The Doubled Exile from Gan Eden (Addendum to The Tree, The Naming, and Eyzer k'negdo)

Genesis 3:22-24
22: Said Hashem-Elokim: Behold! Mankind has [become] like One Amongst Us*, knowing good and bad; now lest he send his out hand, and take also from the Tree of [knowledge of eternal] Life, and consume, living forever.
23: Thus, Hashem-Elokim sent them out, from the Garden of Eden; to work the soil from which he was taken from there.
24: He drove out Mankind; and he established, from Eastward to Gan Eden, the Keruvim, and the flaming overturning sword, to guard the way to the Tree of [knowledge of eternal] Life.

Why is the exile of Mankind from Gan Eden stated twice?

A close examination of the wording reveals an answer: The sending out in 3:23 is the sending out of an agent to accomplish a task - to work the soil.
However, we do not see Mankind then going out of the Garden of his own will and doing so!
I conjecture that in the 'original plan', Mankind was to be sent out to work the soil after having eaten of every tree, ending with the Tree of Knowledge, Good and Bad*.
Having jumped the gun, God gives them the option of beginning their mission, to prove themselves capable of not now subverting the mission.
By refusing the great charge, Mankind denies itself the only route to societal growth left available to it.
Thus, God has no choice but to banish Mankind from the Garden, lest he stagnate and 'consume living forever' - in other words, be only a devourer of the world, and not a builder thereof.
We had proven ourselves not able to be trusted with that power.

A primary consequence of the beginning of the success of the ongoing mission of Am Yisrael to be a light unto the nations is that Mankind regains the ability to safely reenter Gan Eden, and eat of its knowledge. This is why the Aron HaBrit is topped by two unarmed Keruvim, their wings arching towards each other - it is symbolic of those guards now granting Mankind entry, through an open gate!

* See The Tree, The Naming, and Eyzer k'negdo (http://toratmatematica.blogspot.com/2016/03/thefollowing-what-was-original-timeline.html)

A meaning of Shmini Atzeret - 22/7

What is symbolized by the juxtaposition of Shmini Atzeret and Succot?

For seven days, we dwell in nature. By night, we gaze upwards at the stars, the grandeur of the Universe that we can see with our own unaided eyes. By day, we see the plants and creatures, the beauty of Nature.

Through these, we gain an awe and closeness to God.

However, relationship predicated merely on blind, unknowing awe is as flimsy and weak as the booth we are dwelling in.

Therefor, on the Eighth Day, the 22nd Day of the 7th Month, the Pi Day of God - symbolizing the exact and perfect truth of Mathematics, the Language with which God wrote the Universe - and the vehicle by which we can see the Face of God.
Thus, we take the flimsy awe of Succot and place within it the structure built of Math, creating a firm and sturdy relationship, not of slave and master, not just of child and parent - but student and teacher.

May all of humanity merit to dwell in the House of the Lord, learning Mathematics and Torah together all of our days.

A Thought on Newton's Source for his Differentiation Notation

Consider Sir Isaac Newton's notation for derivatives[1]:

It occurred to me that Newton might have chosen this notation for the following reason:

Newton was an avid student of biblical studies and mysticism. He was fluent in Hebrew and Aramaic, and seems to have had at least passable knowledge of Arabic, based on that there are manuscripts with portions of the Rambam’s works, translated into Latin, by his own hand[2].

He produced a large body of works, containing his thoughts on a large number of matters, citing many familiar sources, such as Rashi and the ibn Ezra. From the selections discussed in footnote 2, he seems to have been familiar with Moreh Nevuchim, and professed a philosophy for himself very much along those lines.

Newton was therefore almost certainly familiar with the dot notation of the Tanach – that some letters are at some points written with dots over them, indicating that there is a secondary meaning, that word being also parsable with that letter deleted. I suspect that Newton might have found it pleasing to use that ancient notation for his own work.

