• The Periodic Table

Torah and the Periodic Table
Kabbalah and Chemistry

1. Theoretical Background

One of the most well known and ubiquitous symbols of modern science in general and chemistry in particular is the Periodic Table of the Elements. The modern periodic table has been almost 300 years in the making. Early efforts to group elements produced the tables of Geoffroy (1718) and Lavoisier (1787). The atomic theory formulated by Dalton in the early 1800s provided chemists with a solid basis to classify elements, and the theory stimulated vigorous experimentation that culminated in the development of the modern form of the periodic table in 1869 (See figure 1).

Figure 1

From the early rudimentary groupings of chemical compounds to our modern classification that recognizes the periodicity of atomic elements together, chemical tables are usually based on an implicit theory of the composition of matter . These theories have shared a common axiom: that all of the matter in the Universe is composed of a finite variety of basic building blocks. These building blocks have been known from the ancient Greeks to the present as atoms.
In our modern table of the chemical elements, the different atoms are identified and ordered by their atomic number. Atoms are defined as the smallest unit of an element that can combine with another element. Atoms are theorized as composing of a nucleus, made of protons and neutrons, and electrons that move around the nucleus. The atomic number identifies the number of protons in an element’s nucleus. Atoms can lose or gain electrons, and the ease with which they do so is a measure of their reactivity.
In our modern periodic table of elements, elements are arranged in columns and rows. As its name implies, the modern table is periodic in nature, meaning that elements are placed in it based on their shared and recurring (periodic) characteristics. Periodicity of element properties is found to be strongest down columns of the table. Primary among these periods is that of the 6 noble (or inert) gases which populate the far right column of the table. The property shared by the inert gases is a lack of reactivity ensuing from their inability to gain or lose electrons.
Another example: the first element in the table, Hydrogen (H) is a gas, the second, Helium (He), is a noble gas, and the third, Lithium (Li), is a soft, reactive metal. Going down the table, we find eight elements later Fluoride (F), Neon (Ne) and Sodium (Na), a gas, a noble gas, and a soft, reactive metal, and eight elements later, Chloride (Cl), Argon (Ar) and Potassium (K)—again: a gas, a noble gas, and a soft, reactive metal.

The remarkable predictability of element properties revealed by the periodic table allowed chemists to ‘describe’ as yet unidentified elements based on their supposed location in the table. Such was the case when in 1871 Dimitry Mendeleev, the Russian chemist who originally formulated the periodic law, correctly described the properties of the element between Silicon (14) and Tin (50) which he called ekasilicon. The element in question was not identified until 1886 by a German chemist who dubbed it Germanium.

2. The Kabbalistic counterparts to the Periodic Table

It is our goal in this article to present an exact and full analogy to the modern periodic table within Torah. The motivation for this goal is explained in preceding chapters. To do so in a methodological manner, we must first ascertain that the Torah does indeed include examples of the two central concepts underlying the content and form of the Periodic Table: (1) atoms and (2) periodicity.
The notion of the entirety of creation being constructed out of a finite variety of basic building blocks is central to the earliest Kabbalistic source known (and incidentally the first book of Hebrew grammar)—the Book of Formation (Sefer Yetzirah). From there this notion assumes a central role throughout the entire Kabbalistic and esoteric tradition within Torah.
Specifically, the Book of Formation turns to Genesis and, following a (spiritually) linguistic perspective, identifies 32 non-corporeal elements or atoms. They are the 10 sefirot [which correspond to the 10 utterances (ma’amarim, מאמרים ) spoken by God when He created the world ] and the 22 letters of the Hebrew alphabet [out of which the utterances are constructed]. Together, these 32 atoms form the basis for language and speech, the conduits of the creative act itself.
However, though the Book of Formation provides us with the notion of basic building blocks of the Universe, the atoms it identifies are ill suited for our purposes of correspondence. First, because they are of two separate categories: one (utterances) clearly hierarchically above the other (letters). Second, because we are searching for a one-to-one correspondence between the atoms of the periodic table and some corresponding unit in Torah.
However, one piece of valuable insight to be gained from the Book of Formation is the idea that should the Torah’s equivalent of elements or atoms be found, it would be in the first chapter of Genesis, where the act of creation is described. What better place to search for the Torah atoms from which Creation is constructed?
*   *   *
To explain the correspondence we have found, let us first mention that of the more than 100 elements, only 92 are naturally occurring. Atoms of elements with atomic number higher than 92 can be artificially synthesized, however, they are generally not stable and undergo nuclear rearrangement resulting in radioactive decay shortly after being synthesized.
And now to our correspondence: one of the most important contributions to Jewish scholarship in the recent past has been the work of Rabbi Zalman Pinchas Horowitz . Rabbi Horowitz was (to the best of our knowledge) the first to correctly count the number of times the Tetragrammaton (YHVH) appears in the Pentateuch: 1820 times. Even more surprising and innovative was Rabbi Horowitz’s cataloging of all the distinct words in the Pentateuch, which he also found to be exactly 1820 in number.
This equality still warrants much research, but here we will note a fact related to our own particular interest: of the total 1820 unique words in the Pentateuch, the section describing creation (Genesis 1:1 to 2:3, inclusive) contains exactly 92 distinct words. Indeed, as mentioned already, this section of the Torah literally describes the creation of matter in the universe—it is only fitting that it is here that we find our sought after parallel for the 92 natural elements identified by modern science.
Before proceeding let us copy the familiar periodic table of elements with the 92 distinct words of Genesis placed in order:

