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Stan Tenen
Essay Index
Learning by Copying vs. Learning by Reading 1997
Scientists and Wordsmiths 2003
A Few Notes on Literalism 1994
A Purloined Letter: The Evidence is Not Hidden 1999
Damning By Faint Praise 2003
Man Bites Dog 1996
The Purpose of Prayer 1997
Foundations of Jewish Survival 1997
Determinism vs. Freewill 2003
The Dirac String Trick - First Hand 1997
The Most Assymetrical Spiral 1997
Dini's Surface, Mt. Sinai, & the Human in the Gorilla Suit 1997
Who Wrote the Bible 1994
Squaring the Circle: A Philosophical Solution

The Three Abrahamic Covenants and The Car Passing Trick

Making Peace With Geometry - Index
Spirals as Metaphors:
Some Notes on the Logarithmic and Golden Mean Spirals 1997

Notes on Golden Mean Addendum September 1997

Bible Codes
Index of Collected Articles
Alternatives to Biblical Scholarship 1999
When is the Textual Approach Not Appropriate? 2000
On Immortality 2000
Which Way Up? 2000
The Three Pillars of Love 2001
Eating Our Words: A Purim Drash 2002
HOQ 2002
Shabbos & Resonance 2001
Reconciling the Irreconcilable
©2000 Stan Tenen
This essay was written in response to to the renewal of the Intifada in Israel in 2000-2001, and an increase in the feelings of frustration and hopelessness among Israelis and Palestinians.

Once we use the word "irreconcilable" in ordinary usage, that brings our verbal logic to an end.  When something is literally irreconcilable, we mean that there are not going to be any words, nor any word-smith skills that can possibly solve the problem at hand.

Since most people, including most well-educated people like our scholars, diplomats, businesspeople, and political leaders, think almost exclusively in words - and, since, unfortunately, most word-based scholars believe that we can think ONLY in words - once something is called irreconcilable, we naturally assume that there is little more that anyone can do.  As we will see, this is a fundamentally flawed view, and it easily leads to much misunderstanding, and, of course, to the abandonment of possible, non-verbal, means of reconciliation.

But it is hard to make this case.  Most people do rely on words most of the time.  Trying to tell a highly educated, caring, and accomplished person that, in spite of their best intentions and efforts, they are not qualified for the job of solving and reconciling certain problems is not easy, not popular, and generally not appreciated.  Among accomplished people, it takes a near saint to graciously accept the idea that they are not qualified for a job they have taken on, and an extraordinarily secure and open mind to hear this sort of message - particularly when it comes from outside of their field of expertise.

But, the fact is, we do not ONLY think in words, and word skills are not always adequate for all situations.  As recent published scholarly work has confirmed, all cognition is based on movement, with words taking a secondary, later, back seat.  We know that musicians, dancers, craftspersons, mathematicians, and many other professionals use languages and modes of thought that are non-verbal. They would not do this if ordinary language were usable for their thinking, and able to solve their problems.  Why make it difficult for others to understand your meaning by making up your own language, if ordinary verbal language would do?  So, we can assume that mathematicians, for example, do not use arcane symbols just to be secretive, but because they must.  They cannot reconcile (or even properly discuss) many issues in mathematics with verbal language alone.

We can learn from this.  Here is a simple example of how a mathematician might reconcile the irreconcilable.

Examine a square and an equilateral triangle. They are entirely different.  They use different numbers of parts: 4-lines and 4-corner-points for the square and 3-lines and 3-corner-points for the triangle.  Squares have 4-fold, "square," symmetry while triangles have 3-fold, "triangular," symmetry.  When we limit ourselves to a flat surface, because squares and triangles are flat (2-dimensional), there really is no "non-violent" way to reconcile squares and triangles. We cannot make a square and a triangle equal parts of one greater whole without compromising essential features of one or the other.  For a square to become like a triangle it must lose one of its edges and points - and a square cannot do this without losing its defining "squareness."  Likewise, for a triangle to reconcile itself with a square would require the triangle to lose a vital part of its definition as a triangle.  This sort of reconciliation is no reconciliation at all.

