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The Fluidity of Life

The Fluidity of Life

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Editor’s note: The following essay is an adaptation of an (undated) entry in the notebook of the Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, of righteous memory, exploring the moral and spiritual significance of Pascal’s Law of Hydrostatics. While this particular thesis does not, to my knowledge, exist anywhere else in the Rebbe’s voluminous works, it touches upon several concepts that are at the heart of his teachings, including the supreme importance of translating one’s most sublime talents and experiences into concrete deeds, and the potential of every phenomenon to serve as a lesson in how we live our lives.

It must, of course, be added that the Rebbe wrote these notes for himself, and one can at best offer nothing more than an educated guess as to meaning buried in the shorthand of phrases and references that comprise much of these writings.


Who has not fallen prey to the oh-so-human tendency to compare his life to the lives of others? “I am thirty (or thirty-five, or forty) years old. Do you know what So-and-So had achieved by age thirty? What a meager, inconsequential existence I am leading!” Or: “If only I had So-and-So’s mind (or talent, or money), then I’d be able to make a difference and have some impact on the world!”

Such sentiments express a certain perceptive on life: life as a solid, contiguous body, whose impact and weight are proportional to the volume and density of its opportunities, experiences and achievements. Life, however, can be experienced not as a solid but as a fluid substance, whose impact is measured by entirely different criteria. But we are getting ahead of ourselves; let us explain what is meant when we speak of a “solid” versus a “fluid” vision of life.

The Torah refers to itself as “water.”1 “Just as water descends from a high place to a low place,” explain our sages, so too does Torah descend from its heavenly incarnation as the divine wisdom and will, and gravitate to the lowest possible point of earthly terrain, saturating the most commonplace aspects of everyday life.2 More specifically, we find the Torah compared to the “seven liquids”3–water, wine,4 milk,5 oil,6 honey,7 dew8 and blood9—describing the particular ways in which various elements of Torah impact our lives. Otherwise stated, a life lived by the dictates of Torah is a “liquid” life—a life with the properties of a fluid.

A solid, by definition, is a body that holds its shape, resisting the deforming influence of its own weight. A large pillar of marble may rest solidly on a stone floor and transmit a great deal of pressure to that floor, but it will itself remain unaltered by its own weight. The pillar will not, for instance, bulge outward in the middle, and if you place your hand against the side of the pillar you will not be aware of any pressure thrusting out sideways. Imagine, however, a similar pillar made of water. It could not remain in existence for more than a fraction of a second—the gravitational force of its own weight would cause it to belly outward at every point, and collapse. If this pillar of water is encased in an aluminum cylinder, the weight of the water would press against the cylinder at every point—not only at the bottom. If a hole is punched in the side of the cylinder, water will spurt out sideways by the force of this pressure.

The degree of pressure exerted by a fluid on the inside walls of its container varies in accordance with the height of the column of water above it, but it is the same in all directions: downward, sideways, and even—in containers of a certain shape—upwards. This is illustrated by case of the fluid-filled container in figure A: the fluid presses against all its walls—down against the container bottom (surfaces c and g), sideways against its side walls (b) and upward against the top panels that are below its water level (a). In other words:

Pressure exerted on a solid is transmitted only in the same direction (e.g., the downward pressure of its own weight is exerted only downward, on the area directly beneath the solid). Pressure exerted on a confined liquid is transmitted, unchanged, to every portion of the interior and to all the walls of the containing vessel.

This principle was first clearly stated by the French mathematician Blaise Pascal (1623–1662), and is known as “Pascal’s Law.”

According to Pascal’s Law, the pressure exerted on the bottom of the container represented in figure A is the same on every square inch of the container bottom. At first glance it would seem that the pressure on area c should be twice as much as the pressure on area g, since area c has a column of water above it that is twice the height of the column of water above area g (c has the water of both areas e and f pressing down on it, while g has only the water of area h). However, since the full pressure of the water in area e is being exerted on panel a (as above), Newton’s Third Law (“every action is accompanied by an equal and opposite reaction”) dictates that an equal pressure is exerted downward from panel a. So, area g has the weight of the water in area h pressing down on it, as well as the pressure exerted by the water in area e that is transmitted via panel a; thus, the total pressure being exerted on area g is equivalent to that of the highest column of water in the container.