Following our methodology, we should now seek periodicity, the second organizing principle identified above. To do so, we will first examine and understand in-depth the periodic nature of the structure and form of the table of elements and the model used to explain this periodicity. We will then explore parallel spiritual models found in Kabbalah and Chassidut. In a forthcoming article we will use our findings to examine the periodicity inherent in our parallel Torah table of elements pictured above.

3. On the relationship between spiritual and mundane in the Torah

Before starting our analysis, let’s take a few steps back to say a few words about the rationale for looking to the Torah for models that can describe (directly or indirectly) natural phenomena.
The physical world and its attributes are often spoken of as a reflection or manifestation of the spiritual realm, and as such, by studying the physical we may come to know more about the spiritual worlds, and ultimately our Creator .
It is explained in Jewish tradition that there are two ways to describe the relationship between the Torah and physical reality:
The first, more commonly held view, is that the Torah speaks of mundane matters (e.g. laws of commerce, liability, etc.) but as it were, these mundane matters are also to be found reflected in the higher (or inner) spiritual dimensions of the universe. So we might say that the Torah can be interpreted as saying something about the spiritual worlds as well as the mundane. This interpretation can be as simple as talking about the spirit of the law (as opposed to the letter or the law). Or, it can form the basis of a complex and intricate (anthropomorphic) analysis of the Divine, based on the Torah.
The second approach, advocated by assidism, holds that the Torah’s actual subject matter are the higher (or inner) spiritual dimensions of the universe, and it is actually they that are also reflected, or mimicked, in the lower mundane material dimensions . Thus we may say that the literal meaning of the Torah is spiritual, while a non-literal, or allegorical interpretation of this meaning teaches about the mundane physical world.
The second approach may seem troubling because the Torah does not seem to employ ‘spiritual’ language (note the lack of mention of angels or any other ‘heavenly’ artifacts). In fact, the opposite is more the case—the stories related and the commandments of G-d found in it all seem to speak directly about physical reality as it was a few thousand years ago. The response to this point comes in the shape of the Talmudic dictum that “Torah speaks in the language of men” . In other words, though the subject matter of the Torah is indeed spiritual, its language is mundane—“the language of men”—such that it employs language that refer to objects and states of affair familiar to humans.
Armed with these two basic notions regarding the subject matter and language of Torah, we argue that by studying the physical world using scientific methods (which should hopefully give us a clear picture of physical phenomena) we expect to find parallels between the Torah’s ‘physical’ terminology and the findings of experimental science regarding those phenomena. Relating our knowledge about such physical phenomena to the Torah’s vocabulary (or other non-linguistic forms of communication, as will be explained) will, in turn, lead us to a better understanding of the ‘spiritual’ issues, which are the Torah’s ‘actual’ subject matter. Thus we come to learn more about the spiritual realm using scientific knowledge.
The Torah contains varied types of communicable information, alluded to by the famous acronym: PaRDeS. PaRDeS stands for the four types of textual analysis traditionally used to explore the Torah in order to recover its informative content. These are: pshat (literal analysis), remez (symbolic, or numerical analysis), drash (hermeneutic analysis) and sod (associative, or model-based analysis). In order to quickly orient the reader we will note that drash (hermeneutic analysis) was utilized in the study and development of Halachah (Jewish Law). Sod (associative, model-based) analysis was most fully developed in Lurianic Kabbalah. Our present study will make use of all four types of textual analysis. At times, we refer to the knowledge arrived at using remez and sod analysis as the ‘inner (or esoteric) wisdom of the Torah.’

