample. When this difference is plotted against wavelength an ORD curve results. The other parameter is called circular dichroism and it measures the difference in the molar extinction coefficients ($\ce{\epsilon_{R}, \epsilon_{L}}$) when right and left circularly polarized light passes through the sample. When this difference is plotted against wavelength a CD curve results. The dependence of these two phenomenon on wavelength is termed the Cotton effect.


The following figure shows the uv-vis absorption (blue line), ORD curve (green line) and CD curve (red line) for the two enantiomers of camphor sulfonic acid. Note how the ORD and CD curves for one enantiomer are mirror images of the same curves for the other enantiomer. It is the carbonyl chromophore's $\ce{n->\pi^{\ast}}$ absorption that is responsible for the curves seen in this image. In ORD spectra there are typically 2 maxima, one positive and one negative. The positive maxima is a "peak", while the negative maxima is termed a "trough". If, when moving from longer to shorter wavelength, a peak is encountered first, then the ORD curve is said to be positive (+). Conversely, if a trough is encountered first, then the ORD curve is negative (-).


enter image description here


image source



Chromophores can be divided into two groups, symmetric or inherently dissymmetric. A carbonyl, nitro and olefin are examples of groups that, by themselves, are symmetric. They may be perturbed by asymmetry on other atoms around them, but alone, by themselves, they possess no inherent asymmetry. On the other hand, groups such as helicenes, twisted biphenyls and unsaturated ketones possess a twist or handedness; such molecules are inherently dissymmetric. The intensity of an ORD or CD curve from a molecule containing an inherently dissymmetric chromophore is usually much greater than the peak intensity from a molecule containing a symmetric chromophore.


With that information as background, we can now apply these concepts to the examination of real molecules. One of the most studied classes of molecules where these concepts have been applied are the substituted cyclohexanones. In the early 60's Djerassi, Moffitt, Woodward, Moscowitz and Klyne (some of the greats!) developed an empirical set of rules to predict the absolute configuration of chiral centers in substituted cyclohexanones. The rule became known as the "Octant" rule and came about because of the work they were doing with complex natural products that often contained a substituted cyclohexanone ring. They would run a reaction on a pure enantiomer of a cyclohexanone containing natural product and wanted a method to quickly determine if a chiral carbon in the molecule retained its absolute configuration or if the configuration was inverted in the reaction. After comparing ORD curves from countless cyclohexanone containing natural products, they were able to compile their observations into the Octant rule.


As its name implies, the Octant rule divides the region around a cyclohexanone carbonyl into 8 regions or octants. As the picture below (left part of figure) illustrates, the octants are generated by bisecting the carbonyl group with 3 planes. Two of the planes contain the carbonyl group. One divides the carbonyl into top and bottom regions and the other divides the carbonyl into right and left regions. The third plane actually passes through the middle of the carbonyl and is perpendicular to the 2 other planes. This third plane divides the molecule into front and back regions. There are a few molecules that do have substituents in the front region, but most molecules do not, so we can usually simplify our analysis by only considering the 4 rear octants. Each octant is also assigned a plus or minus symbol telling us whether we would expect a substituent in the octant to contribute in a positive or negative manner to the ORD or CD curves.


enter image description here


image source


The figure on the right shows how a cyclohexanone would be placed in the octant diagram and how its projection appears as a rectangle when sighted down the carbonyl group.


Let's examine the case of 3-methyl cyclohexanone. First let’s draw the possible conformers of both S- and R-3-methylcyclohexanone


enter image description here


Now let’s take the 2 possible conformations for R-3-methylcyclohexanone (axial and equatorial methyl group) and project them onto the octant diagram. We see that the equatorial conformation has a positive contribution to the Cotton effect, while the axial conformer has a negative contribution. At equilibrium, the molecule exists predominantly in the conformation with the methyl group equatorial, therefore we expect the positive Cotton effect from this conformer to outweigh the negative contribution to the Cotton effect from the axial conformer. Therefore, we expect a positive ORD and CD curve for R-3-methylcyclohexanone. Similar analysis leads to the expectation of a negative ORD and CD curve for the S enantiomer. Indeed, experimentally it is found that the ORD curve for R-3-methylcyclohexanone is positive and negative for S-3-methylcyclohexanone. The full name for the R enantiomer is R-(+)-3-methylcyclohexanone


enter image description here



image source


More detail on the 3-cyclohexanone example, as well a nice, concise review of ORD can be found here.


Books have been written on this subject so there is much that I have left out. For those who would like to explore further here are a few phrases that, in addition to the previous link, can help you get started: Cotton effect, ORD biological applications, and magnetic circular dichroism


minhag - Talis Gadol for Unmarried Individuals


In my minhag (and I believe it's minhag Ashkenaz), unmarried men do not wear a Talis Gadol (only a Talis Katan).


Why is this so?



Answer



In D'varim 22, the pasuk commanding placement of tzitziyos on 4-cornered garments immediately precedes the pasuk describing/commanding getting married. The juxtaposition gave rise to the minhag of simultanaizing these two acts.


Extracting instructive meaning from the juxtaposition of two verses is universally acceptable as a method of interpretation only in D'varim. The example used by the g'mara to prove this includes one of the aforementioned p'sukim. In this issue of Yeshivat Har Etzion's Daf Kesher, the topic is addressed. Its mention is attributed to the Sefer Hamanhig, on whom the Mishna B'rura asks exactly @jake's question in the comment below: How could it be that a mitzva from the Torah is pushed off beyond the age of bar mitzva?



