Table of Contents

The ברכה of Listening

את הברכה, אשר תשמעו אל מצות ה’ אלקיכם אשר אנכי מצוה אתכם היום

as for the ברכה; which you shall listen to the Mitzvos of G-d your Almighty, which I [G-d] command you today.[i]

Considering the various blessing enthusiastically expounded upon throughout the Torah, this verse, which should be providing the contrast between the blessings and curses (which Moshe states in the verse before and after) seems to be strange. The verse should have stated that the blessings will be provided, on condition to listening to G-d Almighty’s Mitzvos.

Rashi too seems to anticipate this question and accordingly inserts the grammar of על מנת אשר תשמעו – that this is conditional on listening.

However, this still leaves us with the question: what exactly is the blessing we are comparing to the curses. Why doesn’t the Torah explain what it is, once we listen of course. And why doesn’t Rashi explain why the Torah doesn’t explain the blessings.

The Definition of a ברכה

On explaining the formula of a ברכה, the Zohar[ii] defines the initial word ברוך as follows:

ברוך: דא רזא דמקורא עלאה מכלא לארקא ולאמשכא ולאנהרא כל בוצינין. ואיהו ברוך תדיר שלא פסקין מימוי. ומתמן שירותא דאקרי עלמא דאתי. ואיהו קצה השמים דההוא קצה קצה עלאה איהו. בגין דאית קצה כגוונא דא לתתא, ואיהו עלמא תתאה – ואקרי אוף הכי ברוך, לקבל תתאי, לארקא לתתא ולאתערא מתתא לעילא בברכאן דצלותא. וברוך דא אקרי הכא ברזא דחכמתא עלאה, דאמלי לההוא אתר, בחד שביל דקיק דאעיל ביה.

Blessed: This is the secret of the source above all, to drip, and to draw down, and to illuminate all the torches. And it is always blessed, whose waters do not cease. And from there is the beginning of that which is called ‘the World to Come’. And it is the end of heaven, which end is the upper end. For there is a corresponding end like this below, which is ‘the Lower World’. And it is also called ‘blessed’; to receive below, to ground below, and to awaken from below to above with the blessings of prayer. And this ברוך is called forth here, in the secret of the highest wisdom, which fills that place, in the single slight path by which it ascends.

Rabbi Levi Yitzĉok Schneerson quotes ברוך דא רזא דמקורא עלאה מכלא לארקא ולאמשכא ולאנהרא כל בוצינין and writes as follows:

The three (3) terms:

לארקא – to drip

לאמשכא – to draw [down]

לאנהרא – to enlighten

We can say because ברוך, which is רזא דמקורא עלאה – the secret of the source above, which is יסוד אבא; [the Sefira of] חכמה [is represented by the letter] י of the [tetragrammaton] name [of G-d], which has in it three (3) concepts, which are the three (3) letters יו”ד.[1]

י – point

ו – line

ד – plane[2]

And [the three (3) letters יו”ד] also hint to [the three (3) intellectual Sefiros, whose acronym is] חב”ד, because [the intellect of] חכמה includes בינה and דעת also.

י – חכמה

ו – דעת

ד – בינה

This is [the meaning of the three (3) terms used by the Zohar]:

לארכא –            from the י

ולאמשכא –        from the ו, because [the letter] ו is the drawing down

ולאנהרא –         from the ד, because the illumination of light is in a spread-out fashion, which is a plane[3].

Mathematical Descriptions of the Dimensions

To begin to understand this statement, we have to review fundamental spatial mathematics and then the concept of a ברכה. In doing so, we can retrace the teaching of Rabbi Schneerson; taking us from basic geometry all the way to the theology of how a blessing changes spacetime.

The Classic Spatial Dimensions

In defining a dimension, we first have to explain what is meant by the term. A “dimension” is that aspect of something which can be measured. In a physical world, dimensions are the physical directions you can move through, or “degrees of freedom.”

