248 in Nature and in Man – Lectures 3 and 4

248 and Matter

Let us begin by saying a word about the substance of particles. We know that in physics particles can be either matter particles (that have half spin) or force particles (that have whole spin), but, more abstractly everything is a form of some substance. This is true even though particles are not things. An electron is not a thing, as the famous physicist Dirac was fond of saying. Even matter particles are not what we are used to calling matter. Certainly, force particles, which are messenger particles, are also not “things,” in the usual sense. Virtual particles are even further removed from being what we consider substance. But, more generally, everything is some form of abstract matter—since they are clearly not nothing. In this sense, all particles are a form of substance.

One of the simplest and most straightforward gematrias of 248, which relates it with reality and the substance in reality, the substance of particles, is חֹמֶר , which means “substance,” or “matter,” in Hebrew. This is a very simple 3-letter word. In fact, it is the simplest word that equals 248. This suggests that there is something essential within matter relating it to this number: 248.

Grammatically, this word חֹמֶר is very unique. To understand its uniqueness we have to first know that Hebrew is a very structured language; probably the most structured of all languages. It is based on three-letter roots out of which verbs and nouns are constructed. Since there are three letters in each root, there are six possible permutations, or in the language of the Book of Formation: “3 stones [letters] build 6 houses [roots].” But, not all of the possible permutations are words or roots. There are only 7 examples of three letters where all the six permutations are actual roots or words in the Bible. The most important is חֹמֶר . Clearly then all six permutations relate to this basic abstract sense of matter or substance.

We are not going to look at all six permutations of חמר . Instead, will focus focus on one of these רֶחֶם , which literally means “womb.” This permutation is also the root origin of the word רַחֲמִים , which means “compassion,” or “mercy.” Compassion is the inner property of the sefirah of beauty (tiferet, in Hebrew). In the Zohar, the sefirah of beauty is referred to as “the body of creation” (תִּפְאֶרֶת – גוּפָא ) in the sense that beauty is the all inclusive matter or substance out of which all of creation is formed. All of matter in creation is born from the vacuum of creation. The first stage of creation, as explained in the writings of the Arizal, is the creation of a vacuum or empty void, from which all is born. In Kabbalah, this empty void is likened to a womb out of which everything is born, as it were. Now the new idea that Kabbalah introduces into our understanding of creation is that all is born through a process that reflects God’s mercy and compassion. Of course, science does not normally use this type of qualitative or emotive language, but this Kabbalistic idea suggests that even quantitatively, there is some aspect of creation that exhibits what would be described as a compassionate event. What we see here is that this notion of compassion is reflected first in foremost in this number 248, which is one of the suggestions for the number of particles in our universe.

In our first article on the number 248, we talked in length about its connection with loving-kindness (חֶסֶד ), an attribute of the heart that is very close and related to compassion. Actually, loving-kindness and compassion complement one another.

As we saw, loving-kindness is the attribute of our first patriarch, Abraham, whose name in Hebrew (אַבְרָהָם ) equals 248. For each of the emotive sefirot from loving-kindness through kingdom there is a corresponding archetypal soul that embodied the qualities of that sefirah. The full correspondence is as follows (we have noted both the name of thesefirah and its inner experience or motivation):

As we can see, compassion is the special property our third patriarch, Jacob. The special connection between loving-kindness and beauty is described in the verse: “Jacob, who redeemed Abraham.” As explained in the Tanya, the meaning of this verse is that to arouse loving-kindness and love (the attribute of Abraham), especially when for some external reason it has been concealed and lost, one needs to convey compassion (the attribute of Jacob).

Practically speaking, if there is a soul who is lost in darkness, whether it be an inability to love God, love others, or even love itself, it is difficult to get through to it through acts of loving-kindness. Instead, compassion and mercy should be the focus. These will arouse the dormant love and loving-kindness in that soul. In other words, compassion (Jacob) redeems, that is, reveals love (Abraham). In any event, the two are very close in meaning and therefore related to one another.

So, we have an image of womb, which is the first stage of creation, from which all of creation originates. Through compassion, which is a means of expressing loving-kindness, all of our 248 components of primordial matter, חֹמֶר , are created.

Permutation Theory

Let us take another moment to more deeply understand how compassion is related to a womb. In Kabbalah, we have a topic known as the secrets of permutation, or permutation theory. The goal of Kabbalistic permutation theory is to correctly correspond any three elements, let us call them a, b, and c, with the six emotive sefirot, from loving-kindness to foundation.

Given 3 distinct elements, a, b, and c, clearly, there are six possible permutations: abc, acb, bac, bca, cab, cba. Using a very basic mathematical transformation rule, these six permutations correspond to the six attributes of the heart in the following manner:

This is the bare-bones correspondence and is very straightforward. However, now let us note that the given any three terms, their identification as a, b, and c is not arbitrary. Rather, Kabbalistic permutation theory requires that the three terms correctly correspond to the three intellectual sefirot: wisdom (a), understanding (b), and knowledge (c).

Correctly identifying which of the three terms corresponds to which of the intellectual sefirot is the crux of the issue and requires that one have a great deal of experience with this topic (i.e., having studied how this is done for many 3-letter roots) and a great deal of Kabbalistic intuition (something that obviously cannot be taught).

Now, let us rewrite the above correspondence using more traditional Kabbalistic notation. For a, b, and c we use the three unique letters of God’s essential Name,Havayah, י (yud), ה (hei), and ו (vav), which themselves correspond to wisdom, understanding, and knowledge, respectively. In addition, we will now note the correspondence of the letters י , ה , and ו , to the sefirot as well, including the three heads of the sefirah of crown.

