words - What is the meaning of 幾里?

I took up a personal translation project--lyrics to a song from a game I played--recently, and one of the words is giving me trouble. The line out of the song is 我れ幾里の路を共に往かむ, and I can understand everything except for 幾里. I did have to try to make out the lyrics from the video before it dawned on me to check for a transcript online, and here's the other confusing thing; this word pops up in other transcripts and the video itself. (See: http://010701070107.blog5.fc2.com/blog-entry-3543.html) I seriously cannot find a definition for this word with any dictionary I've been able to get my hands on, part of which I credit to this entire song being written in Classical Japanese, but still. I've tried both English and Japanese dictionaries on the subject, so finally I decided to turn here. Any ideas?

Answer

幾里 means “how many lis.” “Li” is a unit of distance, and 1里 is equal to 4 kilometers (2.5 miles) . 幾 means “how many, how much” as you ask an antique shop owner “これ幾らですか？－How much price is this?” It has nothing to do with the name of town and village.

Thus 我れ幾里の路を共に往かむ means “How many miles should I tread (go) with you ahead the road?” Apparently this is an expression in literary style (文語調) to be found in the writing of authors in Meiji-and-Taisho era, but surely sounds lyrical and solemn.

fourier transform - Properties of Spectral Transformations - Allocation (decomposition into even and odd part)

I am trying to understand the Allocation property of Spectral Transformations. I can't.

I know that every function can be separated into an even part and into an odd part.

My problem is understanding proof for that:

$$s(t)=s_e(t)+s_o(t)$$ where:

• $s_e(t)$ - even part of function


• $s_o(t)$ - odd part of function

The problem is that in next step at every site I looked so far, it goes something like this:

$$s_e(t) =\dfrac{s(t)+s(-t)}{2}$$

Why did they do this? Where did $\frac{1}{2}$ come from, and why is $s(t)+s(-t)$

Can you please explain it to me, or point me to a good resource where I could read more about it?

Thanks!!!

Answer

Let's say that your signal is composed of two parts: even and odd:

$$s(t)=s_e(t)+s_o(t)$$

We also know following properties of this type of functions:

• Even: $f(-x)=f(x)$



• Odd: $f(-x)=-f(x)$

Let's calculate the time inversion of your signal $s(-t)$ and apply above properties:

$$s(-t)=s_e(-t)+s_o(-t)=s_e(t)-s_o(t) $$

So now let's do the trick and add the: $s(t)$ and $s(-t)$:

$$\require{cancel} s(t)+s(-t) = \color{blue}{s_e(t)}+ \cancel{\color{red}{s_o(t)}} + \color{blue}{s_e(t)}-\cancel{\color{red}{s_o(t)}}=\color{blue}{2s_e(t)} $$

Solve it for $\color{blue}{s_e(t)}$, and you will get:

$$\boxed{\color{blue}{s_e(t)}=\dfrac{s(t)+s(-t)}{2}} $$

In the end let's subtract $s(t)$ and $s(-t)$:

$$s(t)-s(-t) = \cancel{\color{blue}{s_e(t)}} + \color{red}{s_o(t)} - \cancel{\color{blue}{s_e(t)}} + \color{red}{s_o(t)}=\color{red}{2s_o(t)} $$

Rearrange and you will get:

$$\boxed{\color{red}{s_o(t)}=\dfrac{s(t)-s(-t)}{2}} $$

fourier transform - How were windows originally conceived?

I am aware of the common types of windows, (Hamming, Hanning, Kaiser, Tukey, etc etc). However while many books describe them - almost none tell me just how exactly they were derived.

What is so holy about the hamming window? What about the hanning? I understand that they all play on the ratio of mainlobe width VS sidelobe attenuation, but how exactly were they derived?

The motivation for my question, is because I am trying to figure out if one can design their own windows, that also play off main lobe width and sidelobe energy.

Answer

This is only a partial answer, but there's a lecture online where Hamming talks about how he came up with his eponymous window. Starting at roughly 15:15 gives the full context.

With a reasonably entertaining story, he credits John Tukey with inventing the theory of windows (for spectrum analysis). However, he introduces the whole subject in the context of using Lanczos sigma factors to reduce Gibbs phenomenon. In addition, in The Art of Doing Science and Engineering (based on the same lectures), he describes how his window is a variation on the Hann window, which he claims was used by von Hann in economics (long before its application in signal processing). That suggests the history goes much further back, depending on how you want to define it.

The book where Tukey first named the Hamming window is The Measurement of Power Spectra from the Point of View of Communications Engineering. Given Hamming's assertion that Tukey invented the theory of windows, it would probably be a good place to start for a deeper understanding of how to design new ones. I think the book is just a reprint of Part I and Part II of his Bell System Technical Journal article, so it's available online.

parshanut torah comment - Not Negah but Like a Negah

Why when calling the Cohen even if you clearly know the Psak you cant say I have a Negah at home Instead of saying "Kanegah Nireh Li Babayis" Like a Negah?

Answer

Tos'fos Yom Tov to N'gaim 12:5 gives the following answers, if I read him right:

1. (from the Mizrachi in the name of his teachers) Since he can't be sure it's a nega until the kohen shows up, he shouldn't say he's sure.


2. (from the Mizrachi himself) He should treat the kohen with derech eretz, etc. [The Tos'fos Yom Tov includes the "etc.", thereby referring the reader to the Mizrachi for a fuller explanation. I didn't check the Mizrachi or, indeed, the other people he quotes.]


3. (from the Mizrachi himself again) So the kohen not be swift to judge it as tame. [I assume this means that he'll be prejudicing the kohen; however, see the Chazon Ish's answer, below.]


4. (from the Gur Arye) It's not a nega until the kohen says it is, and he shouldn't lie. (The Korban Aharon asks that that's not true: the kohen says it's tame, but it's a nega tahor even before pronounced tame by the kohen. The Tos'fos Yom Tov answers that "nega" in the vernacular means a tame one, so he'd be lying to call it that.)


5. (his own) Because of al tiftach pe l'satan.

Midrashim quoted by the Tora Sh'lema say that this is the source of "al tiftach pe l'satan" [which I guess means that they agree with the Tos'fos Yom Tov's own answer].

Rabbi Matis Blum of Queens, in his "Torah Lodaas" weekly d'var-Tora sheet for M'tzora 5771, suggests that according to those who say there never was or will be a house with tzaraas, "k'nega" makes sense, as it isn't, in fact, a nega.

Ralbag says it's because only the kohen can adjudge it a nega. [This is opaque to me, but perhaps he means the Mizrachi's teachers' or the Gur Arye's answer?]

Rav Moshe (in Darash Moshe) says it's so as not to say something bad. [This, too, is opaque to me. Perhaps he means the Tos'fos Yom Tov's own answer, or en m'shivin al hakalkala?]

Rabbi Chayim Zuckerman, in his sefer Otzar Chayim on chumash, quotes רמה״כ‎ (?) as saying that because tzaraas appears on a house because of tzarus ayin, the owner's saying it's a nega is effectively his libeling himself.

Abarbanel says he should make himself seem uncertain and not like he's smart. [This answer seems to me like the Mizrachi's teachers' answer, but I'm not convinced they're the same.]

In Esh Kodesh, the Piazetzner says that the homeowner is unable to see on his own whether the tzaraas is a good thing in disguise (so as to get hidden valuables) or simply a bad thing (a nega), so all he can say is that looks like a nega to him.

Rabbi Avraham Yitzchak Shayn of the Yeshiva of Staten Island writes in his book, Birkas Ish, that the homeowner, if he were sure that he were not guilty and that the tzaraas were so he could get hidden valuables, would be glad to announce he has a nega; on the other hand, if he thought he might be guilty and that the tzaraas were a punishment, he would only say it's k'nega; so the Torah is telling him that he should think he might be guilty and examine his deeds.

The Malbim, if I understand him correctly, seems to be saying that the problem is one like more halacha bifne rabo.

Chazon Ish says that if the homeowner is a talmid chacham then the kohen will need to rule like the owner said, that there is, in fact, a nega, since, although only a kohen can rule on a nega, anyone can check it. (This works, he notes, according to those who hold a homeowner can check a nega on his own home, which he says is a matter of dispute among rishonim.) And if the owner is not a talmid chacham (or if he saw it at night or under other circumstances that don't count) then (a) saying it's a nega is lying and (b) one shouldn't begin talking by saying something bad.

halacha - May a non Ethiopian Jew celebrate Sigd?

Ethiopian Jews recently celebrated their festival of Sigd, which involves reaccaptence of the Torah, communal fasting and feasting, and prayers.

Is it acceptable for someone of a Minhag other than that of the Beta Israel/Ethiopian Jews to celebrate Sigd? I ask because it is a holiday that doesn't exist outside of all non-Ethiopian traditions, but also doesn't conflict with Jewish beliefs. I've been in Israel during Sigd (though I wasn't this year), and wondered about "joining in" with my Ethiopian friends when they celebrated.

Obviously CYLOR, etc.

halacha - How do we know that homosexual relations is a sin?

I recently heard that the Ibn Ezra brings down a minority opinion that the pasukim talking about "laying with a man as you would a woman" are actually talking about androgynous people. The Ibn Ezra disagrees with that, but he cites it nonetheless.

Obviously, modern Jewish Orthodoxy rejects this viewpoint, but after hearing it, I can't help but question why that is the case.

Answer

[Edit for clarification: As DoubleAA mentioned, the interpretation is apparently presented incorrectly in the OP. The rejected interpretation mentioned by the Ibn Ezra merely suggests that relations between a male and a hermaphrodite are included in the scriptural prohibition, not to the exclusion of standard משכב זכר].