1D (The Line): Imagine a universe that is just a taut thread. You only have one degree of freedom: to move along the line from one point to the next. We call this length. The math here is strictly linear. To measure the distance between two points ( and ), you just find the absolute difference: .
2D (The Plane): We introduce a second degree of freedom, but it must be mathematically independent of the first. In this case, instead of existing solely within the first dimension – the ability to move along the line – now we have the ability to exit that line and move differently. To ensure the measurement of this movement is truly independent of the initial line, we measure it by adding an axis at a perfect 90-degree angle from the original line. Now, you can move left/right or up/down as well as forward/backward. The math for is upgraded to the Pythagorean theorem to calculate diagonal distances across a flat plane: .
3D (The Cube): We add a third 90-degree angle, unlocking volume and depth. If we consider that one can start movement on any point of any line, we are left with six directions: Forward/Backward, Right/Left, Up/Down.

The Challenge of the Singularity

However, in considering this fundamental math, there’s an observed phenomenon theorized to exist in a manner different than any of these dimensions: How does this classic math handle a black hole? Seemingly, a black hole is something that is compressed to a theoretical point, and thus there should be no conceptual ability to measure from within the black hole in any direction[4]. Seemingly, the only point of measurement that matters for the singularity within the black hole is a binary measurement: yes/no – does it exist or does it not.

If a black hole is an “on/off” existence where distance from one side to the other is meaningless, is it 1D?

No, because in 1D, distance is the only measurement that exists. To find a state where distance is mathematically meaningless, we have to subtract length entirely and drop to 0D.

The Zero Dimension

Still speaking of dimensions as being determined by their measurements; the 0D means it has no measurements. A 0D point has neither length, width, nor height. This mathematically describes the singularity at the center of a black hole: a coordinate where all mass is crushed into zero volume, and the existing mathematical formulas for distance completely break down.

The Measurement Paradox (Interior vs. Exterior)

This brings us to a crucial question: How can a 0D singularity, which has no space, exist inside our 3D space? Meaning, we have just defined a 0D as having no measurement whatsoever, and yet, to us observing it, there certainly is a measurement. Perhaps one which is warped as compared to other observable phenomena, but certainly something that can be measured. If it truly was 0D, then there should no coordinates in our universe in which a black hole could exist.

To resolve this, we need to identify who is doing the measuring:

The Interior (Intrinsic) Perspective: Measuring from within. If you were trapped inside a 0D singularity, you would have zero degrees of freedom. There is no left, right, up, or down.
The Exterior (Extrinsic) Perspective: Measuring from the outside. Because we are 3D observers, we can point to that 0D singularity and assign it an coordinate in our larger universe.

This realization – that dimensional definitions change depending on whether you are inside the system or looking down on it from the outside – is the key that unlocks the final stage of our thought experiment.

The Creator’s Perspective

When considering the universe from within it – from the created human’s perspective, there comes a point past which we cannot pass. A 0D point behind which we cannot measure, because our measurements are limited to that which is inside the system. However, what if we were to consider the ultimate Exterior Perspective? Imagine measuring existence from the viewpoint of an infinite Creator looking at the universe. A being beyond the concepts of space and dimensions, but one who created these dimensions. If we strip away physical “space” entirely, what do the mathematical dimensions actually represent from that perspective?

1D: Existence (The Spark)

From the exterior, the existence of 1D is not a line on a map; it is the sheer persistence of existence. It is the ex nihilo moment – flipping creation “on” from out of nothing – יש מאין. If a single entity exists, its continuous presence draws a 1D “Worldline.” The math of 1D simply states: Be.

2D: The Ability to Change

Having established a creation out of nothing while not having defined it other than as a created thing, “Be”; the concept of “physical space” is a meaningless concept, because there is nothing to measure distance against. One cannot measure distance from G-d, as a Creator is not within the framework of existence. So, the second dimension becomes Cause and Effect.

1D: Axis 1: The State of the Entity (Exists or not).
2D: Axis 2: The Sequence (Before and After).

From the exterior perspective, 2D math creates something called a Phase Space – a directed graph where the creation can “move” /grow/change in relationship to its previous state. It provides the mathematical engine for growth and time, for time fundamentally is the framework of before and after. In Ĉassidus and Kabbalah, this idea is called סדר זמנים – the ordering of times.

3D: Multiplicity and Interaction

Finally, we introduce a multiplicity from the single unity of creation. If two entities are going to exist, change, and interact with each other without simply crashing into each other on a flat 2D timeline – in other words, if things / entities can grow and change at different rates and in different ways, then the math requires a new degree of freedom.

3D: the mathematical space required for multiplicity. It allows independent worldlines and histories to weave around one another, form relationships, and build a complex universe.

