This article may contain special characters or charts. To view it correctly, you can select the PDF version of this document by clicking here
. (You can also download the PDF version of this document by right-clicking on this link and selecting "save link as...").
If you do not have Adobe Acrobat Reader and cannot view PDF files, please go here
and follow the instruction to install this free software.
This article is based on a recorded lecture. You can listen to part 1 of the lecture by clicking here
. You can listen to part 2 of the lecture by clicking here
Torah and Science: Converting the Wisdom of the Nations - Part 1
(read part 2)
Our topic is converting the wisdom of the nations. The key word is obviously "converting." Normally conversion implies a non-Jew who is converting to Judaism. Now, we know that we are not missionaries and we do not approach non-Jews and tell them that they must convert to Judaism. But if a non-Jew has an authentic desire and arousal to become Jewish—the archetypal case being that of Ruth—so of course, the Jewish people are truly interested in accepting any such person. Such a person after conversion is an inseparable and indistinguishable part of the Jewish people. The verse in the Torah that we learn this from is "There shall be one Torah for those who are born and those who converted…"1 Whether you are born into Judaism or you become a Jew by converting, you are seen as equal by the Torah. A convert is like a sojourner, but all the laws of the Torah and the way that those born Jewish should relate to him (or her) are exactly the same.
In fact, as pertains to the commandment to love your fellow Jew, in relation to someone who is Jewish by birth, you perform only one commandment: "You shall love your neighbor as yourself." But in relation to someone who is Jewish by conversion, you perform actually two commandments, "You shall love your neighbor as yourself," and "You shall love the convert." So the Torah commands us to give, as it were, a double portion of care and love to converts.
Conversion to Judaism will serve as our parable for understanding how to incorporate a piece of true wisdom from the non-Jewish world.
The first two parshahs of the Torah are of a universal nature. The setting is humanity in general. Noach was also a great scientist, he was the first to invent a plow and with that brought a measure of peace to the people of his generation. Then he was able to construct this truly tremendous structure called the ark, a structure that was able to contain all the animals—not a small feat by any measure. Noach was not Jewish; he was almost Jewish and was one of the greatest tzadikim of the generations before Abraham. In this respect, we should mention that if Adam had succeeded in his test and not eaten from the Tree of Knowledge of Good and Evil, he would have become the first Jew. So Adam had the potential to become the first Jew. Likewise, about Noach, the Torah says that he was a righteous and sincere man, still he was not yet Jewish. The first Jew was Abraham. There were many tzadikim before Abraham, but what set Abraham apart was his self-sacrifice for his fellow men. Noach did not sacrifice himself in order to save the people of his generation. Indeed, for this reason the flood was named after Noach,2 because he did not pray and try to save his generation it is attributed to him. The first one to pray for the people of his generation was Abraham,3 even though he was not successful. The high point of self-sacrifice for others was Moses, whom we first meet when he places himself at risk to save another Jew and who later prayed that God forgive the Jewish people and succeeded in saving his generation.
To begin, let us spend some time understanding the following famous statement made by the sages. They tell us:
Believe that the nations possess wisdom, but do not believe that they possess Torah.
On the one hand, we need to know that the non-Jewish nations have wisdom and that we should learn from this wisdom and incorporate it in some way. On the other hand, if non-Jews claim to possess Torah, this is by and by a false statement, and we are told to discredit it point blank. This is the key statement of the sages regarding the wisdom of the nations.
The first question we need to address is what is the difference between Torah and wisdom? More specifically, the Torah itself is God's wisdom. In the Zohar it says that the Torah comes from wisdom [God's wisdom]. So if some other wisdom is true, it must also have come from God. Any true wisdom is God's wisdom. So what is the difference between the two?
As with every statement of the sages, this one too has a multitude of explanations, each uncovering a deeper dimension in the sages’ wisdom.
Torah is a Way of Life
The simplest explanation is that the word "Torah" stems from the verb meaning "to guide."4 In other words, the Torah guides us in how to live our lives, how to go about day after day, whether life be good or not so good.