It is suggested that although an interesting symbolic connection exists between wrapping oneself in a talis and protecting one's wife or imitating God's ways, citing the pasuk is intended to be a postfix hint and not an ab initio source.


(Also see this Satmar publication for extensive treatment of the same question: פרי תמרים)


halacha - Can 'cruelty to animals' render an animal not kosher?



The problem of cruelty to animals is rife in the food production industry. This article brings the reasoning of two Rabbanim to forbid foie gras and veal on these grounds:



Some of the greatest halachic authorities of modern times such as Rabbi Moshe Feinstein and Rabbi Haim David Halevy, both of blessed memory, declared foie gras (goose liver produced by force feeding geese) and veal (the anemic flesh of a calf, denied light and movement) to be prohibited, as their production egregiously transgresses the Jewish prohibition of za’ar baalei hayim, causing cruelty to animals that is not essential for human consumption.





  1. To what extent do kashrut authorities take this in to consideration?




  2. Is this regulated in the kashrut market?





  3. Does the animal become forbidden because of cruelty or is it that you are facilitating it by buying that animal?




  4. Is there indeed a 'threshold for cruelty' beyond which an animal would be considered non permissible to eat?






UPDATE: An article by Rabbi Slifkin was written on this topic called 'How Frum Is Your Food'.





halacha - Was Zerach really the first born?



וַיְהִי בְלִדְתָּהּ וַיִּתֶּן יָד וַתִּקַּח הַמְיַלֶּדֶת וַתִּקְשֹׁר עַל יָדוֹ שָׁנִי לֵאמֹר זֶה יָצָא רִאשֹׁנָה And it came about when she gave birth, that he (the infant) stretched out his hand. So the midwife took and bound a crimson thread on his hand, saying, "This one came out first." (Bereshis 38:28)



Is stretching a hand outside the mother enough to be considered the first born? Would this count today l'halacha? If not, how is this pasuk understood?




halacha - Surrogate mother



If a fetus has been formed in a mother and then deposited in a surrogate mother, who is considered the mother? In other words, does the mother's 'seed' make her the mother?


The story of Yosef and Dinah is well known. Yosef was originally in Leah and Dinah in Rochel. Because of their prayers they were 'changed' round and Yosef is considered Rochels child although made with Leah's 'seed'. Also, since it says one can always be sure who the mother is, that is why you use the mother's name, also proves that the surrogate mother is the one.




grammar - Difference between してこのかた and して以来


These two grammar points seem to be synonymous. Apart from formality このかた being maybe an older expression, are there any significant differences in meaning between these two.


For example, is there any reason that



あの山の写真を見て以来、いつかは登ってみたいとずっと思い続けてきた。



could not be rewritten as



あの山の写真を見てこのかた、いつかは登ってみたいとずっと思い続けてきた




Likewise, is there any reason that



日本から帰国してこのかた、毎日日本のことを思い出している。



Could not be stated as



日本から帰国して以来、毎日日本のことを思い出している。



I took these examples from 新完全マスターN2.




Answer



このかた isn't felt older to me, but they do have a little difference in meaning.


Both ~して以来 and ~してこのかた can be translated "since X", but 以来 tend to focus on X, suggesting it is a notable, important turning point, or reference point to explain the story thereafter. In contrast, このかた puts focus on the period after X, that has significance, being long, full of memories, or whatever special, but X itself is usually incidental. In other words, 以来 actually means "Having begun from X, —" while このかた means "In all the time between X and now, —".


Your



あの山の写真を見てこのかた、いつかは登ってみたいとずっと思い続けてきた



thus sounds stiff to me, as this sentence apparently means you start to want to climb that mountain because you saw the picture. The second rewording is natural and almost synonymous.


Usage-wise, it should be noted that このかた is hardly used when telling objective frequency. Even if you said 就職してこのかた三回目, it would only be understood that you wanted to say "three times" is too rare, or too frequent, compared to such a long, or short, duration.


Grammatically, 以来 has a predicative meaning "be the first time since". このかた can never be used as predicate.




酒を飲んだのは、大学を卒業して以来だ。
= 酒を飲んだのは、大学を卒業して以来はじめてだ。
= 酒を飲んだのは、大学を卒業してこのかたはじめてだ。
× 酒を飲んだのは、大学を卒業してこのかただ。



Sources for celebrating Purim during the Second Temple


(Maybe I'm wrong), in the listing of the Dead Sea scrolls fragments Megillat Ester is missing. That seems strange taking into the account that the Megillah says that memory will never fade away.


The list does include Ruth or Job or Song of Song. Also, the Megillah does not seem to be exclusively related to the Pharisees to claim that others didn't accept Purim.


The Mishna in the Megillah tractate was composed (as the rest of it) long after the destruction of the Temple. On the other hand, the Mishnah describes nicely how Succos was celebrated in the Temple, or Yom Kippur. But how Purim was celebrated in that era?



What sources describe celebrating Purim during the Second Temple era?


Also, are there external testimonies on the Jews celebrating Purim abroad, in the Assyrian or Roman empires?




halacha - Meat right after Milk... make a new bracha?


Suppose someone is planning on having some dairy food just before a meat meal. May the person make a bracha to cover the entire dairy/meat meal, or must he finish his dairy, make a bracha achrona, and then make a new bracha rishona on the meat?



