number - Why isn't the Kabbalistic doctrine of Sefirot considered Shittuf if the Christian Trinity is?

From the answers to this question it seems that most if not all Jewish sources treat Trinitarian Christianity (in particular, their doctrine of the Trinity) as either Shittuf or outright Avoda Zara, both of which (if there is a difference) are expressly forbidden for Jews to believe.

For background, the Christian doctrine of the Trinity explains the Godhead as: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God" (in the Athanasian Creed) and therefore Christians would seem to be monotheists, except that God has parts or aspects which cannot be understood but together comprise God's unity (since the Trinity is classified as a 'mystery'). It is this doctrine which is problematic in Jewish sources (which were, of course, not written by Christian theologians but Jewish ones whose understanding of Christian doctrine was probably similar to the level I just presented).

In the Jewish Kabbalistic doctrine of Sefirot, there are 10 Sefirot which are often described as either parts of God's "body" (each corresponding to a different limb) or manifestations or emanations, which although separate, with unique properties and sometimes male or female associations, nevertheless somehow do not contradict that God remains unified and indivisible. His unity is also, in this sense somewhat mysterious.

The Rivash (Rabbi Isaac Ben Sheshet, 14th Century) famously wrote in a responsum, #157:

.וכל זה הוא דבר זר מאוד בעיני מי שאינו מקובל כמו הם; וחושבים, שזה אמונת שניות. וכבר שמעתי אחד מן המתפלספים מספר בגנות המקובלים, והיה אומר: הנוצרים מאמיני השילוש, והמקובלים מאמיני העשיריות
And all this is very foreign in my eyes, as someone who is not a Kabbalist such as myself; and they think is is dualist theology...and I heard one of the ones who philosophizes speaking to the detraction of the Kabbalists, saying: the Christians believe in 3 and the Kabbalists believe in 10.

If the Christian doctrine of the Trinity as understood by Jews is deemed Shittuf/Avoda Zara by them, is the Kabbalistic doctrine of Sefirot considered that as well?

Is there any reason to distinguish between the Christian divided/united God as understood by Jews (and deemed by them problematic) and the Kabbalistic one?

(Note that I am not interested in whether the doctrine of incarnation is problematic from a Jewish perspective. I would like to explore merely the question of a multipart Godhead and whether there is any reason to distinguish Christian and Jewish beliefs in that regard alone. Is there some difference in the perspective on the "parts"? Or a difference in the interpretation of the level of independence of the "parts"? Or a difference in regards their unification/unity? Or is there not fundamental difference aside from incarnation?)

tzitzis - Why was the use of the tallit instituted as halacha?

This article implies that the mitzvah of wearing tzitzit is required only when one wears a four-cornered garment. If one never wore such a garment, one need not wear tzitzit at all.

Citation:

The style of dress in those olden times was for people to wrap themselves in rectangular garments, but over the centuries styles changed, and in many parts of the Jewish world, this commandment and ritual was faced with extinction.

The Rabbis decided, therefore, to make it a special duty for us to go out of our way to continue wearing four-cornered garments in order to obligate ourselves in this time-honored and deeply significant mitzvah. They instituted two different garments for this purpose.

Why was this mitzvah considered so important that the rabbis had to introduce the wearing of a special garment? This is a "situational" mitzvah - i.e., if one doesn't encounter the situation, he doesn't need to perform the mitzvah.

We have many similar "situational" mitzvot, such as Shiluach Hakan (sending away the mother bird before taking the chicks or eggs.) Its reward is long life - So, it seems important, in some way. Yet, we do not require people to plant a tree and coax a female bird to come there to build a nest.

Why was the mitzvah of tziztzit considered that important?

Answer

Although he does not seem to agree with the full extent of your citation (i.e. that it is an actual duty), Rambam (Hilkhot Tsitsit 3:12) writes that this mitsvah is particularly important, and therefore one should try to perform it:

אף על פי שאין אדם מחוייב לקנות טלית ולהתעטף בה, כדי שיעשה בה ציצית, אין ראוי לאדם חסיד, לפטור עצמו ממצוה זו; אלא לעולם ישתדל להיות עטוף בכסות המחוייבת בציצית, כדי שיקיים מצוה זו. ובשעת התפילה, צריך להיזהר ביותר; גנאי גדול הוא לתלמיד חכמים, שיתפלל והוא אינו עטוף

Even though a person is not required to purchase a tallit and wrap himself in it, so that he [will be obligated] to make tsitsit for it, a pious person should not exempt himself from this mitsvah. Rather, he should always try to be covered with a garment that is required in tsitsit, so that he should fulfill this mitsvah. And during prayer, he needs to be particularly careful with this; it is a great disgrace for a talmid hakhamim to pray without being wrapped.

