Ken (Chanoch) Bloom's Blog

12th September 2010

Chovot HaLevavot's Sha’ar HaYichud

I posted the following as a comment on Stephen Hawking’s Rosh Hashanah Gift By Yitzchok Adlerstein. It was originally supposed to be a tangential thought on something he said about Chovot HaLevavot's Sha’ar HaYichud. It seems to actually be more relevant to the issue of science and Torah than I had originally anticipated.

Chovot HaLevavot's Sha’ar HaYichud is incorrect in its mathematical proof of God's unity. In chapter 5, he introduces 3 mathematical propositions on which he rests his proof. One of these propositions is that "That the infinite should have parts is inconceivable. ... Let us assume that a thing is actually infinite, and that we take a [finite] part from it. The remainder will undoubtedly be less than it was before. If this remainder is infinite, one infinite will be greater than another infinite, which is impossible. If this remainder is finite, then when we put the part we took back together with the finite remainder, the result should be finite [thus contradicting the premise]."

There are two problems with this: he assumes that the size of an infinite quantity decreases when you take a subset of the infinite quantity. (In informal terms) when there is a one-to-one mapping between two infinite sets, they are the same size. There is a one-to-one mapping between the even integer and the set of all integers. Each integer can be doubled to give an even integer, even though the even integers are a subset of the set of all integers. Thus demonstrating that the size of an infinite quantity decreases when you take a subset of the infinite quantity.

The other problem is that there are different sizes of infinity. The integers may be listed (in an infinitely long list) without skipping any numbers in the middle, however the real numbers may not. (If they could, the positions in the list would be a mapping to the set of all integers.) No matter how many real numbers you list, you can always find another real number that should be in the list. So the real numbers are a larger infinity than the integers.

This is not to say chas v'shalom that God is a smaller infinity or a larger infinity (there are an infinite number of sizes of inifinity, so if we assign God to one of them, there would have to be a bigger infinity than Him) -- rather this is to demonstrate the futility of proving God through mathematical reasoning in the first place. Which, if you think about it, actually makes sense. Since we have no Human language to describe God as he is (all the anthropomorphisms we do use are borrowed terms and analogies), formal mathematics shouldn't have the ability to describe or define Him either.

I haven't worked out the details of what this says about the validity of science in dealing with issues like creation, but my feeling is that it does imply that science can't foreclose God's existance...

(I hope my informal explanations of the mathematical arguments are understandable. For mathematically rigorous versions of the arguments I have made informally here, see the following Wikipedia entries Hilbert Hotel, Countable set, Aleph number, Cardinality of the continuum.)

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17th March 2010

Seforim on which to base a mussar vaad

The AishDas Society is looking to start a new online/telephone women's mussar va'ad, and is looking for an appropriate sefer for those who do not have much hebrew skill.

Past va'adim have been based on Alei Shur by R' Shlomo Wolbe, but the hebrew is not easy, and aside from small excerpts, we do not have reshut from his family to translate the sefer (and we have asked).

An explanation of our approach is in the translated excerpts of Ali Shur, but to very briefly summarize, the primary criterion for this list is that the book has practical exercises to be performed over a multi-week period to practice and develop specific middot, before moving onto the next exercise in the same middah.

Other seforim that have been suggested include the following. They almost all involve a bit of a change in hashkafic focus (mostly to be more deveikut-oriented) or methodological focus. Our real challenge here is to choose something that's translated/translatable that has the amount of middot development that we're looking for, so some of these books are more on target, and some are farther off.

I'll try to keep this list updated if other suggestions appear on the AishDas lists.

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12th December 2009

The Beit Yosef's Question about Chanukah

The Beit Yosef famously asked that since there Maccabees found enough oil to last for one day, then the fact that the oil lasted for 8 days isn't a miracle -- only 7 of the days are a miracle. Why then do we celebrate Chanukah for 8 days?

At our shul Chankah party tonight, there was a lot of excitement as we asked the kids to answer this question and they presented a lot of nice answers. One of these answers was that the 8th day is for berit milah.

My problem with this answer is that there are three mitzvot that the Greeks forbid the Jews from performing: berit milah, shabbat, and kiddush hachodesh. It seems odd that this answer singles out only one of these three mitzvot.

