Lecture 9

The camel as a metaphor for wave-particle duality

We all remember the story of Isaac and Rebecca and how Abraham sent Eliezer, his servant, as a messenger (like we learnt before, regarding messenger particles) to find a wife for Isaac. The example brought in the mishnah we discussed earlier in respect to sanctifying a wife by messenger is in this story, which very often is explained in Kabbalah and Chassidut as the most essential shiduch (match) in the entire Torah. Everything that we want to learn about shiduchim, about matchmaking comes from this story. When Eliezer had made the shiduch with Rebecca, even her father and brother, who were not very righteous individuals, had to admit that “from Havayah, this thing came” (מֵי־הוה יָצָא הַדָּבָר). In Hebrew, the value of this phrase is 378, which is also the value of the word חַשְׁמַל, a word that in modern Hebrew has been adopted for “electricity.”

Parenthetically, if you reverse the numerals of 378, you get 873, which is the numerical value of the idiom “the speed of light” (מְהִירוּת הַאוֹר), the one essential constant of our physical reality according to modern physics. A similar example is that if you take the value of “Shabbat” (שַׁבָּת), 702, and write the numerals in reverse order, you get 207, which is the numerical value of “light” (אוֹר).

Every word in the Torah has a particular place where it is especially concentrated, meaning, that the reality that this word represents is concentrated maximally in this place in the Torah. Surprisingly, the most ubiquitous word in the verses describing the shiduch of Isaac and Rebecca is “camel” (גָּמָל), another of the images for a photon. A camel is both a particle and a wave, because if you look at its hunch, it is like a wave. But if you take in the whole camel at once, it itself is a big particle. We mentioned that it has been shown that all elementary particles exhibit wave-particle duality, so in essence they are all camels.

Meditation on the meanings of “camel”

All phenomena of the Hebrew language are amazing meditations. The same three-letter root that means “camel,” גמל, also means “weaning.” In the Torah, weaning appears specifically regarding Isaac. The Torah tells us that on the day that Isaac was weaned Abraham made a celebration[1] (בְּיוֹם הִגָּמֵל אֶת יִצְחָק), another connection between Isaac and this root, and hence another connection between Isaac and wave-particle duality.

Besides meaning “camel” and “weaning,” this same root (גמל) can also mean “acts of loving-kindness” (גְּמִילוּת חֲסָדִים), something that is specifically related to Abraham, Isaac’s father. So what might be the meditation linking the three meanings of this root? The vast majority of the times that this root appears in the Torah is in the sense of “camel.” Incidentally, the English word for camel clearly comes from the Hebrew word gamal. There are certain words in the English language which are a hundred percent from Hebrew.

E=mc²

The same three-letter root, גמל, is also simply the name of the third letter in Hebrew, the gimel (ג). The English alphabet in a certain sense simply mirrors the Hebrew alphabet. In English the third letter is c, which is the first letter of “camel.”

What about in physics? In physics c denotes the speed of light, as in E = mc². It is easy to understand that E stands for “energy” and m stands for “mass,” but what does c stand for? Even physicists are divided on the reason for the usage of c in this convention. One opinion says that c stands for “constant.” Another opinion says that it stands for the first letter for “speed” in Latin.

[But we know what it really stands for: c stands for camel! So, E = mc² stands for energy is equal to the mass times a squared camel! It’s hard to square a camel because he’s round, but this is an important thing for women to know. A woman who wants to have a calm husband can use a technique brought by Rabbi Avraham Abulafia, which involves rearranging the letters of a word or phrase to get something related. In this case, the letters of “calm husband” (בָּעַל רָגוּעַ) can be rearranged to spell “circle the square” (עַגֵּל רִבּוּעַ). A woman who wants to calm her husband down has to know how to make a square into a circle. This is not just cute. In Chassidut, it is explained in length that people are uptight and tense because they have too many corners, too many sharp edges. To calm them down, you have to help them round their edges and get them to change from a square into a circle.]

In the Pentateuch, there are 34 instances of the root גמל. They do not always mean “camel.” As we have noted, sometimes, they mean “wean” or “generous.” The significance of 34 for us is that the Hebrew word for “photon,” egel (אֵגֶל) is equal to 34. The value of this word is twice the value of “good” (טוֹב), reminding us of the verse: “God saw the light that it was good.”[2]

Of all those 34 times, 18 are concentrated in the story of Abraham sending Eliezer with the camels, with gifts loaded on the camels.[3] On average, almost every third verse mentions camels. And Eliezer, the messenger particle, says that he will test the woman to see if she is worthy of marrying the son of the most generous soul on earth, i.e., Abraham. Will she give my camels water to drink? And that was the way that Rebecca proved herself worthy of entering Abraham’s household, by watering the camels. 18 is the numerical value of “live” (חָי). So this story is all about the “live camel.”

Sight and camels

At the end of the story, Eliezer takes Rebecca on the camels back to the land of Israel, where Isaac is waiting. The Torah relates that Isaac had gone to Be’er lachai ro’ee (בְּאֵר לַחַי רֹאִי). Upon his return home, he went out one evening to pray in the field, he lifted his eyes and saw Eliezer and his camels arriving. The sages explain that while Eliezer had gone to find Isaac his wife, Isaac had gone to this place called Be’er lachai ro’ee where Hagar, Abraham’s banished wife was living, in order to make a shiduch for his father, Abraham.