4. Nature and the Divine

One of the most basic findings in the Torah using remez analysis (numerical, in this case) is that the numerical value of the hebrew word for nature (הטבע , hateva) = 86 – is equal to the numerical value of the name of G-d associated with the creation of the natural world: Elokim (א־להים ) = 86. This numerical equivalency is usually understood to indicate that there is an aspect of Divinity that is enclothed within the natural world.
As we shall see, this basic equivalency will form the backdrop for much of our present discussion.

5. 92 naturally occurring elements

The first possibility would be to map each element to its corresponding Hebrew root, simply based on order of appearance (see Table 1 in Appendix A).
Further reflection though reveals an alternative. The 92 distinct roots of the story of creation are divided such that the first 86 appear in the verses relating the first six days of creation (Genesis 1:1 through 1:31), while the last 6 are found in the verses relating the Sabbath (ibid 2:1 through 2:3). This motivates us to correspond the 6 noble gases with the 6 distinct roots found in the Sabbath section in Genesis, while the remaining 86 elements will be corresponded in order to the distinct roots found in the 6 Days section of Genesis.
We mention this second possible mapping here because of our interest in the inert gases, as follows.

6. Inert and non-Inert Elements

Scientifically speaking, there are many ways in which the chemical elements can be arranged to accent different attributes of their periodicity. Briefly, when looking at a periodic table, the elements are normally presented with their name, atomic number, and often their valence electron configuration. The commonly found table of elements highlights various types of periodicity, one of the most central ones being that of the noble or inert gases.
One of the most important and outstanding features of the 92 naturally occurring elements is that they may be divided into two groups, based upon their ability to form compounds: there are 6 which do not form compounds, also known as inert (or noble) gases, while the other 86 do form compounds with other elements.
On the periodic table in Figure 1, the inert gases form the far right hand column. Graphically, our modern version of the table of elements is structured such that the periodicity of the inert gases is highlighted, though, as we shall see below, the table could be (and historically was) arranged entirely around this periodicity.
This basic division into 6 and 86 observed in the naturally occurring elements is to be found (again, using a non-literal analysis of the Torah text) in the very first verse of the Torah:בראשית ברא אלקים את השמים ואת הארץ  (usually translated as “In the beginning G-d created the heavens and the earth”). The first chapter of the Torah recounts the act of creation of the natural world. It is important to note that G-d here is referred to as Elokim alone (and not by His other names), thus leading to the association of this name with ‘nature’.
The 6 letters of the first word, Bereishit (בראשית ) can be split into 2 separate words, each with 3 letters and read as ‘barah sheet’ (ברא שית ), meaning “created six” (in Aramaic, the lingua franca of the ancient near-east).
The next two words in the verse are ‘barah Elokim’. As noted above, the numerical value of Elokim, one of the names of G-d is 86. We have then that the first 3 words can be understood to say: ‘six were created’ (“barah sheet”) and ‘86 were created’ (“barah Elokim”). The sum of these two acts of creation is 86 ^ 6 = 92, the number of the naturally occurring elements.
As mentioned above, 86, the value of Elokim, is also the numerical value of the word hateva in Hebrew, or ‘nature’. Thus “barah Elokim” can be read as “created nature” as well.
There is yet another appearance of the name Elokim regarding the 6 inert gases:
The atomic numbers of the inert gases are 2, 10, 18, 36, 54, 86.  The heaviest inert gas, radon (Rn), has an atomic number of 86 = Elokim.