It appears to me however, that Chanukah's scheduling does hint to each of these mitzvot. Chanukah lasts 8 days long (as a reference to berit milah), it includes Rosh Chodesh Tevet (kiddush hachodesh), and it includes a Shabbat.

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11th March 2009

Birkat HaHamah (Nusah Edot Hamizrah)

I haven't seen any books or pamphlets with the Birkat HaHamah according to sephardic custom yet, so I thought I'd post a couple. According to the Ben Ish Hai, the Petach HaDevir (brought also by the SdeHemed), and according to Rav Ovadia Yosef.

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16th February 2009

Parshat Yitro

וַיֹּאמְרוּ, אֶל־מֹשֶׁה, דַּבֵּר־אַתָּה עִמָּנוּ, וְנִשְׁמָעָה; וְאַל־יְדַבֵּר עִמָּנוּ אֱלֹהִים, פֶּן־נָמוּת. וַיֹּאמֶר מֹשֶׁה אֶל־הָעָם, אַל־תִּירָאוּ, כִּי לְבַעֲבוּר נַסּוֹת אֶתְכֶם, בָּא הָאֱלֹהִים; וּבַעֲבוּר, תִּהְיֶה יִרְאָתוֹ עַל־פְּנֵיכֶם־לְבִלְתִּי תֶחֱטָאוּ. שמות כ׃טו־טז

And they said to Moshe: 'You speak with us, and we will hear; but don't let God speak with us, lest we die.' And Moses said unto the people: 'Fear not; for God is come to uplift you, so that that His fear on your faces, that you will not sin.'

It is odd to see this exchange and not wonder what's going on. The clearest simplest way to understand it is that this experience of at the giving of the Torah was so powerful that the people were afraid that the experience was going to overpower them and kill them. Considering that Am Yisrael has just seen that Hashem has the power to do anything at all (evidenced by the plagues and the splitting of the sea), and the fact that Hashem has just told Am Yisrael that they would be his nation, it is difficult to think that Hashem would now subject them to an experience that would kill them.

Moshe's response is also odd. If the point is for them to be afraid, then why is Moshe telling them not to be afraid?

A better explation of these verses confirms a feeling that I have had about this episode for a while. It seemed to me that the opening that allowed all of our sins in the midbar (and since the midbar) was due to the fact that we felt we could not listen to all of what Hashem wanted to say to us at Har Sinai.

It appears to me that Am Yisrael fully understood that Hashem intended for them to survive the giving of the Torah. They were afraid of a different death.
They were afraid that if they heard the whole Torah directly from Hashem that when in the future they would sin, there would be no remaining opening for mercy, and they would die of their sin. Moshe's response is to counter this fear. He explains to them that they should not fear that this experience will leave them vulnerable to death if they sin, because Hashem has come to give them such a penetrating fear of Him that it would be impossible for them to sin in the first place.

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6th August 2008

Devarim 5768

In parshat Devarim, Moshe Rabbeinu discusses the sin of the spies at length (דברים א׃יט־ב׃א). He mentions the decree forbidding that generation from entering the land, saying "If even a man of these people, this evil generation, shall see the good land that I swore to give to your forefathers..." (דברים א׃לה). Then, strangely, he mentions that he too was forbidden to answer the land, saying "With me, as well, Hashem became angry because of you, waying: You, too, shall not come there" (דברים א׃לז). What is this explanation doing there? How was Moshe Rabbeinu's prohibition related to that of the rest of the generation of the midbar? After all, his sin was 40 years after theirs, when he hit the rock to get water for the people, instead of speaking to it (במדבר כ׃יב).

The Ohr HaChaim explains (דברים א׃לז) this. The paseuk says in connection with the sin of the spies, "and the nation cried that night" (במדבר יד׃א). The Gemara (תענית כט ע״א) explains that this night was Tisha B'av, and because the nation cried on that night for no reason, Hashem decreed that they would cry on that night throughout the generations, because the Bet HaMikdash would be destroyed then. Another Gemara (סוטה ט ע״א), explains that if Moshe Rabbeinu had entered Eretz Yisrael, and built the Bet HaMikdash, then it could not have been destroyed. A midrash (מדרש תהלים עט) further explains that the result would have been the complete destruction of Am Yisrael when they sinned, and not the (relatively) minor destruction of the Bet HaMikdash. Thus, Hashem decreed Moshe Rabbenu's death at that time, so that he could not build the Bet HaMikdash.