Be’er lachai ro’ee literally means “the well of the Living One that was seen,” but it can also mean the “well of living sight,” an allusion to photons of light coming out to give life (as in photosynthesis). We can therefore say that Isaac seeing Eliezer’s camels coming over the desert is like an image of photons, camels, arriving. Isaac is like a scientist who is watching the particle and wave effect. He was contemplating sight, and light, and the electromagnetic radiation, something that is hinted to in the place that he was coming from: “the well of sight….”

When Rebecca saw Isaac and how beautiful he was, the Torah says that she fell off the camel. It is like she fell off of her photon. She was “riding” the beam of light and fell off of it. There are many explanations of what it means that she fell off the camel. In order to get married, Isaac had to lift his eyes and see the camels coming.

Now let us return to the word “camel” itself. We saw that it is formed by adding the letter mem to the Hebrew word for wave (גָל). The addition of a mem to the wave gives the wave a particle reality, just as the addition of an alef to גל, forms the Hebrew name for photon, and gives the photon’s wave reality, a particle reality. Now, why is the addition of a mem very good? Because, the meaning of the letter mem (when treated as a whole word) is “water” (מָיִם)! Clearly, the first image of waves that we have from the natural world is from the waves of water.

The sickle as a metaphor for wave-particle duality

We saw in the previous lecture that there are other ways to create a three-letter root out of the two-letter root, גל. In “camel” (גָּמָל), the mem is added between the two letters גל. What about the addition of the mem before these two letters, which then spells “sickle” (מַגָּל)? The form of the sickle also resembles a wave. Moreover, the sickle is used in the field, which relates it to another important element of our topic: fields. Today, science is looking for a unified field theory.

When searching for a bride for Isaac, Eliezer tested Rebecca’s loving-kindness, her ability to do kindness with the camels (as mentioned, גמל also means גְּמִילוּת חֲסָדִים, acts of loving-kindness).

We saw another root that comes from adding the mem to the end of גל, “golem” (גֹּלֶם). A golem literally refers to a substance without form. It can also mean an unformed mind. In Pirkei Avot,[4] the Ethics of the Fathers, there is a description of the golem as a potentially wise man, who in reality is not a stupid person, but rather one who has not finished his training yet, his mind is as yet unformed. Because he is on his way, everything for him is counter-intuitive. But once he finishes he will become a wise man.

Indeed, what is important about these three words—“camel” (גָּמָל), “sickle” (מַגָּל), and golem (גֹּלֶם)—is that they share the same numerical value, 73, which is also the numerical value of “wisdom” (חָכְמָה). Wisdom is the origin of light. In Chassidic teachings it is called “the beginning of revelation” (רֵאשִׁית הַגִּלּוּי). The numerical value of the first verse of the Torah is 2701, which is the triangle of 73, the triangle of “wisdom” (חָכְמָה).[5] So the first verse of the Torah is like a giant triangular camel. The value of “camel” is thus very important. We should keep in mind that so far this is the largest image of wave-particle duality.

The particle zoo

Camels are force particles, while the horses that we discussed earlier are matter particles. To recap, we said that the three types of particles (real matter, real force, and virtual particles) correspond to horses, living beings (animals), and fiery angels (seraphim), respectively. So now we are adding that the force particles are likened to camels, which act as messengers. We are translating all the particles into a zoo.[6]

What about the virtual particles? What animal should they be likened to? Answering this question requires that we expand our imagination. To do so, we need to have already rectified our power of imagination, an important subject in and of itself in Chassidic teachings.

We explained that there are both virtual matter particles and virtual force particles. In the World of Creation there are both virtual Formation (force) particles and virtual Action (matter) particles. So, actually we need to find two different animals as metaphors for both types.

Without explaining this too deeply, the virtual matter particles would be likened to “elephants” (פִּילִים). The Talmud[7] says that if you dream of elephants, you should expect wonders of wonders to happen to you (wonders are actually greater than miracles). The most wondrous experience is to see an elephant pass through the eye of a needle (פִּילָא בְּקוֹפָא דְּמַחֲטָא). This reminds us of the double slit experiment, which ascertained the wave-matter duality of real photons. Here we are talking about virtual particles.

We saw that according to string theory, size does not matter, so there is no difference between imagining photons passing through a microscopic slit, and imagining elephants passing through the eye of a needle. The elephant is considered to be the biggest animal. In the Song of Creation (which relates the song that every part of creation sings in praise of the Creator—the song reveals the essence of each part of creation), it is written that the elephant sings the verse: “How big are your actions, God,”[8] alluding to itself as the biggest of God’s creations. So a virtual electron, which is a virtual matter particle, would be likened to an elephant. This is what comes to mind in regard to the virtual matter particles.

Now, what about the virtual force particles, like a virtual photon? These we say are symbolized by a butterfly. In Hebrew a butterfly is a parpar (פַּרְפַּר). Virtual particles come in pairs, and the word parpar is like “pair pair.” They also spontaneously appear and disappear, which is also “appear disappear.” These are two linguistic puns on the Hebrew word parpar. In any event, now we have all this imagery of horses, camels, elephants, and butterflies in our quantum zoo.

Camels in the Bible

We mentioned already that in the Five Books of Moses there are 34 instances of the root גמל. In the entire Bible there are 112 instances of “camel.” Now, since the numerical value of גמל is 73, looking at the 73^rd instance of this root in the Bible is most significant (as the 73^rd instance of a root that equals 73 is an example of self-reference). The 73^rd instance is in the verse: “God is God of payments, he will surely repay”[9] (כִּי אֵ־ל גְּמֻלֹות י־הוה שַׁלֵּם יְשַׁלֵּם).