Conclusion: dimensions are not just physical directions. When viewed from the ultimate exterior perspective, 1D is the math of existence, 2D is the math of causality, and 3D is the math of relationship – a סדר השתלשלות.

Kabbalistic Orthography and Topological Mathematics

While the math helps us understand the progression of creation moment by moment, since Torah is the blueprint by which creation is designed, we have to have a source in Torah in order for such concepts to exist. The Yerushalmi[iii] fascinatingly explains that this is derived from the verse[iv] כי בי-ה ה’ צור עולמים – for in י-ה, G-d, the Rock of the Worlds – G-d created the world using a י for the “World to Come”, the spiritual worlds, and a ה for “this World”.

If the letter י, which is consistently presented and understood as being a single point, a singularity of a letter, is what creates the world, then, the world should be a world of 0D – no dimensions, no change, no points of reference. How then can we reconcile the lived experience with the blueprint of creation.

Rabbi Levi Yitzĉok explains that within the singularity of י existence, which truly is an on/off experience, there is also built in the phonetic properties of the spelled-out letter, which expands the point of existence into the spiritual source for the next letter, the ה which creates our physical world. The single point of the letter י inherently contains the line (ו) and the plane (ד) the moment it is vocalized and spelled out as a word (יו”ד).

Mathematically, this represents a topological truth: the 0D singularity intrinsically holds the complete blueprint for the 1D line and the 2D plane within its very definition. When the Creator speaks the “Point” into existence, the phonetic expansion dictates that it must immediately draw down into a “Line” and spread out into a “Plane.”

Here is how the mathematical blueprint of existence mirrors the text:

0D: the י Singularity – לארקא to Drip

In our mathematical model, world-building begins with the 0D point – a singularity of pure potential with no dimensional extension, where G-d tells existence “Be”. This is connected to the י aspect of the spelled-out letter, where the letter י is geometrically written as a single, suspended dot.

The Zohar connects this state of existence to לארקא – to drip[v], as in the line of the קו וחוט that extends from the infinite into creation, starting with a single drop dripping. Theologically, this maps to חכמה – the initial, dimensionless flash of insight ex nihilo before it has been processed or expanded. It is the absolute origin, the mathematical 0 converting to 1 from which everything else will flow.

1D: the ו Wordline – לאמשכא to Draw from Place to Place

Our model established that 1D takes that static 0D point and gives it persistence, not just on and off, but a before/after, creating a causal sequence or Worldline. Reb Levik maps this to the letter ו, which is geometrically a single vertical line. Zohar uses the term ולאמשכא to draw across / down. To draw something from one point to the next is to create a vector—to take the isolated point of existence and extend it in a sequence of cause and effect.

Fascinatingly, in Hebrew grammar, the letter ו serves as the conjunction “and.” It is the ultimate 1D causal link, connecting what came before with what comes after.

2D: the ד Manifold – לאנהרא to Illuminate

Having established the source for change and growth, now comes a second, independent axis (Linear Independence) to create a 2D plane – the Phase Space where multiple variables can interact, grow, and spread out.

Reb Levik writes that the Zohar identifies this with the letter ד. It should be noted; the orthography of the letter ד consists of a vertical and a horizontal stroke – an X and Y axis. Critically, it also includes a י sticking out of the back of the top of the letter – the connection point to that which comes before. The plane is not independent of the other dimension it is an extension of it. As per Reb Levik, The Zohar describes this stage as ולאנהרא – to illuminate, it happens in a “spread-out fashion[5], which is a plane.”

This is the exact transition from a 1D sequence into a 2D manifold. Represented by the Sefira of בינה – Understanding, the cognitive process of taking a single point of data (חכמה) and changing it, by spreading it out into a broad, comprehensive structure where concepts exist in relationship to one another.

The Elegance of the Phonetic Root

Thus, the spelled-out letter יוד is effectively a description of Relational Space and topological emanation. It describes how the Creator translates infinite, dimensionless spiritual potential into a structured, dimensional reality where multiplicity can exist and be the source for actual physical creation.

And this process of the סדר השתלשלות is not limited to the hidden potential spoken in the letter י, instead it continues to be expanded upon, transitioning spiritual potential into the source for physical reality.

the order important is

We’ve established that the spelling of the letter יו״ד represents the process of moving through the Sefiros of חכמה – בינה. However, Reb Levik then proceeds to change the formula. Instead of being limited to the process of constructing the 2D plane of existence, he adds a third component and places it between the other two Sefiros.

