The New Journey to God
Chapter 2 September 29, 1993 continued
The Celestial Hierarchy at work
In which St. Michael discusses the Celestial Hierarchy, comparing their work to that of men. He shows how God can be seen through mathematics and the human experience of nature. Catherine asks a question about quantum mechanics and divine providence.
MICHAEL CERTAINLY LOOKED HUMAN ENOUGH, if simpler and more direct than most, but the illusion of comforting humanity could not be sustained indefinitely. The statement, "this man is no man," until thee merely parked on the edge of my intellect, had sooner or later to reach that portion of the mind that grasps the import of a situation and governs the emotions.
While Michael was saying that we return to God, we turned west into Queen Street and faced the sun. It floated, huge and flaming at the end of the street, slightly above the level of the shops. So just as Adelaide Street seemed to end at the church, Queen Street seemed to be blocked by the sun, and to be running into the fire that burns at the end of the world. I quickly shaded my eyes and looked away; the archangel stared onward into the light.
"There is nothing to fear;" said Michael gently.
"There is nothing to fear," said Michael gently. But it was too late. The reaction to terror had already begun to send sickening waves of shock through my system. My knees lost their support. As I fell, I stuck out a hand to save myself and found that I was grasping hold of something hard and smooth like the rim of a shield. But there was nothing there to see.
"The world is wide open," I said in a panic.
"I know," he replied calmly. I could see the image of the sun, doubled in his eyes, as if he were looking at it still. There was no need to say more. He knew what I meant. Angels are fearsome because they face God, not as priests face him, to mediate his mercy, but simply and directly, unshielded by matter, because that is where God has placed them to be.
For a moment my world was opened and straight, as if the road I was walking did indeed run into the sun and off the rim of the world. I understood what Michael meant in saying that the proofs for the existence of God and our experience of the world were much the same thing; I had simply not known the experience before. And here it was, that reality that the mystics have known and the theologians have demonstrated, when our Lord said to St. Catherine, "I am the one who is; you are the known who is not." The earth upon which we stand and everything in it is as insubstantial as a reflection on the surface of a pool.
Michael steered me along the sidewalk and into a small restaurant at the end of the block. In Toronto it is impossible to find a seat and rest anywhere without spending money on something. We went in and sat down at a small table in the window, where we could watch the action outside through a screen of potted ferns. A waiter appeared and poured coffee into our cups.
A shaft of light passed through the window and drew a geometric shape across the tabletop, ending in a point on my placemat an inch away from the saucer of my cup. Cup and saucer were made of the same thick, white china and they stood out clearly against the dark wood of the tables. I watched the waves in my coffee, until friction damped their periodic motion from one side of the cup to the other.
"You are in shock," said Michael. "I didn't see it coming." He lifted three cubes of demerara sugar from the pot and dropped them into my cup. He poured some cream and gave the mixture a brisk stir with a spoon. The cream spiralled out from the centre of the cup until it blended with the coffee, and the mixture spun several times with decreasing speed about its central axis. A plume of steam rose from his cup sitting untouched on the table in front of him.
"Michael," I said. "What are you, really?"
"I am one of the seven spirits that stand before the throne of the Most High."
"No, I meant, 'what are you made of?"'
"Nothing," he replied. "I am created out of nothing."
I gave my coffee another stir and took a sip.
"What did you mean just now when you said that you 'didn't see it coming?' Can you read my mind and prevent me from ... you know, feeling funny?"
"A glass of wine could change your feelings. These are biochemical reactions ..."
I looked at him accusingly. This was evading the issue. His eyes had reverted to their former shade of blue. He ran a finger around the rim of his cup and then settled his hands on the table as if he had just taken a decision.
"Why do you need to know all this?" he asked.
"Because," I said, "if angels exist, that changes everything." "It would change nothing for God if we did not."
"It changes everything for me." I said.
"Why should the existence of pure spirits change the way you understand the material world?" he asked.