If we look at Noah we can understand that his wisdom was expressed in his ability to build this tremendously complex sea-vessel called the ark. Noah was able to carry out all of God's commandments which led directly to incredible technological success. As we noted, Noah was an inventor even before he was commanded to build the ark. He invented the plow. This, the sages say, is why he was called "Noah," which means "rest," because he bettered the condition of humanity by providing it with new technology. Just as today, the more technology we have, the easier life is and the more the quality of life can increase.5
Noah was really involved with quality of life. Until his generation the Earth was cursed, because of Adam's Primordial sin and Cain's murder of his brother, Abel. By inventing the plow, Noah sweetened (i.e., he dissipated and transformed) this curse, to a large extent. So we can see Noah as a type of applied scientist, someone whose concern for the well-being of humanity fuels his search for new technology that will alleviate suffering and bring tranquility.6 Relatively speaking, the invention of the plow was more important than the invention of the computer.
But, all of this is wisdom, it is not Torah. Knowing how to help people, whether it be physically or psychologically, makes a good technologist. But, this is not the ability to provide people with a way of life. We see this very clearly in our generation. Scientists and inventors do not necessarily know how to live better lives than other people. To be a brilliant scientist or successful technologist does not mean that one knows how to bring Divine awareness to people, to imbue them with the awareness that there is a Creator of the universe. All the more so that they cannot answer questions relating to purpose: Why did the Creator create us in the first place? Based on science and technology alone, there is no purpose (tachlit). This is the simplest explanation of the difference between wisdom and Torah. The Torah is a way of life given by the Almighty.
Torah Totality vs. Points of Wisdom
Now let us explain the difference between Torah and wisdom in more depth. In their statement, the sages use the verb "Believe": "Believe that the nations possess wisdom." The way that this verb is written in Hebrew can be understand as either passive—as we have translated it so far (this is the literal translation)—or a call for action, which would render the translation: “Bring the wisdom of the nations into belief.” In other words, you should not simply passively believe that there is wisdom in the nations, but you should act to discover how the wisdom that the nations possess can become a foundation for belief. This is like bringing the wisdom of the nations under the wings of faith, because the most important thing that it lacks is faith, as we explained. This should be the underlying goal of the Jewish people's relationship with the wisdom of the nations.
The Torah is a totality. When a topic is discussed in the Torah it is seen from all possible perspectives. The Torah is described as a perfectly clarified wisdom (חכמה ברורה ); everything is present, nothing is missing. In contradistinction, the truths included in the wisdom of the nations are considered point-like. Let us explain this terminology.
One of the most important models in Kabbalah is called point-line-area (נקודה קו שטח ). This is a developmental model charting development in stages from the simple to the complex. The terminology that this model uses is of course geometric and there are reasons for this in Kabbalah that are beyond our present scope. [The Arizal also uses a parallel model called point-sefirah-partzuf that we will return to later on.]
Since a point is dimensionless, it represents the simplest geometric structure. A line has one dimension, and an area (or to use more rigorous geometric language, a plane) has two dimensions. Obviously, after the plane, we have three-dimensional bodies called volumes, and there are an infinite number of n-dimensional spaces beyond that. Still, in Kabbalah development is considered complete once a structure becomes 2-dimensional. One of the reasons for this is that in Kabbalah completeness is indicative of maturity and rectification. The most important quality of completeness is known as inter-inclusion, whereby, every element in a structure holographically includes all the other elements.
From the perspective of this model, all structures initially have only a single element. They are still point-like. If the initial structure has vitality, it can develop and finer sub-elements can be explicitly expressed. The structure is then considered line-like and may possess any number of n distinct elements. At its final stage, the structure becomes area-like and each of its n elements is discovered to be a complex structure in itself, which holographically include the same n elements revealed at the line-like stage. Thus in the area-like stage, a structure will have n2 elements—representing its most mature and well-developed state. When its full makeup of n2 elements becomes explicit, the structure is considered characteristically inter-inclusive.7
Now, let us return to our distinction between Torah as a totality vs. the truth found in the wisdom of the nations inherently being in the point-like stage. As a totality, the Torah represents not only a way of life, but a complete portrayal of reality. Whatever topic you may learn in the Torah, know that were you to invest yourself in it fully, you would come out with a full, mature, and complete understanding of it and how it relates to every other topic or issue in reality. That is what we mean by Torah being a totality. But, the wisdom of the nations can only portray fragments of reality. For this reason, the wisdom of the nations can never be treated as a complete system. Whatever true knowledge it is able to glean from reality that knowledge will always remain (on its own) incomplete.
