Editor’s note: Tikkun is delighted to be publishing Michael Kagan’s book Where’s G?d as a series on our website. This is the third chapter. Click here to read “Night Two.” Click here to read “Night Four.”
The focused beam of Daddy’s flashlight cut through the darkness like Luke Skywalker’s lightsaber, throwing silhouettes of my little guardian angels across the ceiling of my room. Their shadows danced and whirled like the dervishes in my picture book as I spun the light source around and around. Which was more real – the angels or their shadows? Would they know the difference, or would they assume that the dancing figures were independent forms? After all, there was a ballet being performed up there while they were passive observers hanging motionless from their invisible strings. Excitedly, I bounced up and down on my bed, causing the silhouettes to approach and withdraw, approach and withdraw.
The rumpus was interrupted by Daddy opening the door. The shadow world faded.
“What are you? A Wild Thing?” he asked. “Hey, isn’t that my new flashlight? I’ve been looking for it everywhere.”
I decided to ignore his diversionary tactics. “Come in. Look what I can do.” He shut the door and sat down at the end of my bed to watch the encore of the dance of light and shadow. He grinned as the angels moved without moving.
“Here,” he said, “let me show you something.” I gave him the flashlight and he pointed it straight up to the ceiling, avoiding all shadows. He placed his hand at arm’s length in the beam of light. Instantly his shadow hand appeared above us. “Now watch.” He slowly lowered his hand towards the flashlight and the shadow hand began to grow. It grew and it grew until it was a giant claw coming to get me. I could feel it surround me. Icy fingers stretching out at me. I screamed. Daddy’s smile turned to a worried look. The door opened:
“What happened?” Mummy turned the light on and moved to hug me.
“Sorry,” said Daddy. “It was only a trick of the shadow. There’s nothing there. Look!”
I looked at his hand covering the glass of the flashlight. I could see Daddy’s blood glowing red. The claw had gone. I was safe. Mummy’s arms surrounded me.
“Show Mummy how you made the angels dance.”
When the performance was over, Mummy and Daddy clapped and I was laughing again. I wondered why the shadow-hand had frightened me so. I’ll pray about that later.
“Now I want to show you something else with the flashlight,” I said, “and I promise not to scare you.” Daddy laughed. Mummy turned off the lamp and I shone the beam of light back onto the ceiling. “Now watch this,” I said, trying to imitate Daddy’s voice. “You remember yesterday I drew a flat thing on a piece of paper and we imagined what it would be like not to be able to look up or down? Well here’s another way to understand the same thing. Look what happens when I put different things into the light. See their shadows.” On the shelf next to my bed was my treasure box. It was square shaped. It was covered with butterflies and inside were my favorite things: little shells that I had picked up on the beach, little crystals that caught my eye on a mountain path, a blue diamond (Daddy said that it was a real diamond), a mysterious ring that I spotted while digging in the garden, a dead scarab beetle, and many other special things. I picked up the box and held it in the path of the light beam, taking care that the lid didn’t open. “There, I’m holding this box that’s square all around…”
“I think that you mean cubic. A square is flat or as we said yesterday, two-dimensional. A cube has volume and is three-dimensional.” I thanked Mummy for her contribution.
“Exactly,” I continued. “Look what happens when I place the box in the light with its bottom facing directly at the flashlight. See its shadow?”
“It’s a square,” said Daddy. “So?”
“So? So look what happens as I turn the box around this way.” I rotated the box but kept the bottom facing the flashlight.
“Well, the square shadow turns as well. So?”
“So? So look what happens now.” I started turning the box moving the bottom away from the flashlight.
Mummy responded: “Why! The square has changed shape. Look. The shadow is now a rectangle. There’s a star shape. That’s a … I don’t know what to call that. And there’s another oblong. How many shapes are there?”
Daddy chimed in. “Every time the angle of the box changes in respect of the light beam, even by a small amount, the shape of the shadow changes.” He was right.
“Yes,” I said, “there are hundreds of shapes, many similar but all different.” I turned the box around again until the square reappeared on the ceiling. “If I could cut out that shadow of the square and hold it end on in the light, what would we see?”
“A very thin line,” Mummy answered.
“And what if I could cut out that thin line and hold it side-on to the light? What then?”
“I suppose we would see a very small dot, wouldn’t we?” Again it was Mummy who answered.