Answer



According to the Mishna B'rura (494:16), one does not need to recite a b'racha acharona in between the dairy and the meat, but the tablecloth must be changed in between the dairy and the meat if both are eaten at the same table. (Nevertheless, he must clean his mouth from the dairy before eating meat).


If the dairy food was hard cheese or the equivalent, however, the person must recite birkas hamazon after his dairy meal and wait six hours before eating meat.


pregnancy birth - Woman attending shul after childbirth


There is a common custom that a woman who has given birth does not travel anywhere until she has gone to shul. What is the source of this custom, and what are its details? (I.e., it is necessary to hear Kaddish, or Krias HaTorah etc.)



Answer



Orach Chaim 282 - see Magen Avraham towards end, also Pishchei Olam and Matamei HaShulchan in Orach Chaim 282 - it is in place of the Korban a lady used to bring after giving birth.



http://hebrewbooks.org/pdfpager.aspx?req=9007&st=&pgnum=563


http://hebrewbooks.org/pdfpager.aspx?req=40431&st=&pgnum=394


See Sefer Panim Meiros Volume 2 Question 124 (published appx 300 years ago in Amsterdam) that when a woman finally has enough strength to leave her house after giving birth, she first visits a Shul.


Shaalos U'Tshuvos Bzail HaChocmo Chelek 6 Siman 78 "It is a Minhag from the Kadmonim that a lady does not go anywhere after giving birth, prior to going to the Shul as a Zecher for the Korban that was brought after a lady gave birth".


Saturday, January 28, 2017

Evolved minimal Hebrew pronunciation in halacha


Inspired by comments on this question: Say a person travels from place to place where there are certain traditional havarot (pronunciations) such that what were likely originally distinct sounds, are instead merged as one (e.g. most Ashkenazi pronunciations of ת/שׂ/ס, or ב/ו, ; Sephardic kamatz/patach; Hungarian kamatz/shuruk/kubutz or shuruk/kubutz/chirik or cholem [ו]/cholem-yud [וי]; Hamburg/Dutch Sephardi ס/שׁ/שׂ/צ; Litvish tzeirei/tzeirei-yud/cholem/cholem-yud; some Yemenite dialects of cholem/tzeirei-waw etc.). (Please correct me if I'm wrong about any of these.) As he moves to a new place, he loses the distinct sounds of past places in favor of the merged pronunciations of the new places.


What is the minimum number of distinct sounds his phonetic Hebrew alphabet might contain once he's visited all Jewish communities in the world?


Would his Hebrew be valid halachically?



Answer



Proper pronunciation and proper distinguishing of letters and vowels is halakha.




How must one enunciate? He must be careful not to pronounce [a letter with] a strong dagesh as if there were no dagesh, or [a letter with] no dagesh as if there were one. Nor should one pronounce the silent sheva or silence the pronounced sheva. Hil. Kriath Shema' 2:9



and



There are six factors that prevent [a priest] from reciting the priestly blessings: [an inability] to pronounce [the blessings properly],...


[An inability] to pronounce [the blessings properly]: What is implied? Those who cannot articulate the letters properly - e.g., those who read an aleph as an ayin and an ayin as an aleph, or who pronounce shibbolet as sibbolet and the like - should not recite the priestly blessings. Hil. Tefilah 15:1



and




The person reading the Torah is not allowed to begin reading until the congregation ceases responding "Amen." If one erred while reading, even regarding the careful pronunciation of one letter, [the reader] is forced to repeat [the reading] until he reads it correctly. Id. 12:6



and



Similarly, the inarticulate who pronounce an alef as an ayin or an ayin as an alef or one who cannot articulate the letters in the proper manner should not be appointed as the leader of a congregation. Id. 8:12



Thus any exacerbation of the problem of inarticulation would be halakhicaly problematic. However, it would be impractical to enforce these halakhoth in today's world where 99%+ Jews fall into the category of the inarticulate. Many authorities, Such as Rav. Kook in Orah Mishpat 16-17, permit one to use any pronunciation they were raised with.


As for the first part of your question, by my count, there are 29 consonant phonemes in the full range of proper hebrew. If you were to not use the double pronunciation for resh, that would bring it down to 28. Except for kaf, at least one community merges all the bgdkft letters. If one were to do this, that would bring the count down to 23. If you were to merge ayin and aleph that would it down to 22. Qaf merges in a variety of ways in different pronunciations, but that would bring it down to 21. Merging heth and khaf brings it down to 20, and merging teth and taw brings it down to 19. Corrupting ssadhi to a combination of taw and sin brings it down to 18. If you want to bring Ephraim into this, that brings it down to only 17. This would be the minimum number theoretically possible. The modern pronunciation merges resh and ghimmel as well as waw and veth, however, you could not merge these and the bgdkft letters simultaneously as these are fricatives and the merged bgdkft phonemes are always plosive. Vowels gets more complicated, but pretty much all of them have been merged or corrupted in one way or another.


This is a chart that I have put together of all the phonemes with a current live tradition for reference.


What is meant by a system's "impulse response" and "frequency response?"


Can anyone state the difference between frequency response and impulse response in simple English?