Two contradictory thoughts flashed through my mind at once; one, that the answer was obvious, and the second, that I had no idea. I took another sip of my too sweet beverage and stared out the window, the view being my nearest representative of that material world whose nature had been called into question by the existence of angels. I saw the usual things: a line of shops across the street, straddling the line between cult popularity and upscale chic, two contrary lanes of traffic and the tracks of the streetcars. There were a few sad and spindly trees in pots, and some fat and stoic squirrels. And directly in front of the restaurant, marked by orange cones, half visible and half below ground, was the inevitable group of men working inside a hole in the road.
Judged philosophically, I saw a diversity of individual things, some inert, like the buildings, some moving like the electric current I knew to be active through the wires overhead, some living like the squirrels, and trying to live, like the trees; some natural, like the clouds, but most artificial. And everywhere I looked, either visible or implied, the thousands of human beings living and working in this city, always planning and building, destroying and disposing it, to suit our restless wants and common needs. Nothing of what I could see was incompatible with the parallel existence of angels.
I turned my attention instead to what I could not see, to what I had only read and imagined nature to be like. There I saw a different, and much simpler picture, one suited to the classroom, rather than to experience. I saw a dark and swirling mass, roughly supposed to contain the fundamental particles from which the atoms are composed. This same substance would then be recombined and rearranged to build up the cells of living things, the bodies of animals and the structure of the human brain: a variety of combinations, but fundamentally, the same dark substance running through it all, like a river.
"I can see," said Michael, "that the presence of an angel might disturb a world-view like that. Materialism!" he added, with a snort of disgust.
"I am not a materialist," I said defensively. "I believe in one God." "Yes, but do you believe in the things he made, the seen and unseen? You can judge for yourself that the world consists of many things, related but distinct; and what makes them so is not some massive, extended substance like molasses, that is divided out and transferred between them."
"What does make things be what they are," I asked, "if it is not what they are made of?"
"Simply what they have been made to be," he said. "But look, you said that the existence of angels changes everything. Do you not see that your own existence does so no less? It is true that you could melt down this knife and make it into a fork, but no one can melt down your soul and turn it into a different person. That seems to be the error of reincarnation: recycled humanity! But it's nonsense. You can't manipulate a spirit that way; you can't even manipulate an idea that way. You can't melt down the idea of a knife and turn it into the idea of a fork.
"So there you are. The universe contains distinct beings, like the two of us for example, that cannot be recombined, interchanged or reworked into other things. It isn't matter that unites the world, nor some common substance flowing through everything, but God; not in the sense that he is the body of the world, which he is not; but because he made it."
"Here," he said. "You should drink this as well." And another three cubes of sugar landed in the coffee. The archangel pushed his cup in my direction, exchanging it for my own, which was now empty. At least the cup moved, while his right thumb and forefinger rested on the saucer. It looked as if the hand were following the cup rather than pushing it.
"You are wondering how I moved that object," Michael said.
"Yes," I said. "And how you always know what I am thinking."
"The principle is the same in both cases," he replied and paused as if searching for a way to explain it. "Strictly speaking, I do not actually know what you are thinking; only what you feel and picture inwardly to yourself in words and images. Only God knows what passes in the human intellect, since he is the one moving it to think in the first place."
"The universe seems to be a very public place", I observed, a bit sadly.
"Of course it is, because it is a serious undertaking. Did you think that your life was intended solely as a private project of your own, unconnected to what anyone else is doing?"
"No," I said very quickly, and then, "I don't know; maybe I did.
Why should anyone be interested in what I am doing?"
Michael was not impressed by my self-pity. "It's not only a question of being interested, although naturally God is interested in everything that happens to the creatures he has made. But don't you think that being known is a part of existence? Think of all the human beings who have made the quest for fame the sole purpose of their lives. It's a bit exaggerated on their part, but there is some truth behind their choice. If they worked as hard to publish the worth of God as they do their own ... But look around you. The world is full of things waiting to be known and understood, and of people suffering because no one knows or cares who they are."
