Is there a special significance of 4 directions as opposed to 6?

Question

According to halacha, when a person says the word "echad" (אחד) in Shema:

בדלי"ת צריך להאריך יותר כדי שיעור שיחשוב שהקב"ה יחיד בעולמו ומושל בד' רוחות העולם

[One should] draw out the dale more [than the Cheis] in order to think that Hashem is one in His world and he rules over the four corners of the world (Shulchan Aruch HaRav 1:61-7).

In Torah Or (נה,ב) the Alter Rebbe of Lubavitch explains that:

ובד' רוחות העולם שהם בחי' ו"ק העולם

...the 4 corners of the world which are on the level of the six directions of the world.

My question is, is there something unique about the number 4 in comparison to 6? In other words, can we learn anything from the number 4 that we would not have learned from 6?

Answer 1

The quote presented here is incomplete, causing some misunderstanding. The larger quote is:

כמאמר רז"ל שהוא אחד בשבעה רקיעים ובארץ ובד' רוחות העולם ר"ל שגם בשמים ובארץ ובד' רוחות העולם שהם בחי' ו"ק העולם בחי' התחלקות ופירוד אעפ"כ שורה ומתגלה יחודו ואחדותו ית'

Like the saying of the sages that He is one in the seven heavens and in the earth and in the four directions of the world. This means that even in the heavens and the earth and the four directions of the world - which are the aspect of the six directions of the world [which is] the aspect of division and separation, nevertheless His Uniqueness and Oneness, may He be blessed, rests and is revealed [in it].

So the point is not to say that the four includes 6 directions, it is just distinguishing the 4 specifically.

I believe the question is why that is. One way to understand it is according what the Alter Rebbe writes in another place:

והתכללותם הראשון הוא רק ארבעה דגלי' דגל מחנה ראובן כולל ג' שבטים כו' שהן ד' מחנות שכינה למעלה כמו בכתות המלאכי' בחיצוני' העולמו' שנחלקים ג"כ לד' ... למעלה בד' מחנו' שכינה מחנה מיכאל מחנה גבריאל מחנה רפאל מחנה אוריאל מזרח ומערב צפון ודרום ד' סטרי עלמא

The first inclusion is only from 4 [in contrast to twelve, which comes from each of the four being subdivided into 3 each] flags, the flag of the camp of Reuven, which includes 3 tribes, etc. which are the 4 camps of the Shechina above, like the groups of angels in the external aspects of the worlds that are also divided into 4 ... above in the four camps of the Shechina the camp of Michael, the camp of Gavriel, the camp of Refael, the camp of Uriel, east, west, north and south the four sides of the world.

(It would be highly interpretative to put punctuation in those lists, so I avoided it in my translation, but at a minimum there are three, if not four groupings there. Machane Shechina groups, Angelic groups, and a north, south, east and west group. There may be an additional four sides of the world group, it depends on how you read it).

In other words each level, higher and lower, has a fundamental initial division of four. So it is not that there is six directions of equal significance, but rather each level (the seven heavens and the earth in the context of Shema) has the basic four directions (with further subdivisions).

Indeed, there is a verse that speaks about ארבע רוחות השמים ...

Answer 2

Without doing too much research, it may be based on this statement from the Shulchan Aruch HaRav, based on the Tur who in turn is quoting the Rosh (Orach Chaim 61:6), regarding the Dalet in the word Echad:

ויש נוהגין להטות הראש כפי המחשבה מעלה ומטה ולד' רוחות

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Also, and I'd like to preface this with the disclaimer that I don't really know what I'm talking about, but you can draw a cube just using 4 corners.

To (try and) explain. Every corner of a cube is made up of 3 edges. For example, in the picture above, corner 0 is made up of 3 edges: 5-0 ; 0-3 ; 0-7

So by starting with just 4 corners (i.e. 0,2,4,6), you could draw a whole cube. Or in other words, with 4 corners you have 6 directions.

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Or perhaps, more simply, 4 directions is 2 dimensional, while adding up and down makes it 3 dimensional.