There is a famous saying of the sages in the Talmud, “‘Knowledge’ is great, for it appears between two Names [of God].” There is a verse: “God is God of knowledge.”[10] In the original Hebrew, the word “two types of knowledge” (דֵּעוֹת) appears between two Names of God, Kel and Havayah. The sages then mention that the word “Temple” also appears between two different Names, Adni and Havayah, which they also explain. The Talmud then goes on to ask about the word “revenge.” Since it too appears between the same two Names as “knowledge,” it too should be great. As we have discussed in the past, the teaching about “knowledge” can indeed be extended to “revenge.” Very significantly, when one checks the entire Bible, one finds that there is one more example of a word that appears between two Names of the Almighty. This is our word here: “payments” (גְּמֻלֹות). Surprisingly, though the sages do not mention this.

Now this word, “payments,” even though it stems from the same root, does not mean “camel” here. It means “payment,” a meaning that is closer to the meaning of “acts of kindness.” But payment can be positive or negative. You can get a reward and you can get punishment as payment. Though it does not mean “camel,” “payment” is still etymologically related to camel, since they stem from the same root. It is in the Zohar that we find that the camel can be a negative image. Sometimes it is so negative that it is a symbol for the angel of death (that should be written on Camel cigarettes). Nonetheless, camels were part of the positive image of the patriarchs and matriarchs, especially Isaac and Rebecca. The camel is also a symbol of acts of loving-kindness. The unified view of a camel is therefore that it is a symbol of just payment: reward or punishment.

The essential message of the letter gimel (ג) is that of reward and punishment, as explained in length in our book The Hebrew Letters. To believe in reward and punishment, the eleventh of the thirteen principles of faith enumerated by Maimonides, is camel-consciousness. That is what the camel represents: reward and punishment. Punishment is also reward, because it too has a positive intent to it—it purifies. This is what this phrase mean: “…God is a God of payments.”

So, now we have that the three words that appear in a verse between the two names Kel and Havayah (this excludes “Temple,” which appears between Adni and Havayah) correspond to the three axes of left, right, and middle.

Right (loving-kindness): “God is God of payments.”

Middle (knowledge): “God is God of knowledge.”

Left (might): “God is God of revenge.”

The simplest reason explaining why the sages do not note our phrase is because it is so similar to the verse on “revenge,” except that revenge is pure might while payments alludes to loving-kindness as well. So now we have the basic understanding that all the forces of nature are camels.

Space as a desert

To complete our meditation on this image of the camel as a force, let us ask what medium the camel travels through? The camel is known as the “ship of the desert.” Its medium of travel is the desert. For a camel the space-time continuum is the desert. So the desert represents the medium through which the forces travel, which is space-time. Thus the camel, which represents the photon, the force particles, traverses the desert, which represents space-time. Just like space, the desert has curvature. The desert is in a sense full of waves. We might ask: Why do camels have humps? Because they are born of the desert! If you are born out of something, you resemble it, you represent it. The camel, which is born out of the curvature of the desert, resembles its origin in that it has a hump.

Another example of this principle that we have already seen is the drop of dew. We said that it seemingly comes out of the nothingness. So the drop itself resembles nothingness. Seeing a drop of dew is like seeing (as much as can be seen) the nothingness from where it originates.

The Dirac Sea

The famous physicist Dirac, symbolized space-time as a sea—even called the Dirac Sea. He called the medium in which the universe exists: a sea. A sea is also full of waves.

What is the connection between the desert and the sea? Based on Psalm 107, the sages learn that four individuals should thank God for delivering them from a dangerous situation.[11] One is a person who has successfully made a journey through the desert and another one who has a made a journey by sea. Dirac envisioned the medium of the universe as a sea. Likewise, one can imagine the entire world as a gigantic desert, part of which we inhabit. Just as a sea has islands in it, so a desert has its own islands: oases. The universe also has islands, which are stars, planets, moons, etc.

Space as a field

There is another concept that is very similar and actually appears more commonly in science: the image of a field. Every force establishes a field. A field also has a wave-like property to it. Like grass growing in a field and then you have to take the sickle to cut down the grass.

How do you say “space” in Hebrew?

You can imagine space-time in modern physics symbolized as a desert, or a sea, or a field. There is one more word that is used by the sages to connote “outer space,” in Hebrew. That word is חָלָל (chalal). The first step of creation is the contraction of the infinite light which results in the creation of “the empty space” (חֲלַל הַפָּנוּי) within which the entire universe was created. Let us give all these images a sign, or acronym.[12] The particular sign in this case is made up of the initial letters of these four symbols for space-time: “desert” (מִדְבָּר), “field” (שָׂדֶה), “sea” (יָם), “space” (חָלָל), which spell the word Mashiach (מָשִׁיחַ). Mashiach has now become our image for the four symbols of space-time in Torah.

Space is not empty!

Let us return to Dirac’s sea. What was he thinking of when he chose this symbol. He was imagining fish jumping up and down. The fish symbolize virtual particles that are continuously being created and annihilated. According to quantum mechanics there is no such thing as a vacuum, because everywhere there are eruptions of virtual particles, which are so-named because they are short-lived, not because they do not exist. So every little piece of space-time is constantly creating and annihilating virtual particles. This is a sea of particles. This is similar to the way the Torah describes the creation of fish and reptiles from water, from the sea, “Let the waters teem with crawling, living creatures….”[13]

The Hebrew word for “space,” chalal, is usually translated as “vacuum.” But, quantum mechanics says that there is no real vacuum. What does Torah have to say about the existence of a vacuum?