He pushed back his chair so that he was sitting at an angle to me, crossed his legs and rested an elbow on the table. It was a very human sequence of movements.
"We — the pure spirits — were created so that the universe would not at any time be blind. We are not necessary, you understand. God could have created many worlds, completely different from this one. He could have made a world consisting only of geometric patterns, or great stands of plants for instance; blind worlds that he could admire, but that would know nothing of their own existence and be unable to praise God for what he had given them. He could have created worlds that were blind for most of their duration, and then added a rational creature at the end. But he chose that from the beginning, this universe would not be lacking in minds and hearts to know and admire it. So yes; you are right. The universe is a very public place. That shows you how much God cares about glory, that creation should know and be known — know its creator and know itself.
"As time and space began their course, and material energy first came into being, we were made also, the pure spirits. We were there to glorify God, to admire the things he had made that were not aware of themselves, and to guide the world in the process intended for it."
"Do you mean that the development of the stars and the planets was your work?"
"Yes. And it continues to be the work of many in the celestial hierarchy. We also assisted in developing life on this planet. You he made himself, so that you would have the same priority that we do. In any case, I can no more create a rational soul than I can create myself."
"I thought all of that happened through the Laws of Nature," I said.
"Hah! And I suppose you think that housework gets done through the laws of housework! Material particles, when left to themselves, converge to highly uninteresting configurations. They tend to clump, oscillate or dissipate; either that, or they are unstable. To produce the variety that you experience, without catastrophe, he would have had to intervene directly and override inert processes; that or direct things through beings capable of understanding the situation and acting responsibly. He chose the latter."
"I know," I said. "Sooner or later, the machine breaks down, and you have to call an engineer. But what I don't understand is why, if there were hosts of angels working on the universe, it took billions of years to bring it to the stage where life could develop and man appeared."
He laughed at this. "Catherine, how long do you think it should take to build a universe?"
"I don't know," I said. "But I assume that it would depend on the workmen. We have factories that now turn out large quantities of merchandise in a fraction the time required with hand tools. I would have thought that you could do it even more rapidly."
He thought about this for a moment.
"Yes. In principle we could, if we simply forced the particles into the necessary configurations. There are certain practical constraints of course. There is a minimal contact time required before you can have any effect on a material particle ..."
"Matter is somewhat unresponsive, even to violent action."
I must have registered surprise at this, because he turned to face me and said with some intensity, "Yes, violence. We would have had to impose on matter in a sense; move it against its natural bent. But that would have been all wrong. For instance, I could support you by your heels so that you could walk on your hands, but it would be inappropriate, since you were designed to walk on your feet.
"You shouldn't be thinking of a factory when you think of our work. In some ways it is more like gardening, where you have to let nature take its course, and you can't force a plant to grow faster than it was meant to go. Actually, the closest analogy to a human activity would be to something like the Liturgy, where man's common praise of God serves as an instrument to restore creation. In a sense, the first creation was sung into its current shape as well."
"So that's why the universe is so luminous to you," I said. "It's a giant score! I wish it looked that way to me. But tell me something.
How much of all this is actually your work, and how much of it came from God?"
"I do not understana your distinction," said Michael, with a tense look.
"I mean, did you figure it out by yourselves, how the stars would be arranged and so on, or did you receive explicit instructions from God as to how everything should be?"
"I see," he said, as if seeing nothing of the kind. "You can't compare the work of the creature with that of the Creator, since everything comes from God, is directed to him, and follows the course he has determined for it; including any work done by you or me. You might as well ask whether the music comes from the pianist or from the piano.
"When it comes to creation, God gave us the instructions when he gave us ourselves; in a way, we are more like blueprints than like engineers. And in part, it is a question of consistency. From knowing the sort of being that I am, I can deduce the properties of other things and direct them accordingly.