Answer



The impulse response and frequency response are two attributes that are useful for characterizing linear time-invariant (LTI) systems. They provide two different ways of calculating what an LTI system's output will be for a given input signal. A continuous-time LTI system is usually illustrated like this:


LTI system diagram


In general, the system $H$ maps its input signal $x(t)$ to a corresponding output signal $y(t)$. There are many types of LTI systems that can have apply very different transformations to the signals that pass through them. But, they all share two key characteristics:




  • The system is linear, so it obeys the principle of superposition. Stated simply, if you linearly combine two signals and input them to the system, the output is the same linear combination of what the outputs would have been had the signals been passed through individually. That is, if $x_1(t)$ maps to an output of $y_1(t)$ and $x_2(t)$ maps to an output of $y_2(t)$, then for all values of $a_1$ and $a_2$,


$$ H\{a_1 x_1(t) + a_2 x_2(t)\} = a_1 y_1(t) + a_2 y_2(t) $$



  • The system is time-invariant, so its characteristics do not change with time. If you add a delay to the input signal, then you simply add the same delay to the output. For an input signal $x(t)$ that maps to an output signal $y(t)$, then for all values of $\tau$,


$$ H\{x(t - \tau)\} = y(t - \tau) $$


Discrete-time LTI systems have the same properties; the notation is different because of the discrete-versus-continuous difference, but they are a lot alike. These characteristics allow the operation of the system to be straightforwardly characterized using its impulse and frequency responses. They provide two perspectives on the system that can be used in different contexts.


Impulse Response:



The impulse that is referred to in the term impulse response is generally a short-duration time-domain signal. For continuous-time systems, this is the Dirac delta function $\delta(t)$, while for discrete-time systems, the Kronecker delta function $\delta[n]$ is typically used. A system's impulse response (often annotated as $h(t)$ for continuous-time systems or $h[n]$ for discrete-time systems) is defined as the output signal that results when an impulse is applied to the system input.


Why is this useful? It allows us to predict what the system's output will look like in the time domain. Remember the linearity and time-invariance properties mentioned above? If we can decompose the system's input signal into a sum of a bunch of components, then the output is equal to the sum of the system outputs for each of those components. What if we could decompose our input signal into a sum of scaled and time-shifted impulses? Then, the output would be equal to the sum of copies of the impulse response, scaled and time-shifted in the same way.


For discrete-time systems, this is possible, because you can write any signal $x[n]$ as a sum of scaled and time-shifted Kronecker delta functions:


$$ x[n] = \sum_{k=0}^{\infty} x[k] \delta[n - k] $$


Each term in the sum is an impulse scaled by the value of $x[n]$ at that time instant. What would we get if we passed $x[n]$ through an LTI system to yield $y[n]$? Simple: each scaled and time-delayed impulse that we put in yields a scaled and time-delayed copy of the impulse response at the output. That is:


$$ y[n] = \sum_{k=0}^{\infty} x[k] h[n-k] $$


where $h[n]$ is the system's impulse response. The above equation is the convolution theorem for discrete-time LTI systems. That is, for any signal $x[n]$ that is input to an LTI system, the system's output $y[n]$ is equal to the discrete convolution of the input signal and the system's impulse response.


For continuous-time systems, the above straightforward decomposition isn't possible in a strict mathematical sense (the Dirac delta has zero width and infinite height), but at an engineering level, it's an approximate, intuitive way of looking at the problem. A similar convolution theorem holds for these systems:


$$ y(t) = \int_{-\infty}^{\infty} x(\tau) h(t - \tau) d\tau $$


where, again, $h(t)$ is the system's impulse response. There are a number of ways of deriving this relationship (I think you could make a similar argument as above by claiming that Dirac delta functions at all time shifts make up an orthogonal basis for the $L^2$ Hilbert space, noting that you can use the delta function's sifting property to project any function in $L^2$ onto that basis, therefore allowing you to express system outputs in terms of the outputs associated with the basis (i.e. time-shifted impulse responses), but I'm not a licensed mathematician, so I'll leave that aside). One method that relies only upon the aforementioned LTI system properties is shown here.



In summary: For both discrete- and continuous-time systems, the impulse response is useful because it allows us to calculate the output of these systems for any input signal; the output is simply the input signal convolved with the impulse response function.


Frequency response:


An LTI system's frequency response provides a similar function: it allows you to calculate the effect that a system will have on an input signal, except those effects are illustrated in the frequency domain. Recall the definition of the Fourier transform:


$$ X(f) = \int_{-\infty}^{\infty} x(t) e^{-j 2 \pi ft} dt $$


More importantly for the sake of this illustration, look at its inverse:


$$ x(t) = \int_{-\infty}^{\infty} X(f) e^{j 2 \pi ft} df $$


In essence, this relation tells us that any time-domain signal $x(t)$ can be broken up into a linear combination of many complex exponential functions at varying frequencies (there is an analogous relationship for discrete-time signals called the discrete-time Fourier transform; I only treat the continuous-time case below for simplicity). For a time-domain signal $x(t)$, the Fourier transform yields a corresponding function $X(f)$ that specifies, for each frequency $f$, the scaling factor to apply to the complex exponential at frequency $f$ in the aforementioned linear combination. These scaling factors are, in general, complex numbers. One way of looking at complex numbers is in amplitude/phase format, that is:


$$ X(f) = A(f) e^{j \phi(f)} $$


Looking at it this way, then, $x(t)$ can be written as a linear combination of many complex exponential functions, each scaled in amplitude by the function $A(f)$ and shifted in phase by the function $\phi(f)$. This lines up well with the LTI system properties that we discussed previously; if we can decompose our input signal $x(t)$ into a linear combination of a bunch of complex exponential functions, then we can write the output of the system as the same linear combination of the system response to those complex exponential functions.