Why is דעת being placed in the center of the Sefiros of בינה and חכמה? Granted חכמה is traditionally placed “on the right” being associated with חסדים – growth, while בינה is traditionally placed “on the left” being associated with גבורות – constrictions: and דעת is placed “in the center” being associated with the מכריעים – deciders… however, those spatial relationships are meaningless in the 2D world of the letter יו”ד. Accordingly, the ו of דעת should come at the end, representing the process of חכמה, בינה, דעת – חב”ד.

If we are to consider the classical iteration of the סדר השתלשלות, after the singularity of the Sefira of חכמה, where the initial flash of creation comes into being, we proceed along the natural path as hinted at in the shapes of the remaining letters of the tetragrammaton:

The First ה: a 2D Expansion

While the י is the 0D point of pure potential (חכמה), the first ה corresponds to the בינה – Understanding. בינה is defined as taking the concentrated point of wisdom and expanding it into length and breadth so it can be analyzed. Mathematically, this is the creation of the 2D plane (the X and Y axes).

Visually, the orthography of the letter ה reflects this transition. It is constructed from a ד with a י suspended inside it. It represents the 0D point (י) expanding into the two-dimensional framework (ד) of relational space.

The ו: a 3D Z-Axis and the Six Directions

To move from a flat 2D plane to a 3D volume, mathematics dictates we must introduce a Z-axis—a downward [upward] vector that establishes depth.

This is visually represented by the letter ו and the six (6) [ו = 6] emotive Sefiros, collectively known as זעיר אנפין.

The Geometric Vector: The letter ו is a straight vertical line. Its Kabbalistic function is to channel or “draw down” the intellectual blueprint from the upper spheres into the lower realms, effectively punching a Z-axis through the 2D plane.
The Six (6) Degrees of Infinity: In mathematics, a 3D space originates from a center point and extends in six (6) distinct directions along its three axes (positive and negative X, Y, and Z). The numerical value of the letter ו is six (6). Sefer Yetzirah explicitly maps these six (6) extremities to the physical universe: Forward/Backward, Right/Left, Up/Down.

Therefore, the ו is the mathematical realization of 3D physical space. It provides the required degrees of freedom for multiplicity—allowing discrete entities to exist, move, and interact within a volumetric universe.

The Second ה: Actualization and Action

A 3D coordinate system though is still just an empty geometric framework. To have a physical reality, something must actually happen within that space.

This action is carried out by the final ה, which corresponds to the lowest Sefira: מלכות – Sovereignty, for to be sovereign, one must have subjects to rule and rules to enforce.

מלכות has no light of its own; it is the ultimate recipient. It receives the six-directional 3D volume of the ו and crystallizes it into solid reality.
In the Kabbalistic four-world paradigm, מחכות corresponds to עשיה – the World of Making.

Mathematically, this is where pure topology and geometry become physics. The Second ה represents the moment the mathematical scaffold is populated with mass, energy, and physical events. It is the realization of the Block Universe, where the abstract formulas of 1D worldlines and 2D causal relationships are finally rendered into a tangible, interactive 3D reality.

From the 0D point of the י to the 3D action of the final ה, the Tetragrammaton serves as a complete mathematical equation for bringing a universe out of nothing and into physical existence.

Coloring outside the lines

The result of this process though, is fundamentally flawed when considered within the fully enunciated letter יו”ד. If one were to organize the Sefiros as the process of moving from one to another along a single line, in effect, that would create a 1D world, in which there was only one line, the line of סדר השתלשלות. Such a spiritual world could not create the world as we understand it.

Therefore, to introduce the concept of the 3D grid, the Sefira of דעת must be inserted between the other two, at a “right” angle to them.

Furthermore, we must consider as to which letter ה of the tetragrammaton is doing the creating of the physical world. There are two ways to consider the name of G-d, י”ה: the mental Sefiros of חכמה ובינה, or the bracketing Sefiros of חכמה ומלכות.