"The same principle holds with human scientists. They deduce the laws of nature by observing particular material occurrences. They assume, rightly, that in a world in which these things happen, certain laws must obtain. At the same time God tells us what he wants done, and we do it."
"Even when it is inconsistent?" I asked.
"God never commands inconsistency. It would be unjust to the things he has made."
"I was thinking of miracles. Don't they violate the laws of nature?"
"Oh that," said Michael with a laugh. "Will we never be clear of the eighteenth-century? Now if you want violations of the laws of nature, beginning with the laws of common sense, eighteenth century philosophy is where you will find them. We have been trying to clean up that mess for the past two hundred years, but once something gets into the school curriculum it takes for ever to get it out again.
"Miracles!" he said firmly. "True miracles come from God, and not from us. By miracles, I am thinking of sudden and complete cures, instantaneous organic transformations ..."
"Turning water into wine?"
"Yes. And of course, the conversion of a sinner is a great miracle, and something which is totally beyond the ability of man or angel to accomplish. It is a direct intervention of God's power and mercy into the world he has made. Sometimes we are involved in producing dramatic effects, like the burning bush, or conveying a verbal message to someone. These are miracles too, in the sense that they are signs of God's particular intent. But none of these events violate the laws of nature, since the first law of nature is that the creature show forth the glory of the Creator. After all, why else are we here?"
I thought about this for a minute, and stirred the sludge at the bottom of my cup. Three lumps was far too much sugar for a cup of this size. I tried to picture the choirs of pure spirits singing the laws of physics and calling the clouds of interstellar dust into the formations of the sky at night and I wondered how many millions of them there must be.
What happened next was very odd, although at the same time, it would be hard to say what actually took place. I was looking out of the window at the traffic on the street outside, suddenly something like a shadow of sadness and disgust passed through my mind. There was no reason for it that I could tell except that it had something to do with the people I could see, rushing about as if they owned the place, and the heavenly host, working quietly for billions of years, controlling everything behind the scenes. At least, I think that is what I was thinking, but it was the mood that I remember now: disgust at the short lived futility of the race of men.
Suddenly, out of the corner of my eye, I thought I saw a flash of light, and a brief tremor passed through the table. I turned to look, but saw nothing unusual, only Michael staring at me with some concern.
"What was the thought that passed through your mind?" he asked.
"I don't know," I said; and I did not, since the mood had passed as suddenly as it came. "I suppose I was wondering why we exist at all. I mean, if it is just a question of having someone to observe the universe and praise God for it, the angels can do that by themselves with no help from us. We don't seem to contribute very much."
"Yes, I thought it was something like that," he said grimly. "As to why you are here, God wanted you, and that should be reason enough for anyone. But I suppose you would like to know how you fit into the scheme of things, how your existence relates to the rest of the universe. There I can only offer my opinion."
"Don't you know?" I said. "I thought you knew everything " "Who is like God?" he said rhetorically.
"Well wouldn't he tell you if you asked Him?"
"Yes, in a way. I can see the human race in my vision of him, but I see it from my own perspective. For instance, if you were to ask one of the cherubim about the purpose of man, they would answer by relating the structure of human nature to the Logos, and describing how your nature participates in the divine Truth."
"That would be interesting to hear," I said.
"Yes it would, but it would take several human lifetimes to hear it. The explanations of the cherubim are not brief. But to me it all comes down to the question of service. I find something very unfitting in the idea of a universe full of creatures with no opportunity to serve anything greater than themselves."
"Doesn't everything serve God just by existing?"
"Not really. We glorify God by being what we are, but we can't render service to someone who is in no need of our help. God does not need the light of the sun, the soil of this planet, nor anything that grows here. And neither do we. You can see the difficulty; since we had to guide the universe in its development, we have to be independent of its structure. We cannot be contained by space, since we were there when it was first extended. And obviously, we could not be composed of matter, or we would have to travel slower than light; but that means that we suffer none of the vicissitudes of the material world, and we require nothing from it. It has nothing to give us beyond an opportunity to serve God.
