Do these words ever appear together as one phrase in Tanach?
Tuesday, October 1, 2019
gentiles - Can a Christian "Grace" invalidate food?
Suppose there's a communal meal in a secular workplace, at which some of the food is reliably kosher. Now suppose that right before anyone takes any food, one of the participants, to general assent, says grace, including a line like "We consecrate this food to Jesus Christ." Is there any problem with consuming any of the food after that?
Answer
There's a rule that "you can't prohibit that which does not belong to you." A pagan can go deify my cow and bow down to it all he wants; he can even slaughter it to his idol; if it's my cow, he did nothing and you can derive benefit from the cow. So the first and major question is, who owned the food in this situation, and who consecrated it? Moreover, what does "consecration" mean? Is that the act of sacrifice, or merely designating it for sacrifice? (The latter wouldn't prohibit it.)
From Rambam's Laws of Foreign Worship and Heathen Practices, Chapter 8:
לפיכך הגויים העובדים את ההרים, ואת הגבעות, ואת האילנות הנטועין מתחילתן לפירות, ואת המעיינות הנובעים לרבים, ואת הבהמה--הרי אלו מותרין בהנאה; ומותר לאכול אותן הפירות שנעבדו במקום גדילתן, ואותה הבהמה. ואין צריך לומר, בהמה שהוקצת לעבודה זרה, שהיא מותרת באכילה: בין שהקצוה לעובדה, בין שהקצוה להקריבה--הרי זו מותרת.
ב במה דברים אמורים שאין הבהמה נאסרת, בשלא עשה בה מעשה לשם עבודה זרה; אבל אם עשה בה מעשה כל שהוא, אסרה. כיצד, כגון ששחט בה סימן לעבודה זרה. עשה אותה חליפין לעבודה זרה, אסרה; וכן חליפי חליפין: מפני שנעשת כדמי עבודה זרה.
ג במה דברים אמורים, בבהמת עצמו; אבל אם שחט בהמת חברו לעבודה זרה או החליפה--לא נאסרה, שאין אדם אוסר דבר שאינו שלו.
The next question would be how to approach Christianity vis-a-vis the prohibitions related to the accoutrements of idolatry, which is addressed elsewhere.
The third question is whether a declaration of consecration alone (even by an absolute pagan on his own food) is enough to prohibit it. If I recall correctly from the whole mess about wig hair coming from Hindu temples, there are different opinions in Tosfos whether any item used in pagan worship becomes prohibited, or does it have to be specifically the object of pagan libations, bowing, incense, or animal sacrifice. I don't see a verbal consecration in any of those.
water - What is the cause of hygroscopy?
Hygroscopy is the ability of a substance to attract and hold water molecules from the surrounding environment.
Why are some compounds hygroscopic and others are not? What is it about their structures that allows them to hold water? Is it due to the atoms being arranged in a certain structure due to bonding?
How can you tell if a compound is more hygroscopic than another?
metal - Why does mercury not form amalgam with iron?
I am learning about solutions and while giving an example of a liquid (solute) and a solid (solvent), my teacher told us that mercury forms an amalgam with all the metals except iron.
I want to know why this is so?
Answer
Iron does not form an amalgam readily, hence the use of iron electrodes in mercury switches. Apparently, iron does form alloys with mercury under specific conditions; see http://www.madsci.org/posts/archives/2011-04/1304143502.Ch.r.html.
By contrast, mercury spilled on gold (e.g. gold-alloy jewelry) soaks in immediately, discoloring the gold, and migrates further into the bulk metal in a few hours, thus restoring the color.
What are the practically relevant differences between various image resampling methods?
Mathematica's ImageResize function supports many resampling methods.
Not being familiar with this area, beyond nearest neighbour, bilinear, biquadratic and bicubic (which are obvious from the name), I am lost.
Can you point me to some source that will explain the basic (mathematical) differences between these methods, and in particular point out the practical differences (e.g. by showing sample images where the choice of method really matters and introduces noticeable differences)?
I don't have a signal processing background, so I'd prefer a "gentle" and concise introduction :-)
I'll copy here the list of ImageResize methods for those "lazy" to click the link:
"Nearest" nearest neighbor resampling
"Bilinear" bilinear interpolation
"Biquadratic" biquadratic spline interpolation
"Bicubic" bicubic spline interpolation
"Gaussian" Gaussian resampling
"Lanczos" Lanczos multivariate interpolation method
"Cosine" cosine interpolation
"Hamming" raised-cosine Hamming interpolation
"Hann" raised-cosine Hann interpolation
"Blackman" three-term generalized raised cosine
"Bartlett" triangular window interpolation
"Connes" squared Welch interpolation
"Welch" Welch quadratic interpolation
"Parzen" piecewise cubic interpolation
"Kaiser" zero-order modified Bessel interpolation
Answer
Given an image $I(m,n)$ with $m,n$ integers, the interpolation of that image at any arbitrary point $m',n'$ can be written as
$$\tilde{I}(m',n')=\sum_{m=\left\lfloor m'\right\rfloor-w+1}^{\left\lfloor m'\right\rfloor+w}\ \sum_{n=\left\lfloor n'\right\rfloor-w+1}^{\left\lfloor n'\right\rfloor+w}I(m,n)\ f(m'-m,n'-n)$$
The result $\tilde{I}$ is still only an approximation to the true underlying continuous image $\mathcal{I}(x,y)$ and all that different interpolating functions do is to minimize the approximation error under different constraints and goals.