Before her complete conversion to Judaism, Rachav, the innkeeper, said to the spies that she knew that, “your God is the God of the heavens above and the earth below.”[14] When Moshe Rabbeinu stated a similar concept he said it with the exact same words, but added another two at end: “there is no other” (אֵין עוֹד).[15] The sages explain that what Rachav did not know is that there is no real vacuum—because the Almighty is even in the vacuum, or in Hebrew “even in reality’s vacuum” (אֲפִילוּ בַּחֲלָלוֹ שֶׁל עוֹלָם).[16] There is no other, even in the apparent vacuum of the universe. Meaning, that God is equally present even in what seems to be a vacuum. In essence, there is no real vacuum.

Rachav did not have this understanding until she became a complete convert. This also teaches us about the difference between a full-fledged convert and a non-complete convert. The full-fledged convert receives a Jewish soul in his or her internal consciousness and therefore can understand this concept.

The word used for “vacuum” in Hebrew, chalal, is also the root of the word “event,” as in מִתְחוֹלֵל, some activity is going on. So it is very significant that in Hebrew, the language of creation, the very word for “vacuum” implies that activity is going on; something is happening in the vacuum. This is exactly the mindset of quantum mechanics. Space looks at first as if nothing is there, but there is an infinite amount of activity going on inside. This is a beautiful example of insight into nature using the Hebrew language itself.

So we have four words in Hebrew that can be used to describe the space-time medium. Because the acronym designating these four words spells “Mashiach,” we may conclude that our becoming conscious of the nature of the medium of the universe is an indication of having Messianic consciousness.

According to many modern physicists, space-time itself is in essence gravitons, it is gravity itself (gravitons are the as yet undiscovered force particles of gravity). From these gravitons erupt all of the other particles, spontaneously, as virtual particles do.

Lecture 10

Classic Determinism

Determinism is one of the great questions faced by modern science. If we believe that we can perfectly know all the causes and their effects, then we should be able to know everything. If we could just put all the initial data into a man-made computer, we should be able to predict all future events. This understanding of determinism, which indeed contradicts the concept of free-will―the basis of the Torah―was a dogma of classical science. Laplace, one of the greatest scientists of the previous century, wrote clearly that if you could tell him the exact position and movement of every single particle in the universe, then he could tell you everything that would happen in the future.

This definitely contradicts the entire Torah, the entire faith system that is built on the principle that man has free choice, and that man is free to determine his own path in life—that it is not predetermined, that it is not fate. If there is a reason to argue that science contradicts faith, it is not the age of the universe, or some other external thing that will eventually be explained by science itself. It is only because of this problem, the problem of determinism. Evolution is not the problem, unless it is entirely based on determinism.

Quantum determinism

Classic determinism was the dogma of science until quantum mechanics. So quantum mechanics was a very good innovation. Quantum mechanics declares that it is impossible to really know the initial conditions, all the more so that I cannot know where things will end up. So, initially it seemed that quantum mechanics was the downfall of classic determinism. About which, we may say: “Baruch Hashem”; “Shehechiyanu.” We can make a blessing that quantum mechanics came along and destroyed classic determinism, for our good, for the good of the Torah, for the good of faith.

But, then quantum mechanics came up with another form of determinism, which is not the same; it seems to be more o.k. than the classic determinism. This is called quantum determinism. What is this? Quantum determinism says that though I cannot know exactly what will happen, I can still know pretty much (maybe 99%) what will happen, because of probability considerations. The foundation of quantum mechanics is probability. Probability is the essence of the wave function, which is actually a probability function. So if there is a tremendous probability that something will happen, I can say with almost complete certainty that it will happen, although there is a miniscule chance for freedom of choice.

This is also sometimes called probabilistic determinism—everything is probable, not 100% determined as thought before quantum mechanics. Even Einstein had a problem with this little bit of choice that was left. Einstein was a Jew, so he should have preferred this quantum determinism, but he had a real problem with it and he preferred classical determinism. It was very hard for him to accept that God plays dice with the universe. We explained previously that there is an inherent mortal consciousness in nature that is the result of Adam’s primordial sin and the descent of nature into an uncertain state.

In any case, this is the second stage of determinism: though science no longer believes in classical determinism, it accepts quantum determinism.

Black holes and determinism

But, then along came Stephen Hawking, who is the greatest authority on black holes. Black holes were already predicted by general relativity, so Einstein knew about them more or less. A black hole is a region of space that has so much matter and so much gravitational pull that even light that approaches the black hole will be drawn and sucked and swallowed by the gravitational field surrounding the black hole. That is why it is called a black hole, because light cannot reflect off of its surface, it is dark. It is the ultimate prison, whomever enters cannot leave. Everything has a verse to describe it. In this case the verse that describes such an inescapable prison is: “All who enter will not return.”[1] This verse actually refers to heresy. Whoever comes into it will not be able to get out of it. That’s what Egypt appeared to be. No slave could escape. It was the absolute prison. Nonetheless, the Almighty delivered us out of Egypt.