I think that Newton might have found it particularly pleasing to do so, as in Moreh Nevuchim, the Rambam seems to be… uncomfortable with the mystical concepts that are associated with the planetary spheres in Aristotelian cosmology[3]. The painful need for the Rambam’s intellectual acrobatics around that is eliminated by Newton’s gravity and the consequences thereof[4].

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[1] https://en.wikipedia.org/wiki/Notation_for_differentiation#Newton.27s_notation

[2] http://moreshetsepharad.org/media/Newton_Mathematics_and_Esoteric_Knowledge.pdf

[3] Maimonides and the book that changed Judaism: secrets of The guide for the perplexed. [Micah Goodman].

[4] Although his largest difficulty would not be eliminated until Hubble and Einstein.

The Covenant of Wonders

A question that has drawn my attention for some time:

שמות לד:י

וַיֹּאמֶר, הִנֵּה אָנֹכִי כֹּרֵת בְּרִית, נֶגֶד כָּל-עַמְּךָ אֶעֱשֶׂה נִפְלָאֹת, אֲשֶׁר לֹא-נִבְרְאוּ בְכָל-הָאָרֶץ וּבְכָל-הַגּוֹיִם; וְרָאָה כָל-הָעָם אֲשֶׁר-אַתָּה בְקִרְבּוֹ אֶת-מַעֲשֵׂה יְהוָה, כִּי-נוֹרָא הוּא, אֲשֶׁר אֲנִי, עֹשֶׂה עִמָּךְ

Sh’mot (Exodus) 34:10

[Translation, initial understanding]:

He [God] said: “Behold, I, enact a covenant: in the presence of your entire nation: I will make wonders that were never created[1] in all the lands, nor in any of the peoples – It will see, the entire nation -  that you [Moshe] are amongst, the makings of God - for He is Incredible – that I do for you.

What bothered me was this: Covenants, both in the world at large as well as those between God and Israel, always have some obligations on each party, or at least a symbolic gesture to ratify the agreement. It is exceedingly odd for there to be a covenant unilateral in both ratification and clause.

I came across some statements of the Rambam in Moreh Nevuchim[2] wherein he comments on the two requests Moshe makes of God earlier on in their discussion[3]:

"Make know to me Your Ways"                                                        אֶת-דְּרָכֶךָ הוֹדִעֵנִי נָא              

"Show me Your Glory"                                                                        הַרְאֵנִי נָא אֶת-כְּבֹדֶךָ

The Rambam states that the former statement is a request to understand Nature, the physical universe (i.e. laws of physics), and the latter is a request to ascend to understand God’s perception and reasoning for the Universe in its entirety, which the Rambam understands to be equivalent to being God (or at least not being a possibility without being Him in the first place).

In response to the latter request, God tells Moshe that he cannot do so – which makes perfect sense to we who understand the vastness of the cosmos – to see in the greatest detail the state of the entire universe, Moshe would need a brain with at least the number of particles in the universe – he literally cannot do this thing and exist in the universe as he is! Given this, an argument could be advanced that the issue with the request of Moshe is not that there is a theological issue, but a practical physical impossibility.

To the former – the Rambam states that God granted his request. But, according to the Rambam: Where does God give over this knowledge? Why does Moshe not teach it? Why did the Industrial Revolution, the age of Science, not start from that moment?

 This can be answered by understanding the Pasuk in a different way:

He [God] said: “Behold, I, enact a covenant: in the presence of your entire nation: I will do wonders that were never created in all the lands, nor in any of the peoples –  all the people[s] will see- that you [The Nation of Israel, singular denoting unity] are amongst, the doings of God - for He is Incredible – that I do with you [The Nation of Israel].

עִמָּךְ is not ‘for you’, it is ‘with you’! That single word changes the entire covenant! This covenant is a promise that God will do these things with us – that we, the Nation of Israel, will have the privilege of being amongst the forefront of humanity as we build the glorious future by the light of our minds, by the skill of our hands – and we will feel the touch of the hand of God on our works. This is a covenant we have merited to see fulfilled for the first time - that we continue to fulfill - in the last centuries!