In signal processing, you'd like the interpolating function $f(m,n)$ to be the ideal low-pass filter. However, its frequency response requires infinite support and is useful only for bandlimited signals. Most images are not bandlimited and in image processing there are other factors to consider (such as how the eye interprets images. What's mathematically optimal might not be visually appealing). The choice of an interpolating function, much like window functions, depends very much on the specific problem at hand. I have not heard of Connes, Welch and Parzen (perhaps they're domain specific), but the others should be the 2-D equivalents of the mathematical functions for a 1-D window given in the Wikipedia link above.
Just as with window functions for temporal signals, it is easy to get a gist of what an image interpolating kernel does by looking at its frequency response. From my answer on window functions:
The two primary factors that describe a window function are:
- Width of the main lobe (i.e., at what frequency bin is the power half that of the maximum response)
- Attenuation of the side lobes (i.e., how far away down are the side lobes from the mainlobe). This tells you about the spectral leakage in the window.
This pretty much holds true for interpolation kernels. The choice is basically a trade-off between frequency filtering (attenuation of sidelobes), spatial localization (width of mainlobe) and reducing other effects such as ringing (Gibbs effect), aliasing, blurring, etc. For example, a kernel with oscillations such as the sinc kernel and the Lanczos4 kernel will introduce "ringing" in the image, whereas a Gaussian resampling will not introduce ringing.
Here's a simplified example in Mathematica that let's you see the effects of different interpolating functions:
true = ExampleData[{"TestImage", "Lena"}];
resampling = {"Nearest", "Bilinear", "Biquadratic", "Bicubic",
"Gaussian", "Lanczos", "Cosine", "Hamming", "Hann", "Blackman",
"Bartlett", "Connes", "Welch", "Parzen", "Kaiser"};
small = ImageResize[true, Scaled[1/4]];
Here, true represents the image which I assume to be the discrete equivalent of the "exact" image $\mathcal{I}(x,y)$, and small represents a smaller scale image $I(m,n)$ (we don't know how it was obtained). We'll interpolate $I(m,n)$ by 4x to give $\tilde{I}(m',n')$ which is the same size as the original. Below, I show the results of this interpolation and a comparison with the true image:
You can see for yourself that different interpolating functions have different effects. Nearest and a few others have very coarse features and you can essentially see jagged lines (see full sized image, not the grid display). Bicubic, biquadratic and Parzen overcome this but introduce a lot of blurring. Of all the kernels, Lanczos seems (visually) to be the most appealing and one that does the best job of the lot.
I'll try to expand upon this answer and provide more intuitive examples demonstrating the differences when I have the time. You might want to read this pretty easy and informative article that I found on the web (PDF warning).
chabad - Nusach Sefard vs. Nusach Ha-Arizal
So I was wondering what differences there are between Nusach Sefard, the traditional Chassidic nusach and Nusach Ha-Arizal, the Chabadnik nusach arranged by the Alter Rebbe (Rabbi Schneur Zalman of Liadi). Does anyone know the difference?
Answer
Nusach Sefard, Nusach Sepharad, or Nusach Sfard is the name for various forms of the Jewish siddurim, designed to reconcile Ashkenazi customs (Hebrew: מנהג "Custom", pl. minhagim) with the kabbalistic customs of Isaac Luria.
https://en.m.wikipedia.org/wiki/Nusach_Sefard
Technically speaking, the Alter Rebbe's siddur is a form of nuschach sefard.
Nusach Ari is a variant of Nusach Sefard, used by Chabad Hasidim.
https://en.m.wikipedia.org/wiki/Nusach
Practically speaking, no one calls it Nusach sephard (even wikipedia separates it from Nusach sefard). My guess would be that's because of the separation between chabad and other Chassidim. Either way, Chabad definitely views it as separate nuschaos. I can't speak for the other Chassidim though, and I haven't asked them. But they're both founded from the same sources, and share many similarities.
halacha - “Worship idols or I kill another Jew” - what should one do?
The Halacha is that one may not serve Avodah Zarah even on pain of death (Sanhedrin 74a).
I was staying by a family for Shabbos, and their 11-year-old son asked a genius question. What happens if the threat is not “worship or I’ll kill you,” but rather “worship or I’ll kill him”? Does this Halacha still apply?
On the one hand, one could argue that what the threatener decides to do is none of your business; let him do what he wishes, and you not get involved.
On the other hand, the source that one must give up his life for Avodah Zarah, as per the above-cited Gemara, is Devarim 6:5 - “and you should love Hashem, your G-d...with all your soul.” One could argue that it’s only your soul one is obligated to give up, and you have no right to give up someone else’s soul for your love of Hashem.
What is the Halacha? I have looked in the Rambam, Tur, and Shulchan Aruch, as well as the commentaries on the above, with no success of anyone talking about anything similar to this case.
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