"But you, on the other hand, are completely supported by the material world, both in body and in spirit. You can't even think without forming a mental image derived from the things you have seen and heard. You need the world, and in serving you, it can serve the image of God; as can we."
"Are you trying to tell me that the reason that I breath air, and consequently risk death by choking every time I take a bit to eat, is so that the oxygen molecule can lead a life of usefulness?" I asked, too astonished to be polite. "It may give matter a goal in life, but where does that leave human freedom and dignity, if we have to be so dependent?"
Michael laughed. "But since you are already completely dependent upon God for your existence, why should it annoy you that this dependence should be exercised through reliance on inert powers? Or are you afraid that you may die sooner than he intended?"
"I don't know what I fear." I said quietly.
"Well, as to that, nature was intended to be dependable; but that is another story."
Michael let this sink in for a few moments before trying another tack.
"You might prefer to think about it in terms of knowledge. After all, we understand things intellectually, from within. We never hear nature tell its story in its own words."
"What do you mean?" I asked.
"Who hears the wind in the trees when no one is in the forest or sees the colours of autumn? I know that these things are taking place, but only you can receive them as they are sent. You can feel the rain and hear the water running through the drain spout and into the street. These things have a right to be known, and to be admired on their own terms."
"Isn't that anthropomorphic?" I said, doubtfully. "You make it sound as if nature wants to be known in some way."
"It is only like man because it is also like God, albeit distantly. Everything is made to be known, and to be loved. It is in the nature of things. Nature is material, so it has to be known materially. Its 'speech' is material: the radiation emitted, the particles released, the wave trains launched. You receive these, and perceive them as colour, smell, sound and texture, and through all this, as beauty. You receive it simply as something material, and appreciate it as something much greater."
I tried to think about the natural world, not indeed the one that constantly claims my attention during every waking hour, with its catalogue of sounds and sensations, but that other world, the one that lies in the physics books — serene and untroubled by the human eye, spying on it over the rim of the universe. I thought about scientists unlocking the secrets of nature. But now Michael seemed to be saying that there are no secrets and no locks; that nature has been screaming for attention, like a "spontaneous" political demonstration to which the media have been issued a prior invitation. It all sounded dangerously subjective.
"Of course, it is because you are subject to nature, that it is subject to you; there would be no justice otherwise," Michael pursued. And now he too looked out of the window. He seemed to be watching the city maintenance crew, who in turn were standing around the hole they had made. They appeared to be discussing it.
"You know," he said, "I only grew to appreciate human work when I served as guardian angel to our Lord. I used to think it was inefficient, but you have to spend time with a man, watching him every day, to see what human nature is."
"What was it like?" I demanded eagerly. "Being a guardian angel."
"It's standard procedure," he said. "You liaise between heaven and earth, neutralize hostile interference, wait for something to go wrong — seldom a long wait where human beings are concerned."
"No, no," I said. "What was he like — Jesus? You were there, during all those years we know nothing about. Tell me everything. I want to know!"
"Ah!" said the archangel, spreading his hands in a shrug. "What can I say about such a life that you don't already know? It was an ordinary life, like any other." But as he said so, a faraway look came into his eye, and a gentler smile crossed his face and for a moment softened the severe joy of his countenance. "If you want to see the child, ask the mother. The guardians guard."
"But I was saying something about human work," he resumed briskly. "I spent hours watching him work, laborious detailed work too. I could have helped — except that it wouldn't have been help, only interference into the natural course of things. In a distant sort of way, it is like watching the Trinity in action; there is a comparable movement of expressing oneself in the form of another and then benefiting from the result."
"You're right," I said. "We always talk about work adding value; I had forgotten that we are adding form as well."