Now, let us return to our 3-letter root, חמר . How do we go about permuting it correctly? In this particular case, the shortest method is by noting that we have already clearly identified the permutation רחם (meaning, “womb,” as above) with the inner experience of the sefirah of beauty. Given this identification, it is merely a technical exercise to reconstruct the full permutation model of the root חמר :

Accordingly, חמר , or “primordial matter” is the permutation that corresponds to loving-kindness. Now, we can see how each of the three root letters corresponds with the three intellectual sefirot: wisdom, understanding, and knowledge. As we shall see, in this particular case, all three intellectual sefirot will, in context, be the intellectual sefirot of the partzuf of wisdom.

The letter ח (chet), corresponds to the sefirah of wisdom. Indeed, ח is the first letter ofחכמה , the Hebrew word for “wisdom.”

The letter מ (mem) literally means “water” in Hebrew. Whereas wisdom is likened to a flash of insight, like an almost impossible to catch lightning bolt, understanding is likened to waters—indicating that the sudden insight has jelled, as it were, into a perceptible substance—water.

Finally, the letter ר (reish) literally means “head.” In Hebrew, the word “head” also means a “mind-set” or “head-space.” After understanding jells wisdom into a useful form, knowledge takes the understanding and converts it into a mind-set, or element of our consciousness.

Now, this particular 3-letter root, חמר , is especially related to the sefirah of wisdom. First, because as mentioned earlier, the numerical value of Abraham’s name is the same as חמר , 248. Since Abraham is the archetypal soul of loving-kindness, wisdom, which is above loving-kindness, is also known as “the God of Abraham.” 

But, the link between wisdom and חמר , meaning “primordial matter” is even stronger because the entire creation of our universe begins with wisdom. As the verse notes: “You have created all with wisdom.” All of primordial matter emanates from God’s wisdom.

The essential quality of water is that it flows from a high place to a low place. This quality is why wisdom is compared to water, for wisdom too (particularly God’s wisdom—the Torah) descends from a high place to a low place and does not change in the process.

Finally, the letter ר , which we said means head is alluded to in the very first word of the Torah, בראשית (“In the beginning”), which literally means “with the head.” The various translations of the Torah into Aramaic translate this word as “With wisdom,” indicting that wisdom is indeed a “head.”

Interestingly, חמר is the root of the word for “donkey.” We know that the prophet pictures the Mashiach coming on a donkey. The way this was always explained even before the revelation of Kabbalah, is that the donkey symbolizes the matter in the universe. The image of the Mashiach riding a donkey symbolizes that the Mashiach has a complete understanding and control of all physical matter in the universe. In other words, the Mashiach will have to be a great physicist. What we are adding now, is that the image of the donkey itself alludes to the (possible) 248 particles in creation.

248 and the Letter Yud

In our previous article on 248, we explained a simple mathematical function how from 2 numbers, 2 and 10 we can derive 248

F[a,b] = a2 + b2 + (a +b)2

Now we are going to introduce another function that will produce the number 248 in another manner. The function we will look at is:

F’[a,b,c] = a(b ^ c) ^ b(a ^ c) ^ c(a ^ b)

As we can see, this function F’ takes three integers: a, b, and c. The numbers that we will substitute for a, b, and c all have to do with the process of creation, as described in Kabbalah. More specifically, they relate to what in Kabbalah is considered the initial or essential point of matter. Again, by “matter” we are referring to the very rawest material that is not yet actual physical matter, as we know it, and perhaps not even affecting what we call physical matter.

Of the 22 letters of the Hebrew alphabet, the letter that symbolizes the very beginning of everything is the letter yud (י ) which is drawn like a point. It represents the seminal, initial point of something that is about to be born. The letter yud thus represents the beginning of all reality. 

Every letter in the Hebrew language has a name. In Kabbalah, when the name of the letter is spelled out, it is called that letter’s “filling.” A full listing of the Hebrew letters and their fillings can be found in the glossary under “Hebrew Alphabet.” Every such filling comprises the root letter, called the mother letter; the additional letters that go into its name, or filling are, to extend the metaphor, considered born out of the mother. In other words, when the letter appears by itself, the additional letters of its name are described metaphorically as pregnant within it.

This is not the case with most other languages. In English, for example, the names of the letters A, B, C, etc., cannot be written out. Thus, the names do not really contain any additional letters. Instead, the names are just insiginifcant vowel sounds that are sometimes not even related to the sound associated with the letter (for example: H, which in English is called an “aich,” in French, an “ash,” etc.).

The name of the 10th Hebrew letter (י ) is yud. When its name is written in Hebrew, it becomes: יוד , the letter yud (י ) with an additional vav (ו ) and dalet (ד ). The word “yud” in Hebrew is very similar to the word for “hand” (“yad”). The letter yud is the first letter of God’s essential Name, Havayah (י־הוה ), wherein it indicates a seminal point of creation; for this reason, the yud in Kabbalah is symbolic of a primordial hand, like the hand with which God created the world. But, the word “yud” also has an additional vavin it, which can be likened to an extended arm, which is then attached to the palm of the hand. In Kabbalah, it is explained that the three letters of the name “yud” denote three stages of development.

In his commentary on Sefer Yetzirah (The Book of Formation), the Gaon of Vilna (theGra) writes:

In every square solid [meaning, a cube] there are 6 planes, 12 pillars—the 12 diagonal borders—and 8 points between the pillars. These three aspects [of the solid] correspond to the three letters of the letter yud [when written out], יוד [meaning, that points are represented by the form of the letter י , pillars (i.e., lines) are represented by the form of the letter ו , and planes are represented by the form of the letter ד ]. And the entire Name is based on these three letters [the first three letters of God’s essential Name, י־הוה ,Havayah, are based on the י , the ו , and the ד ]. And the full value of the Name is 26. When we add the material of the solid itself, which contains them all and is represented by the fourth letter of Havayah [i.e., the final ה ], then we have that the entire value becomes 27, like the number of letters in the alphabet [including final letters], and the value of the Name Havayah with an additional one for the tip of the yud, as explained in Sefer Yetzirah.