7. Spiritual ‘Wholeness’

We now turn to reflect on the spiritual parallel to the presence of both inert and non-inert elements in the natural world.
The spiritual (or psychological) counterpart of physical inertness in the elements can be found in the Torah’s description of Jacob and Lavan’s (Jacob’s father-in-law) working relationship. Regarding the wages that Jacob received for tending Lavan’s flocks the Torah writes (Genesis 30:42):
והיֻה העטֻפים ללבן והקשֻרים ליעקב
This is usually translated literally as:
the weaker (atufim) [flocks] were to Lavan and the stronger (k’shurim) [flocks] were to Jacob.
The literal meaning is that the sheep were characterised as stronger or weaker; the weaker remained the property of Lavan, the stronger were given to Jacob as wages.
However, Rashi, the basic (literal) Medieval commentary on the Torah interprets the meaning of atufim differently. This Hebrew word can be analyzed to stem from the root atf(עטף ) that yields the infinitive la’atof, to wrap. It would then mean “those that are wrapped”.
Likewise, K’shurim the word used to describe the type of flocks given to Jacob, can be analyzed to stem from the root k.sh.r. (קשר ) and the infinitive likshor, to bind. Its meaning would then be “those that are bound”
If these characteristics of the sheep are seen as metaphors for two different types of personalities, then an atuf describes one who is wrapped in wool, keeping warm all to himself, while a kashur symbolizes one who is incomplete without forming bonds with others outside of himself. A ‘wrapped’ (atuf) individual is not in need of a mate and finds sufficient warmth alone. Such an individual needs not receive from nor give to another. On the other hand, a person with a ‘tied’ (kashur) personality seeks completion in relationships with others, at times giving at times receiving.
For the sake of rigor we note that spiritually speaking, these two types of personalities are usually associated with negative and positive qualities, respectively. An atuf attitude (especially in the present case where these flocks are indicated as being the property of Lavan) is considered analogous to that found in Biblical Sodom : “That which belongs to me is mine, that which belongs to you is yours.” While a kashur attitude is normally associated with holiness (though at times it can drift to an extreme form of wantonness which is of course negative).
However, in assidic writings it is explained that a truly whole individual is one who has both qualities. To better understand why how this is so we may take the kaballistic principle stated by Rabbi Abraham Abulafia (1240 – c.1291), the 13th century philosopher and mystic: “being whole is being one and a half”. Or in the famous words of Rebbe Nachman of Bretzlov: “nothing is more whole than a broken heart”. We coin the term whole and half (שלם וחצי , shalem va’chetzi) to designate this special quality of wholeness.
A truly whole (and holy) person is does not feel self sufficient, thereby not requiring others, but rather one who is, existentially speaking, both complete and incomplete at the same time. By virtue of their half-ness, they need to connect or bond with others. By virtue of their whole-ness they are able to offer support and help to others. Real wholeness (and holiness) comes by virtue of an existential feeling of incompleteness – of insufficiency and inadequacy to single-handedly prevail, empowered and strengthened by a sense of whole-ness which saves one from a sense of an inability to rise to the task at hand.
Scientifically speaking, we can immediately note the analogy between these two basic definitions of atuf and kashur and the distinction between inert and non-inert elements. Bond formation is possible only when an electron orbital is half or incomplete. But when an orbital is whole or filled, the element in question is not in need of accepting or receiving electrons and thus does not form bonds. Yet, both exist in nature. Nature reflects these two basic qualities.
The inert gases are also called the Noble gases. The mark of nobility is the air of whole-ness surrounding it. The ‘nobility’ of the elements do not react with any other elements. It is only the 86, Elokim, elements that can do so. Nonetheless, the six noble gases form a sort of axis around which the other 86 elements revolve.

8. Whole-ness of the Patriarchs

The attribute of bonding is found to be associated with the name Elokim in another manner: Elokim is the name of G-d related most closely with the Patriarch Isaac as both manifest the quality of judgment (or din – דין ). When departing from Lavan, his father-in-law, Jacob says:
לולי אלקי אבי אברהם ופחד יצחק היה לי, כי עתה ריקם שלחתני…
If the G-d of my father, the G-d of Abraham, the fear of Isaac, was not with me, then you would have sent me away empty-handed…
Jacob refers to the way in which Isaac (his father) knew G-d as ‘the fear of Isaac’ (pachad Yitzchak, פחד יצחק ). The numerical value of pachad, or fear, is 92, which is again Elokim (86) plus six – the total number of naturally occurring elements.
Yet, Isaac was not always whole in the sense of being both whole and half at the same time. The sages tell us that Isaac was actually 37 years old at the time that Abraham (his father) was commanded to sacrifice him to G-d (see Genesis 22), known as the ‘test of the Akeida’ – the test of the binding of Isaac. The Zohar, the basic book of the inner teachings of the Torah, relates that Isaac was entirely whole, exclusively of ‘noble’, or inert, character and was therefore not suited for marriage, not suited to bond with another. It was the Akeida – literally, ‘the binding’ – which brought him to complete his character with the quality of half-ness. It was only then that he became suited for marriage, to bond with a wife. Thus pachad Yitzchak (= 92) can be understood as the attribute of Elokim (86) plus another 6, the addition of something to Yitzchak’s own wholeness.
By the same token the Zohar explains that Abraham was not truly whole either, as he did not have the quality of Might or Judgment. It was the act of the Akeida – the binding of Jacob – done out of fear and awe of God (as the angel spoke to him following the binding: “for now I know that you are indeed fearful of God” (Genesis 22:12) which complemented his essence with this quality.