Thus, this is a promise from God to his beloved Nation of Israel, that whenever they accept upon themselves the Great Mission to delve into the workings of universe, to perceive its beauty, to give names to its components – God will be with them, delighting in the discoveries of His Children[4] – and that by these discoveries, humanity will attain the capacity to create new wonders[5], in full realization of our Tzelem Elokim.

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[1] It is very interesting to note that the root ברא, here translated as ‘create’ always denotes a truly new or unique creation (ex nihilo). A promise of such in the future is a very big deal, especially in light of the first-order understandings of ‘nothing new under the sun’.

[2]Moreh Nevuchim, 1:54, as explained in Maimonides and the Book that Changed Judaism, by Micah Goodman.

[3] Fragments of Sh’mot: 33:13 and 33:18, respectively.

[4] See “The Tree, The Naming, and Eyzer k’negdo”

[5] Including a way around the Big Whimper, I hope.

The Tree, The Naming, and Eyzer k'negdo

            Consider the following: What was the original timeline God intended for Mankind? In other words, had Adam and Chava not acted incorrectly with regard to the Tree of Knowledge of Good and Evil-“ עֵץ הַדַּעַת טוֹב וָרָע”, what was supposed to happen next? Note that this question holds whether one understands this section to be partly or wholly allegorical. For example, Adam can be read as either a historical person, or as the archetype of Mankind (which is at least somewhat supported by Adam being called “the Adam” throughout).

            First, let us consider the possible meaning of the ancient-Hebrew phrase. It could be better translated (including an attempt to reorder constructs into their equivalent English forms) as Knowledge-Tree that is Good and Bad. It is important to note that “רָע” can mean negative utility as opposed to literal evil. Similarly, “טוֹב” can mean the non-moral-spectrum good. Additionally, the conjunctive “ו” is often used for or as well as and in the Torah. One could also read this, using brackets to indicate application of adjectives, as the Tree of [Knowledge that is (Good or Bad)]. Note that “דַּעַת” means specifically experiential knowledge.

Question: What is this? What experiential knowledge is gained by eating the fruit of this tree?

            Second, let us consider the first command given from God to Adam:

1.      2:16-17

a.       טז וַיְצַו יְהוָה אֱלֹהִים, עַל-הָאָדָם לֵאמֹר:  מִכֹּל עֵץ-הַגָּן, אָכֹל תֹּאכֵל.  יז וּמֵעֵץ, הַדַּעַת טוֹב וָרָע--לֹא תֹאכַל, מִמֶּנּוּ:  כִּי, בְּיוֹם אֲכָלְךָ מִמֶּנּוּ--מוֹת תָּמוּת.

b.      16: God [duplex name, mercy & judgment together] commanded, upon-Adam saying: “From all the trees-of-the-garden, you MUST eat. 17: “And from the Tree of Knowledge that is Good and/or Bad: do not eat, from it; as on that day of your eating from it; you WILL die.

A brief digression to ensure we are all on the same page: The notes according to which the Torah is chanted when it is read in public serve a practical purpose: punctuation. Various notes are either disjunctive or conjunctive to varying strengths (for example, consider the difference between a comma, apostrophe, and parentheses Very often, much information can be unpacked by paying close attention to oddly placed punctuation that might not be apparent from standard translations.

The Ri haKadosh, in the Shem Shel Shmuel, claims that based on this punctuation of these verses, which I have attempted to preserve in my above translation, the prohibition of eating from the Tree of Knowledge only applied on exactly that day.

Additionally, the word ‘וַיְצַו’ is understood to be used to indicate a command of God that is applicable for all generations[1].

Question: Why would it only apply to that day? Why is there an implication that this commandment is directed at all of humanity, for all time?