In other words, the form of the three letters yud vav dalet (יוד ) that spell the name “yud,” correspond to the first three spatial dimensions: a point (the yud), a line (the vav), and a plane (the dalet). In Kabbalah, the point, line, and plane represent the most basic maturation and developmental process. 

So not only does the form of the letter yud (and its “mother” letter—i.e., the first letter in its name) denote the seminal point of the beginning of creation, but when the full name is written (i.e., the two letters pregnant within the yud are revealed), with its additional letters, the yud represents the evolution of multi-dimensionality. Furthermore, the numerical value of the two additional letters vav and dalet (וד ), that are pregnant within the yud, is equal to the numerical value of yud (י ); both are equal to 10. This means that a filled yud is like two yud’s. 

After this lengthy introduction about the significance of the letter yud, let us now take its three letters and plug them into the function introduced above:

F’[10,6,4] = 10(6 ^ 4) ^ 6(10 ^ 4) ^ 4(10 ^ 6) = 100 ^ 84 ^ 64 = 248

What this function is doing is multiplying each letter of yud with the sum of the two other letters. This function expresses a very high level of inter-inclusion within the letter yud. In the end, we see that from the initial point of all of reality, the letter yud, we get the number 248!

In the first article on 248, we took the three components that came out of our function F and used them to make a quadratic series.

Now, let us do the same for the three components that come out of our new function (F’):

So the base of our new series is -4. Let us now extend this series backwards and forwards:

12     40    64   84   100  112  120  124  124   120  112  100   84   64    40    12
28     24    20   16    12     8     4      0     -4    -8   -12  -16  -20  -24  -28
-4      -4    -4    -4    -4    -4    -4    -4    -4    -4    -4    -4    -4    -4

What we have discovered is that this is a symmetric series, shaped like a parabola.

In Kabbalah, this type of symmetry—where there are two identical numbers around which the series repeats in both directions—is dubbed feminine symmetry. In this series, the pair of identical numbers that are at the zenith of the parabola are 124 and 124. There is no mathematical reason that forces this to be the case, but the sum of the symmetry pair—124 and 124—is itself 248, a beautiful example of mathematical self-reference.

In addition, the minimal positive value of the parabola is 12—the value of the word בי , which we used in our previous article to generate 248 using the function F. So this series summarizes much of the mathematical analysis we carried out in the first article.

Primordial Matter

The matter that we encounter in our everyday lives has form. We cannot really imagine what formless matter might look like (since it has no form). Still, the matter that the number 248 relates to is so primordial and abstract that it is exactly this type of formless matter.
Science too discusses formless matter today in the terminology of elementary particles, which are actually matter in a formless state. Among the many elementary particles, we find that there are both matter particles and virtual particles, indicating that indeed elementary particles are a precursor to the matter that we are familiar with in our lives.

In Hebrew, abstract matter (the first thing that was created from nothing) is called chomer hiyuli (חֹמֶר הִיוּלִי ), which literally means “ethereal matter.” The numerical value of the word hiyuli (הִיוּלִי ), which means ethereal, is 61, the same as the numerical value of the Hebrew word for “nothingness” (אַיִן ). This further explicates that this initial matter is still in a totally formless state.

In Chassidut, the hiyuli matter is identified as existing in the World of Creation —the first World (or state) in which there is the possibility of being. When Dirac said that an electron is not a thing, he meant that it is entirely without form; this is exactly what the sages are referring to when they speak of the hiyuli matter.

There is another term used to denote matter in a pristine state: chomer gelem (חֹמֶר גֶלֶם ), which literally means “raw material.” As we will now see, chomer gelem is actually a context-based synoym for hiyuli matter. An example of raw material would be like clay, which the potter will take and soften by adding water and then be able to give it the form he likes by shaping it on his potter’s wheel. The sages use this metaphor to explain the formation of man. 

How is “raw material” different from the hiyuli? Chasidic teachings explain that difference is in context. First, the hiyuli is created in the World of Formation—where reality is still merely in potential —and therefore any potential reality that exists in the World of Creation will be made out of formless matter. Then, in the World of Formation—where reality is already actualized—the hiyuli is used as “raw material”—the precursor to matter as it exists in the World of Formation.

Let us now look at this word “raw” (גֶלֶם ), from a mathematical perspective. Its numerical value is 73, the same as that of “wisdom” (חָכְמַה ). The yud discussed in the previous section is often referred to as a gelem because it refers to the sefirah of wisdom. Another way to explain how the yud is related to the gelem, the raw material, is by imagining how a scribe writes with ink on parchment. First, he dips the quill in ink. As he brings the quill to touch the parchment, the first point formed from the ink on his quill, is the point from which the letter will be formed. This point, or seminal drop, is always a yudand constitutes the “raw material” from which the letter is formed. Every time that the scribe starts writing a letter, he begins with a yud and of course, he ends with a yud. Similarly, when the two most essential Names of God, Havayah (י־הוה ) and Adni (אדנ־י) are inter-weaved, they form the complex name seen in any Kabbalistic or SephardiSidur whose first and last letters are yud. This is called “wisdom in the beginning, wisdom at the end.”

The image of the scribe is applicable to everything in reality. Everything in reality begins with a seminal point of raw material and in the end returns to a point of raw material. Numerically, when we multiply גֶלֶם (meaning “raw”) by 2 we get 146, which is the value of “world,” or “reality” (עוֹלָם ) indicating that indeed all of reality, as we experience it, is enclosed within two instances of raw material.

