Preface
Error! No text of specified style in document.
Preface
The lectures appearing in this volume were given by Rabbi Yitzchak Ginsburgh in Los Angeles, at the then Ahavat Shalom Synagogue, over the course of 3 days, March 18-20, 2007. The 3 day seminar was titled “Beyond the Physical Universe” and it focused on the relationship between modern physics and Torah.
Following the seminar, transcripts were made from recordings of the lectures and both video recordings and the transcripts were posted on Gal Einai Institute’s website (www.inner.org).
The present volume is a lightly edited version of those transcripts. Rabbi Ginsburgh did not edit these transcripts and they did not go through the rigorous and in-depth process that our publications usually do. We believe that even prior to an in-depth review and expansion, the material Rabbi Ginsburgh presented at this seminar is invaluable and should be made available to readers interested in the relationship between Torah and science.
Where relevant, the original Hebrew of verses or idioms is noted. When a Hebrew word appears in bold-print, it indicates that the numerical value (gematria) of that word is being considered.
In order to avoid confusion, God’s Names in Hebrew appear using the proper spelling, with a dash separating the letters, for halachic reasons. We follow the halachic convention of writing out God’s Name in English without a dash. Some, but not all of the sources noted in the lectures have been cited in endnotes, as well as some explanatory points on the discussion.
We have made an effort to retain Rabbi Ginsburgh’s speaking style in this volume and very little has been changed.
Rabbi Ginsburgh has a unique place among the Torah scholars and leaders of our generation, part of it due to his ability to clearly see where Torah and science do indeed unite. Perhaps even more incredible is his ability to recognize those points in which the Torah can guide science in mankind’s quest to understand the secrets of the physical universe.
We pray the Almighty provide us with the ability to continue publishing Rabbi Ginsburgh’s voluminous works on Torah and science, covering practically all fields of scientific inquiry.
During 2007-8, Rabbi Ginsburgh was able to visit Los Angeles every 3 months, thanks to the founding of the Los Angeles Inner Torah Institute by his students: Rabbi Shaya Eichenblatt, Prof. Eliezer Zeiger, Mrs. Chana Rachel Schusterman, and Mrs. Olivia Schwartz, all well-known and active members of the Chabad-Lubavitch community in Los Angeles.
The Inner Torah Institute and hence Rabbi Ginsburgh’s regular visits to Los Angeles that year, were made possible by a generous donation from Mr. David Kaplan. We would like to take the opportunity to thank everyone who put in a great deal of hard work to make these visits possible. They all have a part in bringing the Torah’s inner light to the edge of Western civilization.
Special thank to Mrs. Rachel Gordon for proofreading the transcripts.
May the Almighty indeed open our eyes to see the wonders of His Torah, allowing us to see beyond the physical dimension of our universe.
Moshe Genuth
Chanukah 5773
Lecture 1
In this series of lectures we will connect the issues of modern physics with the inner dimension of the Torah. One of the benefits to be gained from this unification is that the concepts and ideas that form the foundation of modern physics, which appear at first glance to be far removed from our everyday lives, are actually most applicable.
Modern physics is counter-intuitive
The first topic we will address is counter-intuition. It is a simple and well-known fact that all of the most important and successful theories presented and used in modern physics are counter-intuitive. The fact that the accepted scientific narrative of the past century has been utilizing counter-intuitive ideas is a very significant one, indicating that humanity in general is approaching a level that is above and beyond the style of human logic that has been applied since time immemorial.[1]
On a different front, the realization of our long anticipation of the complete and true redemption by Mashiach is imminent. Like science, the redemption that awaits us is counter-intuitive to the redemption that we have been expecting, so much so that the Alter Rebbe of Chabad was known to say that the Mashiach that everyone is waiting for will never come, and the Mashiach that will come, nobody is waiting for! So now, let us begin our journey into counter-intuition and try to see how counter-intuition applies in our lives.
Counter-intuition in Kabbalah
Kabbalah supplies us with the tools for understanding counter-intuition in a much more sophisticated way than does science. By counter-intuition, science means anything that runs against the grain of our common-sense. Special relativity, general relativity, quantum mechanics, and string theory (to a degree), are all theories that run against our common-sense and are therefore considered by science to be counter-intuitive.
The first insight that Kabbalah offers is that everything is relative. This is similar to the conclusion of the first major theory of modern science, relativity. Of course, if “everything is relative” then counter-intuition is relative as well. This means that the blanket statement that counter-intuition is anything that goes against common-sense is not accurate, because common-sense itself is relative!
In the language of Kabbalah, every mind-space, or level of consciousness, is called a World of the and every World has its own “common-sense”[2] [we capitalize “World” in the Kabbalistic sense, in order to differentiate it from the word’s more common meaning; ed.] Thus, given the particular mind-space that I currently inhabit, I would consider the common-sense found at the level above mine to be counter-intuitive to my own. As we progress through each level of consciousness, from Kabbalistic World to Kabbalistic World, our common-sense undergoes a transformation and what is perceived as common-sense in one World becomes absolutely counter-intuitive to common-sense in another World. When we progress from World to World, which are actually levels of consciousness everything that we held to be true previously transforms into something new.
Those readers familiar with our method of teaching know that as we survey a new subject, one of our goals is to describe the appropriate Kabbalistic models that correspond with the particular topic at hand. If the model indeed fits and corresponds correctly, then not only do we gain insight into the model, but we immediately improve our understanding of the topic under consideration.
The model that we have chosen to use to enhance our understanding of counter-intuition is indeed based on the model of the Kabbalistic Worlds, specifically the three lower Worlds which are known as Action, Formation, and Creation. Or, in Hebrew: Asiyah, Yetzirah, and Beri’ah.
The basic state of human consciousness is in the World of Action or more specifically, in the physical dimension of the World of Action. Above our World is the World of Formation and above that is the World of Creation. The common denominator of these three lower Worlds is that in them everything has some degree of self-consciousness, causing it to feel separate from the Almighty; the absolute and unique One.
Above these three Worlds is the World of Emanation (Atzilut) in which there is no distinct self-consciousness at all; everything is purely Divine and there is no separation (or feeling of separation) possible from the Creator.
As mentioned above, every World has its own version of what is intuitive and what common-sense is and anything that contradicts it is considered “counter-intuitive.” When an apparently counter-intuitive insight is attained in any of the three lower Worlds, first we should ascertain that it is indeed counter-intuitive relative to that World’s common-sense.
The picture that we should have in mind as we consider how new insights are attained is that light (i.e., energy, in this case the energy that makes up the counter-intuitive thought or idea) from the World of Emanation has descended and permeated a lower World. Each of the physical theories of the 20th century that has been successfully incorporated into modern science is like a ray of light that has filtered into human consciousness from a higher level of reality. Yet, even though it seems that these theories run against the grain of our common-sense, if you ask a student of Kabbalah and Chassidut, one who is truly versed in the wisdom of the World of Emanation, whether these “counter-intuitive” theories make sense or not, he will tell you that they are in perfect harmony with what is described in the holy books about the reality of the World of Emanation. We hope that this point will be made very clear through the scientific examples we will now consider.
“The opposite makes sense”
The message that scientific progress has delivered in the last century is that the more our understanding of nature increases, the more our common-sense is challenged. In other words, scientific progress means challenging our common-sense about physical events in the world.
If this message about changing our common-sense is indeed true, we would expect to find it echoed in a verse from the Bible or in the literature of the sages. Indeed, there is an idiom the Talmudic sages use to express exactly this idea. In the original Aramaic it is pronounced, “ipcha mistabra” (אִיפְּכַא מִסְתַּבְּרָא). This phrase literally means: “the opposite makes sense,” or in other words, the truth—what truly makes sense—is exactly the opposite of what you initially thought makes sense. This idiom appears exactly 19 times in the Babylonian Talmud, and we will have more to say about this phenomenon later.
The initial letters of this idiom spell the Hebrew word for “mother” (אֵם), hinting at its connection with what in Kabbalah is known as the mother figure, or partzuf Ima. The mother figure is associated with the sefirah of understanding, which is related to common-sense and the analytical skills it employs. The initials of this idiom thus echo the concept of common-sense, that which it is in fact challenging.
Having explained the mother principle, let us add something that will be useful later on. The father figure in Kabbalah is a connotation for the sefirah of wisdom, which represents direct intuition, a state of intellectual insight in which it is impossible to experience that the opposite might be true. Thus, the father principle in Kabbalah represents an insight that can never be refuted.[3]
What is the function of the Talmudic idiom, “ipcha mistabra?” In a Talmudic debate one sage will suggest that, “Given that x is true, such and such follows.” Another sage may then argue “ipcha mistabra”—“Given that x is true, the opposite is the case.” Ipcha mistabra is thus a rhetorical tool that challenges not only conclusions, but the very reasoning being used to arrive at those conclusions. In a certain sense, it is not the facts that are being challenged but their correct interpretation. This therefore exemplifies the idea stated above that the manner in which I am used to perceiving reality defines my “common-sense,” but someone in a different mind-space will find my interpretation a challenge to his perception of reality and hence to his notion of what common-sense is.
The sages compiled two great anthologies of their knowledge called the Babylonian Talmud and the Jerusalem Talmud (the latter is also known as the Talmud of the land of Israel[4]). Many of the same sages appear in both editions of the Talmud, and of course the discourse in both focuses on the same basic text, the Mishnah. Yet, despite the many parallels between the two Talmuds, interestingly, the idiom ipcha mistabra appears only in the Babylonian, but not once in the Jerusalem Talmud. What is the reason for this?