9. Inert Periodicity Historically

Now that we have spent some time studying the periodicity of the inert elements, let us delve a bit into its history. Using the periodicity of the inert elements as the basis for the table of chemical elements was first proposed in 1895 by J. Thomsen and was itself based on an earlier model by T. Bayley (1882). A table similar to Thomsen’s appears in Figure 2. Note that the principal disadvantages of this table was the large space required by the period of 32 elements and the difficulty of tracing a sequence of closely similar elements (for purposes of illustration the inert elements have been marked in blue, and the non-metals, marked in green, in the contemporary table form a triangular shape, but here do not align similarly).

Table 1

10. Orbital Filling of the 6 Inert Gases

It was only in 1922 that Niels Bohr proposed the quantum-theoretical model that forms the basis for our current understanding of the subatomic construct of the elements, and explains the observed periodicity of the inert gases. According to Bohr’s model, the structure of each atom could be singularly described using 4 quantum numbers to identify the ‘orbitals’ in which electrons organize around the atom’s nucleus. The orbitals (sometimes called sub-shells) are grouped into shells, the shells being designated by the letters: K, L, M, N,…, or simply 1, 2, 3, 4,….
Every orbital is classified by two quantum numbers: the primary quantum number and the angular momentum quantum number. The angular momentum quantum number is replaced by the letters s, p, or d. Two other quantum numbers – the magnetic quantum number and the spin quantum number – determine the number of electrons that can ‘fit’ in an orbital.
Looking at the periodic table using Bohr’s model, we find that the naturally occurring elements can be described exhaustively using 7 shells and 4 orbitals, namely (designating the shells by their number, not letter): 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 6s, 6p, 7s. The number of electrons that can fit in each orbital is: 2 in s orbitals, 6 in p orbitals, 10 in d orbitals, 14 in f orbitals
To truly understand the theoretical basis for Bohr’s model is beyond our scope. However, we would like to take a closer look at the mathematical regularities that this model produces. So let us order the elements in a table that will show us how their electrons ‘fill’ the various shells and orbitals:

Table 2
The rows designate the Shells, while the columns the orbitals in each shell. Thus for instance, the first shell (K) can accommodate up to 2 electrons and therefore has room for 2 elements. The second shell (L) can accommodate 8 electrons and therefore has room for 8 elements, and so on. In the K shell, all the electrons are available in the s orbital only. In the L shell, electrons ‘spots’ are available in both the s and p orbitals.
Note that shells are not filled entirely before the next shell is started, due to the fact that electrons in elements always seek the lowest possible energy state they can reach. This is clear if we follow the elements in this table. Up to Argon (Ar), the first shell (K) and second shell (L) are filled completely. Then the s orbital of the third shell (M) is filled, followed by a complete filling of its p orbital. Argon then is the 18th element in the table with electrons completely filling the 3p [3rd shell (M), p orbital] orbital. But the next element, Potassium (K) does not continue to fill the 3rd shell’s d orbital, but rather skips to the 4th shell’s (N) s orbital, because electrons in that orbital actually have a lower energy level then electrons in the 4d orbital. This is due to the interactions between the electrons themselves, an effect known as ‘shielding’. So Potassium’s ‘extra’ electrons do not locate in the 3d orbital but rather in the lower-energy orbital 4s. The rest of the table follows this general trend, with electrons always vying for the lowest energy level orbitals.
There are two interesting facts about this table that should be noted are:

• that the number of ‘spots’ in each orbital is equal to the differences between the total number of elements that can populate each shell.
• all the orbitals that are used are ‘filled’ or ‘populated’ to capacity by elements except for the 5th shell’s f orbital. Though 5f has room for 14 electrons, only 4 ‘spots’ are used by the heaviest naturally occurring elements from Actinium (89) to Uranium (92).

The first fact is the reason that we have drawn the table as 7 x 7 even though the entire g, h and i orbitals have been left blank. Let us explicitly write the first fact out: The total numbers of electrons in the shells are (We designate these as set A):
A = {2, 8, 18, 32, 50, 72, 98}
The numbers of electrons in each orbital are (we will designate these as set B):
B = {2, 6, 10, 14, 18, 22, 26}
Now note that the numbers in set B are the differences between the numbers in set A. This can be clearly illustrated by writing the two sets, A and B, one beneath the other, as follows:

This is truly one of the most astonishing mathematical properties of the periodic table.
But, arranging the elements in the above table also reveals an interesting property of the inert gases and that is that an inert gas is formed each time the p orbital fills. The p orbital of each and every shell has room for 6 electrons. That is to say that each time 6 electrons fill the p orbital, an inert gas if created (excluding Helium, which does not use the p orbital).
Recollect that above we noted that in the story of creation, the first word of the Torah, Bereishit, which can be understood to mean ‘created 6’, should be seen as corresponding to the formation of the 6 inert gases! In fact, the excluded inert gas Helium, is hinted to in the word Bereishit as the letter bet, the first letter of the word is written in the Torah scroll as a large bet (בית רבתי , bet rabati) and the numerical value of the letter bet is 2.