When we consider the classical explanation of the macro-structure of the Tetragrammaton (י-ה-ו-ה) as being the process of the סדר השתלשלות – starting with חכמה, which expands to בינה, is drawn down through זעיר אנפין and realized[6] in מלכות, as indicated in the Gemara, where the letter ה is what created the physical world – we cannot[7] be speaking of the first letter ה’ corresponding to בינה which creates the physical world. Instead, we are talking of the final letter ה’ corresponding to מלכות.

If we are talking about the final letter ה’, then the name י-ה can be read to mean the connection of חכמה to מלכות,[8] in which case these letters serve as the encapsulation letters, containing within it the letters ה”ו which are themselves the letters of G-d’s name.[vi]

To reference this concept, Reb Levik notes that immediately after חכמה represented by the written יו”ד comes the enunciated ו representing דעת, the Sefira that includes the six emotive attributes.

Thereafter, the final enunciated ד represents בינה.

However, considering the order of the יו”ד, which is now being taught as בינה ← דעת ← חכמה, the question arises, why are we moving from a 1D universe to a 3D and then back to a 2D? The order seemingly is out of order.

The Poor Question

This question becomes even stronger when we consider the enunciated letter ד within the letter יו”ד. The letter ד on its own is typically associated with the Sefira of מלכות:

ד when spelled out is דלי”ת – that which has not. The Sefira of מלכות is characterized by its lack of light on its own. Instead, it is the receptacle of the light from the other Sefiros. It is thus represented by the moon which [currently] has no light of its own and only reflects other light.
The shape of the letter ד is formed of the same plane as the letter ה.

Accordingly, one would think that instead of בינה ← דעת ← חכמה, Reb Levik should have explained the corresponding Sefiros as being מלכות ← דעת ← חכמה.

To explain this concept, Reb Levik goes back to the Zohar and stresses that the verbs used there correspond to the process outlined previously, of transitioning from the start of creation into a 3D world. In other words, the יו”ד doesn’t just described a single part of the overall tetragrammaton process of creation. It contains within it the entirety of creation, which is held hidden within the letters that are enunciated when speaking the letter itself.

The Blessing Dimension

To understand this, we have to bring the discussion back to the topic of Rabbi Levi Yitzchok’s commentary; the Zohar’s discussion of the meaning of the word ברוך.

ברוך – bless by definition is the introduction of new light within the closed system of creation. Whether one is asking that new or improved sources of פרנסה be provided, or anything similar, one is asking for the סדר השתלשלות, the fundamental order of creation, to be supplemented with new light which will allow the effect to be created and actualized within this physical world.

One would therefore expect that to be effective, the blessing has to map on to the existing system. And yet we find the opposite in terms of the shapes of the letters:

3D – ב: We start off with the fully expanded ב, representing three axis points in its shape. (Furthermore, its name בית house is a literal description of a 3D defined space[9].)
2D – ר: This is followed by the ר where one of the axis points are removed, rending this a representative of the 2D plane.
1D – ו: Next is the ו where another axis point is removed, leaving only single line – a 1D existence measured only from one point to the next without deviation.
And only then is the final ך introduced which breaks the initial 3D – ב like structure and allows the letter to descend “below the line”. In other words, what we have with the word ברוך seems to be the opposite progression of the enunciated יו”ד, where the reverse order is in place 3D → 2D → 1D.

Furthermore, the associated Zohar starts with the ‘proper’ progression: לארקא ולאמשכא ולאנהרא, but then, when reiterating the description of the process, it concludes with לקבל, לארקא, ולאתערא – to receive, to ground[vii] (as in grounding an electrical charge), and to awaken. Why change the order, and why does לארקא change meaning?

The Interactive World

It seems to me that world-building is not a static thing, but a dynamic interaction between the Creator and his creation. The initial explanation of לארקא ולאמשכא ולאנהרא is the explanation of the יו”ד process, the creation ex nihilo of the spiritual worlds. However, the concept of a ברכה is fundamentally different. It is not the Creator who is initiating this action [we are no longer measuring from without], but rather the creation reaches out to G-d, and initiates a brand-new connection – a request and boon which can be granted / blessed by G-d. This is no longer the blueprint of expansion, it is a reciprocal lightning bolt, introducing new light into the world, and traveling up and down the chain of creation.

The Orthographic Current: ברוך

A closed system, by definition, resists outside energy. If a blessing is going to penetrate the physical world, it cannot just wash over it like a broad 2D plane; it must be concentrated into a piercing point. The geometry of ברוך illustrates this precise compression.