---

This interpretation that the Ibn Ezra mentions and rejects is an interpretation of the simple meaning (p'shat) of the verse (Vayikra 18:22). It is likely that the Ibn Ezra rejects this as the simple meaning of the verse because it's doesn't make sense in the context of Vayikra 20:13, which explicitly refers to two males.

Regardless, for halachic purposes, we are concerned with the exegesis of the verse, not the simple interpretation. Exegetically, the Talmud derives from the phrasing "ואיש אשר ישכב את-זכר" (Vayikra 20:13, "And a man who lies with a male...") that the violation involves a man engaging in relations with another male of any age (Sanhedrin 54a). The Talmud explains that the term זכר ("male") cannot be an exclusive reference to hermaphrodites (Chagiga 4a), even though this particular biblical prohibition applies not only to standard משכב זכר but also inclusively to a man copulating with a hermaphrodite (Y'vamos 82b).

"משכבי אשה" (Vayikra 20:13, "...the manners of lying with a woman...") is interpreted exegetically as a halachic comparison between ביאה כדרכה and ביאה שלא כדרכה for a woman. As far as simple interpretations of that expression in the context of the verse, see the Ibn Ezra (Vayikra 18:22) and Rashi (ibid., 20:13).

idioms - Making sense out of Japanese proverbs

I was never able to make any sense out of the following Japanese proverbs or idiomatic expressions:

豆腐の角に頭をぶつけて死んでしまえ。
'Hit your head against a corner of a cake of tofu, and die.'

...の爪の垢を煎じて飲む。
'take extract from one's dirt/wax under the nail, and drink it'

They are nonsense to me, and the latter is also disgusting. How can you die in such a way? What is the purpose of drinking such thing? How can you make a sense out of them?

Answer

豆腐の角に頭をぶつけて死んでしまえ。

Used to say that a person is so stupid (that he would believe this and real find a piece tofu to die). (source)

...の爪の垢を煎じて飲む。

Use the dirt under the nail of ( some expertise ) as a drug, (you'll get some of his talent). (source)

名人の爪の垢を煎じて飲めば少しは腕が上がるだろうに

It'll be hard to make any sense out of them if you see them alone. I'd recommend you to find some reference.

etymology - Niqqud of the name of the מהר"ץ חיות

What is the correct niqqud to put on the name of the מהר"ץ חיות? Wikipedia claims that his last name is spelled Chajes in English, and that Chayes or Hayot may also be seen. This seems to imply that the correct niqqud should be חַיּוֹת hayoth (a word which can refer to angels). On the other hand, when I encountered the name I had always blindly assumed that it was חִיּוּת ("vitality"), and the same spelling could also be חַיּוּת ("vitality"). Are any of these vocalizations correct? Alternatively, is his original last name a non-Hebrew word pronounced /χajəs/ (in IPA) that was identified with a Hebrew word with niqqud just a folk etymology, and therefore it might not have a "correct" vocalization?

adverbs - What's the meaning of the く in 赤くありません?

The way of turning 赤 into an adjective is adding い, but what does it mean when instead of a い you put a く？

I found it in this phrase:

私のリンゴは赤くありません。

I get the meaning but not the meaning of く.

Answer

Keep in mind that Japanese "adjectives" function differently from English adjectives. You are in this case asking us about a い-adjective, 赤い. Those adjectives differ from the な-adjectives, for example 有名｛ゆうめい｝な:

• The い or な is attached to those adjectives when used as epithets, i.e. they are attached to a noun:
  

  
  

  有名な人、赤いリンゴ.

  
  

  
  


• な-adjectives are used with the copula, dropping the な:
  
  

  
  

  この人は有名(です・でした・ではありません)

  
  

  
  


• 
  

  い-adjectives are "conjugated", you can use them without modifying the copula (sometimes even remove it entirely)! In your example

  
  

  
  

  このリンゴは赤い(です)。

  
  

  
  

  If you to turn this sentence into a negative one, you modify the adjective, by appending ～くない, i.e. このリンゴは赤くない(です). See for example this page or this one.

  
  
  

  
  

  このリンゴは赤いではありません。

  
  

  
  

  is not a correct sentence.

  
  

Then, as mentioned in the related answer ～くありません is the polite form of ～くない. Thus, it is the polite negative form of the adjective.

music - Choir practice for Birkat Kohanim

I am getting a bit tired of having to listen to another "jumbled" Birkat Kohanim this Yom Tov. It seems to be the same in almost every shul. There are always a group of Kohanim that sing a different tune than the others.

I understand that the Levi'im in the Bet Hamikdash had a choir master, so I assume that they must have rehearsed before they sang. Is there any supporting halacha or minhag that would require or recommend that Kohanim rehearse or at least agree to a uniform tune for duchenin before performing it?

halacha - What is the difference between a Ger Toshav, a Ben Noach, an Akum and a Nochri?

These terms get used a lot in referring to gentiles. What are the precise differences, if any, between these different categories? Just for clarity, Akum is an abbreviation of the phrase 'Eved Kochavim v'Mazalot'. Please give specific sources for any definitions mentioned.

Answer

The definition of a ger toshav is discussed in Avodah Zarah 64b. The Gemara provides several definitions of what the term refers to; in common parlance it refers to a non-Jew who accepts upon himself to uphold the Seven Noahide Commandments - not to eat a limb from a live animal, not to "bless" Hashem, not to steal, to have a proper court system, not to murder, not to commit idolatry, and not to commit adultery.

As @DoubleAA noted, Akum is an abbreviation for Oved/Avodas Kochavim U'Mazalos and refers to idolaters.

A Ben Noach literally means "son of Noach" and refers to all non-Jews. Though technically it refers to Jews as well, as everyone is descended from Noach, the term is used colloquially to refer just to non-Jews.

A Nochri is the only term on the list that refers to all non-Jews and only non-Jews. The term literally means "Gentile."

You left off Goy from your list. Literally translated as nation, colloquially this one also refers to any and all non-Jews.

slang - Meaning and level of 死ねばいいのに

I have been hearing 死ねばいいのに twice last week, including once in a context where a bit of formality was required.

What does it mean? Is it as violent as it sounds to me?

I am not looking for a word-by-word translation. I think it has to be taken as a whole expression, a kind of idiom.

EDIT: I just found this usage example on HATENA::KEYWORD:

あいつ「練習なんでドタキャンしたんだよ」って聞いたら、「彼女がデートしようって突然言うからさぁ」だって。ははは。まったくあいつらしいや。死ねばいいのに。

Answer

Context:

Employee talking to the boss, jokingly.

As a joke, anything goes of course, but it does depend on many factors.

Boss: We received another request from our client: ...
Employee: またその話？死ねば良いのに。( -_-;;) Mata sono hanashi? Shineba ii no ni.
"Again? I wish they'd just go away/die! *groan*"

In this case I'd expect the two speakers to be on pretty good, colloquial terms with each other and have a mutual distaste for the client. If that wasn't the case, the employee should be reprimanded for insubordinate behavior (in any culture). It probably shows that he's really fed up with the client and probably doesn't mean it too seriously, but it's still not good taste.

Boss: Do you remember that guy? He's done it again! *lol*
Employee: あはは、死ねば良いのに！（笑） Ahaha, shineba ii no ni! *wara*
"Haha, he should simply die! *lol*"

If they were just bantering with each other I'd find it perfectly harmless, despite the fact that the employee would creep me out to some degree. It's not a nice thing to say in any language, but depending on the personality of the speaker it may be a simple joke or seriously worrying.

In any case, saying it to someone's face is never nice.

あいつ「練習なんでドタキャンしたんだよ」って聞いたら、「彼女がデートしようって突然言うからさぁ」だって。ははは。まったくあいつらしいや。死ねばいいのに。
"So I asked him why he canceled the practice in the last minute, and he said because his girlfriend suddenly asked him out on a date. Hahaha, those guys are just so... I wish they'd simply die."

Apparently this was used in a skit and was likely the punchline (as far as Japanese use punchlines). Here it's funny, exactly because it's rude and unexpected. If the phrase is used in this manner channeling a comedian, it's just good fun. The preceding まったくあいつらしいや and its delivery are quite important to set up this joke.

It's pretty much a case of 空気読めば分かる (depends on the context). ;-)

physical chemistry - Regarding the free energy requirements for reacting gases

Continued from my previous question here.

1. 
   

   With regards to the Boltzmann factor, I am confused on what type of terms we can substitute for E. I know kinetic energy is one, free energy as well, but can we also do internal energy, enthalpy etc.?

   
   


2. 
   

   From this link it looks like internal energy and molecular kinetic energy are related and for real gases the internal energy term contains other factors. Since U is a part of G, is it correct to say that kinetic energy in Maxwell Boltzmann Distributions make up a part of free energy?

   
   
   


3. 
   

   I am still unclear as to whether I can interpret activation energy as a difference in free energy between average reactant energy and activated complex like diagram 1?

   
   


4. 
   

   Is it correct to say that, reaction cannot occur unless the reactant have free energy above that of the activated complex, but even if this was satisfied other factors such as minimum collision kinetic energy, orientation etc. must also be met for reaction to occur?

   
   

Addendum for Q3 and Previous Post:

My confusion is with regards to the relationship between Maxwell Boltzmann Distributions like diagrams 1 and 2, if there even is one.

The M-B distribution implies to me that

1. 
   

   activation energy $E_a$ (which I assume to be that in Arrhenius equation) is absolute given it is marked on an absolute energy scale

   
   


2. 
   

   activation energy refers to a minimum absolute kinetic energy

   
   


3. 
   

   activation energy is constant with temperature.