Hawking’s first insight was that because of Dirac’s sea (which we discussed in the previous lecture), the continuous activity in the apparent vacuum of space, there forms what is called Hawking radiation or glow. Remember that because of quantum uncertainty, pairs of virtual particles are constantly being created spontaneously everywhere in space. Since these pairs of virtual particles comprise a particle and its anti-particle, normally, they just annihilate each other immediately. But, in the case that they are created exactly on the event horizon of a black hole—the event horizon is the theoretical barrier beyond which anything entering will not be able to escape the black hole’s gravitational field—then one particle is ejected and one is sucked into the black hole’s gravitational field. Since one is ejected, even though the black hole cannot be seen, it does have a distinctive glow around it, made up of these ejected virtual particles. This theory is of course all mathematical. No one has actually observed a black hole. This was Hawking’s first insight into black holes. This is very interesting. You would have thought that anything that is black could not be seen. The color black is such because it absorbs all colors of light, yet somehow, here, black does glow, something comes out of it.

As we will explain, black holes are related to how the entire universe was created, and it is surmised that every galaxy has a black hole at its center, including our own galaxy.

Then Hawking had a second insight, which has arguably fueled one of the greatest disputes in the scientific world today. It has to do with information and with the question of if, when a virtual particle is sucked into a black hole, its wave function is forever lost and unrecoverable. This idea is controversial, because if it is correct then quantum determinism does not hold. If I would know the state of the universe now, which is all the information, then I could by probability predict 99% correctly the future. But, if a chunk of information is lost, it would destroy the possibility of determining the future, even within probability. This is because quantum determinism assumes that all of the information (all of the possible outcomes of the wave function) is still present. But, if all of a sudden the universe loses information, due to the black hole, then even probability cannot tell me about the future.

String theory on determinism

Perhaps the greatest innovation of string theory—even greater than the notion of strings, or more dimensions, etc.—has to do with this paradox. String theory says that even after wave destruction, the information lost in a black hole can be retrieved. Not only does a black hole cause radiation to be emitted around it, but even the information that is swallowed up in it can reemerge, meaning that the information is not lost forever. This would seem to return us to quantum determinism.

So if retrieving the information is like resurrecting it, Hawking believes that once something is buried in a black hole, it can never be resurrected. But, string theory believes, like the Torah, in resurrection.

Returning lost information

So all this has tremendous scientific ramifications. But, our goal here is to answer how all of this is alluded to in the Torah, and how it stands in relation to the Torah.

There are two simple and obvious images for “lost information.” The first is that losing information is like forgetting. To lose information psychologically is like forgetting. So the question about information lost in a black hole is: is there something inherent in the universe that allows it to forget. According to the Torah, it is very good to forget, because by forgetting you can open up new directions of choice. But, if the world is never going to forget all of its previous information, it will be a much more deterministic world.

The second, even more straightforward image for information loss is of losing, like misplacing something (in Hebrew, אֲבֵדָה). As King David says in Psalms: “I am lost like a sheep, seek Your servant.”[2] Like “lost and found.” When a person loses something, there is a custom to say, “Elaka de’Meir Aneini” (“God of Me’ir, answer me”) and then he will find it. To lose psychologically is to forget; to lose a physical object is just an אֲבֵדָה.

One of the most important commandments in the Torah is that if someone has lost something and you find it, you have to return it to him. This is a commandment governing our relationship with other people. So if the universe also “loses” things (information), we might ask if we are obligated to return them to it.

Lost and forgotten

The initials for “something lost” (אֲבֵדָה) and “something forgotten” (שִׁכְחָה) spell the Hebrew word for “fire” (אֵשׁ). The sages use the image of finding something that has been lost as an image for the whole topic of finding one’s soul-mate. Finding your spouse is like finding your back-side (your lost “rib”), as originally Adam and Eve were one person joined back to back. Indeed, in Hebrew, the word for woman (אִשָּׁה) etymologically stems from the word for “forgotten” (נשה). The backside represents the unconscious, the “hole” where things are forgotten. There are seven synonyms for “earth” in the Bible.[3] One of them is נְשִׁיָּה, pronounced “neshiyah,”[4] and meaning “the place where things are forgotten.” These are idioms that are thousands of years old and which are black-hole like.

Let us look at the numerical values of these two words:

• Something that is lost is אֲבֵדָה, whose numerical value is 12.
• Something forgetten, שִׁכְחָה, is equal to 333.

Their numerical sum is 345, which is the numerical value of the name “Moshe” (מֹשֶׁה).

This is quite strange as Moshe Rabbeinu signifies memory. The verse in Malachi says: “Remember the Torah of My servant Moshe.” Moshe is the epitome of mind and wisdom. So if Moshe equals “forgetfulness” and “loss” together then that means that he is their opposite. This is a case of a rectifying gematria where one side of the equivalency rectifies the other.[5] So it is very interesting that these two images for information lost in a black hole equal the value of Moshe Rabbeinu’s name. This is once again one of the most important issues in all of modern science, as it can change our entire understanding of determinism in nature, which is especially relevant in respect to science in relation to faith.

The black holes darkness and glow

Now, the root of the word for “something forgotten” is: שכח. The most important permutation of this root is “darkness” (חֹשֶׁךְ). This is the literal meaning of a “black hole,” eternal darkness, a symbol of death, or being buried forever. But, most significantly, these two words “darkness” and “forget” have the same letters in Hebrew.