This brings us to the following conclusion stemming from Pascal’s law:

Pressure exerted by a liquid at rest on any point of the walls or the bottom of the container is determined only by the height of the free surface of the liquid relative to this point (regardless of whether the surface is horizontal, vertical or inclined).

The result of all this is that while the laws of gravity dictate that every physical body exerts a downward pressure upon the surface upon which it rests, there is a major—at times, extreme—difference between the downward pressure exerted by a solid at rest on the ground (or on a table or in a box) and the downward pressure exerted by a fluid in a closed container. To illustrate, let us examine figures B‑1–B‑5, comparing the downward pressure of each of the five solid bodies pictured below with the downward pressure of a liquid body of identical mass contained in an identical mass contained in an identical form. Each block/container is depicted from the side, and is 10 inches deep. To simplify the calculations, we assume that the density of both the solid and the liquid equals 0.1. The results are quite surprising.

Let us begin with a block of granite at rest on the ground (figure B‑1). This is an even-sided cube, with a volume of 1000 cubic inches (10″ x 10″ x 10″) and a density of 0.1 lb. per cubic inch, giving the entire block a net mass of 100 lbs. This means that the block exerts a total of 100 lbs. of downward pressure, which is uniformly distributed along its “nether surface”—the area that is in direct contact with the ground upon which it rests. Since the block has a nether surface of 100 square inches, it exerts a downward pressure of one pound per square inch (psi) on the area that supports it. The sole determinant of the net force exerted by the block is its mass (i.e., its volume and density): the shape, size and height are irrelevant. Thus, the block in fig. 4 (the block is shown from the side, and is also 10″ deep, as are all the five blocks pictured), while twice the height of block 1, exerts the same amount of pressure on the ground (100 lbs.), since it is of an identical mass.

Also irrelevant to the net downward pressure of a solid block of matter is the area of its nether surface. Look at block B‑2. Its mass is the same as block B‑1, so the total pressure its exerts upon the ground is likewise the same—100 lbs. The fact that it has a nether surface of only 50 square inches means only that this downward force will be more concentrated—two pound of pressure per square inch instead of one (this is why a table leg coming down on your foot hurts so much: 25% of the table’s weight is being exerted on the one square inch of foot under the table leg). On the other hand, block B‑3 is only half the mass of block B‑1, so it exerts only 50 lbs. of pressure on the ground beneath it. The fact that it has a nether surface of 100 square inches does not increase this pressure—it only dissipates it: here the distribution of pressure is only 0.5 psi.

By this method (calculating the net mass for net downward pressure, and then dividing this sum by nether surface area for the psi), we arrive at the values listed under blocks B‑1 to B‑5 for “solid.” Note that shape and height are irrelevant: blocks B‑3 and B‑5, being identical in mass and nether surface area, both exert the same amount of pressure overall and per square inch. Also note that the size of the nether surface area in no way affects net pressure.

Now, imagine that these five shapes are not granite blocks but liquid-filled containers. Let us assume that the liquid filling these containers is of the same density as the granite blocks. This would mean that the bodies of liquid are identical in all ways (volume, mass, nether surface, height, shape) to the solids described above. Nevertheless, the pressure they exert on the bottom of their containers is calculated in a different way entirely.

First of all, unlike a solid, a fluid at rest does not behave as a contiguous mass; so we must calculate the pressure exerted by each “column” of fluid individually. For example, with block B‑2, we calculated its entire weight, including that of the two “arms” extending to the right and the left of its nether surface, as pressing down at the block’s point of contact with the ground; concerning the liquid contents of container 2, however, only the column of fluid directly above the container bottom is exerting pressure on it.

Second, with a contained fluid at rest, the pressure exerted on every point of the container bottom will be as great as that of the highest column of liquid in the container. If there is one point on the bottom of the container that has X amount of pressure exerted upon it, the pressure on every other point of container bottom will be no less than that amount. This is due to the principle known as Pascal’s Law, which states that “pressure exerted anywhere on a confined liquid is transmitted, unchanged, to every portion of the liquid and to all the walls of the containing vessel.”