I looked at Daddy. He was playing with his fingers and intertwining his hands. He seemed lost in thought.
“Yes,” I said. “You see, when I hold a three-dimensional box in the light, we get a two-dimensional shape – a square – on the screen. If I could hold a two-dimensional shape in the light, we’d get a one-dimensional string. And if we could hold that in the light, we’d be left with a dot which has no dimension.”
“Here’s an idea. Mummy, hand me the pencil we used yesterday. I put the pencil lengthways in the path of the light, and the shadow cast was a fat line. As I began to turn the pencil, with its end facing the light, the shadow pencil began to shrink. It got smaller and smaller until all we could see was a small circle. “You see, the pencil is almost one dimensional. So when you turn it on its side you see a dot. If the pencil were thinner, like a thread of cotton, then the dot would be smaller. Until…”
“Until it disappeared!”
“That must be zero dimension.” Mummy can be brilliant sometimes.
“Put the box down. I want to show you something not scary.” Daddy put his hands in the beam and suddenly there was a bird flying around the room. He shifted his hands and there was a dog with large ears and a tongue. I started laughing. And now a face of an old man; a giraffe; an alligator. Mummy laughed too. Daddy’s funny.
When he had finished his show, Mummy asked him: “Did you get what we just saw?”
“What, that the projection of 3D gives 2D, 2D gives 1D and 1D gives 0D? So?”
“Well that wasn’t all. Even the simplest 3D shape like that box gives a whole range of different shapes. Just think what would happen when we put a more complicated object in the light beam. The shadows would be endless and endlessly unusual.”
They both looked at me, waiting for the next step.
“What would the shadow of a 4D object look like when placed in the light?”
“4D again?” Daddy said.
“Would the shadow of a 4D object be a 3D object?” Mummy asked hesitantly.
“Yes. For instance, this box would be the shadow of a 4D box – whatever that looks like. And furthermore it would be only one of the many possible shadows that such an unimaginable 4D object would cast in the light.”
Mummy continued: “You mean all these things around us could be shadows thrown by the same 4D object? That they could all in fact be from the same source?”
Daddy added: “And I suppose that you’re going to say that all those 4D objects are just shadows of 5D objects and on and on.”
“Yes! Yes!” I started to get excited.
“And that we are all shadows of some higher dimensional object, some kind of primordial human illuminated by the great light? Wait a minute. Maybe that’s what it means when it says in Genesis: ‘God made humans in the image or shadow of God.’ That’s very interesting.”
I didn’t know what the word ‘primordial’ meant, but what Daddy was describing sounded about right. “And so where is God?” I asked.
Mummy answered: “Why, God must be in the infinite dimension, and is therefore the source of all things in all the other dimensions.” I smiled at Mummy. Daddy was still bathing in the light of his little Biblical enlightenment.
He jumped in again: “Well, if God is the infinite object, then what is the light? Or rather, where does the light come from? Because, because if there is a light, there must be a light source. And if there is a light source that casts its light on an object which is God, then the light and the light source must be independent of God. Isn’t that a problem?”
He continued. “In the infinite dimension, God must be the Source and the Light and the Object of all objects. In fact, at the infinite dimension there is no source, no light, nor any objects. So at some point, God had to say ‘Let there be Light’.”
“Yes,” I said, agreeing with Daddy, “but not in the sense of creating something other than God. Rather, just revealing something in a lower dimension of Godself.”
Daddy was becoming quite animated at this point. “So,” he said, “when the Bible says ‘In the beginning when God was making the Heavens and the Earth, “maybe it means that first God made the higher dimensions and then the lower dimensions, namely our 3D Universe. Maybe we’re at the bottom of the chain. What a strange idea. Can you imagine that we’re at the bottom of the pool? The lowest of the low? The living dimension furthest away from the original Light? Like those organisms living at the bottom of the oceans so far from sunlight, huddled around little geotherms. Now that’s a pretty humbling thought.”
“Maybe that’s why God loves us so much.”
“What?” Mummy and Daddy exclaimed in unison.
“Yes. That’s exactly why God loves this part of Godself so much – because we are so far away from the warmth and Truth of the Great Light.”
Mummy was catching on to my thread. “I suppose that is why we have more compassion for those that are down and out in our society, those that are furthest from the source of power and wealth, those that are living in the twilight zones.”