So what about the Moshe Rabbenu's sin of hitting the rock instead of speaking to it? The Ohr HaChaim hints that if Moshe Rabbeinu had sanctified the name of Hashem at that time, then Am Yisrael would have returned to the level of purity that they had before the sin of the spies, and Hashem would have reversed the decree of Moshe Rabbenu's death.

It seems to me that the peshat behind this is as follows: the sin of the spies was in believing (and convincing Am Yisrael) that they would need to work hard to conquer the land on their own, and that the nations then in the land were too powerful for them to conquer. Moshe Rabbenu was asked to speak to the rock and a miracle would be performed. Had he done that, Am Yisrael would have understood that Hashem would do a lot for them effortlessly, particularly the conquest of Eretz Yisrael, and this would have reversed the sin of the spies.

In the end, it took Am Yisrael 7 years to conquer the land sufficiently that they could settle it, and they never fully uprooted the original inhabitants. There are numerous warnings of the corrupting effect of letting the original inhabitants stay in the land (דברים ז׃א־ה), but since Am Yisrael never fully kicked them out, they were susceptible to the sins that eventually caused the destruction of the Bet HaMikdash. It was possible to have an effortless, complete conquest of Eretz Yisrael, as we see in Sefer Bemidbar that Israel conquered Sihon, Og, and Midian in a matter of days, an area totaling the size of Eretz Yisrael. Why couldn't they do that in Eretz Yisrael? Because Hashem made it hard in accordance with their expectations. Had Hashem granted us this kind of conquest of Eretz Yisrael, none of the inhabitants would have remained to be a thorn in our sides to cause the sins that eventually led to the destruction of the Bet HaMikdash.

May we merit to see the Bet HaMikdash rebuilt, speedily in our days. (Preferably before Sunday, but if not have a good fast.)

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26th July 2008

Parshat Mattot

I composed this post on Thursday afteroon, but got delayed a bit in actually posting it, as I spent Friday afternoon reflecting on a very exciting week, rather than running to the computer to post this.

In Parshat Matot, the torah tells us in great detail the disposition of the spoils of the war against Midian (במדבר לא׃כה־נד), providing multiple reduntant counts of how the spoils were divided between the men who fought, the rest of the nation, and the kohanim. Why so much detail? Our clue is in Sifre in Parshat Balak.

"They conquered sixty cities [in Bashan], all fit to be the capitol of a kingdom, as it says ששים איר כל חבל ארגוב ממלכת בשן (Sixty cities, the entire region of Argob, the kingdom of Og in the Bashan דברים ג׃ד). And Israel came and makde war with them, and took all that was theirs, but when Israel became full from the booth, the soldiers wasted the spoils, tore the garments [they found], and killed the anmials, because they only wanted silver and gold vessels, as it says וכל הבהמ׳ ושלל הערים בזונו לנו (And all of the animals and spoils in the cities we looted for ourselves (דברים ג׃ז)."

The war against Og, King of Bashan, came after the war with Sihon, king of Heshbon. The Jews were filled up with the spoils from Sihon, and didn't feel they needed any more when they conquered Og. The Netziv explains the progression: the soldiers wasted the spoils, this was the beginning of the sin, they devalued the great kindness that Hashem did for them. They tore the garments, thereby transgressing the commandment of בל תשחית (don't waste/destory) and killed the anmials, thereby coming to cruelty to animals. Then end was that they came to idol worship and sexual immorality in the plains of Moav, with the incident of Ba'al Peor (מבדבר כה׃א־ט). The war against Midian was commanded to fix the sin of Ba'al Peor by destroying the nation that had enticed the Jews to sexual immorailty and idol worship. But since the root of this sin was their cavalier attitude toward the spoils of war, the Torah tells us that in this war they fixed up the root of that sin too, by giving us a meticulous accounting of the spoils of that war, that none of it was wasted.

It appears to me (and I found my words were confirmed by the Maharal's Gur Aryeh in Parshat Vayishlach) that the root of the commandment of בל תשחית (don't waste/destory) can be found that God gives us everything we need, and everything Hashem gives us is useful for us in our mission to serve him. By using not using it properly, we deny that we need everything that Hashem has given us, and we thereby do not use it for the mission that Hashem intended it.