Here's where it gets better: exponential functions are the eigenfunctions of linear time-invariant systems. The idea is, similar to eigenvectors in linear algebra, if you put an exponential function into an LTI system, you get the same exponential function out, scaled by a (generally complex) value. This has the effect of changing the amplitude and phase of the exponential function that you put in.



This is immensely useful when combined with the Fourier-transform-based decomposition discussed above. As we said before, we can write any signal $x(t)$ as a linear combination of many complex exponential functions at varying frequencies. If we pass $x(t)$ into an LTI system, then (because those exponentials are eigenfunctions of the system), the output contains complex exponentials at the same frequencies, only scaled in amplitude and shifted in phase. These effects on the exponentials' amplitudes and phases, as a function of frequency, is the system's frequency response. That is, for an input signal with Fourier transform $X(f)$ passed into system $H$ to yield an output with a Fourier transform $Y(f)$,


$$ Y(f) = H(f) X(f) = A(f) e^{j \phi(f)} X(f) $$


In summary: So, if we know a system's frequency response $H(f)$ and the Fourier transform of the signal that we put into it $X(f)$, then it is straightforward to calculate the Fourier transform of the system's output; it is merely the product of the frequency response and the input signal's transform. For each complex exponential frequency that is present in the spectrum $X(f)$, the system has the effect of scaling that exponential in amplitude by $A(f)$ and shifting the exponential in phase by $\phi(f)$ radians.


Bringing them together:


An LTI system's impulse response and frequency response are intimately related. The frequency response is simply the Fourier transform of the system's impulse response (to see why this relation holds, see the answers to this other question). So, for a continuous-time system:


$$ H(f) = \int_{-\infty}^{\infty} h(t) e^{-j 2 \pi ft} dt $$


So, given either a system's impulse response or its frequency response, you can calculate the other. Either one is sufficient to fully characterize the behavior of the system; the impulse response is useful when operating in the time domain and the frequency response is useful when analyzing behavior in the frequency domain.


gentiles - Invited to Engagement of Girl intending to marry out: Attend/Not-attend?


We have recently been invited to an engagement of a Girl who intends marrying someone that is not Jewish. However, the girl and her family are related family members.


Firstly, is it permitted (in general circumstances) to attend such an event? Or, is there a basis that perhaps it may be seen as condoning such a union? Could it even be considered prohibited, or not?


Secondly, does the fact the girl is related change anything, in the sense that we have to consider that she might be hurt and offended by our non-attendance? I.e. If there is a basis for the first question, does anything change in this case?


KT.




Transfer function of double exponential smoothing?


Double exponential smoothing a.k.a. Holt-Winters smoothing tracks level and trend of a time series in coupled IIRs:
$\qquad$ In: $Y_t$, t = 0 1 2 ...
$\qquad$ State: $L_t, T_t \quad$ -- level and trend
$\qquad$ Out: estimate $\hat{Y}_{t+1}$

$\qquad$ Parameters: a, b (a.k.a. $\alpha, \beta$)
$\qquad$ Step equations:
$\qquad$ $\qquad L_t = a Y_t + (1 - a) (L_{t-1} + T_{t-1}) \quad$ -- level
$\qquad$ $\qquad T_t = b (L_t - L_{t-1}) + (1 - b) T_{t-1} \quad$ -- trend
$\qquad$ $\qquad \hat{Y}_{t+1} = L_t + T_t$


How can I calculate the transfer function of this smoother, for given $a$ and $b$ ?


(Two possible approaches:



  • manipulate the step equations into ratio-of-polynomials form

  • brute force iterate with input $e^{2 \pi i f t}$: converges slowly for small $a, b$.



The first of these is beyond me, the second unsatisfactory.)



Answer



I would use the $\mathcal{Z}$-transform. Let me change the notation slightly by using $n$ as the discrete time index, lower case letters for time domain quantities, $x[n]$ as the observed input data sequence, and $y[n]$ as the output sequence, which is an estimate of $x[n+1]$. With this notation, the time domain equations are


$$\tag{1}\begin{align} l[n]&=ax[n]+(1-a)(l[n-1]+t[n-1])\\ t[n]&=b(l[n]-l[n-1])+(1-b)t[n-1]\\ y[n]&=l[n]+t[n] \end{align}$$


Taking the $\mathcal{Z}$-transform of these 3 equations gives


$$\begin{align}\tag{2} L(z)&=aX(z)+(1-a)z^{-1}(L(z)+T(z))\\ T(z)&=b(1-z^{-1})L(z)+(1-b)z^{-1}T(z)\\ Y(z)&=L(z)+T(z) \end{align}$$


From the second equation in (2) we can express $T(z)$ in terms of $L(z)$:


$$T(z)=\frac{b(1-z^{-1})}{1-(1-b)z^{-1}}L(z)\tag{3}$$


Plugging (3) into the first equation of (2), we can express $L(z)$ in terms of $X(z)$:



$$L(z)\left[1-(1-a)z^{-1}\left(1+\frac{b(1-z^{-1})}{1-(1-b)z^{-1}}\right)\right]=aX(z)$$


from which, after some algebra, you get


$$L(z)=\frac{a\left[1-(1-b)z^{-1}\right]}{1+[a(1+b)-2]z^{-1}+(1-a)z^{-2}}X(z)\tag{4}$$


Finally, plugging (3) into the last equation of (2) gives


$$Y(z)=\left[1+\frac{b(1-z^{-1})}{1-(1-b)z^{-1}}\right]L(z)=\frac{1+b-z^{-1}}{1-(1-b)z^{-1}}L(z)$$


and combining with (4) results in a relation between the output $Y(z)$ and the input $X(z)$:


$$Y(z)=\frac{a(1+b-z^{-1})}{1+[a(1+b)-2]z^{-1}+(1-a)z^{-2}}X(z)=H(z)X(z)\tag{5}$$


where $H(z)$ is the desired transfer function, which is of course a second order IIR filter.