The first time that darkness appears in the Torah is even before the creation of light. Before God created light, the earth was dark. This follows the natural order of things as stated by the sages: “first darkness then light.”[6] In respect to science, what this means is that first comes the darkness of the black hole and only then, as a secondary phenomenon, does the light, the glow (Hawking radiation) begin to come out of the black hole. This is the type of light that is described in Ecclesiastes as, “light is more beneficial [when it comes] from darkness.”[7] The order in creation is first darkness then light.

The event horizon

A black hole’s most important phenomenon is its border, its event horizon. What does the Torah say about the primordial darkness? “And darkness on the face of the abyss.”[8] If there is a term in the Torah that refers to the event horizon of a black hole, this is it. The “face of the abyss” is the border of the abyss, where the abyss of course is a beautiful metaphor for a black hole. Everything is trapped in there. What is the only thing that can come out of there; that we can resurrect? It is lost information!

In the Talmud, the image for a case of lost information is that of a talmid chacham, a scholar, who has forgotten his learning.[9] Even if it seems to have totally disappeared, it is destined to reappear. That is why the sages say that you still have to honor him, even if he seems not to remember anything. It will ultimately be retrieved. It will resurface. This resurfacing of information is alluded to in the final part of the verse describing the “event horizon”: “And the spirit of God hovered over the face of the waters.” And then “God said: Let there be light….”

So we have here beautiful images in the beginning of the Torah that represent black holes, event horizons, and darkness before light.

So we could say that all of science (vis-à-vis faith) revolves around the question of whether the universe forgets or not, and whether that forgetfulness is permanent. The answer to this question seems to hinge on whether the wave collapse that the virtual particle entering the black hole experiences is complete or not. If it is complete, then essentially, the information is not retrievable. If it is not, the information may reappear elsewhere, or could be retrieved from the black hole itself.

To date, no one knows how to interpret quantum mechanics in respect to the reality that we experience every day. There are many competing interpretations. Two of these are the Copenhagen interpretation and the many-universes interpretations and they differ on the question of the necessity of wave collapse. According to the Copenhagen interpretation, wave collapse is essential to the quantum mechanical take on our reality, because without it, reality would not be strictly defined and things would stay in a state of indeterminacy. But, according to the many-universes interpretation, wave collapse is not essential as all possible outcomes occur, each in a different universe.

Let us say that Hawking’s notion about black holes swallowing up information forever is found in the verse: “death swallows [things] forever.”[10] Whereas string theory’s notion of information being retrievable from a black hole corresponds to the verse: “It has swallowed strength and spit it out”[11] (חַיִל בָּלַע וִיקִיאֶנּוּ).

The point we are trying to emphasize is the concept of forgetting. It says that the Almighty remembers all that has been forgotten. Everything that has been destroyed is still remembered by God.

We said that sometimes it is good to forget, because it opens up possibilities of choice. Sometimes it’s good to forget, as the Ba’al Shem Tov says that in general it is not good to know your previous incarnations as it will limit your free-will. The Arizal said that it is good to know your past incarnations in order to focus on what your rectification is in this life time. But, the Ba’al Shem Tov felt that such knowledge may well fixate you on a certain image of what your life should be about. It would limit you to a certain rectification. Consequently, you will not be free to progress infinitely in this lifetime to greater things than just seeking one particular rectification. Death is a classic parallel to information that has been swallowed up by a black hole and the question of retrieving the information from the black hole is like the process of remembering one’s previous incarnations.

The paradox of free-will and determinism

Let us now address the paradox of determinism and free-will. It is important to know that in Judaism determinism and free-will are not an either/or proposition. They are paradoxically both true simultaneously. Everything is predetermined and yet, there is free-will. This is because Judaism is inherently paradoxical.

In Jewish philosophy, as for instance in the thought of Maimonides, the two sides of the paradox are known as “[God’s] knowledge and [our] choice,” or “[God’s] decree and [our] choice.” But, in the original way that this paradox was stated by the sages, the paradox is not between God’s knowledge and our choice. There is only one way that this paradox is phrased, which is not the normative philosophical way of putting the question in an abstract way. This singular phrase, which states the paradox of the most important spiritual problem of life, is: “All is foreseen, and permission is given”[12] (הַכֹּל צָפוּי, וְהָרְשׁוּת נְתוּנָה).

This expression is from Rabbi Akiva, the Moshe Rabbeinu of the Oral Torah. He was the only one who could express the essential nature of this paradox in words. This is very poetic language. The poetry here is very significant. It is not a dry, dead intellectual question. It is saying simultaneously: “all is foreseen” and “permission is given.” “Foreseen” does not mean the same thing as “known,” i.e., that God knows all. It certainly does not mean “decreed” (גְּזֵרָה), meaning that God has decreed that we act in a certain way.

By the way, the usual answer given to the problem of knowledge and free-will is to distinguish between “knowledge” and “decree.” Meaning that decree is much stronger and affects our actions much more than knowledge does, but that in reality God only knows, He does not decree. “Determinism” usually implies “decreed.” But, in Rabbi Akiva’s statement the word used is neither knowledge nor decree.

Now, whoever has a fine knowledge of Hebrew knows that the translation of this word is not even “foreseen,” but rather “foreseeable.” This is a nuance in Hebrew. It is like saying that “this was foreseeable,” I should have been able to guess this. Now, this sounds a lot like quantum determinism. It is a very probabilistic way of seeing. But, you are given permission to do what you like. Again the word here is not that you have free choice, or free-will, but that you have permission, you have a green light, to act as you like.