The difference between these two works is that the discourse in the Jerusalem Talmud is concise and promptly arrives at its conclusions, whereas the Babylonian Talmud’s discourse is drawn-out and argumentative in its style. Many arguments and counter-arguments are presented in the Babylonian Talmud before a final conclusion is reached, which is why it is so much longer than the Jerusalem Talmud.
Both the Jerusalem Talmud and the Babylonian illustrate the refined intellect, but the differences between them, such as this one, indicate that a refined intelligence has two different aspects. In Kabbalistic terminology, the two aspects of the intellect (there is also a third, which connects the intellect with the emotions) are identified with the two sefirot called wisdom and understanding and corresponding with the father and mother principles, respectively, as mentioned earlier.
The Jerusalem Talmud echoes the insightful intelligence of the father principle, the sefirah of wisdom. In the model of four Worlds, wisdom corresponds to the World of Emanation, where God’s Presence is absolutely clear and therefore there is no experience of being separate from God. Because of the constant experience of God’s all-encompassing omnipresence inherent in the mind-set of Emanation, the sefirah of wisdom is clear, concise, and most importantly for our purposes here, intuitively secure. The discourse in the Jerusalem Talmud leaves no room for challenges to its conclusions, because they are not arrived at by a critical methodology—they simply are!
But the Babylonian Talmud echoes the mother principle, the sefirah of understanding. As we touched upon earlier, this sefirah reflects the mind-set of the World of Creation (one level below the World of Emanation), where consciousness does include the relative experiences of selfhood. The more the person inhabiting this mind-set is aware of his own being, the more open he is to seeing how relative his methodology and conclusions seem to the subjective experiences of others.
The mind-set of Creation includes relative statements about right and wrong. Therefore, it leaves room for actually being wrong, even in intuitive matters—those things that seem to just be plain common-sense. What follows is that if you inhabit the mind-set of Creation, your first intuition might be correct, or it might be incorrect; in fact, it is often incorrect.
This does not imply that the sages of the Babylonian Talmud were at a lower level than the sages of the Jerusalem Talmud and that therefore their intuition can be challenged. Anyone designated a sage in either Talmud lived in the mind-space of Emanation. Like we said before, many of the sages are mentioned in both editions of the Talmud. It is rather that because the Babylonian Talmud was written outside the land of Israel, its editorial style reflects the mind-set of the World of Creation. Therefore, in the context of the dialogue recorded in the Babylonian Talmud, even the intuition of a great sage may be challenged. It may even be found, in the course of a Talmudic argument, to be incorrect; even completely opposite from the truth, “ipcha mistabra.”
The feminine and counter-intuition
Let’s take another step in looking at ipcha mistabra, the idiom that represents counter-intuition in Judaism. If we search the entire Babylonian Talmud, we find that this idiom is used exactly 19 times; the numerical value of the name “Eve” (חַוָּה), in Hebrew.[5] Eve was the first woman and is referred to in the Torah as the “mother of all life.” This is especially significant when we recall that the initials of ipcha mistabra spell “mother,” in Hebrew.
What this reveals is an implicit but essential relationship between counter-intuition and the Torah’s first female figure, who more than any other character in the Bible, represents the mother principle. The first thing we learn from this connection is that indeed the woman is the ipcha mistabra of the man—female understanding posits a counter-intuitive alternative to male common-sense.[6]
But, more deeply, we often refer to feminine intuition, which is sometimes even hailed as being more potent than its masculine counterpart. Yet, unlike the adamant male intuition, a woman’s intuition is capable of suddenly and completely reversing itself, not only as a response to changing circumstances, but more importantly because the woman who originally expressed the intuition suddenly feels that the exact opposite is true. In a sense, the feminine mind is tuned into intuition (the faculty that is the father principle) and adopts an intuitive stance towards life. But, this is also the reason why feminine intuition knows that it is not always correct. The female mind is thus both open to trusting its intuition, but just as open to completely reversing it by 180 degrees.
Counter-intuition and teshuvah
Those familiar with our methodology know that there is great deal of insight to be gained from looking at the numerical value, called the gematria,[7] of Hebrew words.[8] The gematria of the idiom ipcha mistabra (אִיפְּכָא מִסְתַּבְּרָא) is 815. This is also the gematria of the predicate ba’al teshuvah (בַּעַל תְּשׁוּבָה), which literally means: “a master of repentance.” A ba’al teshuvah is someone who has returned to the Almighty through the Torah, someone who has decided to master the art of self-transformation in order to manifest a bond with God. Self-transformation requires a switch in one’s consciousness. A ba’al teshuvah has to embrace ideas and actions that are counter-intuitive. To seek God from his or her present context, the ba’al teshuvah has to rise to a new level of understanding that is counter-intuitive to his or her current, common-sense approach to life.
Teshuvah—return to God—applies differently to individuals with different levels of religious observance. The more religious a person is, the more his teshuvah can be charted along a straight line, measuring increased attention to the details of observance and the time spent studying Torah. For the observant Jew, teshuvah may not involve the same type of counter-intuitive leap that it does for the Jewish returnee, the ba’al teshuvah of our times. Therefore, most observant Jews will point to the month of Elul, known as the month of teshuvah, as an auspicious time for the observant individual to “do” teshuvah.
But, a cornerstone of Chassidic teachings on spiritual consciousness is that regardless of an individual’s level of observance or commitment to Torah as a way of life, he should always seek to become a full-fledged ba’al teshuvah; meaning that he should always see himself as still distant from God. In the words of one Chassidic master,[9] the more a person feels a sense of spiritual accomplishment and nearness to God, the more spiritually distant he actually is. This foundation of Chassidic guidance is based on the philosophical adage that a person should be practicing teshuvah every single day of his life.[10] Chassidic masters interpret this to mean that relative to God’s absolute nature, we are all equidistant from Him. Therefore, we are all equally in need of a counter-intuitive switch in our thinking in order to better our actions. The path to spiritual progress is not traversed by a series of successive, forward-facing steps that follow a straight line, but rather by a series of mind-spinning and consciousness-altering steps up the landings of a winding, spiraling staircase. At each point in life a person must embrace counter-intuition, i.e., teshuvah, in order to advance spiritually.[11]
Chassidut teaches us that there are two types of teshuvah, which correspond to the two Talmudic opinions regarding whether or not teshuvah is a prerequisite for redemption.[12] Rabbi Eliezer’s opinion is that the future redemption is dependent upon teshuvah, whereas Rabbi Yehoshua is of the opinion that the future redemption does not depend on our doing teshuvah. Maimonides rules like Rabbi Eliezer, that redemption is dependent on teshuvah.
This Talmudic dispute is echoed in another dispute between Rabbi Eliezer and Rabbi Yehoshua,[13] in which Rabbi Eliezer is of the opinion that the future redemption will take place in the month of Tishrei, while Rabbi Yehoshua’s opinion is that the month of Nisan—the month of our deliverance from bondage in Egypt—will be the month of the future redemption by the Mashiach.
It is thus explained in Chassidut that the teshuvah that Maimonides is referring to is a particular type of teshuvah that is uniquely relevant to the month of Nisan. This type of teshuvah is different from the teshuvah that we do during the month of Elul and the High Holy Days in the month of Tishrei. The teshuvah of Tishrei is based on strengthening (hitchazkut) and improvement (hishtaprut); we try to rectify ourselves based on what we know to be wrong in our lives. A person makes an account of his actions and knows that there are things that he should be doing differently. The normal sense of teshuvah is to look at myself and ask whether what I am doing is right, and then deciding to improve based on my knowledge of what is right.
But, the teshuvah of Nisan is based on renewal (hitchadshut). In Nisan we seek a new life, a complete metamorphosis, not just a rectification of the past; we are looking for a new mindset. In Nisan, I come to the revolutionary realization that I have never truly known what is right and what is wrong.
Similarly, the ba’al teshuvah of today is completely different from the ba’al teshuvah of past centuries. A hundred or two-hundred years ago, a Jewish individual would have had a basic Jewish education that imbued him with the knowledge of what constitutes proper and improper behavior. Equipped with this knowledge, he would have been aware of his misdeeds and could decide to improve his actions through teshuvah. But, in our generation, teshuvah often entails actually being reborn and taking on an entirely new understanding of the world. Indeed, seeing things from a completely different perspective is the true essence of teshuvah. This is the type of teshuvah that is required to bring the Mashiach.
As the sages state: “In [the month of] Nisan we were redeemed, and [in the month of] Nisan we will be redeemed.” Clearly, this means that the redemption is a counter-intuitive process. The teshuvah necessary for redemption is a counter-intuitive type of teshuvah. It requires us to rethink everything that we know, our entire perspective on life. I have to understand that my whole perspective on life was wrong. This is the teshuvah of Mashiach. So that is our first gematria. The phrase “ipcha mistabra” teaches us about the essence of the true ba’al teshuvah.
Silence
Now let us turn our attention to a second gematria for 815. This time it is one word whose gematria equals 815, “silence” (שְׁתִיקָה). Now, at first glance, silence may not seem to reveal very much about counter-intuition, ipcha mistabra. So, to help us understand the relationship between the two, let us start by quoting the sages’ saying about the function of silence: “The fence around wisdom is silence.”[14] Since in Torah, wisdom refers to the ability to intuit correctly, according to the sages, it follows from this adage that if a person wants to arrive at true intuition, he has to be totally quiet, totally silent. Silence is the fence that surrounds true intuition.
In Chassidut, silence is further related to the word “chash” (חָשׁ), the first stage in the three stage process taught by the Ba’al Shem Tov as the cornerstone of all spiritual transformation.[15] Silence allows you to give up your previous understanding in order to ascend to a higher level of consciousness.