Preferred approach when behind in Shnayim Mikra


If someone is behind in shnayim mikra, is it better for them to skip to the current parsha or to continue from where they have gotten up to?


What if they estimate that they will be more likely to cover everything if they do it one way and not the other?




Pronouncing Hashem's name in a song


Some people are very careful to say Hashem or Elokim when singing a song with one of G-d's names in it so as not to use His name in vain (related question), but I have also been told this is unnecessary since these songs are equivalent to prayer.




  • If you shouldn't pronounce them, why did the authors put them in explicitly?





  • If there's no problem with pronouncing them, then how does repeating the words (for example, in the chorus) affect that? I mean, now that you're saying the words simply to fit in with the melody does that make pronouncing them in vain?





Answer



http://www.ou.org/torah/tt/5766/miketz66/specialfeatures.htm



Rambam (Sh'vuos 12:9) rules that one who uses Hashem's Name in a meaningless oath or a an unwarranted blessing violates the Torah prohibition to use His Name in vain. One who utters His Name without a purpose transgresses the lower level, Torah commandment to fear His Name (ibid.:11).In the latter case, the Rambam instructs one to rectify an improper utterance of the Name by adding words of praise of Hashem.


As the aforementioned Rambam hinted, it is likewise permissible to use Hashem's Name to praise Him, including in Shabbat zemiros and other liturgy. Indeed, some (incl. Rav Sh. Z. Orbach) pronounce the Names normally. (The rhyming in some zemirot indicates that the liturgist also did so.) However, many have the custom to alter the Names (Nefesh HaRav, pg. 160 reports that Rav Soloveitchik did not utter the Names in zemirot). The explanation of this custom is apparently that we are concerned that we will not be in the proper frame of mind (B'tzel Hachuchma IV, 52) or may stop in the middle of a phrase (see Igrot Moshe, ibid.) or otherwise disgrace the Name. [Ed. or overly repeat phrases in singing the Z'mirot.]


In practice, one can choose either to pronounce normally or change Hashem's Names when reading Torah texts, saying informal prayers, or singing zemirot. When studying b'rachot, he must change the Names; when reading a whole pasuk, it is proper to pronounce the Names accurately.




organic chemistry - What happens when deodorants or perfumes expire


I know that deodorants and perfumes have alcohol as their main ingredient so I was thinking what happens when their expiry date passes?


I tried to search on google but got mixed results. Some say that they do not ever expire but some say that an expired deodorant can burn the skin.


What i think is that as they contain mainly alcohol so maybe a major part of the alcohol gets oxidised to ketones or acids which may in turn harm the skin. Does anyone of you know what happens when deodorants expire?



Answer




The meaning of expiry dates


The date of expiry is widely interpreted by consumers as the date after which a product is known to detiorate. However, the meaning of expiry dates varies widely from product to product, and from country to country. Often times, the date of expiry is not a "first known bad" date, but a "last known good" date. In that latter case, the dates indicates that manufacturers know their product will last up until the expiration date, but after that, they don't know what happen. Their product could last 1000s of years, completely stable and undeteriorated. Or it could degrade instantaneously the day after expiry.


I don't know for sure what perfume manufacturers mean by their expiry dates. You could try asking the manufacturer for clarification. Ask for their data from their product stability studies.


Likely routes of perfume degradation


All of the above notwithstanding, let's suppose that perfumes do degrade over a time span of several years. Subject to that assumption, what could be happening happening? First, I agree with the commenters that ethanol oxidation to acetaldehyde or acetic acid is unlikely to be a major contributor to perfume degradation.


However, the same is not true of other perfume components.


Oxidation




  • Aldehydes such as octanal, benzaldehyde, citral, are an important ingredients in many perfurmes. Citral degradation has been studied and is accelerated by acid and oxygen, with the main ultimate product being p-cymene. Benzaldehyde is oxidized in air to benzoic acid, and octanal is oxidized to octanoic acid.





  • Terpenes are also important pefume components. Limonene is a component of many perfume blends and is a representative terpene. It is also oxidatively unstable, with products such as limonene oxide, carveols, and carvones being formed. Some of these oxidation products can trigger allergic reactions, which while not precisely "burning the skin", could lead to such a perception.




Other possible degradations


Perfume, especially if opened frequently, could also change by absorbing water from the atmosphere, leading to dilution and an alteration of its olfactory properties. Frequent opening or exposure to the atmosphere could also result in differential evaporation of the more volatile components, which would also change its olfactory properties.


The bottom line


Expired perfume or deodorant might be just as good as regular perfume. Or it might be degraded. The degradation products might possibly include compounds that have been reported to form rashes. It is unlikely, however, that the chemical mechanism for this is the formation of large amounts of acid.


tanach - Do Jews accept the Bible as being valid?




Possible Duplicate:
Do Jewish people have a collection of books which are the equivelant of the Christian Old Testament?




