Orientation During Prayer

Has Judaism Lost its Sense of Direction?
Orientation during Tefillah

Guest post by R. Michael J. Broyde

Rabbi Michael J. Broyde is a Professor of Law at Emory University School of Law, was the Founding Rabbi of the Young Israel in Atlanta, and is a Dayan in the Beth Din of America.

This draft article will soon appear in Essays for a Jewish Lifetime: The Burton D. Morris Jubilee Volume, edited by Menachem Butler and Marian E. Frankston, forthcoming from Hakirah Press. In continuation of the discussion begun last week (link), this draft is being made available to the readers of Torah Musings with the permission of the publishers and the author.

I. Introduction

One of the more universally recognized aspects of Jewish prayer is that (at least in our part of the world) it is to be directed to the east, toward Israel. Ideally, synagogues should be designed and built to face Israel. Individuals praying alone are likewise encouraged to orient themselves eastward. We teach this to our children at a young age, and often display mizrach plaques denoting this special direction.

Notwithstanding the commonness of this knowledge, one frequently sees that synagogues and study halls with regular prayer services do not, in fact, face either eastward or toward Israel; indeed, historically, one can find whole communities where not a single synagogue faced toward Israel.[1] The glaring disparity between Jewish teaching and practice raises fundamental questions: How strict is the requirement to face east during tefillah? Is this practice perhaps not even a requirement at all, but merely a hiddur, an enhancement? Might other ideals or requirements take precedence over the notion of facing east? And even if we do conclude that one should face Israel, what exactly does that entail when we recognize that the surface of the earth is not flat but spheroidal?

The second section of this article reviews sources in the Gemara and Rishonim and will demonstrate that there are many positions regarding the direction to face during tefillah, only some of which require facing Israel. This multifaceted dispute is based on conflicting passages in the Gemara, and the way one resolves the sugyot dramatically affects one’s position on the forcefulness of the requirement to face “east” or Israel.

The third section addresses the complications that arise when one takes the location of the Aron Kodesh (Holy Ark) into consideration. Classical and early medieval synagogues did not have fixed arks in the front; rather, the Torah scrolls were stored elsewhere and brought into the synagogue only when they were to be used. The later addition of the fixed Aron Kodesh gave rise to the possibility of two competing focal points for prayer—toward Israel and toward the Aron. Would facing one be a slight to the other? Which one takes precedence? The answers to these questions depend on the position one takes regarding the stringency of the requirement to face Israel. Accepting the obligation to face east as an absolute requirement makes one much less likely to consider the Aron, or other mitigating factors, in deciding upon the orientation for tefillah. Conversely, the less stringent such a requirement, the more likely one would be to weigh other, conflicting issues when they arise.

Finally, the article addresses the complications of geographical direction the farther one moves on the globe from the land of Israel. It will be necessary to distinguish between the “compass route” direction that is the shortest distance between points on a flat surface, and the “great circle route” which is the shortest distance on a spherical plane. The simple, flat map of the earth that we are familiar with distorts the spherical nature of the earth. The straight line between two points on a flat map projection may be relatively correct over short distances, but over large distances it fails to consider the curvature of the earth between those points. The shortest path between such points is not, then, a line that keeps a constant compass heading (say, 45 degrees North-East), but rather an arc whose bearing is constantly changing. Air travelers are familiar with this phenomenon, as the path of an airplane from the United States passes Greenland on the way to Israel. Since it is very likely that the requirement to face Israel is by the straightest, shortest line possible, this question will need to be considered in some detail.

II. Direction in Prayer

A. The Two Talmudic Sources

The Talmud discusses the issue of direction in prayer in two different places—Berakhot and Bava Batra. The two sugyot take different forms—a Beraita about the direction of prayer and a series of Amoraitic statements about the presence of God—and come to seemingly divergent conclusions as to the direction one ought to face while praying.

In Berakhot 30a the Talmud states that one should pray facing Israel and the Beit ha-Mikdash:

The rabbis taught: … One who stands outside the land [of Israel] should direct his heart to Israel, as it says, “And they shall pray to You by way of their land” (I Kings 8:48). One who stands in Israel should direct his heart to Jerusalem, as it says, “And they shall pray to God the way of the city that you have chosen” (I Kings 8:44). One who stands in Jerusalem should direct his heart to the Temple, as it says, “And they shall pray to this house” (II Chronicles 6:32). One who stands in the Temple should direct his heart to the Holy of Holies, as it says, “And they shall pray to this place” (I Kings 8:35). One standing at the Holy of Holies should direct his heart to the house of the ark-covering. One who stands behind the house of the ark-covering should view himself as if he was in front of the ark-covering. One who finds himself in the east of Israel should turn his face to the west. [One who finds himself] in the west of Israel should turn his face to the east. [One who finds himself] in the south of Israel should turn his face to the north. [One who finds himself] in the north should turn his face to the south, so we find that all of Israel are directing their hearts to the same place.[2] Rabbi Avin, or as some say R. Avina, said: What text confirms this? “Your neck is like the tower of David built up with turrets [talpiyyot]” (Song of Songs 4:4)—the elevation (tel) towards which all mouths (piyyot) turn.

This Gemara adopts the view that prayer should be directed toward Israel and when in Israel, toward Jerusalem and when in Jerusalem, toward the Beit ha-Mikdash. The Talmud here gives no hint that this matter is in dispute. The only dispensation for not facing Jerusalem, as the preceding Talmudic passage set out, is for the blind or someone unable to discern the correct direction toward Israel. Such an individual must nevertheless “Direct his heart toward his Father in Heaven.”

Yet, in a series of Amoraic statements, the Talmud in Bava Batra 25a-b seemingly contradicts the aforementioned Beraita.

Rather, [the west] is the constant abode of God’s presence (Shekhinah). As Rabbi Yehoshua ben Levi said: Let us be grateful to our ancestors for showing us the place of prayer, as it is written, “The heavenly hosts bow to You” (Nehemiah 9:6). Rav Acha bar Ya‘akov strongly objected to this: Perhaps [the sun and moon bow down to the east], like a servant who has received a gratuity from his master and retires backwards, bowing as he goes. This [indeed] is a difficulty. Rabbi Oshaia expressed the opinion that God’s presence is everywhere….

Even Rabbi Yishma’el logically inferred that God’s presence is everywhere, as the school of Rabbi Yishma’el said: How do we know that God’s presence is everywhere? Because it says, “Behold, the angel that speaks to me leaves, and another angel goes out toward him” (Zechariah 2:7). It says “toward him” [rather than “after him”] to teach that God’s presence is everywhere. And too Rav Sheishet logically inferred that God’s presence is everywhere, as R. Sheishet [who was blind] said to Shemaya [his servant]: You can set me to pray in all directions but east, and this is not because God’s presence is not there, but because non-Jews pray in that direction. Rabbi Abahu says that God’s presence is in the west as Rabbi Abahu said, What is Uriyah [west in Persian – Rashi], avir-[Y]ah (the air of God)….