The next halakha seems to provide the explanation for why this mitsvah is unique in that pious people should try to fulfill it:

לעולם יהא אדם זהיר במצות ציצית, שהרי הכתוב שקלה ותלה בה כל המצוות כולן, שנאמר "וראיתם אותו וזכרתם את כל מצוות ה', ועשיתם אותם" (במדבר טו,לט).

A person should always be careful with the mitsvah of tsitsit, for the verse (Numbers 15:39) states: "And you shall see it, and you will remember all the mitsvot of God, and perform them".

His son Rabbenu Avraham elaborates upon this point in the halakhic portion of his HaMaspik L'Ovdey Hashem:

אין האדם מחויב לקנות כסות ולעשות לה ציצית...אולם..הנה רצוי ומומלץ...[ש]ישתדל לקנות טלית שהיא חייבת בציצית ויעשה בה ציצת, ויהא לובשה תמיד או במרבית זמניו כדי שתושג אצלו תכלית המצוה הנכבדת הזאת שהיא וראיתם אתו וכו

A person is not obligated to purchase a garment and make tsitsit for it...however...it is preferable and encouraged...to make an effort to purchase a tallit which is obligated in tsitsit, and to make tsitsit for it, and to wear it all the time, or much of the time, to achieve the objective of this exalted mitsvah, which is "and you shall see it", etc. [i.e. and you will remember all of God's mitsvot and do them, and you will not stray after your hearts and after your eyes which you lust after, so that you remember and perform all of my mitsvot, and be sanctified to your God]. (Dana's Hebrew translation pp. 270-271).

Similarly, R. Yonah of Girona writes (Sefer HaYirah) that one should make a point of wearing tsitsit since it will remind him of the mitsvot:

ויהיה לו טלית קטן וילבשנו...כי עיקר מצות ציצית לזכרון ללבשו תמיד

And he should have a tallit kattan and wear it...For the root of the mitsvah of tsitsit is as a remembrance, he should always wear it.

This is paraphrased by the Tur (OH 24) who writes:

טוב ונכון להיות כל אדם זהיר וזריז במצות ציצית שיהיה לו בגד קטן מצוייץ שילבש אותו כל היום כי עיקר מצותה על זכירת המצות ובכל שעה ובכל רגע צריך לכך

It is good and proper for every person to be careful and proactive regarding the mitsvah of tsitsit, to have a tallit kattan with tsitsit to wear all day, for the main [purpose] of the mitsvah is to remember the mitsvot, and one needs this every hour and every moment.

This is in turn cited by the Shulhan Arukh (OH 24:1):

וְטוֹב וְנָכוֹן לִהְיוֹת כָּל אָדָם זָהִיר לִלְבֹּשׁ טַלִּית קָטָן כָּל הַיּוֹם, כְּדֵי שֶׁיִּזְכֹּר הַמִּצְוֹת בְּכָל רֶגַע.

It is good and proper for every person to be careful to wear a tallit kattan all day so that he remember the mitsvot all the time

Importantly, neither Rambam, nor Rabbenu Avraham, nor Rabbenu Yonah, nor the Tur, not the Shulhan Arukh encourage making the effort to wear tsitsit because it is a situational mitsvah, such that you would ask about all other situational mitsvot. Rather, they explain that the particular emphasis on this mitsvh, is due to the unique role of this mitsvah; driving us to remember and perform all of the mitsvot.

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In a different vein, Maharil writes (Shu"t HaHadashot: 7) that one should wear tsitsit simply because it is a mitsvah and one should pursue mitsvot. He makes clear that one is not obligated to acquire a garment with tsitsit, but that it is good to pursue mitsvot:

אין מחוייב לקנות בת ד' אלא דמצוה להכניס עצמו לכלל חיוב כדילפינן ממשה רבינו ע"ה וכי לאכול (מפיריה) [מפריה] כו'

One is not required to acquire a four cornered garment, but it is a mitsvah to bring oneself into the realm of the mitsvah, as we learn from Moshe [who wanted to enter Israel to perform more mitsvot].