   
   
   

My confusion:

• 
  

  My impression has always been that activation energy (in the Arrhenius equation) refers to the difference in free energy between the transition state and reactant and that $E_a = \Delta G^{++}$ as noted in the latter two graphs, which appear to contradict the M-B Distribution. I'm not sure if there's a formal definition for activation energy that defines what "energy" it is.

  
  


• 
  

  The relationship between KE and activation energy (if any)

  
  



• 
  

  The effect temperature has on reactant and transition state free/kinetic energies. I believe that higher temperature lowers activation energy if it is the relative energy between the two.

  
  

Diagram 1:

Diagram 2:

Answer

I think what you are fundamentally saying is you are trying to relate classical thermodynamics to the molecular properties. It is best to have some firm familiarity with classical thermodynamics before attempting this. Classical thermodynamics does not require a molecular interpretation at all! (It helps a lot but is by no means necessary)!. I personally feel the answer I am about to write will help you more than trying to wade through terms and ideas/principles.... I hope so at least. If you don't like it then maybe someone else can provide a more quantitative solution.

1) The whole point of statistical thermodynamics is to provide a molecular interpretation. To do this we have to divide the system up into smaller sub-systems as I described earlier. The key to it is that there can be many "configurations" that give rise to the same macroscopic properties. The aim is to find the most probable one ... which is where your distributions come in.

It is the energy of the microstates that is what you put in so that you can calculate the various macroscopic properties you quote above. This is the best way to think about it. When you get to advanced theories this definition may change slightly. For now just accept that it is the energy of the micro state you are putting in.

In my honest opinion I don't know why courses teach the Maxwell-Boltzmann velocity distribution in a statistical thermodynamics course. I feel while a nice introduction to dealing with ensembles ... it leads to confusion (when I was learning this I had very similar questions with regard to what can be related to what, it only comes with time and exposure to the subject. So I know exactly where you are coming from!).

2) Whenever you see kinetic energy you should be thinking temperature rather than trying to get the individual molecular speeds... what does knowing the instantaneous position/velocity of a mole of gas particles at one instant in time really lead to? (not much)... I haven't really seen anyone combine the thermodynamic potentials with something like velocity. If anyone reading this has then I would love to hear what you have to say!! When I was first learning thermodynamics I clung on to what I was familiar with ... potential / kinetic energies ... now I don't really think about them when you say thermodynamics at all ... I don't think about $G$ as being a "part" of $U$ ... I just treat them as if they were separate (hmm how to phrase this) "properties" of a given system under certain conditions.

In fact I would go further to say that I view them as mathematical tools ... functions of variables of the system that I can manipulate to express molecular properties in terms of measurable quantities ....

3) Yes. You can indeed As is done by most theoretical chemists use Gibbs energies to calculate the thermodynamic activation barrier in the starting material and transition state.... The problem, which admittedly I may have confused you earlier about, is that this is done via the Arrhenius equation A kinetics equation. When in early undergraduate years you don't mix kinetics with thermodynamics. Later on it becomes (bar a factor of $2\pi$ or so ) acceptable to do so ... but you should not attempt this yet ....

A crucial point is that the activation energy graph's x-axis is the reaction coordinate. The reaction coordinate is a generalised coordinate which can be used (whatever it is) to describe the progression of the reaction.

Normally we deal very nicely in cartesian $x,y,z$ coordinates ... the idea of a generalised coordinate is that it can be used to reduce the dimensionality of the mathematical problem with some nifty rethinking of how we choose to describe the system .... for instance when talking about a simple harmonic diatomic molecule .. instead of choosing the location of both atoms in space (requiring 6 position coordinates) to fully describe the system as a function of time (as it oscillates back and forth ) i could use the relative separation (the internuclear distance) relate to the equilibrium bond length.... in this way it becomes much easier to describe the system ....

That was just one example of a generalised coordinate.... something that makes the description of the problem al little easier.... (especially if the system is subject to constraints, the generalised coordinates remove the constraint equation... anyway where were we.)...

Bottom line: ** there is a big difference between reaction coordinate and the Maxwell-boltzmann graph you linked.

4) This question in itself has hit on a very big topic. This is the realm of classical thermodynamics. What you need to understand is the difference between the standard Gibbs energy and the Gibbs energy .... For the following just imagine that $A$→$B$.

In a very brief overview it all boils down to this:

The Gibbs free energy is a mathematical function... don't try to pin down WHAT it is... its just another energy we can describe the system in .... It is a function of $P$, $T$ and $N$. Lets make it easier and say that the number of particles does not change. i.e $dN=0$ ...

Since the Gibbs energy is a function of $T$ and $P$ if we change either of these variables ... $G$ will change too .... The starting materials will have a certain $G$ and the products will have a certain $G$ ... The difference between these under standard conditions is fixed by definition that we are controlling the variables. This is like the thermodynamic drive for the process if it were to occur at our specified standard conditions .... Over the course of the reaction this value does not change since as I said it is the difference between the Starting Material and the Products under given conditions. .... This is also for pure values of the starting material and the product...

So far so good right?

As your reaction proceeds the composition varies i.e $dN\neq 0$. As I pointed out in another answer from the definition of the Gibbs energy this means that the value Gibbs function now changes... if you want a molecular picture it is due to the entropy of mixing adding in another factor to the "disorder" that has so far not been accounted for...

For an illustration please follow this link:

http://www.public.asu.edu/~laserweb/woodbury/classes/chm341/lecture_set5/lecture_set5.html

There are therefore two measures of the Gibbs energy. The one under standard conditions... unchanging for a given reaction... it is this one that has the $\Delta G^{\small o}$.. it is this one you get your electrode potentials off... it is this one that leads to the the equilibrium constant....

The other one is ever changing as the reaction proceeds since the composition of the reaction vessel is ever changing as $A$ goes to $B$. At equilibrium the net rate of change of A to B and B to A is now zero right... this in fact defines an equilibrium point.... shifting it slightly in one way or the other will cause the system to respond to re-establish equilibrium .... Most importantly we define equilibrium as the point where $dN=0$ .... for both types (in this case one would go up as the other went down ... ) but at equilibrium $dN=0$ .... This means that $dG=0$ too from the mathematics I showed you before ....

Therefore equilibrium is the point where the change in the Gibbs energies of two substances in a mixture is zero.... The reaction has no more drive if you like .... You can equivalently say their chemical potentials are equal too ... but leave that for now.....

So thats it ... Im sure if you ask question 4 to someone else they will give you a more complete answer.... but since its getting on for 2:00 am here I think I'm done. Hope that helps and again if I have made any errors ... please edit away :)

edit

What you are describing on the end of question 4 is know as the steric factor... you basically compare the frequency of successful collisions in the transition state geometry "linear" for example with respect to a full sphere of reactivity .... this gives you your factor :)

Edit So the problem is your definition of the energy. I dot know if you have seen this before but perhaps this will help,...

Yes you can indeed use statistical mechanics to obtain a value of $G$ ... The best way to do it is to get an expression for the Helmholtz free energy and then just Legendre transform it to $G$ ... $G=A+pv$.

Whilst yes at a simple level the internal energy does indeed "contain" the kinetic energy ... when you learn a bit more about quantum mechanics .. we never talk about kinetic energy ... I think it would help to actually leave the classical results behind and focus on the actual version of events...

With reference to the uncertainty relation .. how do you think kinetic energy is something we can talk about at a molecular level? The answer is you don't. Once QM comes in it is not useful to talk about velocity.

That being said how do we describe motion ? after all the Schrödinger equation is just an equation of motion. All the Schrödinger equation describes is the time evolution of a vector state in a certain vector space - Hilbert space, Which is the space in which we describe quantum mechanics...

With this in mind ... all motion of the system is quantised ... can only have discrete values .... non-continuous values ... etc etc...

Translational motion is quantised... so is vibrational ... so is rotational ..... each degree of freedom has its own quantised set of discrete energy levels ....

Equipartition theorem uses classical ideas and distributions to distribute all the available energy across these states ... roughly it says that each has energy of $\frac 1 2 KT$....

To say $U$ includes kinetic energy is a primitive way of saying the internal energy is a function that describes the energy of all the modes in the system... (you would need a distribution to see how they are populated mind) ....

Equipartition theorem doesn't get it quite right when you consider the low temperature theoretical and experimental heat capacity of a substance..... Even at low temperature you are still expected to populate all modes with $\frac 12 KT$ ... but this doesn't happen since $KT$ does not have enough energy to populate said modes ... i.e it doesn't reach the quantised energy level requirement .... therefore fewer modes are available at low temperature...

Bottom line is: just try and separate the different preconceived competing ideas you have when it comes to statistical mechanics .... have you had a lecture course on this yet?

it is certainly not about having "enough Gibbs energy to react"... The Gibbs energy between a reactant and transition state $\Delta G ^{\ddagger}$ is not a variable thing as you are saying ... (obviously for a given set of chemicals),.... If it changed all the time then why would we write them down to compare them? The Gibbs energy in your picture is not the same Gibbs energy that goes to zero at equilibrium ... \begin{equation} \bigg(\frac{dG}{dq}\bigg)_{T,P}=\Delta _r G^{\small o}+RT\ln Q \end{equation} at equilibrium the left hand side .... the gradient of the graph in that link i sent you before ... is zero ...

The rate of change of the Gibbs energy with respect to the extent of the reaction is by definition zero at eqm.

When equilibrium is reached $Q=K$ that is to say the reaction quotient becomes the equilibrium constant ....

history - Why Daniel is not Among the Prophets?