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26th June 2008


In Parshat Korach, Korach, Datan and Aviram (and their families and all of their posessions) are swallowed by "the mouth of the earth". The Malbim notices a couple interesting issues with this miracle, which hint at the actual uniqueness of this miracle. When Moshe explains to Am Yisrael that the miracle that is about to happen is a sign of the truth of Moshe's leadership and of Torah, he does so by saying "But if Hashem will create a new creation (בריאה), and the earth opens its mouth and swallows them and all that is theirs, and they will descend alive to the pit -- then you shall know that these men have provoked Hashem" (Bemidbar 16:30). There most obvious peshat (reading literally) would suggest that an earthquake opened up a chasm beneath Korach and his followers and they fell in. But there are a couple of reasons why this cannot actually be the case.

The word בריאה indicates creation from nothing (יש מאין), as indicated by its original context בראשית ברא אלקים את־השמים ואת־הארץ (At first, God created Heaven and Earth, Bereshit 1:1). After God created heaven and earth from nothingness, every other act of creation was to create something from something else. As a side point, the mouth of the earth definitely wasn't created at anew at the time of Korach, because Avot 5:6 says it was created bein hashmashot on the 6th day of creation. But clearly if it's a completely new creation, it cannot be an earthquake -- somehting had to be added to existance, not just reconfigured a little.

Secondly, the purpose of the miracle was to reinforce that Hashem had really chosen Moshe, and that Moshe's transmission of Torah was true (he wasn't just making things up). We see that when Moshe Rabbenu announce the death of the firstborn to the Egyptians, he told them that it would happen כחצות הלילה (at around midnight, Shemot 11:4). According to Rashi, the plauge happened at exactly midnight, but Moshe was vague about the time, so that the Egyptians inaccuracte timepieces wouldn't lead them to believe the plague wasn't at exactly midnight and therefore the plague wasn't from Hashem. The lengths people will go to to disbelieve Hashem. So clearly the plauge couldn't even resemble something natural.

Lastly, we have the location of the people who were eaten. Korach was standing at the enterance to the ohel moed, with the 250 people offering incense. His tent was in the camp of the Leviim. Datan and Aviram were in the tribe of Reuven, so their tents were located there. They were standing at the enterances to their tents with their entire families. (The Malbim says that each of these 3 locations were 2000 amot apart.) But ותפתה הארץ את־פיה (the earth opened up its mouth (singluar), Bemidbar 16:32) and swallowed Korach, Datan, Aviram their families, and posessions, and nothing else (nothing in between). With an earthquake, there could not have been a single opening that hit all 3 locations and left everything in between untouched.

The Malbim describes the miracle that occured as follows: the Earth opened its mouth underneath Korach's tent and devoured it. The mouth looked like the mouth of an animal. It moves, and it opens and closes. After devouring Korach's tent, the mouth closed and stretched out 2000 amot to Korach himself, opened one end, and devoured him. Then it closed again, and streched out 2000 amot (I supposed in the opposite direction) to the tents of Datan and Aviram, opened one end, and devoured them. And any posession of Korach, Datan, and Aviram that someone else was borrowing was magnetically attracted to the mouth.

As an aside, Rabbi Itzinger mentioned to me another reason for כחצות הלילה (at around midnight, Shemot 11:4). Each Egyptian who died in the plague died at exactly midnight, but midnight hits different locations in Egypt at slightly different times. So not all of the firstborns died at once, rather they died in a wave across Egypt, following the progression of midnight across Egypt.

The secret word of the week is הבלה דאגמא (Bava Metzia 36b).

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25th June 2008

Parshat Shelach

The following is a drasha that occured to me over shabbat during kriat hatorah. I've been entirely too busy to blog it until now:

In Parshat Shelach, Hashem permits Moshe to send spies to Eretz Yisrael to spy it out. Moshe selects 12 spies, one from each tribe, including his foremost talmid, Yehoshua bin Nun. Before this spy mission, Yehoshua's name was Hoshea, but Moshe Rabbeinu prayed for him that he not fall victim to the conspiracy of the 10 spies who would speak badly about the land. This implies that Moshe Rabbenu knew (or at least expected) that the 10 spies would speak badly about the land. If this is so, why did Moshe choose these spies? And why would he pray for only one?