So, instead of translating overall mass into pounds of pressure and dividing the sum by square inches of nether surface (as we did with the solid blocks), we take the tallest square inch column of fluid in contact with the container bottom and calculate its mass; this gives us the pounds per square inch of pressure exerted by this column on the square inch of container bottom on which it stands. Then we multiply this psi value by the total number of square inches of area in the container bottom to arrive at the net pounds of pressure exerted by the liquid on the container bottom.

Let us see how this works out in the five containers illustrated above. In container B‑1, which is a simple cube, the fluid level is uniform throughout the container—10 inches high. So the tallest square-inch column of fluid is also 10″ high, giving it a volume of 10 square inches and a mass of 1 lb. Thus, the pressure this column of fluid exerts on the square inch of container bottom beneath it is one pound of pressure. If we multiply this by the total area of the container bottom (100 square inches), we arrive at a value of 100 lbs. of net pressure exerted on the container bottom—the same as if it were a solid block. We have arrived at the same value by a different method.

What happens when we apply this method to container B‑3? Here, too, the highest square-inch column of liquid is 10″ high, exerting a pressure of 1 lb. on its square inch of container bottom. And the bottom of this container also has an area of 100 square inches. So the net pressure exerted by the liquid in this container on the container bottom is 100 lbs.—the same as the liquid in container B‑1, though container B‑3 has only half the volume and mass of container B‑1! Now let us look at container B‑2. The highest column is also 10″ high, exerting 1 lb. of pressure on the container bottom; but the container bottom has an area of only 50 square inches, so the total downward pressure exerted by the liquid on the container bottom is only 50 lbs.—half that of the liquid in container B‑1, though the two containers hold the same mass of liquid.

And so it goes: the liquid in container B‑4 exerts twice the pressure of the liquid in container B‑1, although they are identical in mass and nether surface, simply because the highest column of liquid in B‑4 is twice as high as that in B‑1, giving it a psi of 2 lbs. And, most amazingly, the liquid in container B‑5 exerts four times the pressure on its container bottom than the liquid in container B‑2, although container B‑5 holds only half the mass of container B‑2—because it is both twice as high and has twice its bottom surface.

To summarize: with a solid body, it is the net mass of the body that determines the net pressure it exerts on the area beneath its nether surface; the size of this area, as well as the other parameters of the body (shape, height, nether surface), are not relevant. If a greater mass has a smaller area in direct contact with the ground, it will still exert pressure proportional to its mass; the pressure per unit of area will simply increase. In contrast, when calculating the equivalent behavior of a liquid, it is the mass that is irrelevant. Rather, the degree of downward pressure exerted by a liquid upon the lowest point of its container is determined by the height of the highest column of liquid in the container (no matter how narrow this column might be), and by the area of the liquid’s contact with the lowest point of the container bottom. A comparison of the different sets of values noted in figure B reveals the resultant discrepancies in downward force between solid and liquid bodies of identical dimensions.

The analogy

If life is a liquid, the human being is its vessel. The soul that channels its essence, the psyche and character that give form to its potentials, and the body that actualizes them on the physical level—these contain and shape a life, and also focus its “downward pressure”—its impact upon the physical reality.

Human containers of life come in many shapes and forms. There is, however, one value that is the same in regard to them all: their height. Every soul comes from the same place—each is, in essence, “a part of G‑d Above,”10 a spark of divinity that extends downward to physical earth to animate and sanctify a human life. Other than that, the shape of human potential varies from individual to individual. Some “containers” are broad at the “top,” with the capacity for a rich and profound spiritual life (one might describe such a “container” as similar in shape to the one pictured in Figure B‑2). Others might be somewhat “narrower” at the apogee of life, but are endowed with a broad capacity on one or more of life’s various levels: one might possess a prodigious capacity for intellect, another for depths of feeling, while yet others are blessed with an abundance of creative skills, leadership skills, organizational skills, etc. (cf. Figure B‑4).

Every life has a “nether surface”—a point of contact with and impact on the physical reality. This, too, varies from container to container. Container B‑2 is top-heavy; his area of contact with earth is relatively small. Container B‑5 has but a trickle of life from his supernal height all the way down, until it comes to his broad base, signifying an extensive capacity for getting things done—we might envision him as the simple soul who sustains hundreds of families with his charity. Container B‑1 represents the rare individual blessed with a voluminous capacity for life top to bottom: profound spiritual identity, prodigious intellect, acute emotional sensitivity, and a broad spectrum of involvement with material life.