Thirdly, immediately following the above:

יח וַיֹּאמֶר יְהוָה אֱלֹהִים, לֹא-טוֹב הֱיוֹת הָאָדָם לְבַדּוֹ; אֶעֱשֶׂה-לּוֹ עֵזֶר, כְּנֶגְדּוֹ.  יט וַיִּצֶר יְהוָה אֱלֹהִים מִן-הָאֲדָמָה, כָּל-חַיַּת הַשָּׂדֶה וְאֵת כָּל-עוֹף הַשָּׁמַיִם, וַיָּבֵא אֶל-הָאָדָם, לִרְאוֹת מַה-יִּקְרָא-לוֹ; וְכֹל אֲשֶׁר יִקְרָא-לוֹ הָאָדָם נֶפֶשׁ חַיָּה, הוּא שְׁמוֹ.  כ וַיִּקְרָא הָאָדָם שֵׁמוֹת, לְכָל-הַבְּהֵמָה וּלְעוֹף הַשָּׁמַיִם, וּלְכֹל, חַיַּת הַשָּׂדֶה; וּלְאָדָם, לֹא-מָצָא עֵזֶר כְּנֶגְדּוֹ.  .

18: Said God[name of mercy-name of judgment]: It is not good for the Adam to be by/for himself; I will make for him a compatriot-in-task, as his counterpart. 19: Formed God[name of mercy-name of judgment] from the earth/soil: all the wild animals of the field and all the birds of the skies; and He brought them to-the-Adam, to see what he would call them; and all-that-was-called-to [by] the Adam; living beings – that was its name. [line break] 20: Named the-Man names, to-all-the-animals and the birds of the skies, and-to-all, the wild animals of the field; but [lit. and] the Man did not find a compatriot-in-task, as his counterpart.

            Question: What is the purpose of the naming of the animals? Why does it interrupt the narrative of Chava’s creation?         

            Perhaps, the original – and ongoing – mission of Mankind is encapsulated by this naming –exploring the Universe, seeing its beauty and wonder, and naming its structures and all the creatures that dwell within them. Why? God created us in his image – “בְּצַלְמוֹ”. The Rambam states in his Guide for the Perplexed that צלם means the essence of the being, the essential properties that make the being what it is. According to the Rambam, God created us to ourselves be creators – our mission is to join Him in creating Creation. Consider: God names exactly five things – Day, Night, Heavens, Land, and Sea. Everything else was left for the Adam, and his descendants, to name – and God tells us: “everything the Adam named – that was its name” God approved[2].

            But, the Adam, aware of the immensity of the task, despairs – how can he, but one man, in one small lifetime, name all things, see all sights, explore an entire Universe? This is why he now searches for a partner, a mate – he realizes that this is not a task he can accomplish alone.

            Finally, I conjecture that the other trees of the Garden of Eden, which Adam was commanded in the strongest terms to eat of, are trees of various other knowledges – the Tree of Knowledge [that is] Good & Bad is representative of the knowledge that Mankind, and each individual, needs maturity to wield without causing great harm[3]. The other trees of the Garden represent those things that Mankind can learn without danger – and those that must be internalized prior to ingesting the knowledge that could destroy Mankind– or his world.

The entire Garden of Eden is thus not be merely written and passed to us a tale of an error of our distant ancestors, but as an eternal warning to their descendants - us -  a warning we today understand all too well. Today, never before has our mission been so firmly within grasp – and never before have we been so able to destroy it. We can build the future God desires for His children, so long as we do not drive ourselves out once again.

May we act with these in mind always, and build eternally amongst the stars.

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[1] Talmud Bavli, Daf 29A.

[2] I would like to thank and give credit to David Brin, in whose novel Earth the original formulation of this idea appears (If you enjoy this blog, you will very likely enjoy his novels).

[3] Prime Directive from the Torah!

On conceptualizing the degree of the Presence of God

With regard to the shechina - the "Divine Presence of God, I have noticed that some grapple with the concept of how God can be more or less present in a given place or time.