I saw in the Abarbanel an understanding of this situation which changes the question. The Abarbanel suggests (and then rejects) the following interpretation:

The Jews in the desert tested Hashem's hashgacha repeatedly, Marah, at Midbar Sin, at Masah u'Meribah. The most recent and most pointed test was at Kivrot-Hata'avah (in Parshat Beha'alotecha), after leaving Sinai. It is the Abarbanel's suggestion that because of this test, the Jews were already not on the level to inherit the land, and this was simply intended as a way for them to fall and prove that fact. The Abarbanel does not like this explanation, since he finds it inconcievable that Hashem would give them a test they could not overcome, and since really did want the Jews to inherit the land, and since the generation that left Egypt was the forth generation, which would inherit the land, as promised by Hashem to Avraham in Parshat Lech L'cha (Bereshit 15:16).

Nevertheless, it appears to me that this explanation can be saved with slight modification. It is not necessary to assume that Hashem gave them a test they could not pass, rather we can say he gave them a test to determine their merit and repair the lacking they demonstrated at Kivrot-Hata'avah. In this vein, the Gemara in Sotah (14b) explains that the names of the spies allude to the ways in which they denigrated the land. Here too, we can say not that they would inevitably do so, but that this was their test in life and it was reflected in their names. Thus Moshe Rabbeinu knew that these men were to be tested in this way, and they were the men to send. To address the Abarvanel's last problem with this peshat, we can see Rashi in Parshat Lech Lecha, who is forced to interpret the promise of 4 generations in accordance with what actually happened when the Jews failed to enter the land immediately. These 4 generations are Yehuda, Peretz ben Yehuda, Chetzron ben Peretz, and Kalev ben Chetzron (who finally entered the land).

A new question on Parshat Shelach, for which I do not yet have an answer: on the sixth day of creation, Hashem described the world as טוב מאד (very good, Bereshit 1:31). In Parshat Shelach, Calev and Yehoshua describe the Eretz Yisrael, saying טובה הארץ מאד מאד (Bemidbar 14:7). What madrega does the phrase טוב מאד imply in Bereshit, and what additional madrega is implied by the second מאד in Bemidbar?

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29th May 2008

Parshat Bemidbar

שאו את־ראש בני־ישראל למשפחתם לבית אבתם במספר שמות כל־זכר לגלגלתם׃ מבן עעשרים שנה ומעלה כל־יצא צבא בישראל תפקדו אתם לצבאתם אתה ואהרון׃

The Ramban explains תפקדו (usually translated as counting in this paseuk) along the lines of the verse וה׳ פקד את שרה כאשר אמר (And Hashem remembered Sarah as he had said). He also relates the idea to a פקדון (a deposit) because the shomer (who holds the deposit) watches over and directs the deposit. Hence, the idea of a census is that each person in Am Yisrael should be remembered individually. How? במספר שמות (usually translated "by the count of their names"). The Ramban relates the word מספר to the verb לספר (to tell, as in a story) and explains that when each person deposited his half shekel (Shemot 30:13) he also told the census taker his name.

The Emek Davar interprets similarly, but does not require the half-shekel since it is not stated in the commandment for this census. Instead, he explains that במספר שמות means that each person counted brought a slip of paper with his name on it, and put it into a box to have that counted. Afterwards, the leaders of the tribes each came with their own box and sifted through the names to find the names for their own tribe. (All except for the tribe of Naftali who didn't need to sift. Since he came last, all the remaining names were his, as indicated by the lack of a ל at the beginning of Bemidbar 1:42.)

The Ramban further explores the reason why David HaMelech was punished for his own census. He rejets the idea that it was because David didn't use shekels, since surely he knew the halacha, and if not, Yoav (his general) did. (And Yoav says so in Divrei HaYamim 1 21:3.) Rather, he advances other reasons.

One reason was that David counted for no reason other than his own glory. In this parsha, had it not been for the sin of the spies, this census is the one that would have been used to divide the land after Am Yisrael entered the land just a few days later.

Another reason: David wanted to count men from the age of 13 and up. The Ramban syas that the verse (Shemot 30:14) did not allow the Jews to be counted except from the age of 20 and up. (The punishment of a plague applying to an error here too.)

The Ramban says further that Hashem does not want all of israel counted together in one number, because we are compared to the stars of the heavens and the sand of the sea, which cannot be counted.