If Daniel was one of the Prophets, I do not understand why he is not counted among the Prophets.

Why is his book among the Ketuvim and not Neviim?

translation - すみません came from 済みません?

What's the correlation between 済む and すみません? 済む means to finish and I can't see it a correlation between the two.

Answer

A better understanding of 済む is to be settled or be cleared off. Thus すみません represents the sentiment that one owes a mental debt, something remain to be repaid. Here comes the meaning "I feel guilty to you", or "I'm sorry".

FYI the negative of 済む as such has that lexical meaning besides this cliche.

彼には済まないことをした
= I did something conscience-smitten to him
≈ "I regret what I did to him"

bond - Maximum Pressure of Covalently Bonded Material

At high enough pressure, atomic material no longer exists, for example under the conditions of a neutron star. Is there a different maximal pressure above which covalent bonds no longer exist?

Expression for "lose track of time"

Jim is at home, and it is currently 9:00. He has plans to meet up with a friend later, and has to leave at 9:30 to be on time for it. He decides that, during the half-hour of waiting, he'd get out his computer and work on some stuff he needs to do.

After a while of working, he looks up at the clock, and... oh no! It's 9:45! He's late!

He scrambles out the door and meets up with his friend--late, of course. As he arrives, he wants to explain that he lost track of time, causing him to be late.

And then he remembers he's meeting with the friend that only speaks Japanese.

What expression could he use to convey the same thing as English phrase "lose track of time", or equivalently mean that more time passed than it felt like?

Answer

Most commonly, we would say:

「[時間]{じかん}がたつのを[忘]{わす}れちゃって。」（「～～ちゃって」＝「～～てしまって」）

「時間を忘れちゃって。」

「時間の[感覚]{かんかく}がわからなくなっちゃって。」

Since Jim is talking to a friend, I used the informal form 「ちゃって」. He could add 「パソコン（を）いじってたら」 in front of each phrase above.

I am sure you know you can end a sentence with 「ちゃって」 or 「しまって」 in casual speech.

acid base - MgCl2 acidic or neutral in water?

I'm currently taking chemistry 12. On our test we were asked, when given a $0.1~\mathrm{M}$ solution of certain compounds whether the resulting solution when added to water would be acidic, basic, or neutral.

At first, I thought the solution would be neutral, because we learnt in class that alkali earth metals and chloride are spectator ions and therefore don't interact with water and pH.

However, I then realized that $\ce{Mg(OH)2}$ has low solubility in water, and I assume that adding $\ce{MgCl2}$, would dissociate and then precipitate $\ce{Mg(OH)2}$ from the solution, therefore the resulting solution would be acidic. My final answer was acidic.

The teacher marked my answer wrong, but when questioned could only say that $\ce{Mg}$ and $\ce{Cl}$ are both spectators, but was unable to give direct contradictory proof against my answer.

I looked elsewhere online and Wikipedia states that anhydrous $\ce{MgCl2}$ is a Lewis acid, despite being a weak one. But anhydrous seems to mean without water, so I currently have no idea which answer is correct.

I would like an explanation to why it is acidic or neutral and why the contradicting argument (both spectators vs low solubility of $\ce{Mg(OH)2}$ ) is invalid or flawed.

solid state chemistry - How are the number of tetrahedral voids twice the number of octahedral voids in a CCP structure?

How are the number of tetrahedral voids twice the number of octahedral voids in a CCP structure? Is there some kind of mathematical proof for it? Is there some way I can understand this intuitively?

I have been trying to think about it using this picture but I cannot seem to get anywhere.

kibbud av veim honoring - The 5th Commandment - Who should be financially supported first - children or parents?

During a recent Pirkei Avot shi'ur in my synagogue, our rabbi discussed two concepts.

Jewish Virtual Library citing of Talmud, Tractate Kiddushin 31B

Our Rabbis taught: What is "revere" and what is "honor?" "Revere" means that the son must neither stand in his father's place nor sit in his place, nor contradict his words nor [even] support his words [when he is arguing with another sage]. "Honor" means that he must give him food and drink, clothe and cover him, lead him in and out.

Pirkei Avot chapter 5 (I think Mishnah 18? need to edit, later) states a person's lifetime "milestones" by stating that at age 18 one gets married, and at 20 he seeks work.

The rabbi made a conclusion from these 2 citings. He stated that according to the Talmud's teachings, a parent is obligated to support the children until age 20, after which the child is expected to be financially independent. Yes, he acknowledged that, among current Jewish religious society, there are numerous parents supporting their kids in yeshiva, Kolel, etc. but he pointed out that according to the Talmud, it seems that this is not the recommended method.

However, the 1st citing from Kiddushin seems to make clear that children are continuously obligated to financially support the parents, at least to the point where they must make sure that their parents are fed and clothed. This obligation never ends as long as the parents live.

My question:

If the child has only enough money to feed or clothe his own children or his parent, but not both, who gets the priority - the parent or his own children? Does it matter if his children are below or above age 20, per the above assumption? Are there any other criteria that would favor one priority over another, that I haven't mentioned?

Answer

His children.

The Gemara shortly after the one you quoted makes note that one is not obligated to actively spend money in order to fulfill their chiyuv of kibbud av v'eim, and in the event that they do, they are entitled to reimbursement. While this would seem to indicate only that he takes precedence over his parents, and not his children, there's a Gemara in the third perek of Kiddushin (64b) that notes that personal chiyuvim take precedence over chiyuvim that others imposed upon him. Combining these two sugyos would seem to indicate, then, that a son should be able to feed his children, his personal chiyuv over which he must spend money, over his parents, who are not his personal chiyuv over which he must spend money.

number - Tish'a Ushmonim?

Who knows eighty-nine?

Please cite/link your sources, if possible. At some point in the next few days, I will:

• 
  
  

  Upvote all interesting answers.

  
  


• 
  

  Accept the best answer.

  
  


• 
  

  Go on to the next number.

  
  

Answer

Number of pesukim in the parasha of the korbanos of the nesiim (and the gematria of chanuka)

korban - What is "the door of the tent of meeting" in Leviticus 1:3?

Leviticus 1:3 and many following verses specify that burnt offerings (and various other offerings) are to be brought to "the door of the tent of meeting."

What, exactly, is "the door of the tent of meeting" specified here?

1. Is it the entrance to the courtyard of the Tabernacle? or


2. Is it the entrance to the Holy Place?

Please provide specific references to the Tanakh, preferably to the Torah, to support your answer.

Though this may be a simple question (and I think I know the answer), I am looking for definitive references to support it based on the construction and use of the Tabernacle as commanded and described in the Torah.

In particular, I am looking for references that clearly show that it is one, and not the other, of these two possibilities.

Thank you.

halacha - What do children own?

Is there truth to the saying I heard in orthodox houses, namely that if the parents support the children (even after 13/12) everything belongs to them?

What is the source of this (truth or falsehood)?

Answer

Shulchan Aruch 270:2

מציאת בנו ובתו הסמוכים על שולחנו אע"פ שהם גדולים ומציאת בתו הנערה אע"פ שאינה סומכת על שולחנו ומציאת עבדו ושפחתו הכנענים ומציאת אשתו הרי אלו שלו

(וה"ה אם הרויחו בסחורה או במלאכה (נ"י ססי' קע"ז בשם עיטור) אבל אם מת אינו מוריש מלאכת בן אחד לשאר יורשיו) (הגהות שניות דמרדכי דב"מ)‏

Higher order spline interpolation

I noticed that spline interpolation with a degree higher than 3 (everything beyond cubic splines) have a very high interpolation error, hence the prediction is mostly awful. I've come across various lecture notes, slides and Youtube videos that simply indicate that cubic splines (3rd degree) are optimal and that anything beyond that is a bad idea. These sources however never mention why this is the case.

Can anyone explain to me why this is the case and maybe give me a title/link to a journal/conference paper that explains this or maybe even gives a proof.

Answer

There is no such proof because it's not always true. It's a rule of thumb, because I guarantee that you could come up with a situation- an infinite number of situations actually- where higher order splines would do better than cubic splines. The optimal spline order for any given situation is the exact same order as the system you are trying to model. If the order is the same and your data points are error free (never the case, of course, except for in theoretical problems), then you should be able to model the system perfectly.

The reason they recommend not to go higher than cubic splines is because overfitting is really, really bad. Overfitting can greatly magnify errors, while "underfitting" (choosing a spline method with an order lower than the order of the system you are modelling) introduces some low pass filtering that is either not that bad or sometimes even beneficial.

product recommendation - Can I get the Rambam's correspondence with the French rabbis online?

I recently read an article by Rabbi Yaacov Schwartz in the Journal of Halacha and Contemporary Society (Fall 1988) titled "Jewish Implications of Astrology." In the article, he quotes the Rambam in the letter he wrote to the rabbis of South France. Rabbi Schwartz also quotes one Alexander Marx, who discusses this responsa in Vol. III of HUCA (1926).

Can I find these letters online?

Answer

It turns out that the research I did before asking this question was simply too good.

Marx reprints the letters at the end of his article (starting at page 343), which is available online for free through JSTOR.

hashkafah philosophy - Is it wrong to be racist?

Is there anything wrong about being a racist?

By racist I mean believing that certain groups of people are objectively worse in any qualitative way based on their race.

Do we have old ancient torah manuscript?

http://abcnews.go.com/International/worlds-oldest-complete-torah-scroll-found-italian-professor/story?id=19280022

It is said that this so called oldest complete torah scroll is only 800 years old.

The Christians uses Septuagint that they(or we?) claim is older. I suspected that Christians uses Septuagint to fit their agenda.

