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Q: for mathtalk-ga ( Answered 5 out of 5 stars,   0 Comments )
Subject: for mathtalk-ga
Category: Miscellaneous
Asked by: timespacette-ga
List Price: $5.00
Posted: 28 Nov 2004 21:05 PST
Expires: 28 Dec 2004 21:05 PST
Question ID: 435367
sorry, I cancelled that Tower of Babel question, but you were very
helpful in leading me to my own answer (haven't gotten there yet, but
I have a tome of reading to do!)

would you please post your findings here and collect the fee for your effort?

Request for Question Clarification by mathtalk-ga on 20 Dec 2004 15:16 PST
Hi, timespacette-ga:

Still wording my response, but meantime I discovered a marvelous link
to a short-short story by Jorge Luis Borges:

[Library of Babel]

regards, mathtalk-ga

Clarification of Question by timespacette-ga on 20 Dec 2004 20:09 PST
thanks for the link

take your time

it's Christmas


Subject: Re: for mathtalk-ga
Answered By: mathtalk-ga on 28 Dec 2004 20:24 PST
Rated:5 out of 5 stars
Hi, timespacette-ga:

At first I was caught up in trying to catch sight of philosopher Alain
Badiou's intent behind his curious remark, striking enough to have
been quoted already by several others on the Web.  For example:

[Lost in translation: an idea of world society and the subject it presupposes]

?Every name from which a truth proceeds is a name from before
the Tower of Babel. But it has to circulate in the tower?.
Alain Badiou, Saint Paul: The Foundation of Universalism, pg. 110

Your question, though, asked about mystical interpretations of the
Tower of Babel.  It isn't clear that Alain Badiou would qualify as a
mystic.  Certainly he is not a Jewish, Christian, or Islamic mystic. 
Maybe we could stretch definitions and consider him as an Hegelian

But since you've given me free rein, I decided to take a broader, more
personal approach.  And personally I prefer the mysticism that is
rooted in the mundane, like the observation that we and all earthly
creatures are composed of stardust.

*  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *

Let's begin with the Scriptural account in the first nine verses of
Genesis chapter 11.  This passage is generally credited to J, the
oldest discernable source in the Pentateuch or Torah, dating to about
950 BCE (around the time of King Solomon).

The Book of J, written by literary critic Harold Bloom and translator
David Rosenberg, forcefully exposes the word play and irony in the J
material, and nowhere better than in the Tower of Babel story:

  Now listen: all the earth uses one tongue, one and                1
  the same words.  Watch: they journey from the east,               2
  arrive at a valley in the land of Sumer, settle there.

  "We can bring ourselves together," they said, "like               3
  stone on stone, use brick for stone: bake it until
  hard."  For mortar they heated bitumen.

  "If we bring ourselves together," they said, "we can              4
  build a city and a tower, its top touching the sky -- to
  arrive at fame.  Without a name we're unbound, scattered
  over the face of the earth."

  Yahweh came down to watch the city and tower the                  5
  sons of man were bound to build.  "They are one                   6
  people, with the same tongue," said Yahweh.  "They
  conceive this between them, and it leads up until no
  boundary exists to what they will touch.  Between us,             7
  let's descend, baffle their tongue until each is scatter-
  brain to his friend."

  From there Yahweh scattered them over the whole                   8
  face of earth; the city there came unbound.

  That is why they named the place Bavel: their                     9
  tongues were baffled there by Yahweh.  Scattered by
  Yahweh from there, they arrived at the ends of the

  (trans. by David Rosenberg)

Other translations of this passage 

The more familiar translation of the King James Authorized Version may
be found in this Wikipedia article, together with discussion and other
links of interest:

[Tower of Babel -- Wikipedia]

Without dwelling on the predictable irony, this next site, dedicated
to various writing systems, uses the Tower of Babel story found in
Gen. 11:1-9 to illustrate their capabilities in dozens of languages:

[Tower of Babel in Hebrew]

[Tower of Babel in English]

The latter has five versions, ranging from the Middle English of
Wycliffe (1395) to the modern English Standard Version (2002).