Rabbi Yitzchak says, One who wants to become wise should turn south [during prayer]; one who wants to become rich should turn north, and the mnemonic for this is that the table was in the north [of the Mishkan] and the Menorah was to the south. Rabbi Yehoshua ben Levi said: One should always face south because from becoming wise, one will become rich, as it says, “Length of days in its right, and on its left riches and honor” (Proverbs 3:16). But did not Rabbi Yehoshua ben Levi say: God’s presence is in the west? [Indeed] one stands in a partly turned manner [i.e., south and west]. Rabbi Chanina said to Rav Ashi: Just like you [of the Babylonian community], who are settled to the north of Israel should turn south.

In Bava Batra we are given a glimpse at the differing opinions of, not only where the presence of God resides, but also in what direction one should face during prayer. The Talmud ponders no less than five different opinions:

1. One may pray westward, as God’s presence is in the west.
2. One may pray in any direction, as God’s presence is everywhere.
3. One may pray to the south in order to become wise.
4. One may pray to the north in order to become wealthy.

One may pray to Israel—ostensibly because that is the direction of the Beit ha-Mikdash.

The two sugyot, then, seem to be at odds with one another (and indeed, the sugya in Bava Batra seems to be at odds with itself!). The Gemara in Berakhot mandates that our prayers be directed solely toward Israel, while Bava Batra offers a multiplicity of valid directions in which to pray. The Rishonim and Acharonim recognize this conflict and offer numerous resolutions. How one chooses to reconcile the tension of these two sugyot leads to significant practical differences in ruling on the direction of prayer.

B. Resolving the Tension between the Sugyot: The Views of Rishonim and Acharonim

Although no less than six different resolutions to the conflicting sugyot are put forward, two predominate in the world of halakhah.[3] One widely held position is that the discussion in Bava Batra is rejected in favor of the conclusive ruling in Berakhot, namely that one must pray toward Israel. The second set of views accepts the validity (authority) of both sugyot. As a result, according to those authorities, one may pray in two directions, pointing one’s feet in a different direction from one’s head.

1. Berakhot is Right: Pray toward Israel

Tosafot,[4] addressing the conflict between the sugyot, state:

It is this passage (Berakhot 30a) that we accept as the halakhah. Such a result is also reached in Bava Batra 25b where it states that those who are in the north of Israel face south, and not like those Amoraim in Bava Batra 25a who argue about whether God is eastward or westward. Nowadays, we are westward of Israel and thus we face east.

Tosafot plainly state that the two Talmudic sources are in tension, and that we follow the view of Berakhot, which directs that we pray toward Israel. The logic of this position is rather compelling: The sugya with numerous Aggadic statements by various Amoraim, some of which are relevant to the direction one ought to face while praying, is rejected in favor of a clear Beraita. After expanding upon the exceptional cases presented in the Mishnah concerning prayer while traveling,[5] the Beraita goes on to delineate the proper way to stand during tefillah generally. A simple principle emerges—no matter where one is in the world, one faces Israel when standing in prayer.

Similar rulings are reached by Rambam,[6] Rosh,[7] and Tur,[8] each of whom perceives a dispute between the Gemarot and sets forward a resolution in favor of facing Israel. These sources would say that one praying in a city like Moscow, for example, due north of Israel, should face south, exactly where Israel is located.[9] This idea is echoed in the Chayei Adam[10] and Kitzur Shulchan Arukh,[11] who both say that one should pray toward Israel, because this is the location of the gates of heaven, to which all prayers ascend. This conclusion, however, was seen as incomplete by some as it discards the multiplicity of opinions in Bava Batra.

2. Both Sources are Correct: Feet to Israel, Face Elsewhere (or the Reverse)

While the two gemarot seem to be irreconcilable, Rashi offers an approach that allows for incorporating both Berakhot and Bava Batra into the halakhah.[12] Rashi picks up on a nuance between the language of the two sources. Bava Batra suggests that one should turn[13] (metzaded atzadudei) south (or north), while Berakhot sets forward a requirement to turn one’s face (yechaven panav) toward Israel and the Holy of Holies. Rashi thus solves the seeming tension between these two sources by noting that the Gemara in Berakhot requires only that one should have his or her face toward Israel, whereas the Gemara in Bava Batra instructs where one’s feet should be pointing. One may pray with one’s feet facing any direction one desires (including those suggested in Bava Batra) as long as one’s face is toward Israel.[14] Thus, for example, if one is living west of Israel, one may point one’s feet northward or southward, and merely turn one’s face eastward.[15]

Rama[16] seemingly endorses Rashi’s view. He posits that it is proper to face (in the quite literal sense) eastward while praying, as his community lived west of Israel. Rama does allow, though, that one may direct one’s feet north or south for the explicit reasons stated in Bava Batra (wealth and wisdom, respectively). Nevertheless, he concludes, one must minimally direct one’s face toward Israel.[17] This feet-face combination is supported by the Smag,[18] Beit Yosef,[19] Mahari Abuhav,[20] and Kaf ha-Chaim.[21]

Rabbenu Chanokh, Chief Rabbi of Cordoba, Spain, in the tenth century and a contemporary of R. Hai Gaon, likewise offers the possibility of having different directions for the orientation of one’s feet and one’s face. However, he puts forward the opposite feet-face combination of Rashi. He writes:

That which we say, “One who wishes to become wise should turn south and one who wishes to become wealthy should turn north,” certainly refers to the north of the earth and the south of the earth—for we [ordinarily] direct our faces [i.e., orient ourselves] toward the Beit ha-Mikdash… eastward, since we are in the west. Therefore, one who prays and wishes to be granted wisdom should turn his face southward, since the menorah was in the south[ern part of the Temple] and it illuminated the Temple, and Torah is called light…[22]

Magen Avraham[23] agrees that the correct foot-face dichotomy is for one to have one’s feet toward Israel and one’s face wherever he or she chooses. It is worth noting that the difference between Rabbenu Chanokh/Magen Avraham and the others is fundamentally one of outcome. The combinations of feet to the south (or north) and face to Israel or vice versa both represent attempts to integrate the positions of the Gemara in Bava Batra with the Beraita in Berakhot, rather than reject one out of hand.

Fascinatingly, the Taz [24]posits that both of the above foot-face alternatives are equally valid—feet to the south, face to Jerusalem is inherently no more compelling than the opposite. Indeed, his underlying claim seems to be that the very fact that we allow feet and face to be in different directions demonstrates both (1) that the competing values here are of equal importance, and (2) that facing a given direction is no more significant than orienting the rest of one’s body that way. One could claim that the positions stated in Bava Batra are not the only valid options. The Taz thus allows for other factors, such as the direction that the congregation stands (and perhaps the location of the Aron Kodesh), to influence what one ultimately does in practice. [25](In section three we will fully discuss the possibility of mitigating reasons to face another direction.)

3. Both Views are Acceptable

The Shulchan Arukh[26] does not take only one of these preceding views to be correct: he codifies the views of both Tosafot and Rashi in successive paragraphs. Orach Chaim 94 begins by restating the rules outlined in Berakhot, namely that one should pray in the direction of Israel, Jerusalem, and the Holy of Holies—consonant with the view of Tosafot. In paragraph 2 of that chapter, though, he notes that those who pray in another direction fulfill their obligation by at least turning their face toward the land of Israel, much as Rashi posits. The articulation of both views in Orach Chaim 94:1-2 here indicates that the Shulchan Arukh first agrees that Israel is to be faced, yet also acknowledges validity in the notion that one may ‘face’ one direction and ‘feet’ another, and that the direction that one ‘feets’ need not be toward Israel. By codifying the minhag of facing the non-Israel directions observed by the Mahari Abuhav,[27] the Shulchan Arukh seems to accept either the view of Tosafot or the view of Rashi (or more precisely, of Mahari Abuhav) as a proper way to conduct oneself.