248, the Commandments, and Creation

No discussion of 248 is complete without looking at its relationship with 365, since the 613 commandments of the Torah divide into 248 prescriptive and 365 prohibitive commandments.

In the previous article on this subject, we explained that the most important Torah reference to 248 is the 248 positive or prescriptive commandments. As we noted, every commandment has two aspects to it: a motivational/intentional aspect and an active aspect (the performance of the commandment). Multiplying 248 by 2, we get 496, which is the numerical value of “kingdom” (מַלְכוּת ). 496 is also the triangle of 31, meaning the sum of integers from 1 to 31. The Torah also contains 365 prohibitive commandments. If we add the 365 prohibitive commandments to the 2 aspects of the positive commandment, we get altogether 861. 861 is also a triangular number: 861 = r41. This means that 365 is the sum of integers from 32 to 41. 861 is also the numerical value of “the Holy Temple” (בֵית הַמִקְדָשׁ ), of “Rosh Hashanah” (רֹאש הַשָׁנָה ), and more.

In Hebrew, the word for prescriptive (as in presecriptive commandments) is עשה . If we fill the letters of this word (like we did before for the letter yud), we will get: עין שין הא , whose numerical value is 496, or 2 times 248. This is a beautiful numerical restatement of the notion that every prescriptive commandment actually has two aspects to it. Furthermore, the word “prescriptive” stems from the word for “action” in Hebrew, the name of the lowest of the Four Worlds, the World of Action. Each of the Four Worlds corresponds to a particular sefirah. The World of Action corresponds to the sefirah of kingdom (מַלְכוּת ), whose numerical value, as we mentioned, is also equal to 496!

The number of prohibitive commandments, 365, is a product of the two prime numbers 5 and 73. 73, as we just saw is the value of “raw material” (גֶלֶם ) and the value of “wisdom” (חָכְמַה ). 73 is the 22nd prime number. This refers to the manner in which wisdom reflects the 22 letters of the Hebrew alphabet with which the world was created. In the Bible we find the verse: “You made everything with wisdom,” while in Kabbalah we find that the world was created with the Hebrew letters.

When we break 248 into its prime factors, we find that 248 = 2 ∙ 2 ∙ 2 ∙ 31. There is an important mathematical tool in Kabbalah called finding the “foundation” or “base” (יְסוֹד ) of a number. The base of a number is defined as the sum of its prime factors. So, the base of 248 is 2 ^ 2 ^ 2 ^ 31 = 37 equal 37. Numerically, 37 is strongly related to 73 as 37 is the midpoint of 73, which we write in mathematical notation as:

37  73

This also means that the product of 37 and 73 is the triangle of 73, or the triangle of “wisdom,” which is 2701. 2701 is the numerical value of the first verse of the Torah:בְּרֵאשִׁית בָּרָא אֱ־לֹהִים אֵת הַשָּׁמַיִם וְאֵת הָאָרֶץ .

In the second verse we read, “And the spirit of God was hovering above the waters” (וְרוּחַ אֱ־לֹהִים מְרַחֶפֶת עַל פְּנֵי הַמָּיִם ). The numerical value of these words is 372.

The fourth verse of the Torah reads, “And God saw that the light was good; and God separated the light from the darkness” (וַיַּרְא אֱ־לֹהִים אֶת הָאוֹר כִּי טוֹב וַיַּבְדֵּל אֱ־לֹהִים בֵּין הָאוֹר וּבֵין הַחשֶׁךְ ). Its numerical value is 1776, also a multiple of 37: 1776 = 37 ∙ 48! There are a multitude of appearances of the number 37 in creation.

The prime factors of 365 are: 5 and 73, which means that its base is 78, or 3 times 26, the value of God’s essential Name, Havayah (י־הוה ).

Adding the bases of 248 and 365, we get 37 ^ 78 = 115, or 5 times 23. 23 is the companion number of 37 in Kabbalah, a topic discussed in length elsewhere.

Torah, Faith, and Wisdom

How does 73 relate to 248? It is explained that unlike all of his righteous predecessors, Abraham began his service of God with simple faith, and it was from simple faith that he came to wisdom. In other words, whereas the righteous fathers of the world such as Adam, Noah, and Shem, the son of Noah, learnt the ways of God as Divine wisdom, Abraham began with an earnest and sinere faith in God. His sincere faith was that God is truly here and that He can be found. Seeing his earnest faith in Him, the sages tell us that God gave Abraham wisdom that flowed out of his kidneys. From this we learn that the path of the Abraham’s descendants, the Jewish people, has always been to first believe earnestly in God (and follow His Torah) and then God opens the wellsprings of wisdom. The more a person searches for God, the more God reveals Himself to him.

Now, the numerical value of “faith” (אֱמוּנָה ) is 102. Then, his two kidneys were opened to him as wellsprings of wisdom. Adding one “wisdom” (חָכְמָה ), or 73, to “faith,” we get 175—Abraham’s lifespan. This denotes the first level of Divine wisdom that Abraham attained, which is referred to as the higher wisdom. Adding a second “wisdom,” meaning another 73, we get 248. The second level of wisdom refers to the lower wisdom, i.e., the wisdom of the natural world. That Abraham attained both means that he was able to reveal the Divine wisdom within natural wisdom, or, to use more modern terminology: to unite Torah with science.