Notes about the passage

1.  The designation J for the theoretical Biblical source connected
not only with the Tower of Babel story, but with much other narrative
material extending well beyond the Penteteuch, comes from the German
"Jahve" version of the sacred name of God.  This source distinctively
uses that name in passages preceding the encounter between Moses and
the burning bush where that name is revealed to him.  The basic
analysis of the Penteteuch in terms of sources J, E, D, and P (plus
efforts of a Redactor to smoothly combine these materials) reached a
mature form called the Documentary Theory by Julius Wellhausen, a
German scholar who published Prolegomena zur Geschichte Israels
(Prolegomena to the History of Israel) in 1886.  These were
developments of ideas first presented by French physician Jean Astruc
more than one hundred years earlier and expanded by several German
scholars before Wellhausen.

[The Origin of the Biblical Materials]

[For the Law was given by Moses... ?]

2.  The city of Babylon or Babel is mentioned in the previous chapter
(Genesis 10:10) in connection with the beginning of the kingdom of
"Nimrod the mighty hunter before the LORD" (Genesis 10:9).  Genesis 10
("after the flood") is held by the Documentary Theory to combine text
from sources J and P, which may account for two differing accounts of
the founding of Babel.  However there exists a work of uncertain
provenance, the so-called Book of Yasher, which connects (inter alia)
the terrorizing reign of Nimrod with the birth of Abraham and the
building of the Tower of Babel with a war against heaven.

[The Book of Yasher]

[An Overview of the Book of Jasher]

3.  God's judgement upon the builders is pronounced after "descending"
(in the company of a heavenly host?) to inspect the city and tower, a
procedure which harkens back to the Garden of Eden story.  But a more
mundane set of details, the bricks and bitumen used to bind them,
foreshadow the story of Moses in the reed basket and the Hebrews
forced to make bricks without straw in Egypt.  Bitumen was indeed an
available natural resource in Mesopotamia:

[Hacinebi Excavations: Selected Local Late Chalcolithic Artifacts]

[Tell Sabi Abyad - Archaeology in Syria - Research]

[Sources of mummy bitumen in ancient Egypt and Palestine]

(more to come)

Request for Answer Clarification by timespacette-ga on 29 Dec 2004 10:12 PST

this is already beyond the call of duty

but I will keep watching and rate and tip when you're done


Clarification of Answer by mathtalk-ga on 02 Apr 2005 17:58 PST
Hi, timespacette-ga:

While looking for references to complement my "personal"
interpretation, I was led to this page which links a few "scholarly"
as well as "artistic" images of the Tower of Babel:

[Tower of Babel Gallery]

One point to be made, in connection with Alain Badiou's quote, is that
the reality behind the "tower" architectures of that era apparently
lacked much in the way of interior space, like step pyramids and
related ancient buildings.

Images of the "tower" in the Tarot and later in art such as Brueghel's
show a potential for complex interior spaces never realized in
neolithic constructions.

Hence literally "to circulate in the tower" seems anachronistic.

regards, mathtalk-ga

Clarification of Answer by mathtalk-ga on 30 Dec 2006 18:19 PST
Some final thoughts!

As a mathematician it is natural to interpret the building of a tower
"touching the sky" as emblematic of the finite striving to attain the
infinite, a theme already evoked in the Garden of Eden when the
Serpent says that eating of the Tree of Knowledge of Good and Evil
will not cause Death, and subsequently God fears that Adam and Eve
will eat as well from the Tree of Life and live forever.

[Garden of Eden -- Wikipedia]

Comparing modern science's Big Bang theory with the Creation accounts
in Genesis, it is striking that all concur on the definite beginning
of time and the potential extension of time without end.

[Ultimate fate of the universe -- Wikipedia]

How can we finite creatures apprehend this infinite extent?  A
seemingly simple model of this is found in counting, which begins with
the number one (or zero, arguably) and continues without end.  Indeed
our word "infinite" comes from a Latin root meaning limitless or quite
literally "no end".

[Infinity -- Wikipedia]

Likewise the Tower of Babel has a definite beginning but remains an
unfinished work.  Yet philosophers have struggled with
self-contradictory implications of infinity, from the ancient Greek
Zeno's paradoxes to the antinomies of Kant.

Bertrand Russell (1910) has been quoted (by Santayana et al) as
saying, "The solution of the difficulties which formerly surrounded
the mathematical infinite is probably the greatest achievement of
which our age has to boast."  While the claim may have been premature,
it is indicative of the true progress made by the development of
mathematical logic.  Old paradoxes have been tamed, yet remain a
source of interest, and even mystery.

