613 Degrees of Freedom

Passover has ended.  All Jews hastily remove their Passover dishes into special cabinets or the attic until next Passover.  After an eight-day break, home becomes filled with the aroma of freshly baked bread.  Passover leaves us with the pleasant taste of burnt matzot, memories of the Seder spent with family, and stories of the Exodus.  But did Passover really end?

In the Mishnah (the precursor of Talmud), the holiday of Shavuot (Pentecost) is called “Atzeret.”  This word is familiar to us from Shemini Atzeret—the holiday that follows immediately after the seven days of Sukkot, often simply viewed as the last day (or, in Diaspora, the last two days) of Sukkot.  Either way, Shemini Atzeret is the conclusion of the festival of Sukkot.  By designating Shavuot as Atzeret, the Mishnah seems to imply that it is not so much an independent holiday as it is the conclusion of Passover, just as Shemini Atzeret is the conclusion of Sukkot.

Let us recall that the main idea of Passover is the idea of ​​freedom, freedom from the bondage of Egyptian slavery.  God took the Jewish people out of Egypt and made ​​them free.  But did they really become free?  Sometimes, a slave freed by his master remains in slavery voluntarily, because there is no place for him to go, because he does not know any other existence, does not have a purpose in life.  So what does this really mean, freedom?

In physics, this concept is defined in terms of “degrees of freedom.”  Simply put, a degree of freedom is an independent parameter of the system.  In mechanics, for example, degrees of freedom represent different possible directions of movement.  Thus, a body moving only linearly has one degree of freedom, it has only one choice—to move left or right.  If there is another choice—to move up or down—we say that the system has two degrees of freedom.  If there is still another choice—to move forward or backwards—we say that the system has three degrees of freedom, etc.

Degrees of FreedomEvery degree of freedom can be viewed as a dimension in so-called phase space.  The state of the system can be described as a point in such phase space.  Since every point-particle in classical mechanics is fully described by its three coördinates (XYZ) and three velocities (VxVyVz) (or, in quantum mechanics, it is customary to describe a subatomic particle by its three coördinates and three components of its momentum), the phase space of a single point-particle has six dimensions (three familiar spatial dimensions plus three additional dimensions representing three components of the the momentum).  A system comprising three particles will have a 6×3=18 dimensions of its phase space. In general, N particles has 6N-dimensional phase space.

In addition to the translational degrees of freedom, such as moving in three spatial directions, a system can have rotational degrees of freedom, called pitch, roll and yaw. Rotation around each axis may be clockwise or counterclockwise.

Spin is a quantum-mechanical degree of freedom analogous to angular momentum, although no real rotation is involved. Spin can be pointed down as if corresponding to clockwise “rotation” or up as if corresponding to counterclockwise “rotation” (again, no real rotation is associated with spin).

Spin

In mechanics, therefore, the number of degrees of freedomis equal to the number of “choices” between alternative possibilities, such as left or right, up or down, forward orbackwards, clockwise or counterclockwise.

The same is true of man… Our freedom is the freedom of choice, i.e., the freedom to choose between alternative options.  Since the human being is, in a sense, a two-dimensional being that exists in physical and spiritual worlds, degrees of freedom also exist in both dimensions.

Physical freedom is the freedom move around, to choose one’s residence, occupation, etc.  This freedom is relative and has many levels.  Thus, people in the former Soviet Union, for example, were not completely free, as their movement outside and inside the country was limited.  At the same time, even there, most people had more freedom than a person who was in jail and could not move beyond the barbed wire.  In America people have acquired more freedom—that’s why it is call the “free world.”  However, even here, the choice of residence, if not dictated by the authorities, is determined by the employment, etc.  No wonder that, in the free world, only independently wealthy people are considered truly free; their options are not limited by employment, market conditions, etc.  Everything is relative.

Freedom in the spiritual (or moral) dimension is the freedom to choose between good and evil.  The oldest known book of Kabbalah, Sefer Yetzirah, describes three domains: Olam (“World,” i.e., space), Shanah (“Year,” i.e., time), and Nefesh (“soul,” i.e., the spiritual or moral dimension).  The third domain, Nefesh, is described in Sefer Yetzirah as “the depth of good and the depth of evil.”  It is this choice between these extreme alternatives that constitutes freedom of choice in the moral dimension.  Animals have no spiritual freedom at all, because they do not have ability to choose between good and evil.  Moreover, the very concepts of good and evil lose their meaning when there is no choice between them.  When a wolf kills a lamb, he does not commit an act of evil, because it has no choice—it follows its instinct.  Let us emphasize that freedom is not an opportunity to do what you want (the wolf certainly wants to eat the lamb), but the freedom of choice between alternative possibilities (to eat or not to eat).

Angels do not have freedom of choice either—they can do no evil as their only function is to obey the will of the Creator.  (That is evident in the Hebrew word for an angel – “malach,” i.e., “messenger.”)

Humans are the only creatures in the universe who have freedom of choice in a spiritual sense.  Cain killed Abel, but he did not have to kill.  He committed an act of evil, because it was an act of free choice.  Abraham put up a tent in the desert, which was open on all four sides.  He invited weary travelers to take shelter in his tent from the heat of the desert, to satisfy hunger and quench thirst.  An act of hospitality is an act of kindness, because it is committed voluntarily and not under duress.  As we can see, the concepts of good and evil arise when there is a choice, and freedom is the ability to realize this choice.  In other words, freedom is always the freedom to choose.  And spiritual freedom is inextricably bound with the choice between good and evil.

The Kabbalah teaches that the Divine soul (Nefesh Elokit) has 613 aspects—I call them 613 degrees of freedom.  In the anthropomorphic language of the Zohar, the soul posses 248 “limbs” and 365 “sinews.” Just as in mechanics, a system can have translational and rotational degrees of freedom, our soul’s 613 degrees of freedom are comprised of 248 “positive” degrees of freedom (positive in the sense that they are connected with an action) and 365 “negative” degrees of freedom (negative in the sense that they are connected with cessation of action).  In other words, our moral phase space has 613 dimensions.  As we have said before, freedom is the freedom to choose between alternatives.  But what are these alternatives?

After the Jews left Egypt, they obtained physical freedom; they ceased to be slaves.  What was lacking, however, were moral alternatives to free the soul.  This freedom we have attained at the Mt. Sinai, which is what we celebrate on Shavuot. The freedom we celebrate during Passover is not yet the ultimate freedom.  The ultimate freedom came when God gave us the Torah on Mt Sinai. There is freedom from and freedom of. On Passover we celebrate the freedom from slavery. On Shavuot, we celebrate the freedom of choice—choice between good and evil.

The Torah has exactly 613 commandments—Taryagmitzvoth—one for each aspect of the soul.  We were commanded 248 mitzvot aseh—“positive” precepts of what to do, one for each positive aspect of our soul, and 365 mitzvot lo ta’aseh—“negative” precepts of what not to do, one for each “negative” aspect of our soul.  Now we have moral alternatives: to do or not to do a positive commandment, or to obey or violate a negative commandment (prohibition).  These 613 moral choices liberated our soul.  It is on Mt. Sinai that we received 613 degrees of freedom, thereby obtaining the ultimate freedom in the spiritual dimension.  It is this spiritual freedom that we celebrate on Shavuot—the giving of the Torah, which completes the physical freedom we celebrated during Passover.

Originally published on www.QuantumTorah.com on June 6th, 2014.

About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
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