The Bible has an "Old testament" and a "New Testament". Do Jews use the "Old Testament" of the Bible or do they have a separate book? Is the Bible considered a valid book to the Jews?




halacha - Referring to Gentile Priest as "Father"


Is it permissible to either refer to or address a gentile priest as "Father XXXXXXXXX"?
What alternatives might there be?




bond - What are the prerequisites in hydrogen bonding?


I know when a hydrogen bond is, but - can hydrogen bonds only occur between two molecules containing hydrogen? Or, only one of the molecules should contain hydrogen and the other one may not contain hydrogen, but should have a large electronegative difference between two of its sides?



Answer



Actually, theoretically speaking hydrogen bond is the attractive force between the hydrogen attached to an electronegative atom of one molecule and an electronegative atom of a different molecule. Usually the electronegative atom is oxygen, nitrogen, or fluorine, which has a partial negative charge. A hydrogen bond may occur between $\ce{H-O}$, $\ce{H-N}$, $\ce{H-F}$ (first two are more common). Apart from that, these hydrogen-bond attractions can occur between molecules (intermolecular) or within different parts of a single molecule (intramolecular)


See also the Wikipedia article about hydrogen bonding A hydrogen atom attached to a relatively electronegative atom will play the role of the hydrogen bond donor An electronegative atom such as fluorine, oxygen, or nitrogen will be the hydrogen bond acceptor, irrespective of whether it is bonded to a hydrogen atom or not. An example of a hydrogen bond acceptor that does not have a hydrogen atom bonded to it is the oxygen atom in diethyl ether.


http://chemwiki.ucdavis.edu/@api/deki/files/4680/image115.png?revision=1


gentiles - If I have behaved badly, should I hide the fact that I'm Jewish?


If, G-d forbid, a Jew should behave badly in public (anything from simply doing something quite embarrassing, to being rude, to making a scene/causing a disturbance, to actually [ch"v] committing a major sin or breach of ethics) should he then try to conceal the fact that he is Jewish?


Two cases: both if it would involve another sin to do so (such as removing his kippah [?]) and if not.



Answer



No, he/she should not conceal the fact that they are Jewish. When you do this, you say that you worship men more than you worship God. The Jewish people are called to be a nation of priests to the whole world, and we are commanded to wear certain clothing to illustrate this point. It's understandable that there will be certain points at certain times where you will fall short of this ideal, and you will have sinned against God. But the moment that you become more worried about how others will perceive your sin, rather than being worried about the fact that you sinned against God, you have a much bigger problem. Because you are worshiping men, rather than worshiping God.


It has become commonplace to view tzit tzit or kippot as outward expressions of ones being Jewish. Rather than their actual purpose, which is to remind us of God's commandments, anywhere at anytime, especially when we are sinning. A practical example will be that one will be afraid to be seen wearing a kippah at a McDonalds in which he is grabbing a coke (which is permissible), but feels no remorse about actual sins in which no one is looking at him. Rather than this hypocrisy, one should embrace their Judaism at all times, and all moments, using it as a force toward holiness and repentance to God.



A great example of this is brought down in the Talmud in Menachot 43b-44a



Once a man, who was very scrupulous about the precept of zizith, heard of a certain harlot in one of the towns by the sea who accepted four hundred gold [denars] for her hire. He sent her four hundred gold [denars] and appointed a day with her. When the day arrived he came and waited at her door, and her maid came and told her, ‘That man who sent you four hundred gold [denars] is here and waiting at the door’; to which she replied ‘Let him come in’.


When he came in she prepared for him seven beds, six of silver and one of gold; and between one bed and the other there were steps of silver, but the last were of gold. She then went up to the top bed and lay down upon it naked. He too went up after her in his desire to sit naked with her, when all of a sudden the four fringes [of his garment] struck him across the face; whereupon he slipped off and sat upon the ground.


She also slipped off and sat upon the ground and said, ‘By the Roman Capitol, I will not leave you alone until you tell me what blemish you saw in me. ‘By the Temple’, he replied, ‘never have I seen a woman as beautiful as you are; but there is one precept which the Lord our God has commanded us, it is called zizith, and with regard to it the expression ‘I am the Lord your God’ is twice written, signifying, I am He who will exact punishment in the future, and I am He who will give reward in the future. Now [the zizith] appeared to me as four witnesses [testifying against me]’.


She said, ‘I will not leave you until you tell me your name, the name of your town, the name of your teacher, the name of your school in which you study the Torah’. He wrote all this down and handed it to her. Thereupon she arose and divided her estate into three parts; one third for the government, one third to be distributed among the poor, and one third she took with her in her hand; the bed clothes, however, she retained. She then came to the Beth Hamidrash of R. Hiyya, and said to him, ‘Master, give instructions about me that they make me a proselyte’.


‘My daughter’, he replied; ‘perhaps you have set your eyes on one of the disciples?’ She thereupon took out the script and handed it to him. ‘Go’, said he ‘and enjoy your acquisition’. Those very bed-clothes which she had spread for him for an illicit purpose she now spread out for him lawfully. This is the reward [of the precept] in this world; and as for its reward in the future world I know not how great it is.



Source: http://www.halakhah.com/rst/kodoshim/42b%20-%20Menochos%20-%2027a-58b.pdf


Rather than taking off his tzit tzit when he was on his way to the prostitute, he kept them on. Rather than hiding the fact that he was Jewish when he realized he was sinning, he made it very clear that he was Jewish, and even explained the Judaism to a gentile, and the world was made better for it.



grammar - けど in the end of sentence




無理をしないように言ったけど。。



Is it an incomplete sentence? So she want to say "although I have told him not to overdo things... (he did it anyway).