So, we have that 248 = 102 ^ 2 ∙ 73, or “faith” with 2 “wisdoms.” But, before we saw that 365 is equal to 5 times “wisdom.” What this means is that 613, the number of commandments in the Torah—the essence of God’s will—is equal to “faith” plus an additional 7 “wisdoms”:

613 = אֱמוּנָה ^ 7 ∙ חָכְמָה

The seven wisdoms that divide into 2 and 5 refer very clearly to the candles in the Temple Menorah. The order of lighting the 7 candles in the Menorah divides them into 5 and 2. The Menorah itself was made out of one chunk of pure gold. The word for “gold” in Hebrew is זָהָב , whose letters exhibit this same division of 7 into 5 and 2: the first letter, zayin (ז ) is equal to 7, and the next two letters, hei (ה ) and bet (ב ) equal 5 and 2 respectively.

So, the essence of the Torah as the revelation of God’s will begins with “faith” to which are added seven wisdoms.

The ratio of 1 faith to 7 wisdoms is indicated in the word אז , a very important word in the Torah. The first word of the Song of the Sea sung by Moses and the Jewish people is this word, from which we learn that it inspires the power of song in the soul. In fact, since the entire Torah is called a song, we see once more, form another perspective, that the Torah is inspired by this relation of 1 to 7.

The division of the 7 wisdoms into 2 and 5 and the ratio of 1 to 7 all in relation to faith are found together in a single verse that is part of the Song of Ha’azinu, the second great song of the Torah recited by Moses just before his passing. The verse reads: “God is a God of faith, he is righteous and he is straight” (אֵ־ל אֱמוּנָה וְאֵין עָוֶל צַדִּיק וְיָשָׁר הוּא ). “Faith” (אֱמוּנָה ) is equal to 102. Beautifully, the adjective “righteous” (צַדִּיק ) is equal to 204, or 2 times 102 (“faith”) and the adjective “straight” (יָשָׁר ) is equal to 510, or 5 times 102 (“faith”). So we have, 1 times 102, 2 times 102, and 5 times 102.

This was to give us a sense of how these two numbers, 248 and 365, relate to one another. In our analysis, we found that 365 is produced from 248. Nonetheless, it is important to know that in Kabbalah, it is usually the prohibitive commandments that are considered to correspond to the first two letters of God’s essential Name, Havayah, while the prescriptive commandments correspond to the final two letters—giving the impression that 365 is higher than 248. The explanation for this is that all of the Torah’s commandments represent God’s will and thus originate in the sefirah of crown. But, in the crown itself, the prescriptive (positive) commandments originate in the pleasure aspect of the crown (the second head of the crown), while the prohibitive commandments originate in the will aspect of the crown (the third and lowest of the three heads). The corrolary of this correspondence is that the pleasure caused by the positive commandments is greater than that of the prohibitive commandments. Actually, according to this analysis, the purpose of the prohibitive commandments is to clear a purified path and area through which and into which the positive commandments can draw down light. When a person transgresses one of the prohibitive commandments, a blockage is created inhibiting the drawing down of this light.

248 As a Figurate Number

Now, we are going to turn to another important mathematical property of 248, 365, and 613. There are various types of figurate numbers—numbers that can be represented by a collection of points arranged in some symmetric figure.

The three most basic types of figurate numbers are the triangle (which we have already met above), the square, and the inspirational. Let us draw the first few triangular numbers:

The squares are probably familiar to everyone, so we defer drawing them. The first few inspirational numbers look like this:

The inspirational numbers have a second isomorphic shape, which we will now draw as well:

The function that defines the series of inspirational numbers is §n = n2 ^ (n – 1)2, where §n denotes the nth inspirational number. It is clear from the function and from the figure of the inspirational numbers, that each is a sum of two consecutive squares.

In addition, it is easy to show that every square number is the sum of two consecutive triangular numbers, or:

n2 = rn ^ r(n – 1)

Let us illustrate everything that we have seen to this point with a simple chart:

1     3     6     10    15   21    28    36   45    55    66   78    91   105  120 136  153  171 190
4     9    16    25    36   49    64    81  100  121  144 169  196  225  256 289  324  361
13     25    41   61    85   113 145  181  221 265  313  365  421 481  545  613 685

In the first row, we have written down the triangular numbers. In the second row, underneath each pair of triangular numbers, we have written its sum. Notice that as expected, the second row is the series of square numbers. In the third row, we did the same for the square numbers. Again, as expected, the third row is the series of inspirational numbers.

Now, note that both 613 and 365 are inspirational numbers. §19 = 192 ^ (19 – 1)2 = 613 and §14 = 142 ^ (14 – 1)2 = 365. But, 248 is not an inspirational number. In fact, it is easy to see that because the square numbers alternate form odd to even, and every inspirational number is a sum of squares, no inspirational number can be even.

But we will now see that it is related to inspirational numbers. Let, us write a fourth row following the same scheme we have been using, except now let us fill in the left end of each row with 0’s in order to get the full series in each row:

0     0     0      0      1     3      6     10   15    21    28
0     0     0      1      4     9     16    25   36    49
0     0     1      5     13   25    41    61   85
0     1     6     18    38   66   102  146
1     7    24    56   104 168  248

The fourth row, the sum of inspirational numbers is the series of 2nd order inspirational numbers. The fifth row is then the series of 3rd order inspirational numbers and the seventh of those is 248!

Not only that, but, beautifully, 248 is the sum of the two 2nd order inspirational numbers 102 and 146, which we have seen above equal “faith” (אֱמוּנָה ) and “world,” or “reality” (עוֹלָם )!

Altogether, in order to get to 248, we have used 35 non-zero triangular, square, inspirational, 2nd-order inspirational, and 3rd-order inspirational numbers. On Friday night, as the main part of the kidush, we recite the three verses from Genesis that describe the Shabbat. Between them, these three verses have exactly 35 words. Let us order these three verses in a 5 by 7 array and correspond them with the 35 non-zero numbers in our above derivation:

In a beautiful example of internal reference, the 35th number is 248 and the 35th word is “to do” (לַעֲשׂוֹת ); recall that 248 is the number of prescriptive commandments, commandments that we are obliged “to do!” (עַשֵׂה ). We would not be amiss searching for other meaningful connections between the number and words in this joint array.