4. Other Proposed Solutions

While most halakhic commentary is dedicated to variations of the two positions discussed above, other opinions exist. Notably, the Mahari Abuhav records that the practice in his community was that many did not face Jerusalem at all, but simply faced north or south during prayer. His comments presume that their custom was in accord with the view of the Gemara in Bava Batra (i.e., face north to be wealthy, south to be wise), and gave no mandatory weight to the Beraita in Berakhot. In this view, the sugya in Berakhot is just an elaboration upon one of five views in Bava Batra, but that view is no more or less correct than any other.[29]

Another series of views on the correct direction for tefillah focuses on improper directions to face. One example of this can be found in the writings of Rama, who cites an affirmative custom not to pray due eastward, as that would imitate the local Christian customs of praying toward the sun. He writes in the name of Rabbeinu Yesh’ayah di Trani[30] that:

One of the great sages used to pray in any direction when he didn’t know the precise direction toward Israel except for due east. He was careful not to do this because the Christians pray in that direction, as it says in Bava Batra. And I believe that this was the intention of our predecessors—that we not pray in synagogues directly facing the rising sun. And in our synagogues, we pray toward the middle of the day [southeastward] as that too is toward Israel.[31]

The Rama here seems to imply that facing Israel is undesirable if that also causes one to directly face the sun and thus imitate the pagans. Thus, even a community due west of Israel should not pray directly eastward. Similar sentiments are noted by the Levush,[32] who also proscribed praying in the way of the Christians and notes simply:

Since these lands [that we live in] are northwest of Israel, care should be taken when building a synagogue that they erect the eastern wall with the Ark in it [that one prays toward] inclined to the southeast, as that way one’s face can be turned toward Israel, the Temple, and the Holy of Holies. However, if they erect the eastern wall directly toward the sunrise, there are two problems. Firstly, one is not at all facing the land of Israel; secondly, it resembles the practice of the pagans who pray eastward and bow toward the sun.

Additionally, the Kaf ha-Chaim[33] citing the Zohar (in the Tikkunim) writes that one is forbidden to face west (where the mystical tradition relates that the Shekhinah is located) during tefillah because the west is called “achor”[34] and could come to represent other gods and be worshipped independently. He explains that one who prays to the west from the east is doing so only because God is located in that direction, at the site of the Temple. This would imply (contrary to the view of Tosafot in Berakhot[35]) that those who are situated east of Israel would not face westward, even though that is the direction toward Jerusalem. Indeed, synagogues in Tehran, which is (roughly) east of Israel, face east and not west!

A further view, emerging from the Gemara and Rishonim, but not cited explicitly in the poskim, is that one should always face east, as that is the proper way to face the Shekhinah. This view is related to, but differs from, the opinion quoted in Bava Batra (25a) that one faces west as the Shekhinah is in the west. Rabbi Yehoshua ben Levi derives that concept from the verse “The hosts of the heavens bow to You” (Nehemiah 9:6). As Rashi explains Rabbi Yehoshua ben Levi’s position, the hosts of the heavens, namely the sun and the moon, which rise in the east, bow to the Shekhinah in the west. Rav Acha bar Yaakov understands the direction of “the bow” differently: the sun and moon are like servants who back away from their master while facing him and bow. Thus, they would be bowing in the opposite direction of that which they travel in: as they move west, they face and bow to the east. Hence, God’s presence, according to Rav Acha bar Yaakov, must be in the east. The Gemara ends this part of the discussion by remarking that the interpretation of the verse in Nehemiah remains unresolved. Indeed, Tosafot in Berakhot 30a understand that two different views are presented in this Gemara—the Shekhinah is in either the east or the west.

However, it should be noted that while the subsequent Gemara refers to the notion that the Shekhinah is “be-ma’arav,” in the west, it never explicitly uses the term “Shekhinah be-mizrach.” Perhaps, then, both the explanations of Rabbi Yehoshua ben Levi and Rav Acha bar Ya’akov are expressions of the concept of “Shekhinah be-ma’arav;” i.e., one could bow / pray in the direction of either east or west to God who is “in” the west. In order for this to make sense, one must think of the world as a globe (such that if you start at any one point and want to reach the complete opposite side of the earth, whether you choose to turn to your right or to your left before you start walking, makes no difference at all). Perhaps this is the thinking behind the position of Rabbenu Yitzchak bar Yehudah as quoted in Tosafot.[36] There he is quoted as saying that after Adam ha-Rishon was created, he stood to face east. The prevailing view in Tosafot[37] finds this difficult, because if the Shekhinah is in the west, then Adam’s back was (rudely) toward the Shekhinah! If, however, “Shekhinah be-ma’arav” also includes that one should face east, and meet God’s eye, so to speak, around the other side of earth, then the question disappears.[38] Indeed, this concept was put into wide practice. This writer is hard pressed to find a synagogue in Eastern Europe that was northwest of Jerusalem but did not face due east, and not south or southeast.

This view accounts for an exclusive fixation on mizrach east rather than Jerusalem. Indeed, this explains an otherwise curious matter of iconography: If Jerusalem were the intended focal point, our custom should have been to design plaques displaying the word “Jerusalem” rather than “mizrach.”[39] Such is clearly not the Jewish iconographic practice, which focuses on a direction as opposed to a particular locale, consistent with the view of R. Yitzchak bar Yehudah above.

5. The View of the Arukh ha-Shulchan: Direction Does Not Require Precision

The Arukh ha-Shulchan[40] presents a novel, and indeed compelling, approach to our topic. He begins by assessing the strictness of the requirement to face the land of Israel while praying. This, he notes, is one of eight criteria[41] that are ideally required for prayer, but in case of pressing need, and even if one willfully neglects them, he or she nonetheless fulfills the basic obligation of prayer. And if one realizes in the middle of one’s prayers that he or she is facing the wrong direction, there is no need to interrupt and turn oneself. The most one is required to do in such a situation is turn one’s face. Further, he points out, the language of the Beraita in Berakhot is that one should direct one’s heart toward Israel, Jerusalem and the Holy of Holies.

The Arukh ha-Shulchan then recounts the prevailing views of Tosafot and the Tur stipulating that communities and individuals west of Israel should face east. Those more north than west of Israel, then, ought to face southeast. But the prevalent custom, notes Arukh ha-Shulchan, was to build synagogues facing due east, not southeast. To explain the seeming difficulty of this practice, he reexamines the relationship between the sugyot in Berakhot and Bava Batra.

The many statements in Bava Batra (that one may face west, north, and south), writes the Arukh ha-Shulchan, cannot be in dispute with the Beraita in Berakhot that requires one to face Israel. If that were the case, we would not be able to simply rule that one must always face Israel. After all, the Gemara lists Tannaim and Amoraim whose practice seemingly was to face elsewhere, and the rules of psak would not allow us to simply dismiss their positions. Moreover, it would not be sufficient to accept only a single Amora’s opinion from Bava Batra (as Tosafot do) against a plurality of others there who seemingly differ. Finally, he writes, if the ruling in Berakhot to face Israel, Jerusalem, and the Beit ha-Mikdash is scripturally based in the prayer of Shlomo ha-Melech, how could the Tannaim and Amoraim in Bava Batra have completely ignored it and ruled otherwise?