ב: The Closed System (3D): The word begins with the established world. The ב is geometrically enclosed on three sides and open only on the left (the forward direction of Hebrew text). It represents the physical house of creation; the root of בראשית – In the beginning of everything else that comes after the process of creation has already started.
ר: Removing an Axis (2D): To introduce new light, you cannot operate within the rigid 3D rules of the ב. The ר (which means poverty) strips away the bottom foundation. It is the recognition that as strong as the “house” might be, its foundation is “not real”. Creation is completely dependent, moment-by-moment on the Creator. The one asking for the ברכה is truly a רש – a completely poverty stricken individual.
ו: The Hook of Connection (1D): By removing one’s connection and dependance on the false physical reality, and connecting (the word וו means hook, as in a connection point holding a structure) emotionally (the ו represents the six (6) emotive Sefiros. A request for a ברכה should not be an intellectual exercise. It should come from the heart) to G-d, one asks that additional light and energy be brought into this world: to change reality. The structure is thus stripped down even further, removing the roof entirely. All that is left is the 1D vertical line. The broad energy of the blessing has now been compressed into a single, high-intensity vector aimed downward, following the same line as the ברכה reaching upward.
ך: Piercing the Baseline: Finally, the new blessing is recognized with the ך. This letter completely breaks the horizontal baseline that all other letters rest upon, descending physically below the line. In Kabbalistic orthography, letters[10] that extend below the line represent energy piercing through the barriers of the physical universe and extending down into the lowest, most fractured realms.

The geometry of ברוך is therefore not the idea of world-building, but the idea of world improving. It is a hydraulic press, collapsing a dimension at each step to create enough pressure to pierce the closed system of reality, and bring new light down.

The Shift in לארקא: From “Drip” to “Ground“

This explains why the Zohar changes both the meaning of the word לארקא as well as its placement in the sequential order.

In the initial sequence (לארקא לאמשכא לאנהרא), the energy is moving Top-Down. The term לארקא means “to drip” (a 0D point) – the initial, dimensionless origin of the light.

But in the concluding sequence (לקבל לארקא ולאתערא), the person has hit bottom. The process of creation has been so successful that it reached the lowest levels, where even the righteous need a special blessing for the physical world to improve. Therefore, לארקא here means “to ground,” as in grounding an electrical current into the Earth.

In Aramaic, the root Ara (ארע / ארק) refers to the earth or the lowest floor. To introduce new, high-voltage energy (blessing) into a closed system, to be לקבל – accepted without being destroyed by it, that system must be grounded. The energy must have a place to land, anchor, and awaken that which has been into the realm of “death”.

The Dynamic Circuit: Awakening from Below

This explains the complete reversal of the Zohar’s sequence. World-building is not a static painting; it is a live electrical circuit.

If the Creator just pushed energy downward endlessly, the universe would be a static, one-way system (a DC current) that eventually overloads. But a true blessing transforms the universe into an alternating current (AC).

Here is the physics of that reversed order:

לקבל To Receive: The physical world (the closed system) acts as a vessel, catching the 1D vector of the Vav.
לארקא To Ground: The energy is anchored into the lowest possible dimension (the Khaf Sofit descending below the line), completing the physical circuit.
ולאתערא To Awaken: This is the ultimate goal. In Kabbalah, this is known as the method by which divine inspiration comes about in a way that has a permanent effect is first with an אתערותא דלתתא – an awakening from below in initiating the connection to G-d and asking for a ברכה, followed by an אתערותא דלעילא – and awakening from above, the ולאתערא stated in the Zohar. Because the energy is grounded, the system is now “live.” The creation pushes back up, generating a return signal to the Creator.

World-building isn’t just about constructing the dimensions; it is about establishing a reciprocal feedback loop. The Creator builds the 3D space, but it is the introduction of ברוך the blessing that turns that static geometry into a dynamic, living relationship.

To model a system where the effect reaches back to alter its original cause, mathematics has to abandon simple, straight-line equations and enter the realm of Nonlinear Dynamics and Coupled Systems.

In classic, world-building math (a linear system), A causes B. The flow of time and causality is strictly one-way. But in a reciprocal feedback loop B doesn’t just sit there as a passive result. It generates a signal that feeds back into A, changing A’s next output.

Here is how the mathematics of dynamic systems model this exact theological process, and how it perfectly maps to the mechanics of prayer.