In the verbal arena, we have a similar - irreconcilable - situation in Israel.  Israelis and Arabs seem to hold views which are vital to each of them that are mutually irreconcilable.  Our best statespersons, scholars, diplomats, businesspersons, and politicians have tried and tried, and, apparently, they have failed.  Many caring persons have now thrown up their hands in frustration and some have come to believe that because our masters-of-words have not been able to find a way to solve these problems, there are no other possibilities and the situation is permanently irreconcilable.  Any suggestion that anyone or any other sort of thinking could break the impasse is dismissed.

But this mode of thought and train of verbal logic is not correct.

In mathematics, despite our initial impression, there actually is a way to reconcile a square and a triangle without either giving up anything.  We simply move up and out of the limited, flat, 2-dimensional realm where we initially encountered our square and our triangle.  When we enter the infinitely broader, higher, space of 3-dimensions we immediately find that we can easily reconcile squares and triangles.  We can construct a 3-dimensional form that mathematicians call a cube-octahedron from a selection of perfect squares and triangles.  A cube-octahedron looks like a cube whose eight corners have been cut off evenly.  The result is a 3-dimensional form made up of 6-perfect square faces and 8-perfect triangle faces.  Not only does the cube-octahedron reconcile squares and triangles without taking anything away or adding anything to either, but it also provides some startling, "newly emergent" qualities - possibilities - that neither squares or triangles can offer on their own.  A cube-octahedron, unlike a square or a triangle, is a dynamic form.  It can move in ways that no square or triangle or accumulation of squares and triangles (in 2-dimensions) can ever duplicate.  A cube-octahedron can (in the words of architect Buckminster Fuller) "jitter-bug."  Even though it consists of nothing but rigid (and sterile) squares and triangles, a cube-octahedron can also be compressed until it looks just like an icosahedron.  An icosahedron is radically different from either a square or a triangle.  Squares are 4-fold symmetric; triangles are 3-fold symmetric, but an icosahedron adds a new, primary, quality that is never suspected in a square or a triangle.  An icosahedron has 5-fold symmetry!

But, there is more.  A cube-octahedron can be further compressed until it looks like an octahedron.  An octahedron has only (8-) triangular faces. It is related to both the square and the triangle, but it is also distinct from them (and from their 3-dimensional analogs, the cube and the tetrahedron.  A tetrahedron is a pyramid where all three of the faces and the base are perfect triangles.)
Before we go further, let me assure the reader that this is all kosher.  The cube-octahedron may demonstrate the fundamental geometry of The Thirteen-Petaled Rose, mentioned in the introduction to the Sefer Zohar.  It also can tell us - perhaps for the first time since Rabbi Akiva - how and why nine of our Hebrew letters (including finals) have those unusual tagin and keterim (tags and crowns) on top.  (For a possible geometry that determines which letters get crowns and for an explanation of the shapes of the crowns themselves, see the graphic poster at: .)

Once we realize the extraordinary and heretofore untapped potential of formal, non-verbal, languages for communicating where verbal communication is not adequate and for providing possibilities for reconciling matters that are verbally irreconcilable, we can look to these modes for solutions to the current political, social, cultural, and religious impasse in the middle east.

As outlined above, one common mathematical-geometric means of reconciling entities that are radically different is to move our perspective to a higher "plane" (dimension) where there is much more (actually, infinitely more) "room" to move and arrange things.  This is consistent with common sense. When there is not enough room for a new addition to the family, we add more room.  Mathematically - and I am suggesting also politically - the same process should work.

But, how can we add more room to Israel or to Jerusalem?  Isn't our problem based on there not being enough physical room (Eretz Israel) for both parties to use, and live in and on, without forcing painful changes on one, the other, or both? Where can we find more room in the space available and how do we gain the higher dimensional perspective that shows us how to use it?

From the verbal-diplomatic perspective there is nothing we can do.  There is simply not enough space for both peoples.  Once we accept this, we have no choice but to wait for God to come to us with a solution.  We can only - more or less passively - wait for Moshiach. When Moshiach comes "down" to us, He will solve our problems, defeat our adversaries and rebuild the Temple.  This may be so.....but it may also be a long time to wait - while our friends and neighbors would like to see something positive for themselves and their children right now.

But we do not have to wait.  We do not have to wait for HaShem to send Moshiach.  In my opinion, we do not have to wait for HaShem to come to us, for us to gain a small, but vital, measure of the HaShem's "higher" perspective. From this higher spiritual (and psychological, emotional, theological, hyper-physical) perspective, we could, if we looked and if we practiced, gain a higher dimensional view for ourselves (and, ultimately for our allies and adversaries) right here, right now.  We have always known that HaShem would meet us halfway.  We do not need to wait for HaShem to come to us because we can move towards HaShem, we can gain an empowering overview, and we can allow for the possibility that HaShem/Moshiach could meet us exactly at the right moment, when we have made ourselves ready by our own efforts.