However, after reading the above article, I began to suspect. Septuagint are indeed older.

So how come Jews don't have old surviving ancient scrolls like Christians?

And is that merely 800 years old scroll really the oldest?

particles - とか and など in same sentence

This sentence includes both とか and など.

金魚の食べ物は虫とか水草などです。

Is there a difference in meaning between the two? Is there a reason to use both like this?

Answer

「AとかBなど」+ です・だ・が・を・に etc.
("A and/or B, etc.", "things like A and B")

Both of とか and など are used to give examples. とか is more colloquial/conversational than など.

You can also use:

「AやBなど」+ です・だ・が・を・に etc.
「AとかBとか」+ です・だ・が・を・に etc. ← casual

「AやB」+ です・だ・が・を・に etc.
「AとかB」+ です・だ・が・を・に etc. ← casual

But not

×「AやBや」+ です・だ・が・を・に etc.
×「AなどBなど」+ です・だ・が・を・に etc.
×「AなどB」+ です・だ・が・を・に etc.　

halacha - Should a non-Orthodox Jew wear tzitzit or not?

It seems obvious to me that in general it’s better to keep more mitzvot rather than fewer, but wearing tzitzit seems like a special case. I’ve asked rabbis in my community about this, but I want to ask here to solicit a more diverse response.

Numbers 15:39-40, the section read in the Shema that describes the meaning of tzitzit, says:

וְהָיָ֣ה לָכֶם֮ לְצִיצִת֒ וּרְאִיתֶ֣ם אֹת֗וֹ וּזְכַרְתֶּם֙ אֶת־כָּל־מִצְוֺ֣ת יְהוָ֔ה וַעֲשִׂיתֶ֖ם אֹתָ֑ם וְלֹֽא־תָתֻ֜רוּ אַחֲרֵ֤י לְבַבְכֶם֙ וְאַחֲרֵ֣י עֵֽינֵיכֶ֔ם אֲשֶׁר־אַתֶּ֥ם זֹנִ֖ים אַחֲרֵיהֶֽם׃ לְמַ֣עַן תִּזְכְּר֔וּ וַעֲשִׂיתֶ֖ם אֶת־כָּל־מִצְוֺתָ֑י וִהְיִיתֶ֥ם קְדֹשִׁ֖ים לֵֽאלֹהֵיכֶֽם׃

And it shall be unto you for a fringe, that ye may look upon it, and remember all the commandments of the LORD, and do them; and that ye go not about after your own heart and your own eyes, after which ye use to go astray; that ye may remember and do all My commandments, and be holy unto your God.

I’m sure there’s plenty of commentary on this — and I would be honored to be taught more about it — but p’shat seems to me to be clear that tzitzit are the reminder to perform all mitzvot and not to subordinate them to going “after your own heart.” So what I’m wondering is, if tzitzit are an indication of following “all the commandments,” is it appropriate for non-Orthodox Jews to wear them?

Say one dresses liberally by mainstream American standards, let alone Orthodox ones, but wears tzitzit (and a kippah), too. One eats only foods that are nominally kosher, and only eats hechshered meat, but one does eat (vegetarian/dairy only) at non-kosher restaurants. One prays three times a day at the appointed times, but prefers or is at least accepting of egalitarian prayer. One keeps Shabbat in most ways but will still shut off appliances that are no longer being used on Shabbat in order to conserve energy and reduce environmental impact. One is, in other words, the ideal religious Conservative or Reconstructionist Jew, striving hard to incorporate mitzvot into one’s life but sometimes going against rabbinic interpretations for one’s own, personal, ethical reasons (“after [one’s] own heart”).

Should this person not wear tzitzit? Does wearing tzitzit make it a more serious problem to act in these religious but non-traditionally Halakhic ways because of Torah’s clear instruction to keep “all the commandments” while wearing them?

One obvious concern I can think of is marit ayin. Is it better to be seen by the community living this way without tzitzit than with them?

But even privately, what if one does not intend to follow “all the commandments,” at least as rabbinic tradition has conveyed them? Maybe one does aspire to keep “all the commandments” as they interpret them themselves, or in the way their liberal rabbi might interpret them, but certainly not in the way Halakhic tradition does. Is that not a conflict with the pasuk?

torah service - Can someone called for one of the Shabbat or Yom Tov aliyot be called again for maftir?

I think the title of the question is self-explanatory.Something to consider:

Maftir seems to be separate from the other aliyot specified in Talmud Megilah.

Would it matter if the person who had maftir was the same Cohen that received the Cohen aliyah, or Levi who received the same Levi aliyah?

Answer

It appears from the Aruch Hashulchan in the last line of סימן קמד - שלא לדלג בתורה מעניין לעניין, ודיני ההפטרה that in extenuating circumstances one could call up for Maftir a person who already had an Aliya.

. ובכלל אין לעשות כן שאחד יעלה שני פעמים אלא בשעת הדחק (שם). וכתבו דהמהרי''ל עלה ללוי וגם למפטיר, ואולי היה מוכרח לזה מאיזה טעם.‏

He doesn't specify what counts as extenuating circumstances.

stereochemistry - Are all higher cycloalkenes chiral?

Are all higher trans-cycloalkenes chiral as trans-cyclooctene is?

This question supplements my previous question: Why is trans-cyclooctene chiral? See also the follow-on question: Do more double bonds cause a bigger number of stereoisomers in cycloalkenes?

Answer

Background

One can draw conformations of n-butane with the carbon-carbon bonds oriented in certain directions and the methyl hydrogens pointing in certain directions that are chiral. However, since rotation about single bonds is typically fast at room temperature, these chiral conformers of n-butane would only be resolvable at extremely low temperatures. Therefore we do not typically consider n-butane to be a chiral molecule.

Take-away lesson: If a chiral conformation can readily interconvert with an achiral conformation, then the molecule cannot be resolved into enantiomers and will be optically inactive.

However, there are molecules where rotation about single bonds is restricted (for example due to steric interference) and the rotational barrier is high enough that the molecules can be resolved into their respective enantiomers at room temperature.

Molecules where the rotational barrier about a single bond is high enough to allow different conformations to be isolated at room temperature are called atropisomers.

The biphenyl pictured below (in a chiral conformation) is an atropisomer due to restricted rotation about the central single bond connecting the two benzene rings. The steric interference that would develop between the 4 ortho groups if the molecule were to approach a planar (achiral) conformation prevents the chiral conformer from equilibrating with the achiral (planar) conformer. Hence this biphenyl has been resolved into its two enantiomers at ambient conditions.

Trans-cyclooctene

Trans-cyclooctene is also capable of being resolved into its two enantiomers due to restricted rotation about single bonds - it also belongs to the class of atropisomers.

In the figure below trans-cyclooctene conformation (a) is planar, therefore this conformation is achiral. The two conformers pictured in (b) are chiral - these conformations are enantiomers of each other. Trans-cyclooctene will be achiral if the two enantiomers pictured in (b) can readily interconvert through achiral (planar) conformer (a).

Build a model or draw trans-cyclooctene and notice the two hydrogens on the trans double bond; one of them is "inside" the ring in the planar conformation and would cause severe steric problems as the methylene chain tries to flip through the planar conformation to the other face of the double bond as pictured below. This steric interference makes it difficult for the molecule to achieve the planar conformation.

(Image source: John D. Roberts, Marjorie C. Caserio, Basic Principles of Organic Chemistry. Excerpt available at http://www.organicchemistry.com/cycloalkenes-and-cycloalkynes/.)

Because of this destabilizing transannular interaction, trans-cycloalkenes with up to around 11 carbons do not exist as planar molecules. They exist in a twisted conformation as pictured above for trans-cyclooctene. In your model of trans-cyclooctene, notice how you have to pull and stretch the methylene chain in order to convert trans-cyclooctene into its mirror image. This rotational movement is highly restricted due to the internal hydrogen. It is this barrier to rotation about singles bonds that allows trans-cyclooctene to be resolved into its two mirror image forms at room temperature.

The barrier to racemize trans-cyclooctene (e.g. pass through the planar conformation (a)) is 36 kcal/mole. As you might imagine, as we make the chain longer it should get easier and easier to loop the methylene chain around the internal (protruding) hydrogen on the double bond. Indeed, the barrier to interconvert the two enantiomers of trans-cyclononene is only 20 kcal/mole. Optically resolved trans-cyclononene must be kept below 0°C to prevent racemization. The barrier to racemization in trans-cyclodecene is even lower at 10 kcal/mole.

Are all higher trans-cycloalkenes chiral as trans-cyclooctene is?

First off, these rings can have chiral conformations, just like butane. I think you are really asking, "Are all higher trans-cycloalkenes optically active as trans-cyclooctene is?". That is, do these larger rings also have difficulty reaching the planar, achiral geometry?

So the answer to your original question is - it depends. It depends on the temperature you specify. At room temperature, trans-cyclooctene is the only trans-cycloalkene where the two enantiomeric conformations are stable enough (e.g. the barrier to reach the planar conformation is high enough) to be isolated. If we lower the temperature to 0°C, then we can isolate the enatiomers of trans-cyclononene. If we go low enough in temperature, we could isolate enantiomers of n-butane.

hashkafah philosophy - Why is it important that God created the first pair of tongs?

It says in Pirkei Avot 5:6 that God made the first pair of tongs immediately before creation.

Could not one have made tongs out of bone or wood wrapped in leather or made with a metal, such as gold, that can be "cold forged" and shaped without heat?

Why is it theologically important that noone could have made tongs without tongs and that God made the first pair?

words - What is the term for two kanjis, that when written in the reverse order, have the same meaning?