Indeed, we might sketch any number of differently shaped containers to describe any number of personalities and vessels of human potential, but the principle is clear: man is a multifaceted conduit of life extending from its supernal source to physical earth. If the containers that hold and mold its expanse are of variant dimensions and forms, they all share two common features: each is of an identical “height,” and thus has the full force of its lofty origins behind it; and each has a “container bottom,” an area of physical life, upon which the “nether surface” of its fluid exerts its downward thrust.

If we have devoted much of our discussion to this “downward pressure” (instead of, for example, analyzing the pressure exerted by the a liquid upon various points on the sides of various vessels), it is because this “downward pressure” is the ultimate purpose and function of human life, indeed of creation. In the words of Rabbi Schneur Zalman of Liadi:

This is what man is all about; this is the purpose of his creation and the creation of all worlds, supernal and material: to make for G‑d a dwelling place in the physical world.11

G‑d created many spiritual “worlds” or realities, and man, a microcosm of creation, incorporates all these dimensions of creation in his own soul. But these are not ends in themselves; they exist solely to influence and facilitate the transmission of life’s essence from its source in G‑d to its application as a force to develop and sanctify the material reality.

As elaborated above, the physical laws that govern the behavior of a fluid in a closed container dictate that the pressure it exerts on the container bottom is determined solely by the height of the container and the area of its nether surface, regardless of how broad or narrow the container might be at any point in between. Applied to the fluid of life, this means that since all “containers” of life are the same “height,” the sum of a life’s impact upon physical earth—which is the ultimate measure of a life—depends solely on the second factor. The volume or distribution of a person’s potential in the various “areas” of the ladder of life—spiritual, intellectual, emotional, etc.—is less significant than a far more basic criterion: the area of his life’s “nether surface”—the volume and scope of his deeds and his commitment to fulfill his Creator’s will through the sanctification of physical life.

Furthermore, differences in “nether surface” determine only the net downward force exerted by a liquid, not the degree of pressure “per square inch,” which is identical in every fluid-filled container of a given height. (As has been said above, this is in contrast with the psi of a solid block, which is determined by its overall mass.) Thus, while different individuals may vary in the size of their “container bottoms”—one person might have been granted the opportunities and resources to effect a great deal of good, while his fellow’s capacity for such achievement is more limited—these differences affect only the sum of a person’s impact on the world, not the degree of force exerted on any given point of his “container bottom.” The power and impact of each individual deed is the same in every life, regardless of the volume or shape of that life.

A Full Life

This is not to say that a person need only do good deeds, and needn’t apply himself to the development of his “higher” potentials. On the contrary, as Pascal’s Law dictates, the container must be full for the maximum pressure to be exerted on its bottom. If container B‑1 or B‑4 were to contain only the volume of fluid that fills container B‑5, they would be exerting considerably less downward pressure. If a person has been granted certain potentials by his Creator, it is because their realization is indispensable to his mission in life—he needs their mass in order to exercise his maximum impact on physical earth. Indeed, Pascal’s law states that “pressure exerted on a confined liquid is transmitted, unchanged, to every portion of the interior and to all the walls of the containing vessel.” In terms of Torah’s vision of life as a fluid, this means that a person of integrity does not distinguish between the “higher” and “lower” areas of his life. He certainly does not neglect his potential to positively influence the material reality in favor of his spiritual development; he knows that the ultimate purpose of life is to “to make for G‑d a dwelling place in the physical world.” But neither does he neglect his spiritual, intellectual and emotional life in favor of his tactile life. To him, every cubic inch within of his “container” is a divine gift and assignment, for him to realize and fill. In fact, it is precisely because he exerts the forces of his life equally in all directions that its downward impact is maximized upon the entire area of its nether surface, even upon those areas in which his more spiritual potentials are more limited (as in area g in fig. A above)

On the other hand, one whose “container” has not been blessed with voluminous capacities in its upper areas can nevertheless lead no less forceful a life than his more spiritual peers. As long as his container is full—as long as he realizes his potentials to the utmost of his capacity—the force he exerts downward on each square inch of his container bottom is equal to that of the highest column of fluid in his container, which is of equal height to every other container. So, his every deed is as impactful as a deed that has the weight of the broadest, most voluminous life behind it.