We could go on in length about this point. But, now let us make a “sign” for this teaching.[13] The symbol for this paradox is the bird, as the Hebrew word for “bird” (צִפּוֹר) is an acronym for the two key words of this phrase: צָפוּי רְשׁוּת. God sees everything in a foreseeable way, and everything has freedom to act. So now we have a symbol of a bird to go together with our particle zoo.

The Zohar[14] says that the Mashiach’s soul, before it comes down, resides in the “bird’s nest” (קַן צִפּוֹר). The nest itself represents consciousness since the phrase “bird's nest” (קַן צִפּוֹר) has the same numerical value as “consciousness” (מוּדָעוּת). If I would have perfect consciousness, then I would be like a bird in the nest, like the Mashiach, able to exercise complete freedom of will, but he is still in the nest waiting to fly out and come to us. Like a chick that is waiting to mature sufficiently to fly into the world, into our minds and hearts.

The diagonal of an n-dimensional cube

Let us see some slightly more sophisticated gematria than what we have until now.

Let us begin with a little understanding of what happens when you add dimensions to space-time. When you add a dimension you are really going up, numerically, by square roots.

One of the basic principles in Kabbalah[15] is called the “twelve diagonals” (יב גְּבוּלֵי אֲלַכְסוֹן).[16] If I have a unit square, the length of its diagonal is √2.

If it is a square with length and width n, then the diagonal will be n√2.

In any case, √2 is to be associated with the diagonal.

Rabbi Levi Yitzchak of Berditschev points out that the word “diagonal” (אֲלַכְסוֹן), relates to “seeing the nothing” (סִכֵּל אָיִן). So if you can see the “diagonal” of something, you are seeing the aspect of “nothingness” in it. If you want to see nothingness, do not look straight, look diagonally.

All diagonals are multiples of square roots.

If I have a unit cube, then the diagonal is √3. To compute this we see that it is the diagonal of the diagonal of two of the sides and one more dimension. Or in other words:

The diagonal of two sides is √2, as we said above. And then the diagonal of that with another of the dimensions is, following the Pythagorean theorem:

√(2 + 1) = √3

Now, for space-time, which has four dimensions, the diagonal is √4 = 2.

But, the Book of Formation defines that there are 5 dimensions, 3 space, 1 time, and 1 value dimension which runs from good to evil (we mentioned that if science would take this dimension into account, many of the problems it encounters today would be solved). The diagonal of a unit 5-dimensional cube would be √5. This is also the basis of the golden section, as explained in our book on the golden section. There are books that claim that the most important number in the universe is √2 and there are those who claim that that number is √5.

So first, let us state the general principle: √n is the diagonal of the cube in n-dimensional space.

So the diagonal of an 11 dimensional cube is √11. And, again, the diagonal represents the nothingness from which all somethingness comes.

In string theory, which now surmises 11 dimensions, 10 of which are spatial, the √10 is also very important. This would be the diagonal of space in string theory.

Square roots, the commandments, and God’s essential Name

Now let us write out the three most important square roots to four decimal places:

√2 = 1.414

√3 = 1.732

√5 = 2.236

If we take out the decimal points, as is done in Kabbalah, we get that: 2236 = 2 · 1118 or 2 times the value of the Shema, “Hear O’ Israel, Havayah is our God, Havayah is one” (שְׁמַע יִשְׂרָאֵל י־הוה אֱ־לֹהֵינוּ י־הוה אֶחָד).

2236 = 86 · 26, where 86 is the value of God’s Name Elokim (א־להים) and 26 is the value of God’s essential Name, Havayah (י־הוה). 1118 is the first number that is a multiple of both 86 and 26. This number 2.236 is the basis of the Golden Ratio, which is the basis of the beauty and elegance of the universe.

Now, the sum of the two other numbers is also a multiple of 26, the numerical value of God’s essential Name, Havayah (י־הוה): 1414 + 1732 = 121 · 26, or 11² · 26. It follows then that the sum of all three is “light” (אוֹר) times “God” (י־הוה), or 207 times 26.

What is the geometric relationship between 86 (the value of “Elokim”) and 207 (the numerical value of “light”)? If we draw a square with length 86, the diagonal will be 121, which is the difference between 207 and 86.

Now, let us see what happens when we add √5 to √3. We get, 2236 + 1732 = 248 · 16 = רמח · הוה, where 248 is the number of positive commandments and 16 (הוה) are the final three letters of Havayah. Taken as a stand-alone word, their meaning is “present” (for, according to Kabbalah, the positive commandments rectify the present moment of reality, the inherent reality of the three created Worlds of Creation, Formation, Action, which correspond to these three final letters of Havayah). Now, adding √5 to √2, we get: 2236 + 1414 = 365 · 10 = שסה · י, where 365 is the number of prohibitive commandments and the letter yud (י), whose value is 10, is the first letter of Havayah, which corresponds to the World of Emanation (pure Divine consciousness, above experience of created time and space), the level of consciousness reached by our observing the prohibitive commandments (the level of “no” above “yes,” while simultaneously giving rise to the “yes”).

Lecture 11

Wormholes in tapestries and space

The Talmud in the tractate of Shabbat explains that there are 39 categories of work that are forbidden on Shabbat. These are based on the 39 categories of work that were done in the Tabernacle. The Tabernacle is considered to be a miniature of the world. Science would do well to take a close look at these 39 categories of work and ask what each one corresponds to in nature.