Practically, this not only means that you cannot base your way of life on the wisdom of the nations, it also means that you can never relate to it us a complete systematic portrayal of reality. For example, take quantum mechanics. There is an ongoing argument about whether this portrayal of the sub-atomic realm is complete, i.e., whether there may be some hidden variables or other factors that still lie hidden. Thus, even physicists are acutely aware of the fact that the most advanced physical theory we have today is plagued by the inherent limitations it places on our ability to understand reality.8 If we ask the question from a Torah perspective—is quantum mechanics complete?—the answer is a resounding no! There is no complete theory based solely on the wisdom of the nations.
Incorporating Points of Wisdom into the Torah’s Totality
Something that is point-like cannot develop on its own to become area-like. In fact, the problem with the wisdom of the nations is that because it is discovered by a bottom-up approach—i.e., man observing reality and describing it—it lacks the infinite vitality found in any point of wisdom in the Torah. Thus, even though there are undeveloped topics in the Torah, we consider them to be in a seminal form. The moment that they enter the thoughts and prayers of an individual, who is devoted to the study of the Torah, they will invariably develop on their own and reach a mature area-like state. But, when it comes to points of wisdom originating in non-Jewish thought, the infinite vitality is missing and must be introduced externally in the form a force driving the development.
Of course, the external force that can foster such growth is the Torah itself. To understand this point better, let us turn back to human conversion. Though a convert is considered to have a special connection with the Almighty even before his or her conversion, this connection is considered point-like; the usual terminology for describing this is that a potential convert has a Jewish spark.9 This brings us back to the parallel model of point-sefirah-partzuf mentioned above. It is the point-like spiritual influence of the spark that draws the prospective convert to Judaism. Once the conversion takes place, the convert is able to develop his connection with the Almighty to a fully mature state. As such, there may be no difference in stature and complexity between the connection with God of the converted Jew and the native Jew. Now, just as sparks of humanity need to develop by joining the Jewish people, so points, or sparks of true wisdom need to be fully developed by being incorporated into the Torah.
Lest we imagine that the process of gathering these human sparks is a relatively minor theme in Judaism, Rebbe Nachman of Breslov states that as long as there are still potential converts who have not converted, the Mashiach cannot appear on the historical stage.10 Likewise, by analogy, as long as there are sparks of true wisdom among the nations of the world that have not yet been incorporated into the Torah, the Divine wisdom with which the Mashiach will guide the world, cannot be presented before us.
Yet, as much as the redemption depends on incorporating the wisdom of the nations into the Torah, paradoxically, the Torah remains a complete and unchanging totality throughout the process. Likewise, as much as the Jewish people draw potential converts, this is not because of an inherent lack within us, but again there is a certain paradox at work here. The discussion of the reasons for these two analogous paradoxes is beyond our present scope. Still, let us say that this special relationship can be likened to a complete and whole organism [the Jewish people, or the Torah] that invites into itself those smaller cell-like organisms [potential converts or points of wisdom] that have a strong affinity with it.
The Origin of the Sparks
To pursue these ideas a bit further let us ask: how did sparks of wisdom end up among the nations in the first place. The analogous question would of course be: how did sparks of Jewish souls end up in potential converts? To answer both questions, we have to note that Kabbalah describes two distinct events of shattering. Perhaps the more familiar is the one known as the shattering of the vessels. The second is described in Kabbalah as the shedding of the souls. Both events are similar in that elements belonging to a rectified spiritual reality were lost to the underworld of dissonance and dysfunction, but their scope is different.
The shattering of the vessels describes a fall that occurred relatively spontaneously in the supernal realm known as the World of Nekudim (literally, the World of Points, also known as the World of Chaos, for this very reason), which led to sparks of Divinity being trapped in the realms of impurity. The shattering of the vessels is one of the most defining components of our present confused reality, in which holiness and impurity are mixed together.
The shedding of the souls describes the loss of sparks from Adam's general soul, which until his eating from the Tree of Knowledge included the souls of all humans that were to be born into our present reality.11 As mentioned earlier, had Adam not sinned, he would have become the first Jew; the totality of his soul would have been transferred through his offspring to all of humanity. But, because of the sin, this was not to be and the world would wait for another 19 generations until the birth of Abraham, who became the first Jew.
Among the sparks of Divinity lost to the dissonant mundane realms are the sparks of wisdom discovered by the nations. These need to be converted through the Torah, as we have been discussing, in order to be freed and reconnected with their source. The same is true of sparks of Adam's total soul. These sparks fell into the collective human spirit of the nations and appear from time to time as individuals who seek to convert to Judaism, thus pursuing their original destiny. All souls destined to be Jewish, whether by birth or by conversion, were present at the giving of the Torah at Mt. Sinai.
