To Light Up the Night

Since we have already outlined a little bit of the meaning of the triangle (pyramid), square, and circle, we will now add another dimension of explanation that relates to the holiday of Chanukah. As many know, Chanukah is a holiday of eight nights where Jewish custom has become to light the Menorah starting on day one with a single candle and then adding an additional candle on each successive day until all eight lights are kindled on day eight. If we think of this geometrically, we are literally constructing a triangle or pyramid.

1

12

123

1234

12345

123456

1234567

12345678

If we were to take this geometric figure and try to describe it algebraically (so that we could calculate how many total candles are lit without having to actually count them all row by row) we would express it with the following formula:

n(n+1)/2

So if ‘n’ stands for the number of levels or rows in our pyramid (which in the case of Chanukah is eight) we would write:

8(8+1)/2

Broken down: 8(8+1) is simply 8 times 9 or 72 which is divided by 2 to give us 36. Thus, we light 36 candles over the course of the festival of lights, reflecting our triangle or pyramid of 8. What is truly amazing about this number in both number theory and in Kabbalah is that 36 is the first number (other than the trivial example of 1 [and some would argue 0 which is also trivial]) that is a triangle that is also a square:

36 = 6²

This follows the commonly recognized algebraic expression for a square which is just:

n²

It is important to relate to a square number in visual terms which helps us achieve the unification of algebra and geometry.

Why is the mathematical relationship so important to Chanukah? What does it mean that 8^△ = 6² ?

As explained in Part 20 of our series, the triangle represents a picture of hierarchical reality whereby everything is graded and differentiated. Part of the initial building of reality hinges upon clarifying how one thing is different from another or how everything ‘stacks up.’ Yet once this process is completed (as in this Chanukah example where we have a total of 36 candles) then the next stage can begin which suddenly transforms all of reality into a square (with 6 times 6 cell blocks) that reflects the interinclusion or enclothment of each level within all the others (all six rows can be seen as being present within each other as illustrated by the 6 columns). This reconfigured situation takes hierarchy and turns it into relative equality (so each of the 6 rows gets to have an equal distribution of columns reflecting equal access to each other). The vertical power structure collapses into a much more horizontal ‘democratic’ framework comparatively speaking.

Chanukah articulates a fundamental ‘phase transition’ in the redemption of the world. By flattening the pyramid of power, it becomes ‘hip to be square’ in this day and age. One spectacular example of this has been the open-source courses that have placed the resources of the educational elite into the hands of countless millions virtually free of cost. Whereas the top-tiered universities of the world were once all about limited access to those at the top of the pyramid–those who either had the grades, test scores or financial means of matriculating into these schools attended, while the rest of the world was largely left out at the bottom–now anyone with an internet connection can stream tens of thousands of classes from the top experts on almost any subject. Often referred to as the democratization of education, the eruption of online options certainly has had, and will continue to have, a flattening effect on the world of learning.

With all levels of the social pyramid starting to benefit, we are witnessing the nascent stage of a new world order–the square. In Chassidic thought, this transformation was presented in the teachings of Rabbi Schneur Zalman of Liadi (1745-1812) as the ‘King in the field (Melech b’sadeh).’ Normally access to the King is extremely limited. Unless a person works his or her way through the outer chambers of the castle, dealing with all of the bureaucracy in hopes of eventually gaining an audience with the King in the King’s inner sanctum. Basically, this approach amounts to climbing the pyramid to get to the top where there is precious little room. Such exclusionary practices reflect one of the ages of the world but one that we are intended to work through and eventually transcend.

As the embodiment of the vertical dimension, the King can always walk out of the castle to greet the people in the field which represents the horizontal dimension. In the field, we are all on an equal playing ground with equal access to the King. Top and bottom have become directly connected without the intervening levels adding unnecessary obstacles. This novel arrangement might best be termed a ‘horizontal hierarchy’ in that there is still a vertical dimension (King) just that this dimension is fully present at the lowest of levels (like all of our vertical columns unfolding their respective levels into each other by means of the rows of our square). In the horizontal hierarchy model, there still are distinctions but they are minimized by compressing the vertical which then produces a situation where everyone is now in direct relationship. The big gain involves universal relatability.

Another powerful allusion to this transformation can be found in the difference in perception of ultimate reality and spirituality by the first two patriarchs–Avraham/Abraham and Yitzchak/Isaac. This father-son relationship is described in Genesis 25:19 with the words “And these were the generations of Yitzchak/Isaac son of Avraham/Abraham: Avraham/Abraham gave birth to Yitzchak/Isaac.” Sometimes we think of a person in terms of one of their physical traits, personal characteristics, lifetime achievements or even ‘classic statements.’ We might regard this as a kind of algebraic substitution. Let Avraham/Abraham = some known quality. Evidence of this comes from the Talmud (Pesachim 88a) where Rabbi Elazer asks about the meaning of the verse from Yeshiyahu/Isaiah 2:3: “many people will go and say, ‘let us go up to the mountain of God, to the house of the God of Yaakov/Jacob….’ Why does the verse refer to the ‘God of Yaakov’ and not the God of Avraham/Abraham and Yitzchak?’ Here the Talmud responds that Avraham/Avraham thinks of this Holy place as a ‘mountain’ (Genesis 22:14 “…on the mountain God will be seen.”) while Yitzchak/Isaac perceives the same space as a ‘field’ (Genesis 24:63 “And Yitzchak/Isaac went out to pray in the field…”).

Leaving Yaakov aside for now (in our next article we will deal with his view of this place as a ‘house’), from this we can see that Avraham/Abraham frames reality as a mountain. Drawn abstractly, a mountain is basically just a triangle or pyramid. His entire spiritual journey entailed progressing upwards through the Great Chain of Being complete with all of its levels of reality until he concluded that there must be One God. At every step he would reject the ‘ruling’ forces at that level which he immediately saw as subservient to some still higher cause. In this way, the complete ascent of the ‘mountain’ of reality would be to reach the First Cause that was at the top. From there he would jump even higher to the absolute unity of the entire mountain from top to bottom with God being transcendent to it all.

Once he surmounted the mountain mentality of existence (the God of the philosophers is usually conceptualized atop mountains), then he ‘generates’ his son Yitzchak/Isaac. If we once again abstract the description of reality as a ‘field’ as Yitzchak/Isaac calls it, we can depict this as a flattened mountain or a square patch of land. Our rudimentary ‘field’ reflects the mentality of the ‘world is flat’ (with some intended echoes of the title of Thomas Friedman’s best-selling book).

Connecting back to our key number of 36 candles in Chanukah, we can now understand how a complete triangle (pyramid) of 8 levels–which would be equivalent to Avraham/Abraham scaling his ‘mountain’ (existential verticality)–‘generates’ and ‘gives birth’ at the end of the full figure of 36 or 6 squared. This square would then represent the ‘field’ of Yitzchak/Isaac (existential horizontality) as the legitimate ‘offspring’ of an exhausted hierarchical thinking (Avraham/Abraham). Relative inequality begets relative equality at the conclusion of a unique process, the likes of which we have been living through on the world-historical stage. These images of the triangle and the square are a kind of metaphysical short-hand. The mathematical relationships between them embody some of the most important entrenched structures at the root of our world.

In the continuation of our postscript in Part 22, we will provide additional examples of triangles turning into squares along with an introduction to the function of the circle in these transformations.

 http://www.interinclusion.org/inspirations/circus-of-dreams-part-22/

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