It must be then, that everyone agrees that one who prays must face Israel and Jerusalem, but the statements in Bava Batra are limited to situations where the individuals are east, north, and south of Israel. In those cases (which covered most of world Jewry at the time) one directs one’s body directly westward (according to the opinion that the Shekhinah is in the west) and may also face north or south. The Arukh ha-Shulchan notes that in his time, there were (already) Jews who lived west of Israel, a possibility not considered by the various positions presented in the Gemara in Bava Batra. Those Jews would not be able to face west (the ideal) as then their backs would be toward Israel. Ostensibly, they would face Israel (east), with the option to turn northward or southward.

If one who is southeast of Israel and oriented westward is considered to be facing Israel, concludes the Arukh ha-Shulchan, then the requirement for prayer is that one merely face somewhat in the direction of Israel. This is further emphasized by the language of the Beraita that one should direct one’s heart toward Israel and Jerusalem. He writes:

Thus, because one needn’t stand precisely toward Israel, our custom to face east despite our being northwest [of Israel] is well understood… Moreover, [standing imprecisely toward Israel] is no worse than [only] turning our faces, because the most important part [of this commandment] is to actually have focus on Israel, [rather than face it].[42]

The main point is that one should face somewhat in the proper direction;[43] facing in the totally wrong direction is not permitted.

This makes eminent sense because the objective of direction in prayer is to have one’s heart and mind—one’s emotions and thoughts—directed to our holy sites for what they represent: the ability of humans to establish a connection with our Creator. Orienting one’s body and face is a means to an end, rather than an end itself. As such, precise direction is not necessary; the attempt to face the locus of humanity’s relationship to the Divine according to the Jewish tradition “grounds” us, so to speak, to a higher spiritual plane from which tefillah is to commence.

6. Recapitulation and Summary

While a diverse set of minority opinions exist, the two most prominent opinions entertain the ideas of either having both one’s feet and face toward Israel or either one’s feet or face toward Israel. The Mishnah Berurah,[44] Tefillah ke-Hilkhata[45] and Ishei Yisrael[46] emphasize concentration toward Israel, although each of them seems to recognize the validity of the head in one direction, feet in another as a possibility.[47] The Arukh ha-Shulchan’s view, that directions need only be approximate rather than precise, seems also to have much foundation.

III. The Ark Question

To this point, we have established according to numerous halakhic views that one should orient oneself toward the land of Israel. Yet, what happens when we introduce the concept of a designated symbol for God in a different direction than Israel? (Of course, this issue arises only when the Aron is oriented in a different direction than toward Israel.) This additional conflicting focal point creates a number of practical problems. Should one face toward the Aron or Israel? Would facing one disrespect the other? Should one contort one’s body to face as much of both as possible? These are some of the practical ramifications that the Acharonim struggle with. This also begs a deeper question, which the Talmudic sources attempted to address: Why do we orient ourselves during prayer, so we face towards Israel or towards God?

The Rishonim do not address any of the difficulties posed by the location of the Aron Kodesh. To the modern reader, this seems like a glaring omission. In fact, this is not an omission at all, but reflects a change in practice over the course of Jewish history: The custom to have a fixed Aron Kodesh did not exist in the classical and early medieval periods.[48] In the era of the Rishonim there was no physical focal point at the front of a synagogue; rather, the congregation assembled around a central bimah. The Torah scrolls were in moveable boxes that would be brought into the synagogue when they were to be used. At other times they were removed and stored outside the main prayer hall.

The practice of having a fixed Aron Kodesh was becoming increasingly prevalent by the time of Rabbi Mordecai ben Abraham Jaffe, the Levush (late 16th century). As we noted above, he instructs that synagogues be built with the wall of the ark set to the direction the congregation should face.[49] These later commentators acknowledged that the advent of the set ark created a new focal point that could distract those praying from facing directly toward Israel. Indeed, how much consideration one gives the positions stated in Bava Batra might very much affect how seriously one ponders the possibility that the presence of an Aron Kodesh (on a wall that doesn’t face Israel) should shift one’s direction away from Israel.

The Ark Does Not Change Anything

Regardless of the existence of a new focal point, Taz[50] and Ateret Zekeinim[51] unfailingly support facing Israel. This view would seem to take the harder line in their approach to the conflicting Talmudic sources. Instead of an attempt at reconciliation, it seems to side completely with Berakhot and ignore the question of the location, so to speak, of God, discussed in Bava Batra. This idea is supported by the Kenesset Hagedola and cited by the Baer Heitev,[52] who notes that even if the ark is in a direction that is not toward Israel, one should face toward Israel. The Kaf ha-Chaim,[53] however, uses weaker language when he says that regardless of ark location and where the congregation directs itself, one may still pray to the east.

The Ark Matters Most

Other Acharonim seem to disagree. The Peri Megadim[54] addresses another problem with ark orientation. He suggests that the rabbi of a congregation stand to the north of an ark (which has been placed on the eastern wall) so that when he faces south to become wise, he will actually be facing the ark. If he stood on the other (southern) side of the ark, then when he faced south, he would be turning his back on the ark. That possibility is seen as problematic. Both the Peri Megadim and the Ateret Zekenim[55] note that the Levush’s suggestion of placing the ark and wall in the southeast would be successful in terms of properly facing Israel, but would create a problem for those members of the congregation on the north side of the ark who would like to pray facing north (for wealth) or those on its south side who wish to face south (to become wise). They may not do so, as that would present the unfortunate appearance of people turning their backs on the ark. The Kaf ha-Chaim[56] also addresses the issue of turning one’s back on the ark with regard to turning in one direction or another and tries to avoid this problem. Implicit in all of these arguments is that the ark requires some extra form of consideration that did not factually exist at the time of Rashi and the Tosafot.

These views consistently note a problem of having one’s back to the Aron, but allow for the possibility of having one’s back to Israel. These Ahcaronim are clearly giving significant weight to the views in Bava Batra, even preferring that source to the Beraita in Berakhot.

Ark Location as One of Many Factors

Arukh ha-Shulchan, who rules that orientation need not be exact, notes that if the ark is placed north or south and the congregation prays in that direction and an individual wants to pray to the east, he may not do so, since this could cause others to bow to him.[57] Instead, the individual should pray in the same direction that the congregation is praying, but turn his body slightly to Israel.[58] This is true only when one prays with the congregation. In a situation where one prays alone he should face Israel and not the Aron.[59] This writer suspects that the Arukh ha-Shulchan would adopt the same view if the Aron was improperly set westward.

Recapitulation and Summary

While the directions in which the congregation prays and the ark’s orientation have been considered, most sources still support facing Israel. Even though there are many different opinions as to which way individuals should orient themselves during prayer, today most authorities agree that one faces toward Israel. The Ishei Yisrael[60] cites the Mishnah Berurah[61] to note that it is customary to place the ark in the direction to which one would pray. Much like the Arukh ha-Shulchan, Tefillah ke-Hilkhata says that if one prays in a congregation that is facing the ark in an incorrect direction, he should face that way, too,[62] but turn his face east.[63] The Ishei Yisrael also notes it is important to consider not placing the ark in a place where the congregation would turn their back toward the ark. In sum, the ark is given weight, but it is not important enough to override the original law.