Thus, our sages have said: “Every person is obligated to say: ‘When will my deeds attain the deeds of my ancestors, Abraham, Isaac and Jacob.’”12 The emphasis here is on deeds: not everyone is capable of experiencing Abraham’s love of G‑d, or Moses’ understanding of Torah. But regarding our deeds, we are capable of achieving the same impact on physical earth as the greatest of our ancestors. The greatness of Abraham and Moses lay not in the vastness of their potential—which was a gift granted them by the Creator—but by the fact that they actualized their gifts to the optimum. Because they filled their vessels, their every deed had optimal impact. The same is true of every individual: each and every one of us is capable of filling his own vessel, which—whatever its form or capacity—extends upward as high as every other container of life. And when we do, the impact of each of “square inch” of our life’s “nether surface” is equal to that of that of the greatest vessel of life that ever inhabited our world.

Countless times we have been told, or have said to others, “If you give it your all, that’s just as significant as anyone else’s all.” Often this seems little more than an elitist cliché, or at best, generous if not necessarily empirically accurate words of encouragement to the “smaller players” in life. In fact, this is a fundamental law of reality, which applies to everything from human lives to to the gauge on a water tank. It can even be demonstrated in the laboratory.

Footnotes
1.

Isaiah 55:1, as per Talmud, Taanit 7a and Bava Kamma 17a.

2.

Talmud, Taanit ibid.; Tanya, ch. 4.

3.

Talmud, Machshirin 6:4. A “liquid” has a special status regarding the laws of ritual purity.

4.

Isaiah ibid.; Song of Songs 1:2; Talmud, Avodah Zarah 35a (see Rashi) and Berachot 57a.

5.

Isaiah ibid.; Song of Songs 4:11; Talmud, Chagigah 13a.

6.

Song of Songs 1:3, et al.; Imrei Binah, Shaar HaKeriat Shma 54a.

7.

Song of Songs 4:11; Talmud, Chagigah 13a.

8.

Midrash Rabbah, Bereishit 66:3; Yalkut Shimoni, Isaiah 431.

9.

Likkutei Torah, Bamidbar.

10.

Job 31:2; Tanya, ch. 2.

11.
Tanya, ch. 36.
12.

Tana d’Vei Eliyahu Rabbah 25:1.

Based on the teachings of the Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson; adapted by Yanki Tauber.
From B’Or HaTorah Journal: Science, Art and Modern Life in the Light of Torah. B’Or HaTorah is an English-language journal for wondering Jews, scientists, artists, teachers and students. It examines personal and intellectual concerns through the microscope and telescope of the scientist; the algorithm of the mathematician; the discourse of the philosopher; the imagery of the artist, poet and photographer; and the tested faith and learning of the Torah-observant Jew.
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Yochanon Bogart Boston June 7, 2013

Added visuals I carry from this As an engineer, I especially like this torah. If I ever think one can not have an impact on the world, I visualize a myself as an empty cylinder, a hydraulic cylinder fits the Rebbe's purposes. Like a physical person, this wide cylinder is strongly tied to the ground. It is hollow, has a piston inside and a thin, thin hydraulic line going upward with fluid in it. The pressure is extremely high as the line reaches high. Like the hydraulics on a bulldozer or backhoe, this pressure produces a tremendous force at the base, capable of cracking rocks, lifting many tons, and doing other useful work. The secret is the thin fluid line reaching very high.

We are vessels filled with the fluid of life whose source reaches extrememely high! Thank you, Yanki Tauber! Reply

Lisa Long Beach, CA June 4, 2013

land of milk and honey Is there further discussion on how all this relates to the Land of Israel being the land of milk and honey? Reply

sue Kanata May 29, 2013

Exceptional Thank you- such food for thought, especially having just read that the name Moses means "drawn form water". I have never heard that Torah is defined as five fluids, and having this new information brought tears to my eyes. When I, myself write (or create) about love and profundity, I use titling that defines the events through liquids , e.g. a video sketch I've made called Milk, then Dew, or a poem I wrote about motherhood and agape called Blood and Milk. These are meaningful and logos concepts. Yanki Tauber is the only person who has, to my knowledge ever defined spiritual life and gifts of Yah(m)weh in this manner! Reply

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