What is the term for two kanjis, that when written in the reverse order, have the same meaning? For example, "northeast". I have seen this situation occasionally.

Answer

There is no widely-known specific term for this.

There is a website maintained by a Japanese amateur kanji fan, where you can find the list of kanji compounds that makes sense when written in the reverse order (not necessarily the same meaning). The owner of the site calls such words 反対語（はんたいご, literally "opposite word"）. But normally 反対語 means antonyms such as 男/女 and 大きい/小さい, and he owner admits this is his own definition of 反対語 which is usable only on his site. He just could not find a better specific word, and ended up borrowing the word 反対語 for his own purpose.

Yoshinori Sakai, another amateur kanji researcher, published a book called 可逆語を探す in 2004, where 可逆語（かぎゃくご, literally "reversible word"） appears to be defined as a kanji compound that still makes sense when written in reverse order (again, not necessarily the same or similar meaning). But apparently almost no one have accepted this term after this book.

reactivity - How does steric hindrance cause sulfur hexafluoride to have almost no reaction chemistry?

Sulfur hexafluoride ($\ce{SF6}$) is, according to the Wikipedia page, a hypervalent substance. However, according to the page in regards to $\ce{SF6}$ reactions:

There is virtually no reaction chemistry for $\ce{SF6}$. The main contribution to the inertness of $\ce{SF6}$ is the steric hindrance of the sulfur atom, whereas its heavier group 16 counterparts, such as $\ce{SeF6}$ are more reactive than $\ce{SF6}$ as a result of less steric hindrance

The linked steric hindrance provides many examples of how that chemical process works, but specifically, what steric hindrance (or any other) mechanism results in $\ce{SF6}$ possessing virtually no reaction chemistry?

Answer

As you can see:

Sulfur (16) is significantly smaller than Se (34). That size difference means that there is more room between the fluorine atoms on Se than on Sulfur. That is what steric hindrance means. Think of steric hindrance as limited access. The smaller the atom the less access there is. Oxygen is so small that less than 6 fluorine atoms can crowd around it because of steric hindrance... probably more like four.

So because there is more room between the fluorine atoms on Se there is more opportunity for other atoms to attack the central atom Se, but sulfur is completely shielded by inert fluorine.

grammar - Confusion with だけに vs. だけあって

直子は七歳のときに家出したが、聡明な _______ 、見つかることなく十日間もひとりで生きていた。

a) だけあって
b) だけに
c) だけ
d) だけは

Answers say that A is proper, but according to my knowledge a and b are synonymous (though だけに can be used when the result is negative, while だけあって cannot).

Why isn't B a valid answer as well?

Answer

Sometimes だけあって and だけに are interchangeable sometimes they aren't.

In the case they are interchangeable is when the result is what is to be expected. For example, 彼が自慢するだけあって、彼女は美しい and 彼が自慢するだけに、彼女は美しい are natural.

In the case they are not interchangeable is when the result is whether to be expected or not. だけあって is used for the result that is expected, だけに is used for the result that is not expected. For example, 優秀なだけあって、彼の業績はすばらしい is more natural than 優秀なだけに、彼の業績は素晴らしい because the result caused by the reason is what is to be expected. On the other hand, 優秀なだけに、彼が会社を辞めるのは惜しい is natural, not 優秀なだけあって、彼が会社を辞めるのは惜しい because the result is not what is to be expected.

As for your sentence, the result 見つかることなく十日間もひとりで生きていた caused by the reason 彼女が聡明であること is what is to be expected, so they may be interchangeable. However if I am asked which one is better when the result is what is to be expected , I will answer だけあって is better.

Source:https://dictionary.goo.ne.jp/thsrs/17215/meaning/m0u/

ashkenazi - Why do we do hosha'nos and hakafos counterclockwise?

I have attended services in a number of different Ashkenazic synagogues on Sukos and Sh'mini Atzeres/Simchas Tora. When going around the bima for hosha'nos on Sukos, and, in most cases, when doing so for hakafos on Sh'mini Atzeres/Simchas Tora, people went counterclockwise (when viewed from above). Why counterclockwise?

Answer

Mishna Berura 660:1:3 says that when the Sefer Torah is on the Bimah those on the Mizrach (eastern wall) turn around to face the Torah their right side is now facing Tzafon (north) therfore they start in that direction.

nomenclature - Why do the names of most chemical elements end with -um or -ium?

Why do the names of most chemical elements end with -um or -ium for both primordial and synthetic elements?

Answer

To expand on @BelieveInvis's answer -- in the early 19th century, when the Royal Society was really in the swing of things, the dominant language of scholarship was still Latin. Since Latin didn't have words for the new metallic elements, new words were coined from the existing terms for the substances and given Latinate endings.

From the OED's entry on -ium:

The Latin names of metals were in -um, e.g. aurum, argentum, ferrum; the names of sodium, potassium, and magnesium, derived from soda, potassa or potash, and magnesia, were given by Davy in 1807, with the derivative form -ium; and although some of the later metals have received names in -um, the general form is in -ium, as in cadmium, iridium, lithium, osmium, palladium, rhodium, titanium, uranium; in conformity with which aluminum has been altered to aluminium.

So, I think after that, other elements were simply given the suffix to fit the generally useful naming scheme, and then, metal names which were already in common use kept their common language names (e.g. gold as opposed to aurum) simply by force of usage.

theology - Who are the Rabbis that don't meet Rambam's reqs acc. to Raavad?

In Hilchos Teshuva 3.7 Rambam defines Minim (that can't do a full Teshuvah):

חֲמִשָּׁה הֵן הַנִּקְרָאִים מִינִים. ...3) וְהָאוֹמֵר שֶׁיֵּשׁ שָׁם רִבּוֹן אֶחָד אֲבָל שֶׁהוּא גּוּף וּבַעַל תְּמוּנָה.

There are five categories of atheists: ... (3) he who says that there is One Lord; but that He is corporeal and has a form;

Raavad strongly objects:

א''א ולמה קרא לזה מין? וכמה גדולים וטובים ממנו הלכו בזו המחשבה לפי מה שראו במקראות ויותר ממה שראו בדברי האגדות המשבשות את הדעות:

Who are those "bigger and better than you (Rambam)" that Raavad refer to here?

Answer

R. Joseph Karo in his commentary to that halacha suggests that based on how Ra'avad is quoted in Sefer HaIkarim the text may not have said "bigger and better than" in the first place:

ויש לתמוה על פה קדוש איך יקרא לאומרים שהוא גוף ובעל תמונה גדולים וטובים ממנו ואפשר שעיקר הנוסחא כמו שכתוב בספר העיקרים פ"ב ממ"א וז"ל א"א אע"פ שעיקר האמונה כן הוא המאמין היותו גוף מצד תפיסתו לשונות הפסוקים והמדרשות כפשטן אין ראוי לקרותו מין עכ"ל וגם לפי נוסחתנו זאת היתה כוונתו וכבר הרחיב הדיבור בזה בעל ספר העיקרים בפרק הנזכר

Several other commentaries state that ממנו does not refer to Rambam, but to the members of our nation. Thus, Ra'avad was not saying that the people with these beliefs were greater than Rambam. For example, R. Meir Soloveitchik in his commentary there:

נ"ב עי' ג"כ שם דהכוונה במש"כ טובים ממנו היינו מבני עמינו אבל לא קאי על הרמב"ם ז"ל

R. Moshe Shternbuch in his commentary there (Haderech L'Teshuvah p. 37) claims that there are manuscripts in which Ra'avad's statement does not contain the word ממנו at all, so again there wouldn't actually be any people greater than Rambam that believed this:

אמנם אמת שבמגדל עוז מביא גדולים וטובים ממנו אבל יש בראב"ד כת"י מדוייקים דלא גרסי כלל ממנו וא"ש בפשיטות ואם נגרוס ממנו היינו מאתנו בבית ישראל וכמ"ש ועיין אור שמח כאן

However, all of these resolutions seem to be motivated by the fact that traditional rabbinic authors simply could not conceive that there could be people greater than Rambam that believed in some form of corporeality. Yet that is not necessarily historically accurate from Ra'avad's perspective. Indeed, we know from all of Rambam's writings against corporeality that belief in corporeality was existent, if not pervasive, in Rambam's time. Combined with the fact that a quick perusal of Ra'avad's glosses shows the harsh way he spoke about Rambam in general, it is not so inconceivable that Ra'avad actually believed that (some of) those who believed in corporeality were actually greater than Rambam.

Furthermore, as I mentioned in this answer and this answer, a century or so later, R. Isaiah the Younger of Trani explicitly stated that some of the Talmudic Sages believed in corporeality. He even mentions the same reason that Ra'avad mentions – that they understood verses according to their simple literal meaning. It is entirely conceivable that Rambam's contemporaries and near contemporaries would consider Talmudic Sages to be greater than him. Thus, the answer to who are those "bigger and better than Rambam" that believed this, may be (some of) the Talmudic Sages.

How do I manually plot the frequency response of a bandpass Butterworth filter in MATLAB without freqz function?

I have code like below that applies a bandpass filter onto a signal. I am quite a noob at DSP and I want to understand what is going on behind the scenes before I proceed.

To do this, I want to know how to plot the frequency response of the filter without using freqz.

[b, a] = butter(order, [flo fhi]);
filtered_signal = filter(b, a, unfiltered_signal)

Given the outputs [b, a] how would I do this? This seems like it would be a simple task, but I'm having a hard time finding what I need in the documentation or online.

I'd also like to understand how to do this as quickly as possible, e.g. using an fft or other fast algorithm.