"Yes. Something is being structured in some way. It is wonderful to see. But in addition to a reflection of the internal life of God, which one gets with the actions of angels as well, the act of creation is also reflected. Things that were almost formless and half finished are remade into the image of man.
"I hadn't thought of that, but when things click, it's as if the work is no longer one's own." I said.
"Excuse me?" he said.
"You know," I said. "You work away at something, like designing a computer program or analysing a set of data. At first everything seems confused, and then suddenly, it all clicks into place. It's as if the project has suddenly become public; it can stand on its own. That is what makes the difference between a professional piece of work and a haphazard attempt at something. It is solid, dependable and orderly, as if somehow one's own private efforts have been carried over a threshold, so that they now belong to the common world of human projects and things that work."
"Who is like God?" He said, with a shrug of amazement. "You must be right, but I have never understood how humans do what they do."
"It is meant as a joke," I explained. "Machines moving to no purpose are funny, because in reality they are built to perform specific tasks. Nothing exists for no reason."
"Actually," I said, "this is the store I was intending to visit."
Indeed, the window with the pointless machines fronted a store that sold machines of greater public utility, and ones employing more modern principles than the Newtonian mechanics being lampooned in the display. It was one of a number of establishments in that part of town dealing in computer hardware and software, and where good deals were said to be had. And this was where I had planned to go when I set out in the morning and before I diverted myself to the CN Tower. Computers are to mathematicians what fast food is to teenagers: the employment stop-gap of first resort; the only difference being that the unemployed teenager does not need to purchase his own grill. I was here to pick up a bargain in a C compiler, in the hope of doing some freelance programming on the side. I pushed open the door and we went inside.
The door fell shut behind us. And we stepped into a different world. "It is easy to make fun of the clockwork universe," I thought, "but Newton's age did know something of incomparable beauty." It was the music that prompted my reaction; the great balanced phrases of an Ode by Purcell commanded the interior of the store. The order of the world, parodied as rigid irrelevance in the models outside, was here expressed as it exists, from the inside. The music gathered up its many parts, and as each one rolled into the next, in perfect balance, the music seemed almost to stand still. If we could stand inside mathematics, it would be like this — not immobile marks on paper, but sound, moved by the certitude of logic.
"Can you hear it?" I asked the archangel.
"I can hear what you feel," he said, "and that the music makes you want to cry."
"Christopher Wren was a mathematician before he became an architect," I said. "When he built his churches, he designed them according to mathematical principles, because he thought that if mathematics was the language of nature, it must also be the form of beauty and the language of praise. When his stones cry out to God, they do so in mathematics. I knew that once. But over the past couple of years, I got too busy and forgot what I was doing."
I remembered those animated conversations in second year, when we used to argue about the meaning of mathematics, why it works if it does, and what it is. At some point the effort of passing exams, writing a theses and worrying about a career had dulled the urgency of these questions.
"Michael," I asked. "Is God a mathematician?"
"No." he said. "And neither am I."
"I often wondered where mathematics comes from, whether it is true, or merely a human activity."
"Must knowledge be false if it is human?" he said. The Celestial Hierarchy at work
"Surely if it is knowledge at all, it must be true regardless of who is doing the thinking"
"Yes, assuming that one is thinking about the same thing and in the same way. But consider it from another angle. Supposing that I told you that mathematics is a purely subjective, culturally conditioned activity of Western man, a series of conventional signs bearing no real relation to the natural world, would you be distressed?"
"Yes," I replied at once. And then, "No, I would not, because I would not believe you. I couldn't."
"Why is that?"
"Because I know what culture is. Culture is like 'Amazing Grace' played on the bagpipes, but mathematics is different: it is too certain to be merely cultural."
"Well then, if mathematics is more certain than the word of an archangel or any other created thing, perhaps that answers your question. If it is stronger than creation, it must come from God."