And, of course, we know how to gain a perspective closer to that of HaShem.  We work on ourselves to be better people, we pray, and we study.  But, we already do all of this.  What can we do better than we are already doing?  We can improve ourselves in ways we have not worked on yet, sacrificing a bit of our ego's unhelpful demands with a measure of added humility.  We can pray with more attention and focus, and we can determine to live by the words we pray.  We can expand our studies of Torah by looking more closely at the most challenging depths of Torah - the Sod level.  The Sod (Sood, Yesod - Foundation) level of Torah informs the backbone of halacha and mitzvot.  It also holds the mysteries that our Kabbalah implores us to explore.  Sod and Kabbalah are not easy to understand, and there are risks involved if we approach them immaturely, rashly, or with unrealistic expectations.  Nevertheless, these depths of Torah can provide a means by which we can earn a higher perspective.  However, they do not provide a "free lunch" and they do not offer easy, quick, or simple solutions. Even with the proper Torah-knowledge, we still must do the work for ourselves.

Because they must address issues that are ineffable - which means that these issues cannot be described in words nor appreciated with words alone - the Sod level of Torah and our Kabbalah make use of forms of language that extend well beyond the limitations of ordinary verbal discussion.  Torah is even deeper and more empowering than the mysteries of the Greek Academy, of course.  The Greek Academy insisted that "Only those who know geometry can enter here."  The same is true for Torah - only with Torah there is even more depth and a more profound understanding for us to master.

The language of Kabbalah requires knowledge of geometry.  It has to.  The words and word translations of our Torah and Kabbalah are necessary, and of extraordinary value in themselves, but they are not sufficient for the greatest depths of understanding that we need for us to be able to reach a higher geometric perspective, closer to that of HaShem, where there really is sufficient room to reconcile what otherwise appears to be irreconcilable.

While geometry is required, it is not modern "rocket science."  The geometry we need is based on the hands-on trades that were available in the ancient world. We need to know about weaving (talitot), braiding (making challah) and knotting (tzitzit); simple carpentry, calendar-making, farming, and building our Sukkah.  These are all common skills that we know were known at the time of Moshe, for example, and that we can easily master.
Our first lesson, of course, is that there is One Infinite Omnipotent God and that in some way beyond our simple human sense of it, the One God is a jealous God.  It would be foolish (and arrogant) for me to attempt to write new midrash  on the matter of the Oneness of God and what that implies from a theological or Talmudic perspective.  Our sages have done this and continue to do this.

But, geometrically, there are some possibilities that may have eluded our current sages.  (Or more likely, that have eluded the attention of our modern sages' verbal understanding of what our sages - who had "hands on" experience and who were not limited to word-smith knowledge alone - have taught in the past.)

For example, there are social, psychological, and political implications that can be inferred from the geometry of an utterly singular omnipotent God.  If God were only fairly "big," than all of life would not have equal status. For example, if God were only 100 feet tall, then 8-footers would be closer to God than 6-footers. (Here, I am using physical stature measured in feet as an analogy for all of our desirable measurable qualities.) Because God is infinite, we are all infinitesimal by comparison. That makes the stature of all people equal no matter who they are or what they do or accomplish.  If God were not infinite, then some of us would be better than others and we would not, in any sense, be all equally precious.

Once we accept that God is infinite we cannot deny that our adversaries are as  precious to God as we are - without renouncing our belief in God.  No matter how heinous the actions of our adversaries are, or appear to be, once we accept that God is infinite, we must retain respect for our adversaries.  When we do this, we rise a bit spiritually and we gain a perspective closer to that of God. While this may be personally difficult while we are under siege, this higher perspective is, after all, what we need if we are going to be able to reconcile the irreconcilable.  When the immediate emergencies pass, we can use our "higher" perspective to see solutions that cannot be seen from the ground.

And what of God's jealousy?  Clearly God is not afraid of, nor threatened by, any puny demigod that might be set up.  "Jealousy" for God must mean something higher than our petty human experiences of jealousy.  We are taught that we are to have Yirat HaShem.  We are to be in awe of and fearful of God and ONLY of God.  Why?  Because when we fear anyone or anything other than the One God, we have, in effect set up an idol that we respect as much as God - and that is the equivalent of denying God's unique Oneness.