11. Mathematical Patterns in Inert Elements

Let us now look at the numbers of the inert gases from another perspective.  If we take the atomic numbers of the inert elements and note the differences between them we can construct the following table:

Table 3

The rightmost column shows that the differences between the elements are all values, in order, of the mathematical series f[n] = 2n2 (n starting at 0).
These numbers are known in the inner teachings of the Torah as the double squares (רבועים כפולים , ribu’im k’fulim). Their significance is related to the 32 paths of Wisdom (ל"ב נתיבות חכמה , lamed beit netivot chochmah). The Book of Formation, mentioned above, begins:

ב-לב נתיבות פליאות חכמה חקק י-ה הוי' צבאות וברא את עולמו בשלשה ספרים בסופר וספר וסיפור
Using 32 wondrous paths of wisdom Kah Havayah [God] Lord of Hosts engraved… and created His world, using three books: author and book and story.
It is known that the textual source in the Torah for these 32 paths of Wisdom is to be found in the 32 times that the name Elokim is used in the verses describing the six days of Creation. This, again, is the Name which we have recognized as central in our discussion of the periodic table. We note that no other Name of the Almighty appears in the creation story, and it appears exactly 32 times. 
32 is thus the number associated with Wisdom (chochmah). In the inner teachings of the torah we find the number 50 associated with Understanding: 50 Gates of Understanding (חמשים שערי בינה , chamishim sha’arei binah). There is also another, less well known concept of 72 Bridges (ע"ב גשרים , ayin beit gesharim).
Actually, all three of these concepts are closely related and are part of one larger picture. This basic conceptual scheme identifies the type of energy related to each sefirah and the type of conduit through which it flows:
Thus the energy of Wisdom is identified as ‘mind’ that flows through a path (נתיב , nativ); the energy of Understanding is identified as ‘intelligence’ that flows through a gate (שער , sha’ar); finally the energy of Knowledge is termed ‘psyche’ and flows through a bridge (גשר , gesher). This model is summarized in Table 2.

Table 4
Of course, 72 is also a double square (particularly, 72 = 2 . 62). We have thus, so far, found the mental significance of the double squares for n = 4, n = 5 and n = 6. To complete our understanding of the significance of double squares we need to complete the series beginning with n = 1.
The basic model of the sefirot in Kabbalah indicates that above Wisdom resides the Crown (כתר , keter) that is explained in the Zohar to consist of three heads (תלת רישין שבכתר , tlat reishin sheba’keter). In our present model we will map these 3 parts of the Crown to correspond to the first 3 values of n.
Continuing our previous discussion regarding the various mental powers we note that Wisdom marks the first conscious mental power. Thus, the Crown – which resides, both figuratively and in our Kabbalistic model, above the head – corresponds to the  super-conscious faculties. The three heads of the Crown, or the 3 super-conscious mental powers are known as: Belief (אמונה , emunah), Pleasure (תענוג , ta’anug) and Will (רצון , ratzon).
Table 3 illustrates the double squares for values of n from 1 to 6 with their corresponding mental faculties.

Table 5
Using the sefirot as a model for the series of double squares, we could continue the series until n = 13. For example, corresponding to the double square 128 (n = 8) we would have the sefirah of Might (גבורה , gevurah). For 338 (n = 13) we would have the sefirah of Kingdom (מלכות , malchut).
We have now taken a look at the series of double squares, the differences between the atomic numbers of the inert gases. This series is essentially the backbone of the whole periodic table of the elements.
Extrapolating from our knowledge of double squares in the periodicity of inert elements we would expect the next inert element to be of quantum number:
86 (Radon) ^ 32 = 118. This element has been dubbed Uuo (Ununoctium) by the International Union of Applied Chemists (IUPAC) until its existence is proven at which time its properties will be ascertained.
We would expect to find the next inert element at quantum number:
118 ^ 50 = 168. This element has been dubbed Uho (Unhexoctium).