When Einstein first taught his special theory of relativity, some older scientists said that it looked good on paper, but that they were too old to get into it and adopt its new way of thinking about the universe. In other words, they were already too entrenched in the old perception of the universe and could not counter their common-sense to adopt Einstein’s new intuitions.[16] Given that Einstein’s theory turned out to be a tremendous success, these scientists would have agreed that the moral is that you should never become too old to adopt new ways of thinking.
How can we retain our minds’ youthful virility? By making use of silence—the instrument for embracing counter-intuition! Silence allows us to give up our old way of thinking about the world and accept a new one.
Counter-intuition is the most important faculty that modern science has taught us to exercise. Scientists have to be willing to make existential leaps (existential because for a scientist the paradigm by which his common-sense functions is the essence of his self). They have to be willing and able not just to surrender their common-sense, but to also be willing to abandon what everyone else thinks is true. Uprooting the paradigms of their own intuitions was a prerequisite for scientists to transcend and go beyond the accepted Newtonian and Hamiltonian mechanics of their time. And as it turns out, without these leaps they would not have been able to advance our understanding of nature.
This is the spiritual moral of the scientific story of the last few generations. We have to open our minds, to be willing to change our mind-set in order to open up to a new spring, a new birth, which vis à vis everything we have thought until now, is entirely counter-intuitive.
Now, let us turn to the three great theories of the 20th century—special relativity, general relativity, and quantum mechanics—and see what aspect of our common-sense each challenges. But first, let us note an important distinction between these three theories and the relative newcomer, string theory, in relation to counter-intuition.
Counter-intuition in physical theories
Both special and general relativity were developed by Einstein in the first years of the 20th century. Though their names suggest they are two developmental stages of the same theory, to this day, scientists consider them to be two distinct theories. Special relativity was introduced into scientific consciousness in 1905, the year Einstein presented three ground-breaking papers that literally turned the world of physics upside-down.
Quantum mechanics, on the other hand, was a group effort, developed by many scientists who collaborated over the first quarter of the 20th century.
Finally, string theory was first explored in the late 60s and early 70s, but did not really take-off until the 90s. Like quantum mechanics, string theory is the product of collaboration between many scientists.
But, what string theory clearly lacks is the same degree of counter-intuitive challenge to our common sense that special and general relativity and quantum mechanics pose. String theory’s challenge to our common-sense is quite weak, in spite of the fact that it contains strange sounding ideas like the universe having 10 or 11 or 26 dimensions. It can be compared to a gentle giant that has the power to lift us up high, but in a calm and non-disruptive fashion. The excitement it has generated is not because of its counter-intuitive principles, but more because of its ability to unify the already counter-intuitive realities described by relativity and quantum mechanics.
It is important to note that the first three theories are pretty much accepted across-the-board by scientists, whereas string theory is not. A minor reason for string theory’s relatively weak standing is its relative youth, but the major reason is that string theory is currently unable to produce testable predictions. Indeed, the criticism of string theory does not focus on how counter-intuitive it is, but on its inability to produce testable predictions.
Let us now look at the three main physical theories of the twentieth century and analyze each one’s particular attack on our common-sense, both scientifically and in the language of Kabbalah. Clearly, each of these theories is complex and can be described in many different ways. We will try to focus our attention on each theory’s most surprising counter-intuitive component.
In order to help us orient ourselves, before we begin we will present a bird’s-eye view of what follows. Special relativity is counter-intuitive to the mind-set of the World of Action, general relativity is counter-intuitive to the common-sense of the World of Formation, and quantum mechanics challenges the common-sense of the World of Creation.
theory |
challenges mindset of World of |
quantum mechanics |
Creation |
general relativity |
Formation |
special relativity |
Action |
The counter-intuitive aspect of special relativity
In the World of Action, the lowest of the three Worlds that our consciousness inhabits, we sense that we are moving; we are advancing in life. The most intuitive thing about the World of Action is that we think that everything is progressing. If someone would tell you that you are actually standing absolutely still, that would be totally counter-intuitive. At this level, our consciousness feels that everybody and everything is active. Everyone is on the move, going to work, doing something.
Enter special relativity, which claims that our sense of motion is really just a subjective illusion that our mind (our consciousness in the World of Action) tells us is happening. Obviously this is really counter-intuitive.
What is special relativity’s argument? It starts from the basic idea that motion is always relative. We judge our motion in relation to another physical body we deem to be at rest. But, in fact, even though that other physical body seems to be at rest, it is only at rest relative to us. But, relative to a third object, it is actually in motion. If we continue to follow this chain of relative motion all the way, we find that there is only one thing that is constantly, absolutely moving in respect to everything else. That one thing is light.
Special relativity challenges our basic intuition about the role that space and time play in everyday action and events. Not only does special relativity merge space and time into a single entity (meaning, that from the standpoint of relativity you are always in relative motion, whether it be through space or through time), but it also casts them in a different role.
Until Einstein developed special relativity, our intuition told us that space and time were both constant and absolute, meaning that all observers should measure distances and time in the same way. In other words, 5 hours really do not take any longer whether you are on the red-eye flight from Los Angeles to New York, or whether you are sound asleep in your bedroom. This was the way Newton understood space and time. His (and our everyday) intuition is that space and time serve as the backdrop to events and actions that happen within their framework and context. Space and time neither contribute to nor change because of the events that take place in them.
But, special relativity challenges this so common part of our common-sense. Einstein’s innovation was that space and time are not a context at all, but that they actively participate and are affected by events. If you are traveling at a very high velocity time dilates and space gets shorter (the Lorentz effect). Time and space are variable, not constant.
In his theory of special relativity, Einstein hypothesized that the only constant and absolute motion in nature is that of light. It does not matter how fast you are going, light will always be moving away or towards you at exactly the same speed: about 300,000 kilometers per second. Everything else, including space-time itself, is relative to the observer. This means that while our common-sense treats space and time as purely objective entities, special relativity makes them purely subjective. This is another way of rephrasing how special relativity challenges the common-sense mind-set of the World of Action.
Incidentally, by challenging our common-sense notion of space and time as constant and objective, special relativity requires us to reframe (and perhaps even discard) many seeming contradictions between scientific theory and the Torah. For example, consider the age of the universe. Since we can no longer refer to some absolute reference for the passage of time, we have to get used to the strange counter-intuitive notion that time can move faster or slower depending on our motion. Indeed, if we measure time from the point of view of a beam of light, there is no passage of time whatsoever. According to special relativity, without unambiguously defining “the observer” in the Torah’s account of creation and the observer in the scientific theory of creation, one cannot compare or contrast the two, because they lack a common frame of reference.
As explained earlier in this lecture, the three major theories of modern physics imbue a higher understanding into our lower consciousness. The higher understanding formulates as the counter-intuitive elements in the theory, while our common-sense attitude towards reality represents the lower consciousness that these elements are challenging. The source of this higher understanding, in the language of Kabbalah, is in the World of Emanation. In a certain sense, we can say that these theories not only elevate our consciousness of the universe and our place in it, but more importantly, they change how we imagine our relationship with God.
The role of mathematics
in countering common-sense
We will see how this is in a moment. But, the question first has to be asked: What is the true nature of reality? Is it what our common-sense tells us it is? Or, is it what Einstein and his theory of relativity tell us it is? This is also related to another question: How is it possible that Einstein and other scientists so intuited such counter-intuitive notions?
Above we used the image of a ray of light descending from the World of Emanation and permeating our lower consciousness. Now let us add that the Magid of Mezritch, the Ba’al Shem Tov’s successor, was fond of saying (in Yiddish) that “Atzilus is auch da!” meaning that, “Emanation is also here!” What the Magid meant is that there really is only one reality and it is only different modes of consciousness that cause us to see it in different ways. The mode of consciousness of Emanation depicts reality in the brightest light, without severing it from the Creator. So, if you have attained the consciousness of Emanation, you will see that it is here too. But, if you have not yet, then you can only catch a glimpse of reality through the eyes of Emanation, whenever Emanation-consciousness descends into your own mind-frame.
When it comes to understanding the universe’s mechanics, it is with the aid of mathematics that we can attain the consciousness of Emanation. For this reason all three theories (quantum mechanics and general and special relativity), even though they counter our experiential intuition, were discovered using mathematical considerations and reasoning. When it comes to physical laws, it is mathematics that carries the consciousness of Emanation down into our consciousness. Mathematics is like the ray of light that brings the consciousness of Emanation down into the three lower Worlds.
The value of challenging our common-sense
At this point, we have to take a step back and ask: What is the value of having lower consciousness in the first place? Why did God not just create our minds and senses in a way that they would experience reality as special relativity says it is? Clearly, this is not a scientific question but a religious one requiring us to find an answer in the Torah. So, let us rephrase this question by going back to the idiom ipcha mistabra, which refers to counter-intuition.
As noted, the Jerusalem Talmud makes no use of this idiom because, as we explained, its intuition is correct from the outset and does not require challenges. But, the Babylonian Talmud does, implying that its intuitive understanding is sometimes mistaken and requires corrections attained through the discourse between the sages. The sages described their state of consciousness in Babylon as that of one who dwells in darkness.[17] Like a person trying to judge what objects are in the dark, their initial intuition may be incorrect, until the lights are turned on, so to speak. So which is better? Is it better to always have higher intuition, like the Jerusalem Talmud, or is it better to first err and then be corrected by the light of higher understanding?