I looked up at my band of angels. Mummy must have followed my gaze, because her next question was: “Are angels living in higher dimensions?”
“Yes,” I answered simply, for that was the simplest truth.
“And I suppose that they don’t really look like that?” She pointed to my flying feathered friends.
At first, I shook my head. But after I thought about it a little, I nodded my head.
Mummy and Daddy looked at each other, trying to interpret my dual answer.
“Ah,” said Mummy, “I get it. In their dimension, they don’t look like this at all. But when they come ‘down’ into our dimension, they appear to us as something like this.”
I smiled and nodded.
Daddy interjected, “You know, this reminds me of something. Wait a minute.” He left the room, rumbled through some books, and returned. “Look,” he said, pointing to a page in a book. “Here’s a picture of a mushroom field.” He began to read: “‘Individual mushrooms even though they appear to be independent organisms are actually connected by a common root system underground. Some of these systems can be hundreds of square miles in size.’ So what we see popping out on the surface is only a tiny piece of the mushroom field. Isn’t that very similar to what we’ve just been talking about?” I smiled. What a lovely example of the hiddenness of reality.
Now it was Mummy’s turn to interject. “So maybe what you are describing is the ‘God-field,’ where everything is inter-connected to everything else and everything is embedded in the whole. In physics, we have magnetic fields and gravitational fields and space-time fields. So why not the field of all fields – the God-field?”
“You know,” Dad added, “there’s a verse in the Bible that says: Man is like a tree in the field. I wonder if that’s what it is referring to?”
I nodded again: “I like that idea of a God-field, especially the part that is outside. The flowers are so beautiful. Mummy, could you please explain to me what ‘quantum theory’ is?”
Daddy smiled a challenging smile: “Where did you hear about the quantum theory? Aren’t you a bit young for that?”
“I read it in the encyclopedia when I was looking up ‘Light.’ I think it’s important to understand what things are.”
Mummy looked at my angels as if praying for help.
“OK. Here goes. ‘The Quantum Theory and All That by Mummy.’” She took a deep breath. “Let’s see. Around the beginning of the 20th century, most physicists felt that they knew almost everything there was to know about how the universe worked. They viewed it like a giant clockwork mechanism. Imagine taking apart an old clock – like grandpa’s grandfather’s clock – and trying to find out the connection between each of the cogs, levers, springs and dials. And when you’ve put them all back into place, you discover that you are left with a few pieces that don’t seem to fit anywhere. And it doesn’t matter how much you try, they just don’t seem to belong anywhere. But without them, the clock simply won’t work. Well, that’s what it was like back then. Everything was almost in place – just a few pieces left to fit into the box. But you know what happened? Those few bits couldn’t be put into the box because it turned out that the entire box was the wrong box. And within a few years, the entire understanding of what the universe is and what things are was turned upside down into what we now call quantum theory.” Out of the corner of my eye. I spotted Dad impatiently waving his hand, as if to say: ”Get on with it.”
“I guess that it started with Einstein – you’ve heard of Einstein I suppose?” asked Mummy. I nodded my head and puffed out my hair. “Exactly. Well he began to ask questions about what light was made of. Do you know why? Because, and this may seem very strange, sometimes it appeared that light behaved like little balls of energy. But at other times, it appeared to behave like a spreading wave of energy, like the ripples you see when you throw a stone into a pond. He came to the peculiar conclusion that light was actually both balls of energy and waves of energy, depending on the experiment you were testing it for.” I frowned. I was having trouble absorbing the fact that the meaning of light depended upon us. “I know,” Mummy continued, “it sounds a bit wacky, but that’s what the scientists found. It’s called a paradox – meaning that the answer is both this and that at the same time. Science – or rather scientists – dodn’t like paradoxes. It messes up with what’s called Truth. Something must be either this or that – either right or wrong – either here or gone. It can’t be both. Anyway, with that discovery or conclusion, the previous paradigm began to rapidly crack and fall apart.”
“What’s a paradigm?” I asked. This was fascinating. Things are not what they seem.
“A paradigm,” interjected Dad, happy to have something useful to contribute, “is a particular way of seeing the world or being in the world or relating to the world. For example, as a result of our talks over the last couple of nights, I am undergoing a paradigm shift in how I view God and my relationship to God. This is affecting how I see myself, how I see other people, and how I relate to the rest of the world.” I smiled, and not just because Daddy had succeeded in explaining a new word to me.