Now, the 24^th is tearing in order to re-sew.[1] The Talmud asks: Where do we find this category of work taking place in the Tabernacle? The Talmud replies that this occurred when a worm-hole appeared in one of the Tabernacle’s tapestries and then the fabric had to be torn and re-sewn. When you see this passage in the Talmud in relation to any book on modern physics today, it totally blows you away.

Today, modern science describes space-time as a fabric which can theoretically be torn, as if a worm hole, and then re-sewn. And one of the main questions is whether indeed tears in the fabric of space are possible and whether they could be used to create “wormholes,” theoretic passages through space that would shorten distances considerably.

There were two layers of tapestries in the Tabernacle. One layer had 10 tapestries in it, and the other had 11 tapestries. In modern string theory there are two types of theories: five theories that posit 10 dimensions and an 11 dimensional model (called M-theory), which unites all five by showing that each is a particular case of this more general model. Indeed, in the Tabernacle too, the lower layer of tapestries had 10 tapestries and the upper had 11.

Leaps of distance

Tosafot, the medieval commentary, notes that the only thing that could happen to the tapestry was a wormhole forming in it and that this was the only place that a wormhole could occur in the Tabernacle. A wormhole in physics is like a “leap of distance” (kefitzat haderech) by the Ba’al Shem Tov.

The worm (once again from our particle zoo) is a symbol for King David, who describes himself as a worm: “I am a worm, not a man.”[2] The Ba’al Shem Tov was the one who used to travel through “wormholes” on his journeys, and he is considered to be a reincarnation of King David.

In any case, according to general relativity, the fabric of space-time cannot be torn, the topology can change gently, but it cannot be torn. But string theory allows for this. We are discussing this in short, but the entire issue here in the Talmud has to be studied deeply.

Even more amazing is the fact that in the entire Talmud, there is only one place where it says that there is a commandment to study science. We find this statement immediately after the discussion of the tearing of the tapestry. The Talmud says:

Said Rav: One who knows how to compute tekufot and mazalot and does not do so, you are not permitted to quote his teachings in his name....

Said Rabbi Shimon son of Pazi: Rabbi Yehoshua ben Levi said in the name of Bar Kapara: One who knows how to compute tekufot and mazalot and does not, about him the verse writes, “They do not gaze at the acts of God, and His handiwork they do not see.”

Said Rabbi Shmu’el bar Nachmani, said Rabbi Yochanan: From where do we learn that man is commanded to compute tekufot and mazalot? From the verse, “And you shall keep and perform these, for they are your wisdom and understanding in the eyes of the nations.” What is wisdom and understanding in the eyes of the nations? The computing of tekufot and mazalot!

According to the Smag (an acronym for the Medieval index of commandments called: Large Book of Mitzvot), this is one of the 613 commandments. In his words: “It is a positive commandment to compute tekufot and mazalot and moladot….”[3] These three words “tekufot, mazalot, moladot” refer to the various cycles of the stars and planets (today, we call this astrophysics).

On the verse, “for it is your wisdom and your understanding in the eyes of the nations,”[4] Rashi writes that science is “recognizable wisdom,” because all the nations of the world can recognize it.[5] Science has an advantage over the wisdom of the Torah because it predicts. The Torah does not appear to predict anything and only the Jewish mind fully appreciates it. Torah is like concealed wisdom compared to science. As we know, the strength of any scientific theory is its power of prediction. So, according to the sages, the most important scientific endeavor is astrophysics, which it is a commandment to pursue.

Now, tekufot, which literally means “cycles,” are a time image and mazalot, which literally mean “star constellations,” or “galaxies” are a space image, which also implies that it is a mitzvah to unite time and space. And, once more, this appears at the end of the discussion in the Talmud regarding the tearing of the fabric of the tapestry of the Tabernacle, which we have explained corresponds to the fabric of space-time.

What Rashi says about science being “recognizable wisdom” is extraordinary. We mentioned earlier the cornerstone (or top stone) of the Temple through which all personal Divine Providence is focused. We noted that Zachariah describes this stone as having twice חֵן (i.e., grace, or symmetry). But, the two letter word חֵן is also an acronym for “concealed wisdom” (חָכְמָה נִסְתֶּרֶת), one of the names by which Kabbalah is referred to. So now we can add that חֵן is also an acronym for this new connotation for science that we just learnt from Rashi, “recognizable wisdom” (חָכְמָה נִכֶּרֶת). So now, we can say that these two types of wisdom are the two types of חֵן that the cornerstone (top stone) possesses.

This passage from the Talmud even says that whoever is qualified and capable and has the mind to study science according to the Torah but does not do this and only studies Torah, even if he becomes a great Torah sage, you are not allowed to say a teaching in his name. It is forbidden to learn Torah from him. One of the commentaries appearing in the Shulchan Aruch itself is the Eliyah Rabbah.[6] He tries to explain this harsh statement. He says that a person who has the ability to be wise in recognizable wisdom, in science, but does not do so, he himself has proven that he is not worthy of the title of a “wise man.” So he himself has prevented himself from taking on the title of a sage. And, in principle, anyone who does not have the title of a sage you cannot repeat his teachings in his name, even if they are Torah teachings.

So we recommend strongly that this passage of the Talmud be studied in depth by everyone. God should grant us the talent and ability to learn, understand, and teach both types of wisdom, both the hidden wisdom, which is Torah, and the recognizable wisdom, which is science.

Endnotes