The essence of this question is disputed in the Talmud in a different context.[18] There is a question of who is greater: the tzadik, who never transgresses from the start, or one who transgressed and then did teshuvah (repented)? One opinion is that the tzadik is always greater than the ba’al teshuvah (Maimonides does not rule this way in his code of law). Following the logic of this opinion, the Jerusalem Talmud, which never needs to have its intuition challenged, is greater than the Babylonian Talmud, which often has to do exactly that. But, according to a second opinion, it is the ba’al teshuvah who is greater than the consummate tzadik. The ba’al teshuvah has arrived at the correct conclusion after having spent time living with mistaken intuitions about life. Indeed, his experience has led him to a more profound understanding regarding the depth of the Torah’s advice than the tzadik who has never overstepped the boundaries of the Torah. Maimonides and others rule according to this second opinion, which when applied to our question implies that countering one’s intuition and forging a corrected common-sense is in the end more rewarding and revealing than having the right intuition from the outset.
In Chassidic teachings a similar idea is stated with regard to light: light that comes out of darkness is greater than light that did not come from darkness.[19] In retrospect, it is a positive thing that your initial common-sense was wrong and that you spent some time in relative darkness, as long as you had enough courage to silence your own mind and counter your intuition when it became clear that this was the right thing to do. In that case, the entire journey was worthwhile, because the light that comes from the metamorphosis of one’s heart and mind is the light of teshuvah, which allows the ba’al teshuvah to attain levels that even a perfect tzadik cannot. So this is an example of how the World of Emanation illuminates the relative darkness of each of the three lower Worlds.
Let us restate what we have seen:
Special relativity is a total reorientation of our approach towards the universe. It does two things: it connects and unites matter and energy, by the most famous equation in all of science: E = mc2. And, not only does it do that, but it also makes space and time part of the events and not just the backdrop in which they occur. This means that space and time are relative concepts, relative to the observer, while the only thing that is absolute is the speed of light.
Interestingly, one of the most recent scientific developments is that perhaps even the speed of light itself, Einstein’s one and only absolute, changes with time. Scientists conjecture that at the beginning of creation, the speed of light was much faster than it is now. This is an idea that is gaining popularity, even though it still cannot be proven. In a similar vein, scientists have hypothesized that the fine-structure constant may also have changed.
These new discoveries could also explain many things in accordance with the Torah. Indeed, the Rebbe taught us that none of the laws of nature should be assumed to be necessarily constant. What this means is that contrary to the assumption that nature is and has always been uniform, we cannot extrapolate about the speed of light in the past based on our current measurements.
To summarize, special relativity states that everything depends on the observer, but this is counter-intuitive to the normal mind-set of the World of Action. What this boils down to is that a person could be running his entire life and in the end realize that he has gone nowhere. The only one who is really going anywhere is one who is attached to light. “Light is Torah.”[20] If you are on a beam of light you are moving. This is absolutely counter-intuitive to the consciousness of the World of Asiyah.
The counter-intuitive aspect of general relativity
Now what about the World of Formation (Yetzirah)?
General relativity takes into consideration gravity, one of the four fundamental forces. It is the most elusive of the forces. But what Einstein realized is that from an observer’s perspective, the experience of acceleration and the experience of gravity’s pull are equivalent. This has very far-reaching consequences. The example that is usually given to demonstrate this is that if you are traveling up in an elevator, when the elevator accelerates you feel yourself being pulled into the floor. The experience of being pulled down is identical to what you would feel if you were suddenly affected by a gravitational field. This insight forms the basis for general relativity and is known as the equivalence principle.
The most important consequence of the equivalence principle is that space is not flat, or in other words, it cannot be described using Euclidean geometry. Until Einstein, everybody envisioned space as being flat. Thanks to Riemann’s work, Einstein had the necessary mathematical tools (or “vessels”[21] to use Kabbalistic terminology) to consider that space might be curved, which means that everything indeed moves in a straight line, while at the same time following the curvature of space created by the masses lying in it. Gravity, as Einstein realized, actually curves space. The idea that space is curved is counter-intuitive to what we normally conceive its geometry to be like. After having studied geometry in high school, general relativity requires us to re-conceive what space is like. Instead of space being flat it is either convex or concave.
What does this symbolize, that you take something that you thought was straight and now it is either convex or concave? In Hebrew, this is described by the idiom, “Like clay in the hands of the artist” (כַּחֹמֶר בְּיַד הַיּוֹצֵר). This is a deep insight into what the word “formation” means. The artisan has a potter’s wheel, on which he places the raw material, the clay, and he curves it. In Halachah, a vessel that has no curvature, meaning it does not have an inner space, convex or concave in which it can hold something, such a vessel cannot be defiled (it cannot become ritually impure), thus it is not a vessel at all. The idea that space-time itself has intrinsic curvature is the absolute formative quality in the World of Formation. So what is being revealed here is that space is a malleable material, not at all what we thought it was. Counter-intuition in the World of Formation challenges what formation is really about: curvature (of space-time). Similarly, we may say that in the World of Action the one true constant of nature, the speed of light, is the essence of action, what action really is. In Chassidic thought a good deed (an action, performed in the World of Action) is only one that shines light in the world.
The counter-intuitive aspect of quantum mechanics
The counter-intuitive principle introduced by quantum mechanics is Heisenberg’s famous “uncertainty principle.” What it started out as is that we cannot know both the location and the momentum of an elementary particle at the same time. At first people thought this was a limitation introduced by the observer. But, later it became clear that quantum mechanics is saying something far more profound. It is telling us that in truth, in essence, a particle does not have exact position and exact momentum at the same time. Uncertainty is not the result of limited powers of observation, rather it is built into the very concept, the very nature of the particle. This means that particles are no longer “things,” as Dirac said. Elementary particles, like electrons, are not physical objects, they are wave functions, meaning probability functions. There are many ways to mathematically formalize this.
Feynman, one of the greatest American Jewish physicists used to say that there are perhaps a few people who understand, who grasp, what relativity is saying. But, there is no one at all who can fathom the meaning behind quantum mechanics.
Let us for a moment restate what the counter-intuitions of the Worlds of Action and Formation say about our service of God. In the World of Action, we said that the counter-intuition boils down to changing our comprehension of what motion is, what it means to be in motion. This is what the prophet says that relative to everything else a person is a walker, a mover.[22] Relative to everything else, only a human being possessing a Divine soul can really move because he is on a beam of light (the light of the Torah).
In the World of Formation, curvature is a statement about the human heart. The heart is not something flat, it is something that needs to be formed, that needs to be shaped (sometimes, it needs to be broken) in order to become a receptacle. You have to make your heart into a vessel. You have to be a craftsman, an artisan in order to make your heart into a vessel.
Uncertainty, the World of Creation’s counter-intuition, is a statement about the mind. The paradox of the mind is that physical matter is intangible. In Kabbalah, it says that when consciousness reaches the World of Creation, it no longer relates to “things,” there is only raw material, i.e., the potential for things. This can alternately be described as conceiving of the appearance of physical matter and events as they will evolve in the lower Worlds, but not their physical reality itself. At the level of the World of Creation, the mind has to divorce itself from thinking about “things.” The mind has to reform itself completely around this idea of uncertainty which takes away our notion of things. As we noted above with regard to the World of Formation (and the World of Action), here too, in the World of Creation, counter-intuition—the recognition that things do not really exist as we experience them (only in potential or as mathematical expressions)—is the essence (from the perspective of the World of Emanation) of what Creation (ex-nihilo) is.
Lecture 2
Introduction
We will continue now with a famous saying of the Ba’al Shem Tov: “No matter what the chidush (innovation) of any of the great Rabbis (and in his time there were very great sages), I can contradict it.” This is truly a remarkable statement. What was the Ba’al Shem Tov trying to say by this? Clearly, he was not trying to make himself out to be the smartest of all the sages. What does it mean that he can find a loophole in any innovation in Torah, or in any line of reasoning for that matter?
The Ba’al Shem Tov himself explained his meaning. What he meant is that every theory that is proposed by any Torah authority is a thought experiment in the realm of a particular World. But, in the middle-most point of that reality, there lies an essential nothingness. There is only one great soul—called the “Moshe Rabbeinu [Moses] of the generation”—that is in tune with this zero-point[1] that lies in the middle of every theory, and the Ba’al Shem Tov was in tune with that zero-point.
What is the purpose of the central point of nothingness? The points of nothingness in each World, at each level of consciousness, are connected to one another. Together, all the zero-points through all the Worlds are like a tube, or pillar, through which the person who is in tune with them can ascend and descend through all the Worlds. Now this is a very deep and important realization for science in general.
Every scientist, as great as he is, to the extent that he is really honest must ask the question whether science can ever really reach the end of understanding. Is science able to present a theory or equation that will completely encompass and represent all of creation? There are many audacious scientists who think that we are on the verge of formulating exactly such a description that will indeed explain everything. We will know everything with one formula. When that happens, all the scientists will have to retire, because then there will be nothing more to discover about the world. With one formula we will know the entire story of creation.
It’s truly an amazing thing that some scientists, who are usually very smart people, do not learn from experience. The sages say that a wise person is one who learns from experience.[2] The experience of the last few hundred years has shown time and again that every theory has always been consumed by a successor. There has always been a small loophole left over in every theory posited, some phenomenon or data that could not be explained, the existence of which eventually led to the creation of a new, more encompassing theory, which then consumed the previous theory. And then scientists think that, “Now we have it made.” But, again there is always one little loophole left that cannot be explained. And yet, every time that a new theory is developed, scientists think once more that they are on the verge of understanding it all, if only that one little thing that we can’t explain would just go away. In fact, that one little thing is exactly what reveals the shortcomings of the theory. And then, some new theory comes about. So how naïve is it on the part of some scientists to think that we are on the verge of explaining everything, leaving no room for doubt and no loopholes.
