The Hebrew words taharah and tumah, which are the subjects of the Torah portion of Chukat (Numbers 19:1–22:1), are usually translated as ritual purity and ritual impurity respectively. This, of course, has nothing to do with physical purity or impurity, as these are strictly spiritual concepts.

But what is a “spiritual concept” in the first place? The word “spiritual” is thrown around a lot by religious pundits and new age gurus. This word is anathema to scientists as anything spiritual is deemed to be antithetical to science. However, this word can be given a simple, precise and strictly scientific definition. (As Descartes famously said, most arguments would disappear if people bothered giving definitions to the concepts they argue about.)

Well, one thing everyone would agree with, that spiritual is not physical. Since all physical phenomena take place in three-dimensional physical space (or four-dimensional Minkowski spacetime, or ten-dimensional space of the string theory), we shall define “spiritual” as anything that takes place in extra dimensions of space outside our physical space. In other words, whatever one may consider our physical world (three-dimensional space, four-dimensional spacetime continuum, or ten-dimensional space of the string theory), the spiritual world is the world made of extra dimensions above the dimensions of the physical world.

Indeed, the oldest known book of Kabbalah, Sefer Yetzirah, describes our world as five-dimensional reality – the familiar four-dimensional spacetime plus the fifth “moral dimensions.” The opposite extremes of this dimension are described as the “depth of good” and the “depth of evil.” Thus, already Sefer Yetzirah, whose authorship is attributed by tradition to Biblical Abraham or, by modern scholars, to the school of Rabbi Akiva, expresses the spiritual realm as an extra dimension in spacetime.

This extra dimension of space can itself be a multidimensional world. Let us take, for example, a string, which represents a one-dimensional reality. Then let us imagine balloons hanging off this string. The balloons, of course, are three-dimensional. If we can image these balloons hanging off every single point on the string, we can essentially replace (or create one-to-one correspondence – an isomorphism, in the language of mathematics) all one-dimensional points on the string with three-dimensional spaces represented by our balloons. In topology (a branch of mathematics closely related to geometry), it is called a fiber bundle. Another intuitive example of a fiber bundle is a cylindrical hairbrush where one-dimensional fibers are sticking out of (or “replacing”) one-dimensional points on the two-dimensional surface of the cylinder.

In the Lurianic Kabbalah, the “moral dimension” of the Sefer Yetzira is expanded into the ten-dimensional fiber bundle, wherein each dimension corresponds to one of ten sefirot (or sephirot) – divine emanations. (Notably, the topology of the five-dimensional world of Sefer Yetzirah may be viewed itself as a fiber bundle. The word “time” – in Hebrew, is ZeMaN – is viewed as an acronym for Zeman (time), Makom (space), and Nefesh (soul, which is a euphemism for the spirituality). Thus each point on the one-dimensional timeline is replaced by the familiar to us four-dimensional world we call the spacetime and a one-dimensional spiritual world – five-dimensional universe. This one-dimensional “spiritual” world termed here as the “soul” or, in the terminology of Sefer Yetzirah, a moral dimension of good and evil is then expanded into a ten-dimensional fiber bundle of ten sefirot.)

Now, that we have defined the spiritual world as a world made of extra dimensions above our physical world, the question arises – what does it really mean? What is the meaning of the points in this spiritual realm? How do we measure distance in this spiritual world? After all, coordinates of points and distance between points are familiar characteristics of the 3D space we live in. As Rabbi Kaplan explained in his book, Inner Space: Introduction to Kabbalah, Meditation and Prophecy (Moznaim; 2nd ed., 1991), spiritual world is a conceptual world. That means, points in this world are various concepts, and the distance between them is the measure of similarity between two concepts. If two concepts A and B are identical (A=B), then we say that they occupy the same point p in this conceptual space p(A) = p(B). If B is the negation of A (B=⌐A, read as B is not A), then we say that these concepts are infinitely far from each other. Therefore, in religious terms, if a man wants to get closer to G‑d, there is no other way to do so but to become a little bit more like G‑d, i.e., to emulate G‑dly qualities and attributes. If G‑d is kind, we should be kind. If G‑d is giving, we should be giving. If G‑d is just, we should be just. If G‑d is forgiving, we should be forgiving, etc. If G‑d is holy (i.e., separated from this physical world), we should be holy  too (separated from the vanities of the physical world), as it says:

“For I am the Lord your G‑d. You must consecrate yourselves and be holy, because I am holy.” (Lev. 11:44) 


“You shall be holy to me, for I the Lord am holy.” (Lev. 20:26)

The more we are like G‑d, the more we emulate him – the closer we get to Him.