It seems to me that these last two reasons are related. That Hashem wanted a count only from 20 to 60 so that the exact number of adult males would not be known exactly, and only a portion of the number would be. Furthermore, I have heard from my teachers that something whose count is known exactly cannot be a recipient of blessing, so it seems to me that the purpose of a plague killing people was a way to restore the nation to its previously uncounted state and make it worthy of blessing. (Though Shmuel 2 24:15 mentions that 70,000 men died, surely nobody knew the exact count besides Hashem, and the Navi who later recorded sefer Shmuel.)

May you all be blessed with the blesings of an uncountable people, and with the blessings that flow from the Kedusha of Eretz Yisrael. Amen.

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21st April 2008

Will the final redemption be bigger than Yetziat Mitzrayim?

A thought I had at last night's seder.

The Haggada (from the Mishna in Berachot 12b) discusses whether we will still remember the Exodus from Egypt in the time of the Mashiach. The Maharsha on the Gemara there mentions that the we will no longer have a daily rememberance of Yetziat Mitzraim (according to Ben Zoma) or that it will be secondary to the final redemption (according to the Sages) because the miracles that take place at the time of the future redemption will eclipse those of Yetziat Mitzrayim.

I find this difficult because Yetziat Mitzrayim was supposed to be the final redemption. Had we not committed the chait haegel, when Moshe Rabbeinu descended the mountain with the luchot, we would have succeeded in restoring the damage caused by Adam's chait. We would have been unable to sin, and there would be no further need for a future redemption. Since the chait haegel had not happened yet, Yetziat Mitzrayim should have all of the miracles needed for the final redemption, and it doesn't make sense to me that the real final redemption should have larger miracles. Hashem pulled out all the stops the first time, why should it be bigger the next time.

Thus, it seems to me that the reason why our memory of the final redemption will eclipse our memory of Yetziat Mitzrayim because we will associate the final redemption with the knowledge that this time our teshuva was complete and the redemption would be permenant because of it.

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21st January 2008

What did Yitro hear?

וישמע יתרו כהן מדין את כל־אשר עשה אלקים למשה ולישראל עמו כי־הוציא ה׳ את־ישראל ממצרים.

Yitro, the priest of Midian, the father-in-law of Moshe, heard everything that God did to Moshe and to Yisrael, his people -- that Hashem had taken Yisrael out of Egypt.

On the words וישמע יתרו, Rashi brings two things that Yitro heard: the splitting of the sea, and the war with Amalek. Later in the same verse, on the words את כל־אשר עשה, Rashi brings a different list: the well, the manna, and the war with Amalek. What can we learn from these two different lists?

The Maskil L'David comments on Rashi, explaining that the manna and the well were kindnesses that Hashem gave us despite our sins -- our improper complaints against Hashem -- in each of these instances. But we know that the nature of each of these was to teach us something.

Water (from Rashi's second list) is symbolic of Torah, as is the tree that Moshe threw into the water to make it drinkable. And lest we doubt this explanation as just symbolism, Moshe also gave the Jews a couple of Torah laws there too. And the manna (also from Rashi's second list) was a daily lesson for us in trust of Hashem.

Compare that to the Egyptians who were drowned in the sea (Rashi's first list), and we can pretty clearly see the difference between the Jews and the non-Jews. When we misbehave, Hashem gives us a way to improve. No wonder Yitro wanted to join the Jewish people.

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1st May 2006


This is Rabbi David de Sola Pool's formuation of the prayer for the State of Israel, found in the Sephardic Siddur he compiled. (This page contains shemot, so be careful with printouts).

מי שברך אבותינו, אברהם יצחק ויעקב משה ואהרן, ודוד ושלמה, הוא יברך את מדינת-ישראל את-שריה את-יועציה ואת-יושביה׃ מלך מלכי המלכים ברחמיו יתקנם בעצה טובה מלפניו׃ וישרה אל שוכני אדמת-הקדש, ריח דעת ויראת-יהוה׃ שם חסד ואמת יפגשו לכל-בני אדם כי מלה הארץ דעת את יהוה׃ ויקים בנו מקרא שכתוב ״כי מציון תצא תורה ודבר יהוה מירושלים״ וכן יהי רצון ונומר אמן

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