Answer

We know that in general transfer function of a filter is given by:

$$H(z)=\dfrac{\sum_{k=0}^{M}b_kz^{-k}}{\sum_{k=0}^{N}a_kz^{-k}} $$

Now substitute $z=e^{j\omega}$ to evaluate the transfer function on the unit circle:

$$H(e^{j\omega})=\dfrac{\sum_{k=0}^{M}b_ke^{-j\omega k}}{\sum_{k=0}^{N}a_ke^{-j\omega k}} $$

Thus this becomes only a problem of polynomial evaluation at a given $\omega$. Here are the steps:

• Create a vector of angular frequencies $\omega = [0, \ldots,\pi]$ for the first half of spectrum (no need to go up to $2\pi$) and save it in w.


• Pre-compute exponent $e^{-j\omega}$ at all of them and store it in variable ze.



• Use the polyval function to calculate the values of numerator and denominator by calling: polyval(b, ze), divide them and store in H. Because we are interested in amplitude, then take the absolute value of the result.


• Convert to dB scale by using: $H_{dB}=20\log_{10} H $ - in this case $1$ is the reference value.

Putting all of that in code:

%% Filter definition
a = [1 -0.5 -0.25]; % Some filter with lot's of static gain
b = [1 3 2];

%% My freqz calculation
N = 1024; % Number of points to evaluate at

upp = pi; % Evaluate only up to fs/2
% Create the vector of angular frequencies at one more point.
% After that remove the last element (Nyquist frequency)
w = linspace(0, pi, N+1); 
w(end) = [];
ze = exp(-1j*w); % Pre-compute exponent
H = polyval(b, ze)./polyval(a, ze); % Evaluate transfer function and take the amplitude
Ha = abs(H);
Hdb  = 20*log10(Ha); % Convert to dB scale
wn   = w/pi;

% Plot and set axis limits
xlim = ([0 1]);
plot(wn, Hdb)
grid on

%% MATLAB freqz
figure
freqz(b,a)

Original output of freqz:

And the output of my script:

And quick comparison in linear scale - looks great!

[h_f, w_f] = freqz(b,a);
figure
xlim = ([0 1]);
plot(w, Ha) % mine
grid on
hold on

plot(w_f, abs(h_f), '--r') % MATLAB
legend({'my freqz','MATLAB freqz'})

Now you can rewrite it into some function and add few conditions to make it more useful.

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Another way (previously proposed is more reliable) would be to use the fundamental property, that frequency response of a filter is a Fourier Transform of its impulse response:

$$H(\omega)=\mathcal{F}\{h(t)\} $$

Therefore you must feed into your system $\delta(t)$ signal, calculate the response of your filter and take the FFT of it:

d = [zeros(1,length(w_f)) 1 zeros(1,length(w_f)-1)];

h = filter(b, a, d);
HH = abs(fft(h));
HH = HH(1:length(w_f));

In comparison this will produce the following:

parshanut torah comment - How would Yaakov's plan to divide into two camps have worked?

Yaakov divides his family into two camps stating that if Eisav attacks one the other will flee and be saved. However his whole family seems to be be there when Eisav arrives, furthermore Yaakov himself states (and it seems to be a metzius) that families with belongings travel far slower than Eisav and his warriors. As such how would sending one camp away have worked in practice and why didn't he actually send the camp away at all?

Answer

After struggling and overcoming the angel of Eisav, spiritually Yaakov now knew that his encounter with Eisav would be successful and that there was no need to send away the second camp. Furthermore Yaakov felt that his method of bribery/appeasement, which had worked with Eliphaz would be successful enough to abate Eisav's anger.

I believe the way it could have worked in theory had it been necessary would be that they would leave the animals and most of the belongings behind so as to be able to travel more quickly. Yaakov specifies that traveling with children and all of the family belongings are what slows them down; it is reasonable to assume that traveling with servants (especially angelic ones) and women and children only would be able to move more quickly.

maseches kilayim - Why is a dog considered a wild animal?

Kilayim 8:6, in listing various animals and whether they are considered wild or domesticated, says:

כלב מין חיה

A dog is a type of wild animal

Why is this? We’re not talking about wild dogs or wolves - just ordinary dogs. Why are they not considered domesticated?

(I should note that R’ Meir argues with the Tanna Kamma. I am asking specifically on the Tanna Kamma’s opinion.)

kohen priest - Kohanim Dating Ba'alot Teshuva

Is it necessary for a Kohen to clarify that a prospective match who is a ba'alat teshuvah has not had sexual relations with a non-Jew before dating her, or can one rely on a chezkat kashrut? If the former what steps need to be taken to clarify her status?

halacha - Self inspection of a bris milah

Is it possible for an adult to inspect his own milah to determine if the milah was done in a halachically proper manner? Are there any picture guides or some other type of resources that would help someone who is completely ignorant in the details of what a bris milah entails, to educate himself to the actual practical details of the laws and in turn allow him to inspect his own milah?

What are the statistics of the discrete Fourier transform of white Gaussian noise?

Consider a white Gaussian noise signal $ x \left( t \right) $.
If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?

Answer

We can do the calculation using some basic elements of probability theory and Fourier analysis. There are three elements (we denote the probability density of a random variable $X$ at value $x$ as $P_X(x)$):

1. 
   

   Given a random variable $X$ with distribution $P_X(x)$, the distribution of the scaled variable $Y = aX$ is $P_Y(y) = (1/a)P_X(y/a)$.

   
   


2. 
   

   The probability distribution of a sum of two random variables is equal to the convolution of the probability distributions of the summands. In other words, if $Z = X + Y$ then $P_Z(z) = (P_X \otimes P_Y)(z)$ where $\otimes$ indicates convolution.

   
   


3. 
   

   The Fourier transform of the convolution of two functions is equal to the product of the Fourier transforms of those two functions. In other words:

   
   

$$\int dx \, (f \otimes g)(x) e^{-i k x} = \left( \int dx \, f(x) e^{-ikx} \right) \left( \int dx \, g(x) e^{-ikx} \right) \, . $$

Denote the random process as $x(t)$. Discrete sampling produces a sequence of values $x_n$ which we assume to be statistically uncorrelated. We also assume that for each $n$ $x_n$ is Gaussian distributed with standard deviation $\sigma$. We denote the Gaussian function with standard deviation $\sigma$ by the symbol $G_\sigma$ so we would say that $P_{x_n}(x) = G_{\sigma}(x)$.

The discrete Fourier transform amplitudes are defined as $$X_k \equiv \sum_{n=0}^{N-1} x_n e^{-i 2 \pi n k /N} \, .$$ Focusing for now on just the real part we have $$\Re X_k = \sum_{n=0}^{N-1} x_n \cos(2 \pi n k /N) \, .$$ This is just a sum, so by rule #2 the probability distribution of $\Re X_k$ is equal to the multiple convolution of the probability distributions of the terms being summed. We rewrite the sum as $$\Re X_k = \sum_{n=0}^{N-1} y_n$$ where $$y_n \equiv x_n \cos(2\pi n k / N) \, .$$ The cosine factor is a deterministic scale factor. We know that the distribution of $x_n$ is $G_\sigma$ so we can use rule #1 from above to write the distribution of $y_n$: $$P_{y_n}(y) = \frac{1}{\cos(2 \pi n k / N)}G_\sigma \left( \frac{y}{\cos(2 \pi n k / N)} \right) = G_{\sigma c_{n,k}}(y)$$ where for brevity of notation we've defined $c_{n,k} \equiv \cos(2\pi n k / N)$.

Therefore, the distribution of $\Re X_k$ is the multiple convolution over the functions $G_{\sigma c_{n,k}}$: $$P_{\Re X_k}(x) = \left( G_{\sigma c_{0,k}} \otimes G_{\sigma c_{1,k}} \otimes \cdots \right)(x) \, .$$

It's not obvious how to do the multiple convolution, but using rule #3 it's easy. Denoting the Fourier transform of a function by $\mathcal{F}$ we have $$\mathcal{F}(P_{\Re X_k}) = \prod_{n=0}^{N-1} \mathcal{F}(G_{\sigma c_{n,k}}) \, .$$

The Fourier transform of a Gaussian with width $\sigma$ is another Gaussian with width $1/\sigma$, so we get \begin{align} \mathcal{F}(P_{\Re X_k})(\nu) &= \prod_{n=0}^{N-1} G_{1/\sigma c_{n,k}}\\ &= \prod_{n=0}^{N-1} \sqrt{\frac{\sigma^2 c_{n,k}^2}{2\pi}} \exp \left[ \frac{-\nu^2}{2 (1 / \sigma^2 c_{n,k}^2)}\right] \\ &= \left( \frac{\sigma^2}{2\pi} \right)^{N/2} \left(\prod_{n=0}^{N-1}c_{n,k} \right) \exp \left[ -\frac{\nu^2}{2} \sigma^2 \sum_{n=0}^{N-1} \cos(2\pi nk/N)^2 \right] \, . \end{align} All of the stuff preceding the exponential are independent of $\nu$ and are therefore normalization factors, so we ignore them. The sum is just $N/2$ so we get \begin{align} \mathcal{F}(P_{\Re X_k}) &\propto \exp \left[ - \frac{\nu^2}{2} \sigma^2 \frac{N}{2}\right]\\ &= G_{\sqrt{2 / \sigma^2 N}} \end{align} and therefore $$P_{\Re X_k} = G_{\sigma \sqrt{N/2}} \, .$$

We have therefore computed the probability distribution of the real part of the Fourier coefficient $X_k$. It is Gaussian distributed with standard deviation $\sigma \sqrt{N/2}$. Note that the distribution is independent of the frequency index $k$, which makes sense for uncorrelated noise. By symmetry the imaginary part should be distributed exactly the same.