The Mathematics of the Feedback Loop

In calculus and systems theory, this is modeled using Differential Equations with Feedback. Instead of a static equation like (where dictates , end of story), the system is written so that the rate of change of the source depends on the current state of the receiver.

Imagine two variables:

(The Source/Creator): The origin of the energy or blessing.
(The Receiver/Creation): The physical world.

A standard, one-way creation looks like this:

(The change in the Receiver over time is driven entirely by the Source).

But a reciprocal feedback loop changes the math entirely. The system becomes coupled:

(The change in the Receiver is driven by the Source, BUT the change in the Source is now simultaneously driven by the Receiver).

By grounding the energy (the ך of ברוך – piercing the baseline), the creation completes a circuit. The moment is energized, it exerts a force back on . The Creator has intentionally built a mathematical system where His output is mathematically dependent on the reaction of the creation.

Resonance and the Math of Prayer

If world-building is the establishment of the system, prayer is the tuning of the feedback loop. In physics, when two coupled systems interact, they are subject to Resonance. If the Receiver () pushes back at random, chaotic intervals, the feedback loop experiences destructive interference. The energies clash, and the flow of new energy from the Source is mathematically dampened or restricted.

However, if the Receiver aligns its frequency to match the natural frequency of the Source, it creates constructive interference. The amplitude of the entire system spikes. The circuit opens up, allowing a massive influx of new energy to flow through the system without breaking it.

This is the exact Kabbalistic mechanism of תפילה.

Prayer is not about informing the Creator of a need (which implies the Creator lacks data).
Prayer is an act of tuning the Receiver to the will of the Creator.

By articulating the words of the ברכה – the blessing, the person praying is aligning their intellectual, emotional, and physical state (the lower dimensions) to resonate with the divine blueprint (the upper dimensions).

Our Blessings are a Component of Creation

This is what Reb Levik is teaching us. The concept of a ברכה causing new light and life to enter the world is not something unnatural or extra that requires a complete rewriting of creation. It is built into the very fabric of the underlying first letter of G-d’s name that begins the entire process of creation.

In Ĉassidus and Kabbala there is a concept called השתלשלות הכתרים – the chain of the crowns. What this means is that there is a separate system of connection between the Creator and his creation which doesn’t follow the normal chain of השתלשלות. The Sefira of מלכות is not just the lowest level of the world above, it is the highest level of the world below – and crucially, when we speak of אור חוזר, the light generated by our service in this world, מלכות is at the top of the chain, its start and purpose. Thus, there is a direct connection between ה גדולה – the greater ה, and ה קטנה – the smaller ה.[11] Which is why they both utilize the same letter – they can be interchanged one for the other.

The Creator built a system of transmission from above to below; the י – חכמה to the ו – דעת, followed by the ד – בינה because the transmission of light and life is not unidirectional – it is bi-directional. We receive G-d’s light, crown him as our king, and turn / return to him with ברכות and prayer, which in turn changes the world into the world G-d desired from the beginning – a dwelling place for him.

The Listening Blessing

This explains our verse and why Rashi does not elaborate on the definition of the blessing. A ברכה is fundamentally the obedience and performance of the Mitzvos. The drawing down of new light and life into this world and changing the world into what it was meant to be. The material blessings that are promised elsewhere, and that we ask for, are not ends in and of themselves. They are provisions of resources so that we can work on the ultimate blessing of changing the world into a Dwelling Place for G-d.

In short, listening and obeying the Mitzvos are a blessing to the world and to G-d himself.

SOURCES

[1] Since letters are both the letter itself and the word which forms the spoken version of the letter – which spoken version is spelled out, therefore, the letter י is actually made up of the three (3) letters which form the spoken version of the letter יוּד.

[2] As the shape of the ד has both an X and Y axis.

[3] Unlike the linear 1D vector, light in a 2D manifold spreads radially outward (unlike in 3D where it spreads in a sphere as can be measured by the inverse-square law) as an expanding circle across the plane, mirroring the Kabbalistic concept of עיגולים.

[4] Nevertheless, blackholes seem to have spin (Kerr metric), which of course implies that physically speaking they are not infinitely compressed. But for the purposes of understanding the concepts here, we will proceed as if the singularity is truly infinitely compressed and dimensionless.