The sum of these 35 numbers is 1449, or 7 times 207, where 207 is the value of “light” (אוֹר ). Abraham, whose name equals 248, has a strong affinity to light. The the sages say that “Abraham began to shine forth light,” that is, Divine consciousness, and he is the archetypal soul that corresponds to the sefirah of loving-kindness, the sefirah of the first day of creation on which light was created.

248: The Channel of Prophecy

In the previous article on 248, we concentrated on how 248 is the channel through which God created the world. From the Torah it is clear that God created the world through His Divine speech (“And God said…”). Altogether, the sages count 10 such measures of speech in the account of creation.

Though our physical reality bears witness to the Creator, it does not reveal His will or intent. To this end, God created man with the ability to prophecy, that is, to experience and relate the Divine speech that continually reverberates throughout reality. Indeed, in the previous article we saw that the ability to hear God’s word is a result of man being made “in God’s image” (בְּצֶלֶם אֱ־לֹהִים ), an idiom whose numerical value is also 248.

A related point is that one of the phrases that repeat many times (more than 70!) in the Torah is “And God spoke” (וַיְדַבֵּר י־הוה ). In the vast majority of cases, these two words appear when God is addressing Moses. The numerical value of these words, “And God spoke” (וַיְדַבֵּר י־הוה ) is 248. Moses is considered the “father of prophecy.” When God addresses him, He is actually opening the channel of prophecy to Moses and through it, all of the Torah was given to us. It is thus very significant that this channel is equal to 248.

In our first article on the significance of the number 248, we saw that there are two distinct aspects to Abraham himself and hence two aspects to the number 248. Earlier in this article, we explained that these two aspects of 248 correspond to the intentional and active dimensions of each of the 248 prescriptive (positive) commandments. Now we have seen another explanation for the duality inherent in 248. The first, and lower aspect of 248, is found in God’s words that imbued man with the potential for prophecy during creation. The second, and higher aspect of 248, is found in the channel that God opens in order to deliver prophecy to Moses. Though Moses is considered the father of all prophecy, the first person to be described as a prophet in the Torah is Abraham. As such, whenever God addresses Moses, He does so through the channel that corresponds to Abraham’s higher soul-root—i.e., through Abraham’s role as the archetypal soul of loving-kindness. Abraham’s soul-root is the conduit through which God reveals His will, i.e., the Torah, to the world. In fact, the Torah is called “A Torah of loving-kindness.”

Loving-kindness was the energy with which God created the world initially. The Zohar describes loving-kindness as, “The measure that flows through all six days of creation.”And, loving-kindness is the energy with which the world is perfected through prophecy and the giving of the Torah, as the verse states, “The world will be built of loving-kindness.” These two aspects of loving-kindness reflect Abraham’s higher and lower soul-roots.

The Dualism of 248: Patriarch and Firstborn

But, the way in which they equal 248 is interesting in itself. The gematria of the first word “He spoke” (וַיְדַבֵּר ) is 222, or 6 ∙ 37. Recall that 37 was the base (i.e., the sum of the prime factors) of 248). Since 37 is the numerical value of “Abel” (הֶבֶל ), which has 3 letters in Hebrew, 6 times 37 is the sum of all six possible permutations of the 3 letters of “Abel,” הבל הלב בהל בלה להב לבה = 222. The second word, God’s essential Name, Havayah, of course equals 26.

But, more importantly, 222 is the value of “firstborn” (בְּכֹר ). Thus, Abraham (אַבְרָהָם ), who is the archetypal embodiment of “God’s image,” is also “God’s firstborn” (בְּכֹר י־הוה). Normally, we are accustomed to relating to Abraham as our first patriarch. What does it mean that he is God’s firstborn? In Kabbalah, all Jewish souls are considered to come from a single common origin called a womb. , The first soul to come out of that womb was Abraham—the first Jew. This is another beautiful way to understand Abraham’s duality. On the one hand, he is our first patriarch; on the other hand, he is our eldest brother.

We see this duality exhibited in the Ten Commandments as well. The fifth of the Ten Commandments is to honor one’s father and mother. The sages explain that this includes honoring one’s elder siblings, especially the firstborn. According to Kabbalah, the reason for this is that all the siblings in a family are born through the conduit opened by the firstborn child. The firstborn is like a second father, which is why he gets a double portion of the inheritance.

In our first article on 248, we explained that the three-letter root of “matter,” חמר is one of the 7 three-letter roots whose six possible permutations are actual roots. The three-letter root whose letters are the same as “firstborn,” בכר is another of these 7 special roots. Alphabetically, it is also the first. In addition, its numerical value, 222, is very special as it is the sum of 2 ∙ 100, 2 ∙ 101, and 2 ∙ 102, and each of its three letters, in order equals one of these: ב = 2 ∙ 100; כ = 2 ∙ 101; ר = 2 ∙ 102.

The phrase “And God spoke” also alludes to primordial matter. This is because the first word “He spoke” (וַיְדַבֵּר ) stems from the same root as the word for “thing” (דָבָר ). This can allude to formless matter, and thus the words “And God spoke,” can be understood as referring to God’s bringing forth matter through His speech. Furthermore, because the word for “thing” also means a “leader,” specifically the king, like the Mashiach, this tells us that the leader of the generation is the one who truly understands how to manipulate and order matter.

248, Adam, and Eve

Let us look at how 248 figures into the creation of Adam and Eve. Had they not sinned by eating from the Tree of Knowledge, Eve would not have been called “Eve,” but rather “Chayah” (חַיָה ), which literally means “alive.” This word stems from the idiom, “a living soul” (נֶפֶשׁ חַיָה ), which is how the Torah describes the creation of man: “And God formed man, soil from the earth… and man was a living soul.” Thus, to be a living soul, Adam had to be attached to his wife. But, once she convinced him to sin, Adam decided that her name would be “Eve.”