Following the Ba'al Shem Tov's model of worlds-souls-Divinity, we can thus say that the breaking of the vessels affected the dimension of "worlds," whereas the shedding of souls affected the dimension of "souls." But, because these dimensions are cumulative in nature,12 that is to say that a change in souls affects the world dimension as well, and Divinity affects all three together, Adam's sin led not only to the shedding of souls but also to an additional distortion in the worlds, causing them to collectively descend 14 levels. This in turn led to more sparks of wisdom being scattered outside the realm of holiness.
Abraham's purpose as the first Jew was to begin to glue the original pieces of holiness back together. He began to do so in the context of his own family, which led to the creation of the Jewish people, whose purpose is to redeem and bring together all the sparks of holiness.
Wisdom, Understanding, and Knowledge
The sages tell us to believe that there is wisdom among the nations, but not to believe that they have Torah. We have been looking at the difference between Torah and wisdom. Let us now see another Kabbalistic approach to answering this question.
In Kabbalah, wisdom is one of the three intellectual faculties called wisdom, understanding, and knowledge. The Hebrew acronym for these is Chabad.13 Human intellect is incomplete without the combined contribution of all three faculties. In fact, we find that these three faculties correspond to the structural make-up of the human brain: wisdom to the right lobe, understanding to the left lobe, and knowledge to the posterior lobe. Thus, when the sages tell us that we should believe that there is wisdom among the nations they are also pointing out there is no true understanding or true knowledge among the nations. Without the Torah, it is next to impossible for a person to develop clarified faculties of understanding and knowledge. Hardly a prejudiced belittling of the nations’ intellectual ability, this statement can only be understood by first defining the differences between wisdom and understanding, and wisdom and knowledge.
To do so, we must first stress that we are now looking at these three sefirot—wisdom, understanding, and knowledge—as different methods of human reasoning. Because wisdom is the first of the three faculties, we might jump to the conclusion that it also represents the highest type of reasoning. However, the Torah recounts that when Moses set about to search for qualified judges to appoint to the high court, he was able to find wise men, but he was unable to find men who possessed true understanding. Thus, wisdom is more common and natural than is understanding.
Rashi offers us definitions for wisdom, understanding, and knowledge as methods of reasoning when he comments on the gifts given to Betzalel, the artisan named by God to design and construct the desert Tabernacle.14 The Torah describes Betzalel as a man whom God has filled with wisdom, understanding, and knowledge. Rashi explains that wisdom is the ability to learn new ideas or points of wisdom from one's teacher, whereas understanding is the ability to "understand [on one's own] one thing from another."
Rashi's definition of understanding includes both the power of deductive reasoning—the ability to logically derive "smaller" constituent parts from within the context of a "greater" whole—and the power of inductive reasoning—the ability to extrapolate, induce, or abstract new, "greater" knowledge from what one already knows.15 True understanding, we are taught in Kabbalah, refers to inductive reasoning (while deductive reasoning is considered a lower form of understanding). Let us continue to elucidate this distinction.
Inductive and Deductive Reasoning
Understanding includes both deductive and inductive reasoning, but deductive reasoning is likened to the fruit of the Tree of Knowledge while inductive reasoning is the fruit of the Tree of Life. Deduction fosters a sense of certainty in one’s conclusions while the knowledge attained through induction is always subject to revision by the changing reality around us. As such, the use of deductive logic tends to be (at least initially, and especially as developed in ancient Greek philosophy) motivated by an egotistic search for self-aggrandizing knowledge, which can crown its possessor with laurels of self-importance. This follows the Kabbalistic identification of the Tree of Knowledge with the source of the impure realm of kelipat nogah, the source of the ego.16
The Torah is equated with the Tree of Life, “It [the Torah] is a tree of life to those who cling to it.”17 Logically, clinging to the Torah, translates into accepting its inductive method and inductive conclusions regarding reality, which can lead at best to an approximation of reality at any given moment. Inductive reasoning is based on a statistical appraisal of reality, forced upon the human mind by the realization that reality as we perceive it is the sum total of the actions of human beings who possess free will and together with God’s own absolutely free will.
As stated above, deductive reasoning begins with generalities (givens) that are then analyzed to yield particular truths. Inductive reasoning phrases a general principle after studying related particulars. Anyone learning Torah will immediately recognize that the sages reason inductively: first, they study the particular verses pertaining to the matter at hand together with the sayings of the sages that preceded them, and then they generalize. From the general conclusion, new particulars can be deduced. But, if a new piece of information is brought forth, the general principle may need to be revised. Thus, the rectified human reasoning of the Torah relies on both induction and deduction, but necessarily in that order: first induction (the Torah), then deduction (logical analysis of principles in order to yield particular statements).