Interestingly, many note that praying in the incorrect direction is acceptable, including cases where the majority of a synagogue are praying in the incorrect direction.[64] Also, if one recognizes that he has prayed in the wrong direction, many say that he can turn his head to correct his mistake.[65] Most authorities, including the Tur[66] and Baer Heitev,[67] note that the direction itself is only an ab initio (lechatchila) consideration and one who cannot turn (i.e., is facing 180 degrees in the wrong direction) has still fulfilled one’s obligation.

However, other less-commonly cited opinions exist. In accordance with a stringent opinion, saying that prayer is absolutely dependent on direction, the Yad Eliyahu[68] says that one who discovers that he is praying in the wrong direction should actually move his feet to point to the proper direction in the middle of prayers. The Ishei Yisrael (23:7) cites the Mishnah Berurah (94:10) and concurs with the Yad Eliyahu only if one was praying communally, as deviation from the communal norm (independent of the presence or absence of an Aron) is itself problematic.[69] Were one praying alone, however, one needn’t make the change. The ramifications of this statement seem to connote that prayer is unfailingly dependent on direction. However, the Rambam,[70] Taz,[71] Kitzur Shulchan Arukh[72] and Mishnah Berurah[73] posit that post facto (bedi’avad), one who prays in an incorrect direction need not repeat his prayer, since the Shekhinah is everywhere.[74]

IV. Measurement Problems

We have seen that the orientation of the ark, although important, is not paramount in determining the direction of one’s prayers. Let us now turn to a deceptively simple question: Exactly how is one supposed to determine the direction toward Israel? At the time when most of the rabbinic writings were being recorded, there was little knowledge of how to correctly determine a synagogue’s orientation. In light of new scientific/geometric thoughts on measuring, we can now accurately determine the shortest route to Israel.[75]

The truest miniaturized representation of the earth would be spherical—a globe. A significant drawback to this representation is that only half of the sphere can be viewed at a given time. But even allowing for multiple sections to be displayed side by side, the globe has an even greater failing: because the laws of planar (Euclidean) geometry do not apply to spherical objects, it is extremely difficult to portray large segments of the earth in two dimensions, i.e., on paper. In order to achieve a flat rendering, the globe must be “unpeeled” in segments and laid flat. The resultant map, though, ends up with large gaps between what should be adjacent areas, making it difficult to convey relationships between various locations on that map.

Numerous simplifications and projections dating back to antiquity were developed to address the complexity of representing a three dimensional curved surface in two dimensions. Fundamentally, they all involve some degree of distortion as they, in essence, “stretch” the earth’s surface to make it lie flat. One of the most commonly encountered is the cylindrical[76] Mercator projection. This map turns the curved grid of latitude and longitude into a rectangular grid, with its edges representing the four cardinal directions. On all such flat maps, it is no longer evident that when moving from point to point, one is really moving along a curved surface. This leads to a considerable amount of confusion about how to calculate distance when traveling on a globe, and what exactly is the shortest route from one point to another on the surface of a globe.

On a flat surface, the shortest route is a straight line determined by a compass. Geographers refer to this distance determination by the term “compass route” or “Rhumb line.”[77] On a spherical globe the compass route is not the shortest distance; rather it lies along what mathematicians term a “Great Circle.” A great circle is the perimeter of the circular plane created when a circle is bisected (cut through its center). Any two points on the surface of a sphere can be connected by an arc along this circle. Geographers refer to this as the azimuth equidistant route or “great circle route.”[78]

To quickly imagine the incorrectness of our perception of compass direction or Rhumb line as producing the shortest route, imagine that there is a circle of people holding hands around Jerusalem, each of them looking directly at the Temple Mount. Now imagine all of these people begin to back up, one step at a time. Ponder the individual who is facing due south. That person is walking directly backwards due north. Just before he reaches the North Pole he is still facing south, and—where he is standing—the shortest distance to Jerusalem is due south. As he passes beyond the North Pole he is facing north, even though he is still facing in exactly the same direction with respect to Jerusalem. That route is the great circle route, and it is not the compass route. The shortest distance to Jerusalem for that person is due north, until he passes the pole, and then it is due south. The same thing happens to all of the other people circled around Jerusalem as they walk away. They remain pointed in exactly the same direction with respect to Jerusalem, but their compass direction changes continuously as they get farther and farther away. Until they have walked backwards a step more than halfway around the earth, each of these people will have walked the shortest distance from Jerusalem to where he or she is now. Each has walked along a great circle route. Confusion about this fact arises from the common usage of flat (Mercator) map projections of the world.[79] For all practical purposes, even five hundred years after Columbus, most people still perceive the world as flat, as when traveling a short distance that appears to be true.[80] Indeed, over short distances the curvature of the earth is less relevant and the difference between the great circle and the Rhumb line calculations is very, very small in terms of distance and heading. Consider the route from Moscow to Jerusalem, for example: The shortest distance between Moscow and Jerusalem is along the great circle route; however, because Moscow and Jerusalem are relatively close, the difference between the two routes is hardly noticeable. The great circle route from Moscow to Jerusalem is a distance of 1659 miles and involves heading[81] 185 degrees south. If one wishes to travel the compass route, the distance is 1661 miles, and the heading is 184 degrees south.

Indeed, as Table 1 demonstrates, when traveling between any point in Europe or the Middle East (or North Africa for that matter) and Jerusalem, there is very little difference between the great circle route and the compass route, and there is also very little difference between the respective directions in which one would head. Map 1 and Map 2 portray this visually.

However, the farther away one moves from any given point, the more the difference grows, both in mileage and in heading. The movement of vast numbers of Jews to locations thousands and thousands of miles away from Jerusalem, in hemispheres and continents uninhabited by organized Jewry until the last century, has caused the question of closest distance and heading to be revisited.

Consider Table 2 above, which demonstrates quite clearly that the direction and heading from a variety of points in North America, South America and the Pacific is quite different when one uses the Rhumb line direction instead of the Great Circle heading.

Thus, while it is clear that one may take an infinite number of paths between any two points on the globe and reach the intended destination, any one of these approaches can hardly be called following the shortest route. If one is going to maintain the same sense of direction to Israel, which is experienced by someone who is within sight of Jerusalem, or claim to head via the shortest route, one can do so only by following what is called a great-circle route.
Let us give two simple,[82] and practical, examples of this.

1. The shortest route between New York City and Jerusalem is 5686 miles, and it travels the great circle route from New York with an initial heading of 54 degrees East-North.[83] If one wished to travel to Israel by the compass route from New York, one would have to travel 6091 miles (over 400 miles farther) at a heading of about 95 degrees East-South.[84]

2. The shortest route between Los Angeles and Jerusalem is 7580 miles and traces a straight line on a great circle with an initial heading of about 24 degrees North-East.[85] If one wished to travel to Israel by the compass route from Los Angeles, one would have to travel 8920 miles (1340 miles farther), at a heading of 91 degrees due East.