“Can I go on?” Mummy asked. We nodded. “Well, one of the most significant conclusions of the new theory is that the more we know about something, the less we can know about it. That’s called Heisenberg’s Uncertainty Principle. Of course it applies particularly to electrons and very small things like that. But it also seems to describe exactly what happened when people thought that the old paradigm could explain everything. Suddenly, we realized that we actually knew very little about anything. Strange, eh?”
She continued. “But I think that THE most important conclusion of quantum theory, and I think that this is what you are looking for, is that not only can light be thought of, or rather seem to behave as, little balls of energy, but that electrons, which we always imagined as little balls whizzing around atoms like planets around the sun, are in fact just packets of energy surrounding the atom like morning haze on the fields.”
This shocked me into asking: “You mean they’re not really there?”
“Well, sweetie, they are there, but they are not exactly anywhere.”
This proved too much for Daddy. “But that’s impossible. Either something is there or it’s not there. You’re sitting on the bed and I’m sitting on the chair. Or is this another ‘paradox’”?
“Not exactly,” Mummy answered. “You see, it’s only a paradox from our world or, as you so correctly defined it, from our paradigm. The big world seems to behave itself: everything seems to be in its proper place, at the proper time…”
“Except when you’re late for school.” Daddys joke made us laugh. All this quantum stuff was very serious.
“But for very small things like electrons, the world is very different,” continued Mummy. “That’s what quantum theory comes to explain. Our macroscopic world behaves very differently from the microscopic world.”
I was puzzled again: “But if our big world is made up of many, many pieces of the small world, how can it be so different?”
Mummy thought about this. “Well, the strange effects on the small scale just average out and disappear on the large scale. So that the big world seems to behave normally to us big people.”
Daddy suddenly sat upright as if he had received a small electric shock. “I think that I can help out here. You remember when I took you to the art museum to see the pointillist exhibition and you saw those painting by Georges Seurat? Remember when we looked through a magnifying glass and looked at a small number of dots of paint and how they didn’t seem to have any connection to the big picture? Each dot with its own hue and brightness somehow contributing to the whole in ways that would be almost impossible to predict by just observing it on its own. And if we had used a stronger magnifying glass, we would have been able to view just one single dot, and we would have seen how non-uniform that dot really was. But when combined with all the other dots and viewed at a distance, all the small imperfections and variations disappear and we’re left with a magnificent, beautiful painting.”
“Thank you, dear.” Mummy looked at me, waiting to see whether she should continue. While Daddy was speaking, I had closed my eyes and was back on the banks of the Seine. The yachts drifted past in the slight breeze of that gorgeous Sunday afternoon. While Mummy and Daddy strolled hand-not-in-hand at a respectable distance, I had skipped and danced around in my new orange dress, my red hair bouncing behind me, trying to keep to the beat of the trumpeter while twirling my hoop around my hand. Everyone was so stiff and proper. Everyone tried to keep out of the light by hiding in the shade of the trees or under their parasols. Even the monkey was kept under a tight leash. Only the butterflies and me were free to play. I remembered laughing and thinking: who’s making a monkey out of whom?
I opened my eyes: “Mummy, if the smallest particles are actually not made of … of hard stuff but of light, and if all the things in the world are made up of these small particles stuck together, doesn’t that mean that all the things we see and feel are actually made up of light? Maybe they are not solid in the way they seem if everything is made up of light.”
Mummy hesitated before answering: “It’s true, everything is made of light – very, very dense packets of light – even we’re made of light. So when we touch something, say the table, it feels so solid because our thick light cannot penetrate the table’s thick light. Even regular light cannot penetrate it. But actually you’re right. It is all light. And one more thing: most of the seemingly solid matter in the world is made of nothing. Yes, nothing at all. Empty nothingness. The spaces between the electrons and the atoms and between the molecules and other molecules are so enormous that it compares to the empty space between the earth and the sun.”
Daddy was astonished by this revelation. “So you’re saying that there’s nothing really here except for some condensed light?”
“I think,” said Mummy, “that it is time to remove some of the light from this room and let this young lady go to sleep.” I didn’t resist. She kissed me on the forehead. “God bless,” she said.