Intuitively we expect adding more integration should reduce the width of the resulting noise distribution. However, we found that the standard deviation of the distribution of $X_k$ grows as $\sqrt{N}$. This is just due to our choice of normalization of the discrete Fourier transform. If we had instead normalized it like this $$X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n e^{-i 2 \pi n k /N}$$ then we would have found $$P_{\Re X_k} = G_{\sigma / \sqrt{2N}}$$ which agrees with the intuition that the noise distribution gets smaller as we add more data. With this normalization, a coherent signal would demodulate to a fixed amplitude phasor, so we recover the usual relation that the ratio of the signal to noise amplitudes scales as $\sqrt{N}$.

names - Why isn't Shimson's mother named?

Why isn't Shimson's mother named in Pesukim that tell the story? She is featured rather prominently, and the angel appears to her before speaking with both her and Manoaḥ. It would stand to reason that she is as important a character as other barren mothers who prayed for children and were blessed with great leaders for sons. (Aside, to preempt comments comparing Shimson to some of those other leaders: Perhaps he wasn't the greatest leader or a true Navi, but he was great enough for his story to appear in TaNa"Ch, and it's not like his father isn't named.)

quotes - What is the use of て-form at the end of this sentence?

何かヒーロー友に守られ血を流させて。

I interpret this sentence from the manga 「僕のヒーローアカデミア」to mean "Some hero I am, making my friends spill blood to protect me." However, I have two questions:

What is the use of the te-form of 流させる at the end of the sentence? Usually, when I see the te-form alone, I assume it's a request (i.e. shortened form of 〜てください), but I don't see how this quote could be construed as such. It's part of a character's inner monologue.

Also, though not my main question, is it acceptable to drop the る from 守られる as is done above?

minhag - Is one allowed to drink from the wine spilled out of the cup at the Makkos?

It is a widespread minhag that during the mention of the makkos at the Seder one should either spill out wine or dip a finger into the cup and put it to the side.

I have heard that one should not drink this wine, or even the wine left on the fingers from dripping it on the plate. I'm told that just like the malachim were unable to sing shirah because it's rejoicing at others' downfall, we should not drink from the wine used to represent the Egyptians' downfall and gain benefit from it. Is this accurate, and if so, what is the source (i.e. sefer that discusses this)?

Artscroll's The Answer Is... Haggadah (page 148-149) quotes Rav Yechezkel Abramsky and Rav Eliyashiv as saying that this is why we spill it, and the Alter of Slabodka as saying that we should not be happy about human beings, created b'tzelem Elokim, being killed. It does not say. anything about drinking the wine, however.

Highly related: Is the wine spilled at the Seder "cursed"? This is not a duplicate, as that discusses actually discarding the wine, not refraining from drinking it.

Answer

The Chok Yaakov (473 s"k 37 - the small print on the left) gives 2 reasons to avoid drinking the spilled wine: Because the Makos were mentioned when they were spilled, and because it became נמעס upon contact with one's fingers.

However, the Hagadah Or Yesharim writes that the Gaon of Vilna would spill the wine into a vessel so it shouldn't go to waste.

Similarly, Rav Shlomo Zalman Aurbach would gather the spilled wine from the plates and pour it into one of the cups (Halichos Shlomo 9 footnote 242).

audio - What does one need to know in order to build a software synthesizer?

For someone who has some experience in software development, loves his synths and knows the [very] basics of digital audio representation, what are the first steps he should follow in order to program a music synthesizer, DSP-wise?

Answer

Get Real Sound Synthesis for Interactive Applications, and download the Synthesis Toolkit. That will give you practical introductions and quality source code for most digital synthesis methods in use. Then pick whichever method you find most interesting, and start modifying the corresponding STK code to do what you want. Then try building something similar from scratch.

In addition, like hotpaw2 suggested, anything from JOS is also great introductory material. In particular, Introduction to Digital Filters with Audio Applications and Mathematics of the Discrete Fourier Transform both start from the basics, and don't assume a lot of background.

From a digital filter/effects perspective, another good starting point is to check out Faust. You don't even have to learn their block-diagram signal processing language, you can just use the examples to dump out VST, LADSPA, etc. template code as quick way of getting something running [which you can then modify].

That being said, it's even easier to start out with sound rendering, which is basically the same thing, but without worrying about real-time operation or interactivity. You just save wav files to disk. It's a great way to experiment with new techniques before going through the trouble of making them run quickly.

organic chemistry - Is carbonyl-enol tautomerization only intermolecular or can it be intramolecular?

During workup of a conjugate addition reaction, it is likely that protonation occurs at the oxygen of the enolate formed. See discussion here: Do enolates get protonated at the carbon or oxygen atom? In that discussion, it is essentially said "The oxygen is probably protonated, but it really doesn't matter." However, I think this could be important in select instances, specifically in the protonation of enolates with diastereotopic faces (which isn't all that rare). But this mostly depends on if tautomerization can occur intramolecularly.

---

An example of what I'm getting at:

This is an example I just made up. This reaction likely would not actually happen like this. In actually, I could see some γ-deprotonation happening.

In this reaction, one chiral center is formed, and an enolate is formed, and the most likely atom to be protonated upon addition of an acid is the oxygen:

That enol could go on to form one of two products. The intramolecular reaction, I think, would likely give much more of the thermodynamic product (shown below) than an intermolecular reaction, though I'm not certain on that. The reactions here are simplified; I realize both would most likely make some mixture of the two products:

My thoughts are that the four-membered intermediate required for the intramolecular reaction will just be too strained for this to occur. I realize that in basic or acidic solution, catalysis will occur, as the Wikipedia page mentions. I guess the best way to phrase my question is this: In the hypothetical situation that a single ester enol molecule (like that shown as the product of O-protonation above) is dissolved in pure hexane, would that molecule be stuck in in the enol form or would it be able to rearrange? I realize this is more feasible with an dienol, but I'm specifically trying to figure out if the enol can do this.

For the sake of this question, ignore the basicity of the nitrogen. Maybe I should have used the diphenylmethane anion or something. Doesn't matter, it wouldn't reach the proton, either.

Answer

tl;dr: The intramolecular variant is an impossible rearrangement. Only intermolecular proton transfer can be observed.

---

This is actually a very nice example to discuss sigmatropic rearrangements, because the desired [1,3]-rearrangement would be one. In general, these can proceed in four possible ways, depending on the configuration of the migrating group and whether it remains on the same side of the π system or not. We would have to draw orbital schemes to determine whether or not the orbital of the migrating group is able to interact both with the point of origin and the point of arrival favourably.

With regards to the configuration, the two possibilities are:

• migration under retention


• migration under inversion

A migration under retention is always possible because the corresponding orbital’s lobe is already pointing towards the π system it is migrating along. A migration under inversion is only possible if the (atomic) orbital whose bond is broken and later reformed has lobes on two different sides; typically for migrating atoms, this means a $\mathrm p$ orbital.

In the case of a proton shift, we must consider a hydrogen atom. It’s only occupied orbital through which it bonds to the carbon chain is $\mathrm{1s}$. This orbital does not have two lobes, therefore a rearrangement mechanism under inversion is impossible; we need only consider the retention mechanisms.

With respect to the π system, the two possibilities are:

• suprafacial (remaining on the same side)


• antarafacial (switching sides)

Again, a suprafacial migration is practically always possible. For an antarafacial migration to be considered, the chain must be flexible enough so that both sides can interact with the migrating group; ideally at the same time.

Since the thought experiments are rather hard to perform, here are some depictions to make it easier.

Figure 1: Suprafacial [1,5] (left) and antarafacial [1,7] (right) hydrogen migrations. The depicted π orbital corresponds to the HOMO of a full π system including the $\ce{C-H}$ bond.

Generally, the full π system and the neighbouring $\ce{C-H}$ bond that is to be broken must be considered as I have done in figure 1. This π system can be drawn up with the standard rules for linear π systems. In the [1,5]-rearrangement, the system is penta-2,4-dien-1-yl while in the [1,7] case it is hepta-2,4,6-trien-1-yl. The $\ce{C-H}$ bond is considered part of the π system with the proton being the migrating group. Therefore, the HOMO (the orbital of importance) will be the one in question. (If the $\ce{C-H}$ bond is considered part of hydrogen, we must consider the π system’s LUMO, meaning that the orbital will remain the same. We must always have an occupied and an unoccupied orbital for consideration.)

The image shows us that the [1,5]-migration — over two double bonds — can only occur in a suprafacial manner with hydrogen. If we had a group capable of inversion, an antarafacial manner would be possible given the correct geometry. In the [1,7] case — over three double bonds —, hydrogen can only migrate in an antarafacial manner under retention; the only possible suprafacial manner would be under inversion which hydrogen cannot do.

This has been turned into a general rule of thumb: If your migration is [1,$4n+1$], it may proceed suprafacial under retention but if it is [1,$4n+3$] it must proceed in an antarafacial manner. In the [1,3]-case, only antarafacial migration would be possible, but there is no way that the π system can twist so it would allow for antarafacial migration. The π orbital in question is shown in figure 2 below.

Figure 2: The π orbital relevant for a [1,3]-migration.

Therefore, an intramolecular proton transfer is impossible and an external source would have to protonate.

---

One thing to note: the molecule itself is able to deprotonate/reprotonate another molecule of its type intermolecularly. So the compound would not be stuck in the enol form but a second molecule would provide the much desired proton to allow the keto form to be regenerated, even in pure hexane (if it is even soluble in that).