As we get a sense of the spiritual dimension, let’s not forget that spiritual dimensions do not need to be all continuous. Let’s look at some examples. The standard model of quantum theory predicts elementary particles with certain qualities such as mass, electric charge, charm, spin, etc. While three-dimensional space is a continuous space where each of the X, Y, Z coordinates continuously vary from -∞ to +∞ (∞ is a sign for infinity) and an elementary particle can have any value of these coordinates, other characteristics, such as electric charge or spin, for example, are not continuous – they are discrete. For every particle, the Standard Model predicts an antiparticle with the opposite charge. Electron, for example, has an antiparticle, positron, which is an identical particle but with electric charge +1 instead of electron’s -1. Proton has electric charge +1, but antiproton has -1. The antiparticle of the neutron is antineutron, which has the opposite baryon number (-1 for antineutron and +1 for neutron). We can represent these discreet values as points in a discreet dimension, but it is more convenient to describe them as properties arising from a symmetry group, as it is done in the Standard Model.

Image result for half black half whiteThe Torah portion Chukat deals with the concepts of tumah and taharah. Without defining what they are, we can say for certain that tumah is an “antiparticle” of taharah, as it were. Needless to say, there are no “particles” involved here. These are two spiritual states that are mirror reflections of each other. Whatever “taharah” is, tumah is anti-taharah or -tahara (taharah with a minus sign implying the opposite of taharah). A Jew in a state of taharah may enter the Bet HaMikdash (Jerusalem Temple) and eat kodshim (produce given to a Cohen-pries and a Levy as truma and maaser-tithe), whereas a person in a state of tumah, may not. In this sense, tumah and tahara are opposite values in an extra dimension that is discreet – the +1 value is taharah and -1 value is tumah.

The natural state of a Jew is tahor (spiritually pure). There are few different types of tumah:

  • Tumat met – spiritual impurity of death;
  • Tumat nidah – spiritual impurity of a woman during her menstrual cycle;
  • Tumat eledet – spiritual impurity of a woman after childbirth;
  • Tumat negoiim – spiritual impurity imparted on a man suffering from tzorat – a spiritual disease (often incorrectly translated as leprosy or psoriasis);
  • Tumat tzorat – spiritual impurity imparted on a house, vessels within the house, or a garment afflicted by a form of tzorat (which looks something like mold); and
  • Tumat zaav – spiritual impurity imparted of a man suffering from venereal discharge.

All these categories of tumah have the same common denominator – removal or diminution of life, actual or potential. Life is viewed in Kabbalah as the state in which the soul is within the body. The opposite of life is consequently viewed as a separation of soul from the body. It is no wonder that in this conceptual framework, death causes the impurity of tumah. Similarly, during her period, the woman loses unfertilized egg, which had an unrealized life potential. Because the lost life was only in the potential, tumat nidah is not as severe as tumat met and does not require purification of the red heifer.

Image result for black and white baby feetOne may wonder, how giving birth fits into this picture. Surely, giving birth is opposite of death! However, during pregnancy, a pregnant woman has an extra soul – the soul of yet unborn child – in her body. At birth, this soul (together with the child) leaves the mothers body. This loss of an extra soul causes the impurity of tumah. It is interesting to note that the birth of a girl leads to twice as long a period of impurity as the birth of a boy. The explanation is that a girl, one day, herself will become a mother and a source of a new life. Thus, giving birth to a girl, the mother not only “loses” one life – the daughter which leaves the mother’s body to assume an independent existence – but it “loses” a potential of future life that will come from the daughter. Again, this type of tumah is not as strong as tumat met and does not require a purification of the red heifer.

Tzorat, albeit a spiritual malady, causes skin lesions – the decay of the outer layer of the skin, which is “dying” on the live body. This dying skin results in the tumah impurity of tzorat. The tzarat impurity on a house or on a garment are viewed in the same light because in Kabbalah, the house and the garment are considered external levushim (garments) of the soul.