[The Philosophical Importance of Mathematical Logic -- B. Russell(1911)]

"To sum up, we have seen, in the first place, that mathematical logic
has resolved the problems of infinity and continuity, and that it has
made possible a solid philosophy of space, time, and motion."

Yet there was another shoe to fall in this connection.  Having neatly
reduced the problematic character of the continuity of points on a
line and other notions of "advanced" mathematical analysis to "simple"
matters of arithmetic, it remained for Godel to illuminate the
extralogical character of our belief in the consistency of arithmetic.

Kurt Gödel in 1931 (as tweaked by J.B. Rosser in 1936) proved that a
widely accepted formal axiomatization of arithmetic is only capable of
proving the consistency of arithmetic (ie. of itself as expressed as a
formal theory in mathematical logic) if in fact it (arithmetic) is
inconsistent.  Moreover this inability to prove self-consistency is
inherited by every logically consistent formal extension of the
theory; the "deficiency" cannot be cured!

[Gödel's incompleteness theorems -- Wikipedia]'s_incompleteness_theorem

Yet we "see" that the counting numbers are a model of this formal
theory, and therefore arithmetic must be consistent.  Such a result
says (to me) that our belief in the certainty of arithmetic has an
extralogical or "faith-based" component.

*  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *

To close I would like to reflect, with the benefit of hindsight, on
some of these issues in connection with the words and ministry of

Clarification of Answer by mathtalk-ga on 30 Dec 2006 20:33 PST
1. The Parable of the Good Samaritan

A nice sermon on this well-known parable, utilizing another
architectural device, is here:

[The Labyrinth - A Place of Healing (Rev. Nancy Bloomer, Ph.D)]

The parable's context is a Question asked by "an expert in the law...
to test Jesus" in those days before Google Answers:

"Who is my neighbor?" Luke 10:29b

Under Mosaic Law one has an obligation to "Love your neighbor as
yourself" (Lev. 19:18), as the lawyer cites.

The legal mind (if we may for convenience so label matters) expects
there to be somehow an absolute delineation between those who are my
neighbors and those who are not.

A similar expectation frustrates our comprehending the continuity of
space and time.  Of all points on the real line, what pair truly lie
next to each other?  Yet the real line as a whole seems obviously
connected.  How is this?

The proper resolution of this puzzle requires overturning any
legalistic/absolutist concept of neighbor, a lesson amply drawn out by
Rev. Bloomer's sermon above.

Jesus turned the lawyer's question around, from the narrow whom am "I"
neighbor to, to whom (among the priest, Levite, and Samaritan) was a
neighbor to "me" under a circumstance of great need.

Likewise the mathematical concepts of "neighborhood" and "continuity"
capitalize on a relativized notion (that some points are nearer than
others) by asking if, whatever the need is (given epsilon > 0), is
there a nonempty pool (delta > 0) that avails the need?

The real line is connected, despite no two points being "next to" each
other, because no matter how the real line is divided into two
nonempty subsets, and no matter what distance epsilon > 0 is chosen,
inevitably there are pairs of points, one from each subset, that are
closer than epsilon to one another.

Clarification of Answer by mathtalk-ga on 30 Dec 2006 21:54 PST
2.  Curse of Babel, reversed at Pentecost

Jumping around a bit, let's look quickly at the passage in Acts 2:1-21
reporting a striking manifestation of the Spirit of God.

[Pentecost: Babel Reversed (Rev. Adrian Dieleman)]

Where mankind was scattered to the ends of the earth and hampered by a
multiplicity of languages at Babel, here people from many nations are
gathered together and understand the speech of Galileans as if in "our
own tongue, wherein we were born".

Where those at Babel proposed to make a name for themselves, to
"arrive at fame", in Acts 2:21 " shall come to pass, that
whosoever shall call on the name of the Lord shall be saved."
timespacette-ga rated this answer:5 out of 5 stars
hi mathtalk!

I took a quick look here; recently had a vivid dream about one of
those towers . . .

I'm way busy these days, so not in research mode, but enjoyed this link.

Hey, there's a book you might enjoy:  Maps of Meaning; the
architecture of belief . . .  by Jordan Peterson, at

best to you


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