Near a bad smell, one might want to do Sh'ma, the Amidah, blessings, study, or think Torah. Is halacha equally strict about all five acts?

"Just as one separates oneself from excreta, urine, a foul odor, a corpse and the sight of nakedness for Kri'at Shema, so too, he should separate himself for Shemoneh Esreh". —Rambam. Hilchos Tefillah 4:8 in translation.

The Rambam just discussed:

1) Sh'ma.
2) Sh'moneh Esrei.

He didn't discuss the acts of:

3) Saying blessings.
4) Studying Torah aloud.
5) Thinking about Torah matters.

When there's a bad smell nearby, is Jewish law equally strict about all five acts? Or is it stricter about some and more lenient about others?

Please cite sources.

word choice - Difference between [行く末]{ゆくすえ}, 将来{しょうらい} and 未来{みらい}

I've been looking around and I got that the three words can mean "future". Is there a way to differentiate them? Can they be used the same way?

Answer

未来 and 将来 are pretty similar to each other. 大辞泉 breaks down the differences under the 用法 section of 「将来」 entry (explanation translated):

将来 and 未来 can both be used in situations where you're talking about the time that will come after the present, e.g. 「将来（未来）への夢」 ("dreams for the future") and 「明るい将来（未来）」 ("a bright future"). 「未来」 cannot be used instead of 「将来」 in an expression like 「私は将来、弁護士になりたい」 ("in the future, I want to be a lawyer"). Also, it's awkward to use 「将来」 in an expression like 「二〇〇年後の未来を空想する」 ("imagine a future 200 years ahead of now"). If it was only 10 years later, 「将来」 would be more common. 「未来」 has a strong sense of a more distinct, intangible future. 「近い将来」 is a common expression, but 「近い未来」 is hardly ever said. The term 「近未来（きんみらい）」 is a recently-coined expression.

To summarize: they're very similar, but when used as an adverb, it's almost invariably 将来, not 未来, and 未来 by default has a farther-off, less tangible connotation.

As for 行く末, it's less common and seems to me to be a more personal sort of future. But I'd stick with 将来 and 未来 for almost all contexts.

infinite impulse response - IIR filters with variable roll-off

I have a filter design problem in which lowpass filters have to be designed with varying roll-off. E.g: 2.7 db/ocatve or 1.4 db/ocave. See picture below.

This is easy to achieve with a FIR filter, yet its computational cost is too large. Therefore, if at all possible, I would like to do this with an IIR filter. Sadly, most IIR filters have multiples of 6dB/octave rolloff.

image processing - Haralick features, am I approaching this correctly?

I'm trying to personalise a custom CBIR by adding more features not only based on colour, but based on textures' features.

What I don't know is if I'm approaching this well with Haralick's features.

I'm doing this:

I've used 10 images, 8 for different "textures" and 2 for tests:

All px.jpg are sand images, and all rx.jpg are squares. The test image is squares and test2 image is sand. (NOTE, I don't want to classify, I want a value for each image).

Well, when I query the image test (squares) on the rest of the images (r1, r2, r3, r4, p1, p2, p3, p4) I got the Haralick's features such as Angular 2nd moment, Contrast, Correlation... but I can't find a relationship with the squares, or a not-relationship with sand. I'm making a euclidean distance in this case:

    double features[15]; // I'm introducing other things as well
    Haralick h;
    h.CalculateCoocurrenceMatrix(features);
    correlation();

    for (int j = 1; j<=11; j++) {

        float result = sqrt(pow(featurestest[j]-features[j],2));
        if (result > f_max[j]) {
            f_max[j] = result; // to normalize later
        }

        jsonFeatures["F"+to_string(j)] = result;
    }

My question is: am I doing this approach well? if not, how should I do it?

Thank you in advance.

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EDIT: If it wasn't clear, I don't want to classify such like I'm doing in the example. I'm using "sand" and "squares" only to make the results more visually when sorting (for example seeing p1 p2 r1 p3 p4 r2 p5 r3 r4 r5 on the final match feature).

organic chemistry - Can a benzyl ether be removed in the presence of an ester?

I'd like to deprotect a benzyl group for a Fráter–Seebach alkylation. Would it be possible to do this with a Birch reduction using Li/NH₃ (or Na/NH₃), without also reducing the ester carbonyl group?

If not, hydrogenation over Pd/C seems to be a plausible alternative. How else can I remove the benzyl group on oxygen?