As Map 3 shows, the great circle route from New York passes over England and France; from Los Angeles, over Scandinavia and Poland. The compass route for both, by contrast, passes through Algeria and Morocco.

One who examines the literature concerning the proper location of the International Date Line in Jewish law[86] sees clear support for the proposition that the direction one should face (assuming one follows the view that one faces Israel) ought to be measured by distance and not compass. Both[87] the analysis of Chazon Ish and Rabbi Yechiel Michel Tukitchinsky are predicated on the basic mapping proposition that Israel is to be mapped at the center point of the globe with the clear recognition that distance is to be measured through the curve of the earth, in a great circle route. This approach can also be well derived from the simple reading of the Ba‘al ha-Maor on Rosh Hashanah 20b and the Kuzari II:20, each of which seeks to map the earth as a ball (globe) with distances measured across the globe on an arc, with the center of the arc being Israel.[88] That image of the earth produces great circle routes.

As an additional proof to this basic proposition, one needs look no further than the Talmudic citation of Israel as the ‘center of the earth’ (tabor ha-aretz) found in Sanhedrin 37a.[89] Israel becomes the center of the earth only when one declines to map the earth on its polar axis. Once one ceases mapping on a polar axis (see Map 2 and Map 4, for example), it becomes clear that all distance in prayer is determined by the great circle route—including direction of prayer toward Israel.[90] The compass route becomes an irrational form of measuring distance, with no foundation in Jewish law.[91] Tosafot in Berakhot, who simply posit that one faces toward Israel, could reasonably be referring as well to directions measured by shortest distance, which would seem to this writer to be a very logical way to think about “shortest direction,” and “facing” a particular direction. Indeed, the Perishah explicitly links the proper direction one is to face with the shortest direction possible, by describing the path of prayer as an arrow aimed at a target, which certainly must follow the path of the shortest distance.[92]

An Azimuthal equidistant map projection whose center is Jerusalem (Map 4) would seem the best way to portray this concept. This map has the properties of preserving direction and distance from its center point. (Land shapes, though, are distorted.) A straight line radiating from the center point to any other point represents the shortest distance between them—along the great circle route. Of course, there are an infinite number of other paths between the two points, but on this map they are demonstrably longer.

All of this analysis is hardly relevant when one is in Europe, northern Africa or most of Asia, as the compass direction and the great circle route do not differ dramatically in terms of distance or heading. However, it is profoundly relevant in Anchorage, Alaska, where the compass route is due west and the great circle route is due north, and is even quite relevant in a city such as Los Angeles where the compass direction is due east and the great circle route is north-east. Of course, as the Arukh ha-Shulchan notes[93] there are ample grounds to assert that all that halakhah requires of one is to face in the rough direction of Israel.

An interesting example of following great circle route heading can be found in the main Bet Midrash at Yeshiva University in New York. In New York City, the great circle route inclines one to east by north heading, and not due east[94] as the Rhumb line would dictate. In the main Bet Midrash at YU, the Aron Kodesh faces Israel via the great circle route (actually, northeast at about 30 degrees, which is relatively close to the great circle heading of 54 degrees). It would seem logical to this writer that since the great circle route has considerable halakhic foundation as the proper direction to face to Israel as a manifestation of the proper halakhah (lechatchila) and the Aron Kodesh is also placed roughly in that direction, facing due east would not be halakhically preferred over facing northeast toward the Aron Kodesh and Israel (via the great circle route).

Conclusion

The Talmud recounts, in two different places, two different views of the direction one should face during prayer. Most Rishonim accept that normative Jewish law rules that either one’s feet or one face (and according to many, both) should face Israel and Jerusalem during prayer. However, as noted by many halakhic authorities over the centuries, this is not an exact formulation, but merely an exhortation of ideal direction that is roughly fulfilled by approximation and imprecision. Indeed, synagogues in Europe commonly headed east, even in situations where south or southeast would have been far more precise. This model continues to this day in America, where synagogues and study halls are not positioned to precisely face Israel, but merely approximate some sort of heading. Finally, even when we aim for precision, determining the correct direction toward Israel from far-off lands is not a simple matter according to halakhah, as the Talmudic instruction to face Israel may very well require measurement not by straight lines drawn on a distorted rectangular map projection, but rather according to the shortest distance. Logic contradicts minhag Yisrael and points to the shortest path rather than the compass direction.