Mathematically, the sum of “Adam” (אָדָם ) and “Eve” (חַוָה ) is 64 = 82. In the mathematical analysis of the Torah, square numbers represent a state of consummate wholeness or completion. One of the reasons for this is that in Kabbalah, inter-inclusion always involves a square number. Inter-inclusion means that given two corresponding models—i.e., both have the same n number of elements—their inter-inclusion involves n2 elements. One example of this is the Counting of the Omer, which lasts for 49 = 72 days, because we are counting through the inter-inclusion of the seven lower sefirot, from loving-kindness to kingdom. There are many tens of thousands of examples of the occurrence of square numbers in the Torah text and in the various sayings of the sages.

What then was to have been the relationship between “Adam” and “Chayah.” Thegematria of “Adam” is 45, while that of “Chayah” (חַיָה ) is 23. 23 is the midpoint of 45. So, originally, the female was to have been the midpoint of the male. In Kabbalah, the empty void within His infinite light that God created in which to create our reality is called the midpoint of the womb. In Hebrew, “Chayah” also means “midwife,” as the midwife helps women manifest their power to give birth out of their womb.

But, if we add “Adam” (45) and “Chayah” (23) we get 68, which is the gematria of “life” (חַיִים )!

But, astoundingly if we apply what is the equivalent of a “dot product” (i.e., multiplying the first letter of one word by the first letter of the second, the second letter of the one with the second letter of the other, and so on) of the two names “Adam” (אָדָם ) and “Chayah” (חַיָה ), we will get:

א ∙ ח ┴ ד ∙ י ┴ מ ∙ ה =
1 ∙ 8 ┴ 4 ∙ 10 ┴ 40 ∙ 5 =
8 ┴ 40 ┴ 200 = 248!

Notice that 8, 40, and 200, are the numerical values of the three letters ח , מ , and ר , in exactly the same order that they appear in the word “matter” (חֹמֶר ). It is clear then that the union (symbolized by the “dot-product” operation on their names) of Adam and Eve, in their ideal state of being, gives us 248, the value of “in God’s image” (בְּצֶלֶם אֱ־לֹהִים ), as above.

Let us take this mediation on Adam and Eve another step further. In Kabbalah, the masculine is represented by direct light, but the feminine is represented by reflected light. This suggests that instead of applying the “dot-product” as we have above, we should first reflect (that is, reverse) the order of the letter of “Chayah” and then carry out the operation. Let us see what happens when we do this:

א ∙ ה ┴ ד ∙ י ┴ מ ∙ ח =
1 ∙ 5 ┴ 4 ∙ 10 ┴ 40 ∙ 8 =
5 ┴ 40 ┴ 320 = 365!

This is truly astounding result and one of the most beautiful mathematical analyses in the Torah that we are aware of. Multiplying “Adam” by “Chayah” (in reverse order) yields 365, the number of prohibitive commandments that we have discussed in great length above. This beautiful relationship tells us that the purpose of all the commandments is to help us return to the ideal Edenic state. In that state, our consciousness is in naturally tuned to the 248 components of the universe and to the 365 components of time, as mentioned in our first article.

248 and Resurrection

The number 248 is not only connected to the creation of the world and to the transmission of God’s will, it is seminal in the ushering in of the final stage of our reality, the resurrection of the dead.

The sages teach us that the resurrection of the dead is possible thanks to a mysterious bone that does not rot in the grave. That bone will serve as the seminal yud, or point of matter from which the entire body will be reconstructed. The bone is called “the luze bone” (עֶצֶם הַלוּז ) and its numerical value is 248!

That the body will be reconstructed from this bone offers us another angle on the notion that 248 indeed expresses the essence of matter. Here it lies at the core of our biological life. Since Abraham’s name also equals 248, we now know that it is Abraham’s soul that is the seminal, or “luze bone,” of the entire Jewish people. The sages liken our state of exile to the state of a deceased person lying in the grave. Coming out of the exile is like coming out of the grave.

The Talmud tells us that when we are dreaming we can see paradoxically impossible images, the likes of which we cannot see elsewhere. This is during dreaming, the mind exercises its inherent power to carry, or bear opposites. The sages tell us that the most amazing paradoxical image that is impossible to see even in a dream is that of “an elephant passing through the eye of a needle.” Indeed, this is more than just an amazing image; it is also a “funny” (מַצְחִיק ) image, as the value of “funny” in Hebrew is also 248.

The Aramaic words that they use for “eye of the needle” are קופא דמחטא . The Hebrew words for “eye of a needle” (קוֹף הַמַחָט ) are very similar to the Aramaic and actually can also mean “the monkey of a needle.” In any case, the Hebrew idiom for “eye of a needle” (קוֹף הַמַחָט ) also equal 248. In this particular idiom, the first word “eye” (קוֹף ) is equal to 3 ∙ 62, while the second word “of the needle” (הַמַחָט ) is equal to 62. So within the idiom we have a ration of 3:1.

What this implies is that the “luze bone” is “the eye of the needle” itself. The word “elephant” (פִּיל ) in Hebrew comes from the word for “wonder” (פֶּלֶא ) and according to the sages, the elephant represents “wonders of wonders.” Every creature sings a song to God, the elephant sings: “How great are Your actions God, Your thoughts are so deep.”This is probably what the elephant thinking as it passes through the eye of the needle, for this is truly the greatest wonder.