This is what the Ba’al Shem Tov was saying. Whatever theory you present, because I am connected with the inner point of nothingness, I can find the loophole in it. And this is actually a good thing, because by finding the loophole, the unexplainable nothingness that lies at the core of every theory, the Ba’al Shem Tov forces you to uncover a higher theory.
We have to say that it is by Divine Providence that scientists are naïve in this respect, because, were they not, they might just give up on studying science. They might prefer to become historians or musicians or something else. But because they have this initiative and vigor and momentum that, “we are on the verge of knowing it all,” they stay on their toes, constantly excited by discovery.
The Ba’al Shem Tov also did not mean that his statement cause Rabbis to stop studying Torah, or that they refrain from teaching and/or writing their understanding of the Talmud; on the contrary (ipcha mistabra!). He just told them that whatever deep understanding they will arrive at, he could find the loophole in it.
Now, the loophole in your understanding is called a “stirah,” which means a “contradiction.” But, the root of this word in Hebrew is the same as that for the word that means “concealed” (hanistarot, as in the verse “The concealed things are for Havayah our God”[3]).
There is another point to be made here. Rav Chaim Vital once asked his mentor, the Arizal, why it is that things that were supposed to be concealed even from the greatest Kabbalists, were now being revealed by him, the Arizal. The Arizal answered that no matter how much you reveal there will always be nistarot, there will always be something more that remains concealed. It will simply be at a higher level. Every revealed level has a loophole.
Applying this to my own personal life, this means that regardless of how I live, there is always a loophole in my lifestyle. There is always a concealed element, an unconscious or concealed contradiction and loophole that can serve as the gateway to ascend to a higher level. And, just as with the Ba’al Shem Tov, if I connect myself to the person who can show me this loophole, I can ascend through it to a higher level of consciousness.
In Hebrew, the word for “contradiction,” stirah, also means “to tear down,” meaning, that this little loophole will ultimately lead to the destruction of the previous theory and allow us to ascend to a higher level of understanding. But, regardless of how high we ascend, our new theory will also have its own nistarot, its own concealed loophole, or contradiction.
The equivalence principle revisited
Now, let’s fill in a few things related to what we said in the previous lecture. General relativity is based on the equivalence principle, which says that the experience of acceleration and gravity are equivalent. Both special and general relativity are based on concepts that stem from our subjective experience. The uncertainty principle of quantum mechanics was at first thought to be a subjective experience or subjective limit, but it was then realized that it is a purely objective limit, one not imposed by the shortcomings of our subjective mind, but by the objective nature of reality. This realization led to an entirely counter-intuitive conclusion, one that contradicts all our subjective experience, i.e., that “an electron is not a thing.” We do not know what it is. It is the formless matter,[4] which is the substance of the World of Creation. It is also called a golem, as we will explain later.
Let us turn now to the World of Emanation as it is revealed in the World of Formation in the form of the theory of general relativity. What is the verse from the Bible that best encapsulates and thus best alludes to the essence of general relativity? In the very beginning of the Song of Songs (1:4) we find the phrase, “Attract me, [and] we will run after you” (מָשְׁכֵנִי אַחֲרֶיךָ נָּרוּצָה). This is a beautiful encapsulation of the equivalence principle.
Gravity in Hebrew is called meshichah (מְשִׁיכָה), which means to draw, or to attract. As we will go on to explain, gravity is the only one of nature’s forces that is purely attractive. If we would compare it with the electromagnetic force, we would say that its “charge” is mass and it is all positive. So even though it is very weak relative to the other three forces in nature, it has the greatest effect on the universe. The first word of this phrase means, “Attract me [to you],” or “Make me gravitate [towards you]” (מָשְׁכֵנִי), and then the next two words mean, “We will run after you” (אַחֲרֶיךָ נָּרוּצָה). What is the second half of the phrase alluding to? It is actually describing acceleration. This short, 3-word phrase, contains a beautiful statement of Einstein’s equivalence principle, the equivalence of gravity and acceleration.
An innovative distinction between gravitation and acceleration
Now, there is a slightly irregular grammatical feature in this phrase. The first half is in the singular (“Attract me”), while the second half is in the plural (“And we will run after you…”). In Chassidic writings, it is explained that attraction (the force of gravity) affects the Divine soul alone, while running (acceleration) is felt by both the Divine and animal souls together.[5] This is certainly something more than what Einstein knew. There is definitely an equivalence in experience between gravity and acceleration. But, the experience of acceleration is shared by both the Divine and animal souls, while the initial gravitation is an arousal that God arouses the Divine soul alone with. The “gravitational pull” attracting the Divine soul to God is Divinity attracting Divinity. The soul is a part of the Divine, so the part gravitates to the whole, and the whole draws the part towards it. In this parable, Divinity is symbolized by mass, and the soul gravitating to God is like a stone falling to earth. This relates to the Ba’al Shem Tov’s famous saying that when it comes to “the essence,” when you hold on to a part of it, you are actually holding on to all of it.[6] That is what spontaneous gravity is like.
But, the second part, “We will run after you,” describing acceleration, means that both the Divine and animal souls experience acceleration towards the Divine. The reason for this is that acceleration is felt as something that “I am doing,” which in order to be experienced this way requires that the animal soul, which can simply be described as “my feeling of self,” also be involved. In any case, we find from this verse that indeed there is equivalence between the experience of gravity and the experience of acceleration.
This is another example of our method of searching for models that can illustrate scientific ideas in a verse, or in a gematria, etc. It is most important to find an asmachta, an allusion in the Torah for scientific concepts and ideas.
Energy, matter, time, and space
Now let us go back to the special theory of relativity. The famous equation here is E = mc2. We will need to investigate this equation in much more depth later. What this equation does is it equates mass, or matter (denoted by the letter m), with energy (denoted by the letter E). We have here matter, which in Hebrew is called chomer (חֹמֶר). Energy is called ko’ach (כֹּחַ). So Einstein’s famous equation means that matter is just another form of energy. But, every little drop of matter has a tremendous amount of energy in it, since it is multiplied by the square-value of the speed of light, a very large number.
Because of this equation, for some mysterious reason, space and time now become affected by events and by motion that takes place in them, the essential discovery of special relativity. So now we actually have four different concepts grouped in two pairs: energy and matter, and time and space.
In Kabbalah,[7] these four concepts: time, space, force, and matter correspond to the four letters of God’s essential Name,[8] as follows:
Time corresponds to the letter yud, or chochmah (wisdom). For instance, it is said, “Who is wise? One who sees the future.”[9] Intuition about time has to do with wisdom.
Space is a binah (understanding) concept, and there is a verse that states this explicitly, “Where is the place of understanding?”[10] This verse equates space and binah (understanding); meaning that the experience of space is a mother experience, while the experience of time is a more fatherly experience. How can we explain this in simple terms? The womanly sense is to know where everything belongs in the home, everything has its proper place. This is a sense of intuition regarding space. There are modern psychological systems, especially geared towards women, that build on this form of intuition. Womanly intuition is that everything has its proper place. To have your child grow-up with a consciousness that is based on Torah study, that is the father’s responsibility. This includes planning the future, the child’s career. This is a more time-oriented consciousness. The two together, wisdom and understanding, the father and mother principles, which here correspond to time and space, are called in Kabbalah: “Two partners that never sever from one another.”[11]
So what Einstein did is to connect time and space into one unit, one entity; together, they are one thing. In the terminology of Kabbalah, this is called “the higher unification” (yichuda ila’ah). Einstein also put together energy and matter, which corresponds to the unification of the bottom two letters in God’s essential Name, vav and hei. This is called “the lower unification” (yichuda tata’ah). Einstein had unified space and time corresponding to the unification of the first two letters in God’s essential Name, yud and hei. Then he unified energy and matter, corresponding to the two final letters in God’s essential Name, vav and hei.
But, then came the truly innovative result: that space and time, which before were viewed as, let us call it “transcendent”—taking no part in the exchanges of energy and matter—were now understood to be affected by physical events involving matter and energy. In Kabbalah and Chassidut, this corresponds to the manner in which the lower unification affects the higher unification. This is called the drawing of mochin, or brain-power, or life-force from the father and mother principles, which correspond to time and space as they are unified together, into the lower levels of energy and matter, which correspond to the lower unification.[12] Space and time change as a result of events that take place in the realm of energy and matter, which have now become one.
Now we will see something interesting about these four words (time, space, energy, and matter) as they are written in Hebrew: זְמָן מָקוֹם כֹּחַ חֹמֶר[13]. If we look at the middle letters of these four words we see that they are: זְמָן מָקוֹם כֹּחַ חֹמֶר. Just the middle letters together spell the word מָקוֹם, “space.” What this reveals is that it is specifically space (which, as we mentioned, corresponds to the mother principle, the first hei in God’s essential Name) that unites all four of these concepts. This is similar to what the Ba’al Shem Tov said that there is an inner point of zero, of nothingness within everything, and if you connect to it, you can be drawn up to a higher level. Indeed, more than the word for “time” (זְמָן), the word for “place” (מָקוֹם), in Hebrew, is a connotation for the Almighty. For example as we say in the Passover Hagaddah, “Blessed is the Place [God], blessed is He” (בָּרוּךְ הַמָּקוֹם בָּרוּךְ הוּא). The word for time, z’man (זְמָן), has many Kabbalistic gematrias and explanations, nonetheless, it is not a connotation for God. So there is something about space that is more Divine, more primordial, than even time. Still, Kabbalah teaches that time is more internal than space. It is time that enters space, which is more primordial. If there were space without time, it would be a continual present; there would be no flow of time.