1. Historical examples include Moscow, where synagogues faced east even though it is due north of Israel (see Table 1, Map 1 and Map 2), as well as much of Eastern Europe, where synagogues faced due East instead of South and some-what East. Even today, synagogues across the world are built facing directions other than Israel.
2. A similar such view is found in the Tosefta, Berakhot 3:15 (Lieberman): “Those standing outside of the land [of Israel] should direct their hearts toward Israel, as it says, ‘And they shall pray to You by way of their land.’ Those standing in Israel should direct their hearts toward Jerusalem and pray, as it says, ‘And they shall pray to God the way of the city….’”
3. See, for example, Siddur Rav Amram, s.v. amar rav, who acknowledges the dispute without resolving it.
4. Berakhot 30a.
5. Mishnah Berakhot 4.4–6.
6. Rambam, Hilkhot Tefillah 1:3.
7. Rosh, Berakhot 4:19, see also Beit Yosef O.H. 94:1-3
8. Tur, O.H. 94[:1].
9. Synagogues in Moscow, however, invariably face east—an incorrect orientation according to the Tosafot in Berakhot.
10. CChayei Adam 22:10.
11. Kitzur Shulchan Arukh 18:10.
12. Rashi, Bava Batra 25b, “demetzaded atzdudei.”
13. Or perhaps more accurately, step sideways.
14. Rashi and Tosafot apparently had a slightly different text of the Gemara, which allowed them to arrive at different conclusions. Rashi’s Gemara in Berakhot included the word “panim” (face) while Tosafot’s did not. Rashi’s Gemara would thus read: “One who stands outside of Israel should direct one’s face to Israel…” In contrast, Tosafot’s would say: “One who stands outside of Israel should direct oneself toward Israel.” See Bah O.H. 94 s.v. “ubemekomo,” who defends this view textually, and notes that there is a dispute as to whether the word ̀“lev” or “panim” is in the Gemara.
    The Bah, seemingly operating on Tosafot’s Talmudic text, elucidates the probable differences between the text problems in the form of the definition of “kavvanah.” If the kavvanah refers to one’s face, then the dichotomy between feet and face can exist. Alternatively, it would be referring to the heart, which could be interpreted more precisely as the body (Tosafot) or less precisely [as what?] (Arukh ha-Shulchan).
15. Furthermore, according to this approach, most, if not all, of the views of the various Amoraim in this sugya are now reconcilable with the Beraita in Berakhot. At the very least, the answer of metzaded atzadudei indicates an acknowledgement of the competing values in facing two different directions. From there it is but a small step to replace the rationale of Shekhinah be-ma‘arav as one of those two values with the need to face Israel. (One might even suggest that according to the opinion that the Shekhinah is everywhere, though one may theoretically face any direction, nevertheless, one’s back may not be toward Israel and the Beit ha-Mikdash—at least lehathila. See Taz and Levushei Srad O.H. 94:1.) It is left to the reader to explore whether the notion that the Shekhinah is in the west is at least partly reconcilable with a requirement to face Israel and the Beit ha-Mmikdash.
16. Darkhei Moshe, O.H. 94: 1.
17. Taz (O.H. 94:1) notes that this is limited to one’s feet pointing north or south. Certainly one cannot face west and turn ones head 180 degrees to the east!
18. Smag, Positive Commandments 19:101:4, cited in Beit Yosef.
19. Beit Yosef, O.H. 94:1, s.v. “u-mah she-katuv u-k-hakh shematta.”
20. Quoted in Beit Yosef, ibid.
21. O.H. 94:6.
22. Teshuvot ha-Geonim (Harkavi, ed.) 529.
23. Magen Avraham O.H. 94:5. Indeed, Magen Avraham believes this to be the correct understanding of Rashi.
24. O.H. 94:3.
25. The Arukh ha-Shulchan (94:6-7) records this not as an argument between facing Israel versus facing north or south, but rather as an argument between facing Israel and facing west, because the Shekhinah is in the west. Yet, he also says that one can choose either of the permutations.
26. O.H. 94:1-3.
27. Mahari Abuhav, Orach Chaim 94, s.v. “v-teima.”
28. See footnote 20. Although no Rishon suggests this possibility, it might be that the community of the Mahari Abuhav adopted the practice of completely disregarding the Berakhot obligation to face Israel during prayer by positing that the Berakhot source was the proper direction only when the Temple was in existence.
29. It should be noted that Mahari Abuhav himself thought that his community’s custom would be much improved if the people would turn their faces toward Israel.
30. Cited in Shiltei Giborim 3, Berakhot 20b in Rif pagination.
31. See Darkhei Moshe O.H. 94 [:1-3].
32. O.H. 94:3.
33. O.H. 94:7.
34. See Tosafot, Bava Batra 25a, s.v. “ru’ah ma’aravit.”
35. In Berakhot 30a.
36. Bava Batra 25a, s.v. “hagah.”
37. Expressed in Tosafot, Bava Batra 25a, s.v. “ruah ma’aravit,” which explains that the Divine presence is in (or perhaps, emanates from) the west and faces east. Accordingly, west is referred to as “ahor” (the back) and east as “kedem” (the front). Furthermore, south and north are referred to as right and left, respectively. According to this understanding of Tosafot, it is appropriate for people who are praying to stand face to face with the Divine presence, so to speak. Thus, if the Shekhinah emanates from the west and “faces,” so to speak, east, people praying should face west.
38. The underlying logic of Shekhinah be-ma’arav, necessitating that one face east, can be found in the Kuzari’s presentation on the need for a fixed halakhic date line on the globe. For more on the Kuzari’s position, see R. Shlomo Yosef Zevin, “Ha-Kuzari ba-Halakhah” in his le-Or ha-Halakhah: Be’ayot u-Veirurim (2nd ed., Tel Aviv: Tsiyoni 1957). In addition, see Rabbi Benzion Firrer, “Be-din ha-mitpallel be-hutz la-aretz tzarikh le-khavvein panav le-Eretz Yisrael,” No‘am 2:171-173 (1959), who also cites this as the opinion of the Kuzari, though with a slight variation.
39. As, le-havdil, the Islamic practice does with plaques oriented toward Mecca.
40. O.H. 94:1-14.
41. Drawn from Rambam, Hilkhot Tefillah 5:1, they are: 1) standing, 2) facing the site of the Temple, 3) with proper posture, 4) dressed properly, 5) in a suitable place, 6) in a low tone of voice, 7) bowing five times, and 8) complete prostration.
42. O.H. 94:9. In previous paragraphs as well as in the omitted section here, one may reasonably see Arukh ha-Shulchan envisioning a longitudinal (north-south) line running straight through Jerusalem—a repositioned prime meridian, if you will. Anyone west of this “line” may face east; anyone east of this “line” may face west—irrespective of north/south positioning. In addition to the additional support for the idea of imprecision, this echoes the discussion of Jerusalem being at the geographic center of the world; see below, text accompanying notes 86-90.
43. Other Rishonim and Aharonim disagree and require precision in one’s heading. See sources cited by R. Yaakov Medan, “Praying Towards Jerusalem,” on the Yeshivat Har Etzion Virtual Beit Midrash, including Talmidei Rabbeinu Yonah on Berakhot, 20b in Rif pagination, s.v. “hayah,” Ma’adanei Yom Tov to Rosh, Berakhot 4:19 (no.6), Responsa Hatam Sofer 19, and Yad Eliyahu 1.
44. O.H. 94:1,8.
45. 12:4.
46. 23:6.
47. In addition, Rabbi Joseph B. Soloveitchik, mirroring the Rambam’s words, notes that a synagogue should be built in order for those who pray to face the direction of the Beit ha-Mikdash, and cites this ruling as a de-oraita ruling. See mi-Peninei ha-Rav, p.47, 5.
48. http://www.jewishencyclopedia.com/view.jsp?artid=1778&letter=A. As noted by others, the liturgy said in the Ashkenazi rite reflects this change. Initially, the Aron Kodesh was carried into the sanctuary, and the worshipers chanted the verse “Vayehi binsoa ha-Aron…” to reflect the fact that the Aron is moving, akin to the traveling Aron (of the Mishkan) in the desert; once the Aron became fixed in location, the verse “Ki mi-tzion tetze Torah…” was added to reflect the common custom of the ark being affixed to the wall facing Israel—the direction from which the torah was now “emanating.”
49. See above, the text accompanying note 32.
50. O.H. 94:2.
51. O.H. 94:1.
52. O.H. 94:2.
53. O.H. 94:9.
54. Mishbetzot Zahav, O.H. 94:2.
55. O.H. 94:1.
56. 94:13.
57. O.H. 94:13.
58. This ruling is similar to the practical rulings of Ishei Yisrael (23:7) and Mishnah Berurah (94:10) that depend on congregational action instead of only on what is proper.
59. The Levush, while addressing the question of the ark location, notes that one should not put the ark in the direction of the rising sun. The Taz echoes this idea by noting that the ark and the proper front wall of the synagogue should be in the same place, perhaps connoting that people do not need the complication of two separate focal points.
60. 23:6.
61. 94:9.
62. Ideally, however, the whole congregation should face the correct direction even if that is not the direction of the ark (Mishnah Berurah 94:9).
63. 12:7.
64. Kaf ha-Chaim O.H. 94:8.
65. Tur, O.H. 94[:1].
66. O.H. 94[:4].
67. Ibid.
68. Responsa Yad Eliyahu, siman 1.