The mistake of the modern academic approach to the Torah is that it places its belief in human reason (i.e., deductive reasoning) above its belief in the truthfulness of the Torah. This mistake is what turns the Torah into just another field of human study, on par with all other fields of inquiry. The end-result is that mistaken generalities (fostered by an egotistic certainty in one’s logical abilities), which contradict the Torah, come to taint one’s outlook on the Torah and one’s ability to experience it as the source of life: the Tree of Life.
Now, it is clear why Moses could not easily find people who had true understanding, because it is only by the devoted study of the Torah—in a state of true selflessness in the presence of the Torah's ever unfolding revelation of Divine truth—that an individual can develop his understanding, that is, his capability for inductive reasoning. The wisdom of the nations does contain within it the ability to understand, but primarily in the sense of deductive reasoning, the intellectual ability to analyze and reduce. Thus, when the sages say that the nations possess wisdom they mean to say that their wisdom does indeed include the the lower dimension of understanding, i.e., deduction, but not the higher dimension, induction. But, one who studies Torah in depth develops his inductive reasoning.
There is of course a limited state of inductive reasoning in science as well (actually at the heart of modern science, for the empirical scientific method of today is based on the progression from particulars, observed details, to hypothesized generalities, from which are deduced yet unknown particulars to be tested by experiment). Perhaps the best example of this is Einstein’s theory of General Relativity. Given the classic view of the cosmos known as Newtonian gravity, Einstein did not arrive at General (or Special, as was the case at first) Relativity by deduction but by induction.
Likewise, it seems that for the current state of physical theory to produce a Grand Unifying Theory, inductive reasoning is called for. Still, the moment that true unification is sought, it should be clear that such a level of insight into the mechanisms at work in the universe cannot be attained without including the eternal and ever-present contribution of the Creator Himself. For induction to produce absolute results, knowledge of the Torah and an awareness of the Creator are necessary. Einstein was able to arrive at the General theory of Relativity without these because his end-result was to sever gravity from the other three forces in nature. Though he gave us a far more complete understanding of gravity than had Newton, his inductive reasoning, being as it was void of Torah, in the end left gravity hanging as the odd-man-out.
In short, we should be aware that any book that we read that contains ideas and theories that do indeed work but do not incorporate the wisdom of the Torah (and are not under the wings of faith), such a book is based on wisdom, but it does not contain true understanding or knowledge. These are good things, because they can be used to better the quality of life. But to truly understand the workings of the universe, one must convert this wisdom by incorporating it into the Torah.
Now, let us analyze the difference between wisdom and knowledge. On the same verse describing the spiritual gifts bestowed upon Betzalel, Rashi continues to explain that knowledge represents an even greater intellectual faculty than understanding, which is called ru'ach hakodesh, or literally, the holy spirit. The holy spirit is the mind's power to be totally tuned into God's will. Rationality is not necessarily aligned with the Creator's will. In other words, God's will does not always agree with what a person would think to be rational.
As a sefirah, knowledge is located on the middle axis, just under will, the lowest aspect of the sefirah of crown.18 As such, knowledge is a hundred percent aligned with God's will. This is expressed in the Kabbalistic principle that many times, when the sefirah of crown is counted, the sefirah of knowledge is not. This is because knowledge represents the super-conscious manifestation of the crown, hence the two sefirot—crown and knowledge—are actually two representations (one conscious, the other super-conscious) of the same faculty.
One of the best illustrations of knowledge as we have explained it in our present context is that of the advice offered by a tzadik, a righteous and holy individual. Many people go to tzadikim for advice. The Bible describes the advice offered by a tzadik, as advice from afar, meaning that even if you would learn the entire Torah through and through, even if you were the greatest student of Torah (a true talmid chacham, a real gadol) you would never come up with the advice given by the tzadik to a particular problem. This is because the tzadik is blessed with the holy spirit and is able to tap into, as it were, the Divine will. There are innumerable stories told about the surprising advice given by tzadikim and by their even more surprising results.