Actually, from a ray of light’s perspective, there is only space, there is no time. There is a famous explanation of this idea that says that a ray of light that leaves the sun takes 8 and a half minutes to reach Earth. Light is not said to travel with infinite velocity, but it is said that light never left the sun. But it did leave the sun. Let us explain it like this: if we have a ray of light that left some far away star so many light years ago, it has left. But, we say that the ray of light is really still in that star, it is still clinging to its source, to the star from which it emerged. Why is this so? Because from the perspective of the ray of light there is no time! Even though the light has definitely spread into space—it has traversed space—nonetheless, it is still clinging to the star. If the light would experience time, it would have left the star. But since there is no experience of time, there is no time-lapse; no time has passed from when it left to when it reaches its destination, so it is instantaneously both at its starting point and at its ending point. The light is still clinging to its source. This is a very important concept in Chassidic teachings which is referred to by the idiom “light clings to its source.”[14] This most important principle in Chassidic teachings, which states that no matter what, light always clings to its source, is the Torah equivalent of the special theory of relativity. What this itself means is that there is space without time.
Once more, space is in a certain sense more essential than time. When time enters space, it becomes the male presence within the female. But space is more primordial than time, which is why it is a connotation for the Almighty. And, what happens in special relativity is that both space and time together become the mochin, part of the experience or the reality of ze’er anpin, the “Small Countenance,” corresponding to the emotive attributes of the soul, to the letter vav of God’s essential Name, and to the concept of energy in nature.
Every theory has a black hole
Let us go back to the Ba’al Shem Tov’s saying that no matter what theory you might come up with, I can always find a loophole in it. The loophole in a theory can be likened to a very important idea that comes out of the general theory of relativity—the black hole.
A black hole cannot be observed, by definition. Nonetheless, most scientists believe they exist. It is even theorized that at the center of our own galaxy, the Milky Way, there is a gigantic black hole that is 2.5 million times more massive than our own sun.
Some scientists even claim that a black hole creates a new universe. A black hole is a parent of a new universe. This is exactly what the Ba’al Shem Tov said. To say that a theory has an internal contradiction is at most a philosophical statement. Now we are saying that there is an actual, a physical “nothing” that is theorized to exist at the center of our physical reality. So the physical black hole at the middle of a galaxy is like the potential nothing that creates a new something. This is just like how the loophole in every theory is the point of origin for the next theory.
We said that some scientists do not learn from experience, they are naïve, not wise. Had they learnt from experience they would recall that every theory has fallen to give rise to the next one. Why do some scientists not understand this? This idea is even more pronounced in mathematics. In mathematics, which is far more theoretical than science, this has been proven, in what is called Gödel’s theorem. This theorem states that given any axiomatic mathematical system there is always an inconsistency, a mathematical black hole, if you will.[15] So if Gödel already proved that every mathematical structure has its own black hole, why not do the same for science? Why not prove that every scientific theory has a black hole by definition. Meaning, that not only would we be learning from experience that every theory has a black hole, but also prove that this is indeed the case. It is one thing to learn from experience that you will always be wrong. The next stage is not just to learn this, but to prove that this is the case.
Once more, the black hole is the physical analogy to the Ba’al Shem Tov’s loophole. In string theory a galaxy and a photon are considered equivalent, something that we will reflect on later. Everything has its black hole, even the smallest thing has a point of nothingness inside.
So we have our black hole analogy, and our saying from the Ba’al Shem Tov and we have Gödel’s proof, which was definitely, without question, the most important mathematical discovery of the 20th century.
In the end, what this all boils down to is that there is only one way out which is akin to the exodus from Egypt—i.e., riding God’s beam of light, which makes us into real movers amongst all those standing.
Lecture 3
Symmetry in the Torah
We have in the past explained a number of times that the word for “symmetry” in the Torah is חֵן, as in the verse usually translated as, “And Noah found favor in God’s eyes”[1] (וְנֹחַ מָצָא חֵן בְּעֵינֵי הוי'). If you take the mirror image of the name “Noah” in Hebrew (נֹחַ) you get the word chen (חֵן), which is the Hebrew word for “symmetry.” So, we might say that Noah was the first symmetry physicist and he found favor in the eyes of God because he contemplated the mirror image of his own name, symmetry.
Physical symmetries
In modern science there are three basic symmetries. First let us explain what symmetry means in physics. In physics symmetry is defined more broadly than the way it is in art. In physics it means that if a system is changed in a certain way, but it still appears to be the same, then it exhibits symmetry under that change. For example, if you have a ball and you rotate the ball, the ball will still look the same, so the ball is said to be symmetric under rotation. So symmetry at its heart says that if it looks the same, it is the same. All types of symmetry, like rotational and angular, all follow this principle.
The three basic symmetries that modern science addresses are called CPT, which stands for Charge, Parity, and Time. As we will explain, the order is not correct, but this is the order in which they always appear in physics. We will explain that time is the highest, then comes charge, and the lowest is parity. They correspond to a threefold division of the sefirot into: intellectual, emotional, and behavioral. In Kabbalistic language, each group of sefirot is denoted with a different acronym: the intellectual sefirot are called chabad, which stands for the initials of the Hebrew words for wisdom, understanding, and knowledge, the intellectual faculties; the emotional faculties are called chagat, which stands for the initials of the Hebrew words for loving-kindness, might, and beauty; and, the behavioral group of sefirot are called nehi, which stands for the initials of the Hebrew words for victory, acknowledgment, and foundation.
Parity, charge, and time
Parity means that if you look at the world through a mirror you will see the same thing. So the mirror image being the same means that the world is equivalent under a parity transformation. Another way of saying this is that left and right can be interchanged.
Symmetry of charge means that if you change every electrical charge in the universe to its opposite, you would still have the same universe. Once more, symmetry means that if you change something and it appears to be the same, then it is essentially the same. If you change the charge of every electron into a positron and every positron into an electron, then in essence you will have changed nothing, because everything appears to still be the same.
Time symmetry is the most difficult for us to comprehend because it says that if I change time such that the future is the past and the past is the future, then nothing really has changed. This is the most counter-intuitive symmetry, because obviously the past is not the future and the future is not the past, so how can a change in the direction of time leave the universe the same. The easiest to understand is parity, the mirror image. Charge is a little more profound. But time symmetry is the most difficult to understand.
In the language of the sages, the description for all of these reversed realities (the universe after a certain symmetrical transformation) is: “I saw an upside-down world.”[2] What happens when you see the world backwards in some way? As said, time symmetry is the most difficult to imagine. So how do scientists explain this? They do so by using the concept of entropy.
The principle of entropy, the second law of thermodynamics, states that as time passes, everything becomes more and more disordered. This is not just an objective experience; it is within the “psyche” of the universe itself. What this means is that under a time reversal (the past would now be the future and the future would now be the past, meaning that we would be headed forward into the past), I would still experience the future as the past, even though it is now my future. Therefore, nothing has changed, even if I change the direction of time. The universe still appears the same; the past even though it is now the future still appears to me as the past and the future, even though it is now my past will still appear as the future. All because of entropy. I can’t say that I understand what this means, but let us believe that this is the case. This is time symmetry.
Gauge symmetry
Now, general symmetry, which means changing something throughout the entire universe, is much easier to understand than if you change things only in a particular phenomenon and then look to see if there is a change in the rest of the universe. So, if I find a particular phenomenon within which I perform the change, the transformation, and yet, the universe stays the same, then this is considered a much more profound symmetry. This is called gauge symmetry and it is this type of symmetry that string theory is based on.
The most important example of gauge symmetry is in relation to the strong force, which keeps the nucleus of atoms—the protons and the neutrons in the nucleus—together. The elementary particle which acts as the messenger for the strong force is called the gluon. Gluons carry a charge that is designated in terms of a color/anti-color pairing.[3] The three “colors” in this description of the gluon’s charge are red, green, and blue. Now, the particular gauge symmetry governing gluons states that if all the reds turned into greens and vice versa, even though this is a change within only one of the four forces of the universe, nonetheless, the universe would remain exactly the same. This is different from taking the entire universe and placing it in front of a mirror and seeing nothing change. Therefore, this is considered a more profound symmetry.
Symmetry broken, symmetry complete
Up until several decades ago, each of these three symmetries was considered to be complete. Parity was complete, as was charge, as was time symmetry. Then came the surprising discovery that for the weak interaction, which is responsible for phenomena like radioactivity, right and left are not the same, meaning, that the symmetry of parity does not apply to the weak interaction (force).[4] This was a great discovery because it turned over what was previously believed to be true about parity symmetry: that it is universally applicable. This is a beautiful example of how quantum mechanics breaks our intuition, which feels that there should really be no difference between right and left. It is totally counter-intuitive to us to say that there should be a difference between right and left, between looking at an experiment directly or watching it through a mirror. Once more, there are four fundamental interactions in physics, the strong force, the weak force, the electromagnetic force, and gravity. Only in regard to the weak force was it shown that parity conservation is violated.
So now we have set the ground work for understanding symmetry.
Parity: the behavioral sefirot
Now we would like to explain that parity symmetry (or conservation) corresponds to the behavioral aspects of the soul, which comprise the sefirot of victory (netzach), thanksgiving (hod), and foundation (yesod). Parity conservation specifically refers to the two sefirot of victory and thanksgiving, which are considered in Kabbalah to be like two sides of one coin.[5] They constitute the ability to take initiative to reach some goal (victory) and the perseverance to see that thing through until it is accomplished (thanksgiving). Victory and thanksgiving are the two sides of one’s powers of action in the world, the “active powers” (kochot ma’asiyim) of the soul. They are considered so complementary that sometimes (especially in the World of Chaos) they are considered to be one and the same—one sefirah.[6]
The allusion in the Torah that clearly indicates that parity is related to victory (netzach) and thanksgiving (hod) is found in the Zohar in the expression, “he is in victory, she is in thanksgiving.”[7] Once again, victory spiritually corresponds to the self-confidence needed to get up and take initiative and is relatively the masculine half of the picture and thanksgiving (hod) spiritually corresponds to the strength to persevere in one’s endeavor and carry it through, the relatively feminine half of the picture. So at the level of action, these are the male and female principles in the soul.