So, no matter how frightening our adversaries may appear and no matter how terrible the situation seems and no matter how painful our loses, we simply cannot afford to fear our adversaries - nor to act on that fear - without denying the Infinite, Exclusive, Oneness of God.  Of course this is difficult.  But, if we succumb to fear of our adversaries or the results of their actions, we have denied God.  When we deny God, we can expect God to (temporarily) deny us in turn.

Geometry teaches us that the verbally irreconcilable can be reconciled when we approach a geometric problem from a higher dimensional perspective, and God's Torah gives us the opportunity to do the same thing in the real world.

If there is interest in this approach, I will try to provide additional theoretical and real world examples and suggestions of how a Sod-Kabbalah geometric approach can offer perspectives where there really is enough room for all parties to live in peace in Jerusalem without the need to compromise or bargain away anything vital to ourselves or our adversaries.

For now, I am merely trying to point out that the irreconcilable is definitely not irreconcilable from HaShem's perspective - and that the Torah-means for finding peace in the city-of-peace is available to us right now.

A few notes on Kabbalah:

There are many aspects to Kabbalah.  Most public attention has focused either on relatively trivial aspects or on "Jewish meditation."  The trivial aspects, such as gematria, numerology, palmistry, astrology and the like are the most popular and the most widely known.  But they are also the least important, and the most discrediting to the modern critical scholarly and scientific mind.  Whatever their virtues, they do not represent the deepest, most useful and most empowering levels of Kabbalah.

Jewish meditation is as good as the Torah-quality of those exploring this path.  In the hands of serious, caring persons with a desire to learn more about themselves and about Torah and HaShem, this can be a very positive and effective path for personal and spiritual growth. But there is a limitation.  Meditation is naturally inward directed.  It helps the meditator directly, but it does not address worldly concerns directly.  When the meditator gains maturity, self-confidence, and a solid experiential spiritual center, they then can be more effective in the world.  But this is a secondary blessing, and it is a general situation that does not offer explicit pragmatic advice.  In other words, meditational Kabbalah practiced responsibly can be a very positive pursuit , but it is not all of Kabbalah and, by itself, it does not offer explicit real-world, problem solving insight.

The Kabbalah that empowers us in the real world is not only inner-directed (and/or God-directed, internally) but also outer-directed.  The so-called philosophical or theoretical Kabbalah can be extraordinarily practical in the real world.  This knowledge is carried not only in the personal meditational experiences of dedicated individuals, but also in the geometric precision of the "science of consciousness" that is really at the heart of Torah, Talmud, and Kabbalah.

The geometric aspect of Kabbalah has not been adequately explored _in our time_ and consequently it has not empowered us as it could.  But, just as geometry and mathematics have empowered the physical sciences, they also empower our Kabbalah and ourselves in turn.  Geometry is not (usually, for most people) a spiritual experience in itself, but it can provide a precise map for spiritual experience.  We know there is a holy mountain to climb.  This is the task of the meditator.  But we also know that even when we are well-trained, even when we have worthy companions, even when we have the sage advice of those who have gone before us, we still have a vital need for a precise map that shows where we are, were we are going and how to get there.  This map is in Torah, and it is explicated by Kabbalah.  We can continue to try to climb our holy mountains without a good map, and we can achieve real spiritual heights by doing this.  But without a good map, few can reach the highest levels, and then only by virtue of personal merit - which is not generally enough to take others without such merit along.

When we wish to make something objectively real so that others can see it, appreciate it, and use it, we need the precision of a good and true map.  When we have such a map, we can go forward with greater confidence and we can show each other how to go further yet.

Thus, in my opinion, it is time for us to study the Sod level of Torah and Kabbalah with new eyes, now, in our time, for the benefit of all.  This can be part of our personal tikkun (repair) and it can be a means by which we can speed along tikkun olam (repair of the world.)  Logically speaking, if we are not able to see how this could be so, it may be because we have not looked closely enough at the parts of Torah that hold the knowledge we need. Certainly Torah does provide us with guidance in dealing with the current situation. It is our job to find it.

Stan Tenen
Sharon, Mass.,
2 November 2000

© 2000 Stan Tenen / MERU Foundation

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