What does this strange and wondrous image symbolize? In Modern Physics, we would answer that the eye of the needle represents an infinitesimally small point through which elementary particles are created and subsequently annihilated (an idea that is the basis of quantum electrodynamics). But, this only takes care of the eye of the needle. What does the elephant represent. Like we said it represents a miracle or wonder. Thus, if something as large as an elephant were to be able to pass through such an infinitesimally small point, the wonder that would be revealed would be the resurrection of the body—like a human body being created and a soul entering it. These are all visualizations meant to help us meditate and understand the significance of 248.

The greatest wonder is the infinite power of God entering the infinitesimally small vacuum—the eye of the needle, which ultimately serves to sow (that is, connect) all of reality together.

248 and the Shema

The Torah commands us to say the Shema twice a day, once in the morning once in the evening. The Shema is the essential statement of our faith in one God: “Hear O’ Israel: God is our God, God is one” (שְׁמַע יִשְׂרָאֵל י־הוה אֱ־לֹהֵינוּ י־הוה אֶחָד ), whose full value is 1118. This number is the lowest common multiple of God’s essential Name, Havayah (י־הוה ), which equals 26 and Elokim, which equals 86, the two names that are equated in this verse.

In the Shema, the three words that have a middle letter are שְׁמַע יִשְׂרָאֵל אֶחָד , and the middle letters are: מ , ר , and ח , whose sum is of course 248! The three middle letters themselves are one of the six permutations of חמר . So this is a beautiful allusion to 248 in the declaration of our faith in one God.

Going back to what we saw earlier, this particular permutation corresponds to the sefirah of victory and its literal meaning is to spread or to smear. Victory is the soul-root of Moses, who is the one teaching us the Shema, because unlike the first four books of the Torah, the Book of Deuteronomy, where the Shema appears, was said by Moses, with the Divine Presence speaking out of his mouth. So, this particular permutation of חמר , gave Moses the power to spread out eternally, forever and ever. Our faith is firm and victorious when we say the Shema! And, it is Moses who brings us to this level of faith.

There is another pair of words that is related to Moses and whose numerical value is 248: “the fountain of wisdom” (מַעְיָן הַחָכְמָה ). Earlier, we saw that 248 is the gematria of “faith” and two “wisdoms” (אֱמוּנָה חָכְמָה חָכְמָה ), where just “faith” and one “wisdom” is equal to 175, Abraham’s lifespan and then with another “wisdom” it equals his name. “The fountain of wisdom” is the name of one of the earliest works of Kabbalah attributed to Moses.

What does this add to our understanding? We can say that when a person merits to reveal how he has been created “in God’s image” (בְּצֶלֶם אֱ־לֹהִים ), he becomes a “fountain of wisdom” (מַעְיָן הַחָכְמָה ). In the terminology of the Ba’al Shem Tov, such a person uncovers his infinite wellsprings, which can then proceed outwards and rectify even the farthest extremes of reality.

The sages tell us that a sage in the Land of Israel is always called a “Rabbi” (רַבִּי ), as opposed to a sage living outside the Land of Israel who is called a “Rav” (רַב ). The difference between the two titles is the letter yud (י ), which represents the special infinite fountain of wisdom that can only be attained by being connected to the Land of Israel, whose “air makes one wise.” In practice, the fountain is the simple faith that the person has in the Almighty.

248 Particles and 92 Elements

In our first article on 248, we mentioned the relationship between the numbers 248 and 92. As we began, 248 has been proposed as the number of particles in nature—it is still a hypothetical statement. But, science today recognizes that there are exactly 92 naturally occurring elements in nature.

In the Torah’s account of creation, we find a beautiful connection between these two numbers. The 248th word in the account of creation is “the great” (הַגְּדֹלִים ), whose numerical value is 92! This word appears in the account of the fifth day and describes the “great serpents” that God created. Even more amazingly, this is also the only word in the account in creation that equals 92!

This word already appeared once earlier in the account of creation. On the fourth day, it appears in reference to “the two great luminaries” that God created—the sun and the moon. According to the midrash, before its luminescence was diminished, the moon illuminated space just as strongly as the sun. What happened to the moon parallels the primordial sin of Adam and Eve, which diminished their stature.

We bring this up because there is a well-known principle in Torah that “the whole follows its beginnings.” In this case, we see that the state of “greatness” (הַגְּדֹלִים ) within creation is (as yet) impermanent and unsustainable. Likewise, the sages reveal that the greatness of these “serpents,” which are actually sea creatures, was also impermanent. They explain that there were two such sea serpents, a male and female. Though God had willingly created both, He saw that if both would remain alive and allowed to produce offspring, no other form of life would be able to survive in the world. Therefore, God killed the female and salted her meat so that it could be eaten in the World to Come.

In the first account of creation, there is no word whose numerical value is 248. Instead, it is only through Abraham—who is described as the “greatest among great men”—that the final rectification of “greatness” can be attained.

Conclusion

Let us conclude this part of our study of the number 248 with a partial verse from Psalms whose numerical value is altogether 248: “God is known throughout Judah” (נוֹדָע בִּיהוּדָה אֱ־לֹהִים ). Since one of the words is God (Elokim), the same as the “God” in “in God’s image,” it follows that the two other words “Known throughout Judah” (נוֹדָע בִּיהוּדָה ) equal the value of “in the image” (בְּצֶלֶם ). Furthermore, the first and third letters of “in the image” (בל ) equal “throughout Judah” (בִּיהוּדָה ), while the second and fourth letters (צם ) equal “known” (נוֹדָע ). So, there is a lot of self-reference going on between these words.

What can we learn from the fact that this phrase equals 248? The idea here is that throughout Judah, that is throughout the Jewish people, there is shared the consciousness that the universe is divided into 248—first and foremost as it pertains to Torah, but also as it pertains to physics.