Parity in the Tabernacle’s wash basin
The allusion to this is found in the Torah reading of Vayakhel. The last of the vessels described (which was also the first one used by the priests serving in the Tabernacle) was the wash basin (כִּיּוֹר) and its base. The basin was made from the mirrors of women.[8] Halachically, a man is not permitted to look at himself in a mirror. A mirror is in essence a feminine object. What this means is that parity (symmetry between left and right) is in its essence a feminine principle.[9]
The word describing the mirrors that were used to make the wash basin, “tzov’ot” (צֹבְאֹת), literally means “hosts.” Rashi explains this unique word. He explains that these were the mirrors used by the Jewish women in Egypt to beautify themselves for their husbands, even in the midst of slavery. The men were very fatigued and had no strength to be with their wives and have relations with them because of their hard labor and this could have spelled the end of the Jewish people. The women had these special mirrors. When the husband came home late at night they would call him and say “Let’s take a look at our faces in the mirror [see our mirror image] and see who is more beautiful.” In this manner, by having the husband and the wife together look in the mirror, they would awaken and arouse their husbands. From this came out the 600,000 children that were finally redeemed from the severe servitude in Egypt, the people that the Torah refers to as “tzivot Hashem” (the hosts of God) and went on to receive the Torah at Mt. Sinai, thus beginning Jewish history.
It is said that because mirrors are used to arouse the evil inclination with the desires of the flesh, when the women brought them as their contribution to the building of the Tabernacle, at first Moshe Rabbeinu did not want to receive them. But God told him to take those mirrors because it was due to them that the people merited being fruitful and multiplying. The entire birth of the Jewish people was thanks to these mirrors. God professed that these mirrors, out of which the wash basin was made, were the most cherished part of the Tabernacle.[10]
Just as these mirrors united husband and wife during the terrible slavery in Egypt, so in the Tabernacle and later in the Holy Temple in Jerusalem, water taken from the wash basin was used to make peace and reunite a husband with his wife who he suspected of infidelity.[11]
On a daily basis, the basin was used by the priests to sanctify their hands and feet before serving in the Tabernacle. To do so, the priest would place his right hand on his right foot and his left hand on his left foot and pour water from the basin on all four together. If he did not wash in this way, then his entire service was disqualified.
From these two instances we see that the basin is a symbol of connecting left and right together. The right hand and the right foot were unified, then the left hand and the left foot were unified, and then all four were washed together.
In Kabbalah, each of the different vessels of the Tabernacle corresponds to a particular sefirah. The basin and its base correspond to the sefirot of victory and thanksgiving. In fact the word tzovot (צֹבְאֹת), when pronounced a little differently (but spelled with the same letters) is God’s Name, the God of Hosts (צְבָאוֹת). This particular Name corresponds to the sefirot of victory and thanksgiving.[12] This we refer to as mirror symmetry.
A Torah insight into parity conservation
Before, regarding our discussion of the equivalence principle (that gravity and acceleration are equivalent) we saw that the Torah offers us an additional insight. Here we also see a similar innovative insight.
When the husband and wife looked in the mirror they were the same except their position changed. It is interesting to ask, when is mirror symmetry most apparent in Jewish life? Let us think about the bride and groom standing under the chupah, the wedding canopy. Who stands on the right and who stands on the left? According to the prevailing custom, we place the bride to the right of the groom.[13] Why should that be? In the sefirot, the feminine half of the victory-thanksgiving pair is thanksgiving and it is the left of its masculine counterpart, victory. But, relative to the Rabbi who is sanctifying the couple it is the opposite. For him the groom is to his right and the bride is to his left. This is a very simple way to explain how left and right interchange, it is still the same universe; the same two people are getting married whether I look at it from their perspective or from the perspective of the Rabbi.
Now, surprisingly, when the husband and his wife looked in the mirror together, the mirror acted. The mirror image was not passive. The mirror image was active. First of all it connected them together. The husband and the wife are sitting together on a bench and the husband is about to fall asleep because he is so tired from his work, there is no connection between them. All of a sudden the wife takes out her mirror and says to her husband, “Let’s look in the mirror.” And then something new happens, by seeing themselves together, the husband is aroused, etc. And once again, the Almighty said that this was the most beloved of all contributions made to the Tabernacle. So the symmetry made the husband take initiative and made him interested in his wife. This means that the symmetry awakened in him his power of victory. About the feminine it says that “understanding extends to thanksgiving.” This is the perseverance to see things through mentioned earlier. And with this power of thanksgiving, of perseverance, the wife was now entrusted with the responsibility of carrying the pregnancy through to term. But, the arousal of victory was achieved by the symmetry.
So, we have seen how parity symmetry, the conservation of parity, is related to victory and thanksgiving.
Charge and the emotional sefirot
Let us now turn to charge symmetry. Charge symmetry is the symmetry of the heart’s essential emotions. To be charged is to have an emotion, an emotion is a charge. People are charged, everyone who has emotions is charged.
Now, here is the amazing thing about emotions. Imagine two people, one who is all love and one who is all fear or awe. Now imagine that they switch. If all the lovers became fearers and all the fearers became lovers, the universe would remain exactly the same; meaning, that in a certain sense, it makes no difference. “These and these are the words of the living God.”[14]
In the terminology of Kabbalah, charge symmetry is called chasadim (attributes of loving-kindness) and gevurot (attributes of judgment). The sefirah of knowledge is the origin of both loving-kindness and might, or fear. It is the source of both aspects of loving-kindness and aspects of judgment, which when they manifest in the heart become the two sefirot of loving-kindness and might, which are experienced as love and fear.
In Kabbalah, the definition of the interchange between loving-kindness and might is referred to as achlifu duchtayhu (אַחְלִיפוּ דּוּכְתַיהוּ)[15] and in Aramaic literally means, “they change places.” What happens in such a case is that the light of loving-kindness enters the vessel of might and the light of might enters the vessel of loving-kindness. Such a cross-over is to be experienced every day when we read the first and second paragraphs of the Shema, as explained in the intentions of the Arizal. The first paragraph, which begins with the words “And you shall love Havayah, your God…,” is the paragraph of love. But, the Divine Name that illuminates it is the Name of 42 letters,[16] which is associated with gevurah, with might, or fear. The Tzemach Tzedek, the third Lubavitcher Rebbe explains that this is because the light of gevurah, of might has entered into the vessel of loving-kindness. In the second paragraph, the opposite occurs, the Name of 72, associated with loving-kindness, illuminates this paragraph which in and of itself is the vessel of might.[17] So what takes place when we say the Shema twice every day is a charge symmetry phenomenon, which is called achlifu duchtayhu.
What this means for each of us individually is that we should remain open to a total metamorphosis or change, but that things will still remain symmetric. For example, if my primary emotion is love and I know someone who’s primary emotion is fear, then the easiest way to give him an experience of love is if I assume a state of fear. If I do so, he will take on love. Charge symmetry will ensure that everything remains the same, but as we mentioned above, there is something better about the symmetric state then the original state.
The best example of charge symmetry taking place in the Torah is found in the story of the binding of Isaac. Abraham who was loving-kindness acted with might (overcoming his love and acting to sacrifice his beloved son), and Isaac who was might acted with loving-kindness (by lovingly accepting his father’s judgment, willing to be sacrificed for God).
Charge symmetry, and good and evil
On a deeper level, we can say the same thing regarding the good and bad inclinations. It is explained in Chassidut that the good and bad inclinations (yetzer tov and yetzer hara) derive from the chasadim (the aspects of loving-kindness) and the gevurot (the aspects of judgment) of knowledge. What happens if throughout the universe they switch? This would also be charge symmetry. Inclination is an emotion, a charge, it is a drive. Just like an electron has a charge and there is a positron with an opposite charge. Understanding that the state resulting from such a switch between all the good and bad inclinations in the universe would, on the whole, leave the universe unchanged is very profound.
Very often, people think they are doing good but they are actually doing evil. Other people may think that they are doing evil, but they are really doing good. This is much more subtle. But this too is an example of charge symmetry.
(What it really boils down to is that the universe remains unchanged. Based on the verse, “And Noah found grace in the eyes of God,” we can say that symmetry (grace) is the beauty of creation.)
We saw such an instance of good and evil being reversed in the previous example regarding the mirrors that made up the wash basin. Moshe Rabbeinu thought that the mirrors came from a bad inclination (they were used for sexual arousal). But, God revealed to him that the opposite was true, they were from the good inclination, used to ensure Jewish survival. Thus, the previous example of parity conservation can be used to explain charge symmetry. For Moshe Rabbeinu, the good was that there should not be sexual arousal, which he believed was driven by the evil inclination. But, God understood that the sexual arousal was actually good. This is very strange since in general we are taught that Moshe Rabbeinu sees things from God’s perspective.[18] But, here we see that he sees things opposite.
As we said, regarding parity symmetry, the weak force was considered a loophole. Still scientists thought that charge symmetry held universally. But, then it was found that charge symmetry also has a loophole. Then it was thought that parity and charge symmetries hold when taken together. But, finally it was found that only when all three symmetries are taken together does universal symmetry hold. Essentially it all depends on time symmetry.