69. Mechzei ke-shtei reshuyot. Perhaps the ruling from the Mishnah Berurah is not as stringent as that of the Yad Eliyahu since it depends more upon what the congregation is doing.
70. Hilkhot Tefillah 5:1.
71. O.H. 94:5.
72. 18:10.
73. 94:10.
74. Bava Batra, 25a. The Chayei Adam (22:10) and Kitzur Shulchan Arukh (18:10) also do not consider Jerusalem’s direction to be an absolute halakhic factor. Instead, they both note that if there are paintings or images in the direction of the ark, one is to pray in another direction. The Chayei Adam also commands one to close his eyes if there are imaged garments hanging on the wall. To them, there must be other considerations that could possibly outweigh the Beraita in Berakhot.
75. Our calculations are not necessarily new ones. Much responsum has been written for Qibla direction in the Arab world as well. They also found facing Mecca difficult in light of the Great Circle route’s prevalence. See http://muslim-canada.org/qibla.html for more details.
76. So called because it is the mathematical equivalent of having an imaginary light source inside the globe project the details of the earth onto a cylinder wrapped around it (in the case of the Mercator projection, tangent to the equator). Mathematically, vertical distances are stretched by the same proportion as horizontal distances, preserving shape and direction on the map. However, an area’s size is increasingly distorted as it moves away from the equator and approaches the poles.
77. From the French word for straight.
78. The great circle is a mathematical term for a surface of a sphere that has the same diameter as the sphere, dividing the sphere into two equal hemispheres. It can also be expressed as being a circle on the sphere’s surface whose center is the same as the center of the sphere or as the intersection of a sphere with a plane going through its center. A great circle is the largest circle that can be drawn on a given sphere—other circles around the sphere that do not contain the diameter are called small circles. Great circles in spherical geometry are analogous to “straight lines” in planar geometry. Thus an arc along a great circle is the shortest path between two points on the sphere’s surface.
    A (hopefully) helpful visualization: Imagine a cardboard square bisecting the earth; you should have two equal hemispheres. Square yourself to face one hemisphere head-on. You should now be able to draw an infinite number of arcs from one point where the earth meets the cardboard to any other. Look at only the perfectly vertical arcs. The longest one, perfectly bisecting your hemisphere, is half of a great circle. The distance between any two points on that arc represents the shortest distance between those two points. Angle your original cardboard slice differently if the distance between two points you would like to measure is not on this great circle arc. There are an infinite number of great circles on the earth’s surface.
79. See Map 3.
80. Just a few minutes with a globe and a piece of string can easily disabuse a person of these notions. Merely by placing the string on the globe so that it touches the origin and destination of the route, and then tightening the string so that there is no slack, while keeping it touching the origin and destination points, will illustrate quickly the shortest route between the two points. For example, when an airplane flies from Chicago to London, the pilot does not just set a compass direction and maintain it until the arrival at the destination. In a flight directly to London, the direction that the compass shows will change continuously along the entire route. The airplane could fly along a constant compass direction, but it would take it far out of its way, and would burn a great deal more fuel. Over short distances the difference is small, but over thousands of miles the difference can be considerable. Thus, the great circle route from Chicago to London involves an initial heading of 46 degrees northeast, and entails traveling 6181 miles by air. Traveling the compass route entails traveling 6806 miles at a heading of 96 degrees east.
81. Due North is expressed as 0 degrees; due East as 90 degrees; due South as 180 degrees and due West as 270 degrees.
82. See www.info.gov.hk and www.movable-type.co.uk/scripts/LatLong.html for how to do these calculations. See maps 3 and 4, which portray the difference between a flat map and an adjusted map.
83. 54 degrees is described as East-North because it can be described as taking five steps eastward and four steps northward.
84. 95 degrees is described as East-South because it can be described as taking 18 steps eastward and one step southward.
85. 23 degrees is described as North-East because it can be described as taking five steps northward and two steps eastward.
86. For a full discussion of the many different sources and citations, one is well advised to examine Rabbi Asher Zimmerman’s classical work Agan ha-Shachar, which quotes nearly all of the sources on this matter.
87. Rabbi Menachem Mendel Kasher’s analysis (which supports the use of the secular international date line) follows a different approach which is not inconsistent with this analysis, but provides no support for it either. It is worth noting that contemporary communal practice follows the view of Rabbi Kasher and not either Chazon Ish or Rabbi Yechiel Michel Tukitchinsky. Thus, Shabbat is observed in Hawaii on Saturday (against the view of Rabbi Tukitchinsky) and Shabbat is also observed on Saturday in New Zealand and Japan (against the view of the Chazon Ish).
88. See also She’alot Uteshuvot Eretz Tzvi 44 for a similar analysis.
89. See also Ezekiel 38:12 for a similar reference.
90. Indeed, Rabbi BenTzion Fuerer in a teshuva written in No’am 2:171-173 (1959) notes this exact problem, and proposes that the solution is found in the approach of the Arukh ha-Shulchan (which he does not cite directly) that one need not face the exact direction of Israel but can approximate direction.
91. Indeed, it is generally an irrational manner of measuring distance, as explained above. However, until the invention of the refined sextant and its more modern cousin, the global positioning system, the compass provided the only accurate way one could travel over extended distances, as one could never determine latitude and the compass could determinate longitude. Thus, on a practical level, travelers 500 years ago traveled by compass as the long way was more practical than the short way, which could not be measured accurately.
92. Perishah O.H. 94:1.
93. Living in Novordok, a city nearly due north of Israel, but with all the people praying eastward.
94. Indeed, the correctness of this approach was recently the focus of a series of exchanges in the Torah journal Kovetz Beit Aharon ve-Yisra’el, beginning with an article by R. Baruch Shovkes, “Berur tzad she-keneged eretz yisrael be-tefillat shemoneh esrai be-New York,” Kovetz Beit Aharon ve-Yisra’el 16:5 (no. 95, Sivan-Tammuz 5761), 113-15, which inspired 2 letters to the editor in the following issue. R. Shovkes continued with part two of his article in the next issue, “Berur tzad she-keneged eretz yisrael be-tefillat shemoneh esrai be-New York II,” Kovetz Beit Aharon ve-Yisra’el 17:1 (no. 97, Tishrei-Cheshvan 5762), 106-10; three other letters to the editor on the topic appear in the same issue. R. Shovkes then replied in a letter of his own, “Teshuvot le-he’arot be-inyan tzad she-keneged ertz yisra’el,” Kovetz Beit Aharon ve-Yisra’el 17:2 (no. 97, Kislev-Tevet 5762), 150-54.
    In a letter (Kovetz Beit Aharon be-Yisra’el 16:6 [no. 96, Av-Elul 5761], 125-26), R. David Yehoshua Koenig challenges R. Shovkes’s assumption of the correctness of the great circle route, and suggests, based on an article by Rabbi Yehudah Hershkowitz, “Be-Inyan le-eizeh tzad tzarikh le-hitpallel,” Yeshurun: Me’asef Torani 3 (Elul 5757): 586–602, that the difference between the compass and great circle routes is in fact a matter of dispute between the Levush (O.H. 94:3) and the Emunat Hakhamim (Chapter 24). This, however, seems to be incorrect. The Levush makes no real reference to compass direction rather than great circle routes, contrary to the claims of the Emunat Hakhamim cited by Rabbi Hershkowitz. Instead, the Levush is simply referring to the exactness of the measure, rather than the way one is measuring. “North,” “south,” “east” and “west” could just as well be understood as directions relative to Israel as they can be taken to be compass directions. (To understand this point, orient a globe with Israel taking the position normally taken by the North Pole; the Mediterranean Sea is eastward, Amman is westward, Egypt is southward and Turkey is northward by this definition. There is no reason to read the Levush to be inconsistent with the Great Circle direction. The magnetic compass is the only reason that the rhumb line route might be considered, and the Levush—as well as all those who preceded him, including the Talmud—were completely unaware of it.