A scalar field is a function that assigns a value to every point in space. One way to picture an approximation of this is to imagine a three dimensional grid overlaying the scene in your mind's eye, and place a small LED at each juncture of the lines of the grid. The larger values of the function can be indicated by a brighter light.

To extend this visualization to the shechina, one can identify the degree of the presence of God with the intensity of the light in the above visualization.

However, I have not discerned a satisfactory interpretation of this model with regard to the underlying theological question - of what God being more or less present means - or if it a thing entirely internal, not having an existence in our Universe at all.

Axioms of Torah

Within Judaism, there are matters of belief and practice. For each smallest question, there tend to be many, many answers. However, there are some statements that can be whittled down to the point that there exists only one formulation that is consistent with Judaism - if that statement is rejected, then the whole system fails (such as the 'exactly one God exists' - any negation of that statement is not consistent with Judaism). However, there are other statements on which there exist multiple 'kosher' positions (almost any detail of almost any thing... although some would disagree).

Similarly, as Rav Kook notes in his discussion of Science & Torah, in particular in I:134 of אגרות הראיה (the 2nd of a series of three on this subject) - The Rambam sets out a relatable dichotomy - that Tanach includes language (i.e. metaphors such as 'the hand of God') and laws that are not 'intrinsic' to the nature of God, or the Godly state to which we strive. Rather, these things are included because they are necessary to achieve God's goals - we, mankind, need these things both to uplift ourselves to the level to enact those goals, as well as to be vehicles to deliver these concepts into our minds as they are.

We can imagine alternate scenarios, histories that might have been, where God would have communicated some things differently, and some things different. For example, if our species had come to be with four arms instead of two, or a secondary heart located elsewhere in our bodies, the verses describing the mitzvah of Tefi would have had some differences, to accommodate that different physiology. Had Avraham said "Sarah is my wife" rather than "Sarah is my sister", events might have played our very similarly, other than the details of the words, and perhaps a Divine intervention to save Avraham rather than protect Sarah.


One way to conceptualize this (the difference between 'Truths that must be so' and 'Truths that could be otherwise') is to relate it to undecidable statements in mathematics. For simplicity, I will assume that any particular gestalt of one's position on every matter is reducible to a self-consistent set of axioms.

Then, consider the axioms of Euclid's Elements:

1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. Given a line, and a point not on that line, exactly one parallel line exists that intersects that point.

For the first four axioms, if you try to build a framework where one is not true - it does not work, the logic falls apart.

For example, you could change axiom 1 to give two unique lines for every pair of points - this is kind of like saying that 2+2=4, but also that 2+2 = 'other 4', and furthermore, 4 does not equal 'other 4' - neither arithmetic nor algebra can function, as you lose one of the most fundamental properties of all - that a thing is equal to itself!

The fifth axiom (It is often referred to as a 'postulate', for reasons which might interest those who enjoy knowing the history of these things) has alternate formulations that are different - each one contradicts the others, yet each generates its own world.

The Parallel Postulate of Euclid can be true - and you end up with 'regular' straight-line-grid, Euclidean geometry. It is true, and Spartanly elegant.

But - you can also reject it.

You can construct a Geometry (a world-measuring from the original Greek, after all) in which no such point exists - and you have the system of geometry of the surface of a sphere - such as the one on which we live*.

You can declare that there exists no limit to the number of lines which can be drawn through that point - and you have hyperbolic geometry (which is rather harder to simply describe).

Each choice yield a different, and true totality - and the existence of each version does not make the others untrue - they are merely describing different things that share much of their underlying nature (they do share 4 axioms out of five, after all).

Similarly, Judaism has statements which are ironclad, absolute. It also has statements which have many possible iterations - each one true, and each not inimical to the others. And - to only ever have but one of those many is too great a tragedy to bear.

*An oblate spheroid, if you wish to be very מדקדק.