Time and the intellectual sefirot
So now let us explain time symmetry and how it corresponds to the intellectual faculties of the soul called chabad, which stands for the three sefirot chochmah (wisdom), binah (understanding), and da’at (knowledge).
In Sefer Yetzirah (the Book of Formation), it states that, “the depth of beginning” (omek reisheet), meaning the past, corresponds to the sefirah of wisdom and that, “the depth of the end” (omek acharit), meaning the future, corresponds to understanding. So the direction of time is from wisdom to understanding, from the past to the future. It follows then that knowledge corresponds to the present, which is in between the two. Before we said that relative to one another the origin of space is in understanding, while the origin of time is in wisdom. This still fits, since time is still in wisdom, but it is moving towards understanding. The classic example of this is that the future tense of a verb in Hebrew is formed with the 4 letters איתן,[19] which when treated as a word means “strength” or “power” (אֵיתָן). For example, “I will be, he will be, you will be, we will be” (אֶהְיֶה יִהְיֶה תִּהְיֶה נִהְיֶה) all examples of the future tense of the verb “to be”. These letters indicate a vector force of the time coordinate from the origin of time to the end of time, which corresponds to understanding.
So, time symmetry means that if the direction of time would reverse, time would flow from understanding to wisdom, from the mother principle to the father principle. But, because of entropy, the universe would still look the same. The past would still be experienced as the past even though it is now the future, all due to the second law of thermodynamics, the law of entropy.
type of symmetry |
in sefirot |
time |
intellectual |
charge |
emotional |
parity |
behavioral |
A Shema meditation on symmetry
Now we will relate the correspondence just explored to the word “one” (אֶחָד), echad. We mention this word in the first verse of the Shema: “Hear O’ Israel Havayah is our God, Havayah is one.”[20] The word “one” (אֶחָד), pronounced echad, has three letters.
There is a basic meditation that we are taught in the Shulchan Aruch regarding this word, “one” (אֶחָד). The first letter, the alef (א, whose numerical value is 1), alludes to God’s essence. Since I cannot know God’s essence, there is little to meditate upon, so I say this letter quickly, without dwelling on it.[21] A bit more meditation can be done on the second letter, the chet (ח). However, the mitzvah, the requirement that we draw out the pronunciation of this word “one,” specifically refers to its final letter, the dalet (ד).
What is the significance of these three letters? The chet (ח, whose numerical value is 8) represents the up-down dimension of reality, which includes 8 levels: 7 firmaments and the earth. The dalet (ד, whose numerical value is 4) represents the four lateral directions of the earth itself. The alef (א) is the root, referring to God, but also to the soul, as it is one with God, before it descends through the seven firmaments to the earth, where it is given its task of spreading the knowledge and light of God throughout the four lateral directions of the earth to reach the four corners of the earth. This is a simple meditation on the word “one,” echad.
Just as we cannot conceive God’s essence, so we cannot conceive the true unity of the soul with God and so the alef (א) is said quickly, without much meditation on it. The meditation truly begins with the experience of descending through the seven firmaments and the earth, by which we can then come to understand our mission in life of spreading knowledge of God through the four corners of the earth, “And you shall spread out to the west and east, north and south”[22] (וּפָרַצְתָּ יָמָּה וָקֵדְמָה צָפוֹנָה וָנֶגְבָּה). This verse literally means giving birth to many, many souls throughout the world, like the “mirrors of hosts,” mentioned above. This is also the literal meaning of the verse “May your wellsprings spread out”[23] (יָפוּצוּ מַעְיְנוֹתֶיךָ חוּצָה) i.e., to have many children who will spread around the world, inhabit it, and bring God’s light to it.
In any event, there are three physical dimensions, which we will refer to as up-down, right-left, and front-back. When we refer to string theory, we will see that it adds many more spatial dimensions. For some reason that we cannot explain they add only spatial dimensions, they do not add a time dimension.
The time dimension in space
Charge is not a spatial dimension. Time is certainly not a spatial dimension. Nonetheless, both time and charge project themselves upon one of the three spatial dimensions.
When considering the three spatial dimensions, time is reflected in depth, meaning, front and back. Depth is called the third dimension, like 3D which is in and out, or front and back. How do I know that time is reflected in the front-back spatial dimension? We are talking about how time unites with space and we are asking in what particular manner time unites with space. From a spiritual perspective, we say that time specifically unites with the front-back dimension of space. We know this because the Hebrew words for “front” (פָּנִים) and “back” (אָחוֹר) stem from the same roots as the words for “before” (לִפְנֵי) and “after” (אַחֲרֵי). But amazingly, the word for “before” (לִפְנֵי) referring of course to the past stems from the root that also means “front” (פָּנִים), while the word for “after” (אַחֲרֵי), referring to the future, stems from the root that also means “back” (אָחוֹר).[24] So we have here an amazing example of direction reversal similar to what we discussed before regarding the symmetry of changing the direction of the flow of time. What was the past is now the future, what was the future has now become the past.
Now, time affects the alef (א) in “one” (אֶחָד). What does it mean for a Jew to be moving towards the future and yet to always experience it as the future. We mentioned already that this is the most profound of symmetries. It is the most intellectual one. It means that just like God, a Jew is always looking at the Torah as the blueprint of creation, the blueprint that God used to create the world.[25] The Jew is always looking at the past, at what the Torah has to say. Every day we re-experience the giving of the Torah. As a Jew is moving forward through time, he is actually looking at the past and basing his entire life on what he knows to be the past, but somehow this is now also the future, since from his perspective he is always moving forward in time. Again, just like the Creator, by looking at the Torah—both the primordial Torah with which the world was created, and especially the Torah that was given to us at Mt. Sinai—the Jew creates a world, creating and forming his future.
Indeed, in Zachariah there is a vision where he sees the Torah as having a front and a back. It’s called the flying scroll of the Torah.[26]
The parity in space
Parity, describes left-right symmetry, they correspond to the four lateral directions. These are the four directions of the letter (ד) of echad, “one” (אֶחָד). Parity again is right and left, and more generally it is the dalet (ד).
Let us go back for a moment. We said earlier that parity reflects the sefirot of netzach (victory) and hod (thanksgiving), they are called two “sides” of the same body. This is like “taking sides.” Netzach and hod are two sides. Side in English derives etymologically from the word “side” (צָד) in Hebrew, pronounced tzad. Even though they are only two sides (right and left), they correspond to all four lateral directions. So parity corresponds to the final letter of “one” (אֶחָד), the dalet (ד), symbolizing the four lateral directions.
The charge in space
Spatially, charge corresponds to the up-down dimension. Scientists cannot explain why they chose these strange words, but the charge on quarks, which gives them their names, are “up” or “down,” or “top” or “bottom” (this means that “charm” and “strange,” the two remaining quarks, also follow this peculiar convention—charm is up and strange is down). The up-down terminology especially applies to the statement in Sefer Yetzirah (the Book of Formation) that, “There is no good higher than pleasure (עֹנֶג) and no evil lower than “plague” (נֶגַע).”[27]
Once more, when we discussed charge, we started with the five chasadim and five gevurot. They manifest either as love and fear, or even more extremely, as the good and evil inclinations. But really what this applies to is up-down, since the good rises all the way up to oneg (pleasure) and the evil descends all the way down to nega (plague). In any event, charge abstractly means that either you are charged “up” or “down.” But, the amazing thing is that it does not matter in which way you are charged, because if the entire universe were to switch we would not be able to tell the difference. Like we said before, sometimes you have to change your own charge in order to bring out the opposite in someone else. Going back to our meditation on the word “one” in the Shema, we have that there is a mysterious projection of charge upon the letter chet (ח) in “one” (אֶחָד).
type of symmetry |
spatial direction |
letter in “one” (אֶחָד) |
time |
front-back |
alef (א) |
charge |
up-down |
chet (ח) |
parity |
left-right |
dalet (ד) |
The gematria of symmetry and unity
We will conclude this lecture with the following very beautiful expression. We saw that in the word “one” (אֶחָד), the alef (א) corresponds to the intellect, the chet (ח) to the emotions, and the dalet (ד) to the spreading out in actions. We also used this word to correspond the 3 symmetry categories in physics.
In Kabbalah, we are taught that every word can be written in a symmetrical form. In practical terms, pretty much the only way to illustrate symmetry is with a mirror. We have no other model for thinking about symmetry. In the Shema as it is written in the Torah scroll, the word “one” (אֶחָד) is written with a large letter dalet (ד). Now if I take the dalet as an axis of symmetry and write out the word “one” in both directions, I will get:
א ח ד ח א
The value of “one” (אֶחָד) is 13. Writing it this way, the value becomes 22. Now, what will happen if we do this not in one but in three dimensions?
א |
א |
|||
ח |
ח |
|||
א |
ח |
ד |
ח |
א |
ח |
ח |
|||
א |
א |
The value of this symmetry of “one” in 3 dimensions is easy to calculate. There is the dalet (ד) at the center, plus 6 pairs of the two letters, alef and chet (אח), whose value is 9. So, the total value will be 54 (6 times 9) plus the value of the central dalet (ד), which is 4, totalling 58. The value of the word “one” (אֶחָד), in three-dimensional symmetry is 58, exactly the value of the Hebrew word for “symmetry” (חֵן), which we have been discussing.
A much simpler phenomenon is that in reduced numbering, the value of “symmetry” (חֵן) is 13, the normative value of “one” (אֶחָד). But, as we saw, in three dimensions, “one” (אֶחָד) expands and becomes equal to 58, the value of “symmetry” (חֵן).
© כל הזכויות שמורות למכון גל עיני. הטקסט מיועד ללימוד ולשימוש אישי בלבד.