[5] As light itself naturally does. It is only with special equipment that we can “force” light to proceed along a single point (a laser), and even that will eventually diffuse as it encounters tangible existence.

[6] Which incidentally might explain why the Jewish people use the letter ה to represent G-d’s name rather than the traditional method of inscribing the first letter – in this case a י – followed by the dash to indicate ‘etc.’ But the Jewish people, who ‘if they aren’t prophets are the descendants of prophets’ instinctively use the letter ה’, the final letter of the name, to abbreviate G-d’s name… because the ה’ is the source for this world, and in reality is the only letter to which we can claim the connection of Creator to Created.

[7] A physical world created by בינה would be fundamentally flawed as compared to the world G-d wished to create: 1) The Sefiros that come “after” בינה would thus be fundamentally on par with or below the physical world, Heaven forbid. It would be a world in which obedience to G-d’s commands was subject to the rationalization of humans. In effect, it would be the world imagined by the Reform movement. 2) It would be a world in which there would be no way to relate to G-d emotionally. 3) Most importantly, due to its degree of “closeness” to G-d, one would not be able to believe in a degree of autonomy or separation from G-d. In the same way that בינה and חכמה are תריין רעין דלא מתפרשין – the created world would be a fully realized and obvious extension of G-d’s intellect. 4) It would be an infinite world, as part of the reason this world is capable of being finite is because the light used to create it passes through דעת and מלכות, the ובכן of the emotive and intellect.

[8] As in אבא יסד ברתא. This also explains why the Yerushalmi noted that Dovid (מלכות) was especially effected.

[9] Especially considering the phrasing of Sefer Yetzira שתי אותיות בונות שתי בתים וכו.

[10] כן קפץ

[11] In reference to the two daughters of Lavan, Leah and Raĉel, who correspond to בינה and מלכות respectively.

[i] Devarim 11:27

[ii] רעיא מהימנא 271א

[iii] Yer. Ĉagiga 2:1. The full text of which is:

Rabbi Avahu in the name of Rabbi Yoĉanan [said], ‘With two letters, two worlds were created; this world and the world to come; one with the letter ה and one with the letter י. What is the reason. As stated in the verse כי בי-ה ה’ צור עולמים – for in י-ה, G-d, the Rock of the Worlds. And it is not known (the Gemara records an argument as to whether Heaven was created “first” or whether the physical world was created first. This doubt mirrors that argument. This is beyond the scope of this work) which of these was created with a ה and which of these was created with a י. Rather, from the verse [Beraishis 2:4] אלה תולדות השמים והארץ ב^הבראם – these are the outcomes of heaven and earth as they were created. [The word בהבראם can be read as] בה בראם – with a ה they were created. Therefore, this World was created with a ה and the World to Come is created with a י:

Just as a ה is topographically opened below – this hints that all those who come to this World descend into the Pit.

Just as a ה has a dot (a serif) on top – [this hints that] at the time they descend they ascend.

Just as a ה is open on all sides (Technically, a ה is not “open” on all sides. The opening is from below and from the left as you look at the letter. However, since the letter is represented as a 2D item, its “sides” are the X and Y axis. Thus, it has an opening in each of them, which are “all” the sides) – [this hints that] so too there is an opening opened for all Ba’al Teshuva (Since we are talking about 2D, we can say that the requirement to have an opening on “all” / both sides represents the two possibilities to engage in Teshuva – סור מרע, which is turning aside from Evil, as in an opening on the Y axis, allow a person to change directions from the path he was on. And ועשה טוב, the performance of Good, as in the opening on the X axis, allowing the person to elevate the line he is on).

Just as a י is bent – [this hints that] all those who come to the world shall be bent, and their faces shall turn green [in jealousy of the righteous – the heights they have obtained is perceptible in the World to Come].

When Dovid saw this, he began to praise with [these] two (2) letters, [as in the verse Tehillim 113:1] הללו י-ה הללו עבדי ה’ הללו את שם ה.

[iv] Yeshaya 26:4

[v] See Gem. Eiruvin 104a ומטיפין מיארק לחולה בשבת – and one may drip from a dropper for a sick person on Shabbos.

[vi] See Gem. Shabbos 104a ה”ו זה שמו של הקדוש ברוך הוא – note the use of ברוך.

[vii] See Yirmiyahu 10:11

The ברכה Dimension