Here's the full story for the context...



今日、鈴木くんに会った時、手があかくなっていておどろいた。木からおりられなくなった 子猫をたすけにいって 子猫にかまれたらしい。 鈴木くんは、子猫がけがをしなくてよかったと言っていたけど、鈴木くんは優しすぎるから、とても心配だ。無理をしないように言ったけど。。




Answer




It is a common idiom to leave the second half B of "A but B" phrases empty, leaving the meaning implicit. This works in English in some cases as well, but is extremely common with most Japanese versions of "but".



In this case, it reads like "(I) said not to overdo it, but ...", or tweaked a little:



"Even if (I) say not to overdo it, ...".



Here, the implication is that the speaker believes in the wisdom of the advice to "not overdo it", but also sees some not-explicitly-stated reasons (at least in that sentence) for why 鈴木くん may still go against the advice. (Side note, the "he is kind" from the previous sentence is almost certainly being alluded to in this case).




Aside: Japanese also often abbreviates the A part, resulting in sentences starting with だけど、ですが、etc. In these cases, A becomes whatever is appropriate from prior context, likely including something from the prior sentence. It is actually not uncommon to see just a lone 「ですが……」. For example, one speaker states a long explanation. There is a pause, then the other speaker says 「ですが……」, and then falls silent again. This could mean something along the lines of "Well, I see what you're saying, but ... (I can't completely agree with your conclusion)"



「AだがB」という表現のBを省略し、言外に含ませるのは、日本語では慣用的な言い方です。英語でもこういう使い方ができることがありますが、日本語の逆接ではきわめて一般的なことです。


この例の場合、「(I) said not to overdo it, but ...」、もしくは少し言い換えて、




"Even if (I) say not to overdo it, ...".



とでも訳せるかと思います。


ここで言わんとしているのは、「話し手自身は『無理をしない』という忠告が最も賢明だと思うが、同時に鈴木くんがこの忠告に反するだろう​(少なくともこの文では)明言されていないもっともな理由も思い当たる」ということです(ちなみに、この場合は直前の文にある「鈴木くんは優しすぎる」というのがほとんど答えのようなものですが)。




余談: 日本語では、Aが省略されて「だけど」や「ですが」などで始まる文章も多くみられます。この場合、前の文脈(例えばすぐ前の文)にある適切な要素がAとして用いられます。さらに言えば、「ですが……」だけの文も珍しくありません。例えば、Aさんが長い説明を言い終わり、一瞬間を置いて、Bさんが「ですが……」と言って、また無言になる、という具合です。これは言うなれば「確かに言いたい事はわかりますが、……(でもその結論にはちょっと納得できない)」のような意味合いになります。


physical chemistry - A quick method for separating liquids?


I'm looking for a way to take 3 separate liquids (liquids which function as paint -- they will all be different colors), put them together into a container, and then rapidly separate them back to distinct colors.


I can handle all the electrical engineering aspects of my project, but this portion is beyond me. Does anyone have any ideas?



When I say "a quick method", I mean something that can be done easily without an excess of time or equipment. Ideally an way to make the paints intrinsically immiscible, but I need to be able to separate them entirely, so that when they are poured together into a container, I can then separate and reuse them.




Friday, January 27, 2017

tanach - Is there a surviving Jewish translation of the entire Masoretic Text in Greek?


Please don't say "the Septuagint" because I know that this has fallen out of favor among most modern Jews (the only exception being Beta Israel, which I believe still uses it - correct me if I am mistaken on that.)


I know that the Torah was translated into Yevanic Greek in 1547 by Romaniote Jews for the "Constantinople Pentateuch," but this is just the first 5 books. Has the remainder of the Masoretic Text been translated into Greek specifically by Jews and specifically for Jewish use?



I also know about the Greek translation by Aquila/Onkelos but this has not survived apart from a few fragments.




sefirat ha omer - can a person take music lessons during sefirah?


Someone who is learning a music instrument for pleasure alone, is it allowed to take music lessons during the period if sefirat haomer?



Answer



I believe Rav Nachum Rabinovitch, shlit"a, is meikil. (I believe Rav Yoshe Ber Soloveichik,z"l, was meikil regarding listening to music in general during sefira.) Similarly, Rav Belsky is lenient with regard to continuing music lessons during sefira:



Refer to opinions of Harav Elyashiv Shlita and Harav Korelitz Shlita quoted in Piskei Shmuos page 53, see Chut Shani Shabbos 4:page 379 who permits it if one is just starting lessons since it is not music.




However, the Tzitz Eliezer (Sh"t Tzitz Eliezer 16:19), even year-round is lenient only if it is not for pleasure (as one part of the year-round ban zecher l'churban (in commemoration of the destruction of the Temple). Furthermore, even if it is not for pleasure and even year round...



Kaf Hachayim 551:41 writes that preferably it should not be done, and even if one is lenient it should only be sad songs. Miyum Hahalacha 1:83, Emes Liyaakov 551:footnote 506 also say that it is preferable not to. The Pri Megadim Eshel Avraham 551:10 writes that parallel to the concept of davar ha'aved on chol hamoed, the rabbis permitted somebody who needs to dance or play music for livelihood to do so. )



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{...