Let us end the first part of our topic by noting a beautiful numerical relationship. We have already noted that, quoting the language of the Zohar, “Torah comes from wisdom,” implying that Torah and wisdom are not the same thing. Though the revelation of the Torah is from wisdom, the ultimate source of the Torah is above wisdom in the very essence of God (as explicitly stated in the Zohar: "the Torah and the Holy One blessed be He are one"). The Torah unites all three faculties of the intellect wisdom, understanding, and knowledge, which indeed can only fully develop in the mind through the study of Torah. The numerical value of these four words in Hebrew, תורה חכמה בינה דעת , is 1225, which is a unique number; it is both a square and a triangular number: 1225 = 352 = 49. We mentioned in passing above that square numbers symbolize completeness, maturity, and inter-inclusion, the properties of rectification. Whenever the numerical value of a number of words together equals a square number, it tells us that these words go together and complete one another.19
Elsewhere, we have dealt with the significance of numbers that are both triangles and squares. The only 2 numbers before 1225 that share this property are (the trivial) 1, and 36; 36 = 62 = 8.
Because 1225 is an odd number, it shares another property with 1 that 36 does not have: it has a midpoint. The midpoint of 1225 is 613, the total number of commandments in the Torah.20 Indeed, the most notable phrase in the Pentateuch whose gematria is 1225 is זֶה שְּׁמִי לְעֹלָם וְזֶה זִכְרִי לְדֹר דֹר (“This is My eternal Name, and this is My memory from generation to generation”21). The Zohar notes that this verse implicitly refers to the 613 commandments, exactly as they are divided into 248 positive and 365 prohibitive commandments. The value of the word שְּׁמִי (My Name) with the first two letters of Havayah (י ־ה ) is 365; the value of the word זִכְרִי (My memory) with the final two letters of Havayah (וה ) is 248.
Based on a class given on the 30th of Tishrei, 5769 in Chicago
Continue to part 2
2. "For the waters of Noach…" (Isaiah 54:9).
3. Who prayed for the people of Sodom and Gemmorah (parshat Vayeira).
5. By leaving more time for spiritual pursuits.
6. We may surmise that Noah was also the first psychologist, able to alleviate suffering not only through technological means, but through the spiritual weight of his character as a tzadik.
7. This is the central reason that in our teachings we attribute “completeness” to square numbers, those numbers that can be expressed as n2, where n is some integer. These numbers clearly express an inherent state of inter-inclusion.
8. For a philosophical perspective on this debate see Karl Popper's Quantum Theory and the Schism in Physics.
9. See Kabbalah and Meditation for the Nations, pp. ??? for a deeper explanation of the nature of a prospective convert's connection with God.
10. In fact, we know that the lineage of the Mashiach is paved with converts, the most important of which is Ruth the Moabite princess who converted and married the judge Bo'az.
11. There are also so-called "new souls" that were not part of Adam's original soul. These souls were not affected by Adam's sin and descend in righteous individuals in every generation and serve as beacons of purity and direction.
12. As the Ba'al Shem Tov writes in his well-known letter.
13. The Chabad Chassidic movement was so-named because of the central role that the intellect plays in it.
14. To construct the Tabernacle, Betzalel had to both be a scientist and an artist. The sages note his ability to permute the letters with which the heavens and the earth were created. This suggests his scientific prowess. Betzalel, constructed the Tabernacle as a microcosm mirroring the cosmos in all its complexity. The Tabernacle was also full of tremendous physical beauty, reflecting Betzalel’s gifts as an artist.
Numerically, the sum of the Hebrew words for “art” (אמנות ) and “science” (מדע ) equals the gematria of “Torah” (תורה ), indicating that Torah indeed reflects both aspects of human knowledge and creativity.
15. For a full discussion of this topic, see our Hebrew volume, Teshuvat Hashanah, pp. 291ff.
16. For the reader well-versed in the language of Kabbalah, we may now add that deductive reasoning stems from the lower two-thirds of the partzuf of Ima, which are left naked and therefore lead eventually to self-consciousness and self-aggrandizement. Inductive reasoning stems from the top third of the partzuf of Ima, which always remains concealed by the extending foundation of the partzuf of Abba, and therefore their mental processes do not fall into self-consciousness.
18. The sefirah of crown is divided into 3 heads, whose inner experience are faith, pleasure, and will.
19 One of the most beautiful and simple examples is from the beginning of the Torah. The combined value of Adam (אדם ) and Eve (חוה ) is 64 = 82!
20. 613 is therefore likened in Kabbalah to the number 1, as both are the midpoint of a triangular-square number: 613 is the midpoint of 1225, and 1 is of course the midpoint of 1!