I waited a moment, expecting the question that did not come. "Aren't you going to say 'who is like God?"' I said. "Even if mathematics comes from God, it cannot be about him. Arithmetic derives from the perception of individual units; geometry comes from the experience of space; calculus from change; group theory from pattern; and probability is a way of describing a diversity of results obtained under similar circumstances. These are all attributes of nature, and I suppose that nature could have been different, and mathematics as well."
"Only God could not have seen otherwise," he replied calmly. "But that is not to say that anything is possible. You could not have a four sided triangle, for instance, because the notion makes no sense, not in any universe."
"Does that mean that God has to think logically, like the rest of us?" I asked, and then quickly backtracked. "No, that can't be right. That would make logic bigger than God, in which case logic would be God. But now I don't know what to think: you said that God is not a mathematician, and yet mathematics must come from God because it is certain, and yet it describes nature, which might have been totally different. So where are we?"
"We are," said the archangel, "where we have always been: in the act of creation, where God and creation meet. As Scripture says, 'God has ordained all things by measure, number and weight'. Number is, in a sense, the first pattern for creation, and it derives from certain attributes of the divine nature."
"Is the world created through mathematics, then?" I asked.
"No. It is created through the Son. But you can think of it as a reflection of the divine Wisdom in the structure of physical things. In a distant sort of way, mathematics reminds me of the Trinity: you can think of the Father, when you consider that no material thing falls outside its principles; you can think of the Word, when you consider its logical structure; and you can think of the Spirit, because mathematics determines how things move. It also deterthines their beauty. It is the mathematics in things that makes them beautiful."
I thought of the music we were hearing, and agreed.
"But if mathematics is true," I said, "why don't angels do mathematics?"
"Because we don't have to. We experience the structure of things through intuition, in much the way that you know music. Number is essential to things, the whole balance of measurable order, but mathematics as you practice it is an activity of the human mind. Whenever you participate in the physical world, so as to study its causality and predict its movements, the result, at its most precise, is mathematics."
"Yes," I added, "and what we don't have the math for, we can't see. There is an example right here." I lifted a book on programming fractal models from a rack of eye-catching manuals. "Do you know that I never really looked at a twig, a crack in a wall, or the shape of a mountain range until I learned how these jagged shapes can be derived from simple formulae? It's scary!" I paged through the book, and we saw colour plates of great forests, lichens on a rock, the edge of a leaf or the outline of a coastline; all utterly plausible, and all totally fictitious; the results of simple mathematics and a fast computer.
"But surely you must have seen such things before," said Michael. "They are ordinary enough, after all."
"Yes, they are. But that's the problem. They belonged to my ordinary experience; not to what I considered to be scientific or worthy of note. Then, when pictures like these began to appear, I realized that I had superimposed upon the natural world a mathematical world drawn from first year calculus, where everything is smooth. A twig is jagged, so a twig doesn't count. Anyway, that is why I was beginning to think that mathematics is only subjective."
"No. Mathematics is true enough as far as it goes; but like any human endeavour, it is a project that accumulates over many generations."
During most of this conversation we had been circulating around the store in the manner of genuine, if unhurried customers. And since the sales clerk was busy filling a complicated order for the computer illiterate father of a technophile son, we passed largely unnoticed. However, the efficiency of my native city began to pull at my conscience. I located the software I wanted, a carton containing ten small disks and seven large manuals, added the book on fractals to my load and charged it all at the cash.
From thinking about large models, it was only a small step to thinking about models at the other end of the scale, where human knowledge penetrates only to the point of seeing its intuitions crumble. But perhaps, if one were not human ... it was not an opportunity to be missed. I hurried after Michael who, with some destination clearly in mind, had set off down the street from the computer shop without the usual pause for orientation that accompanies a human transit from indoors to street.
"Michael," I said, "There is something that bothers me, and I would like to know the answer. How do sub-atomic particles appear to you?"
"They are too small to be seen," he said. "They don't appear."
"Yes, I know. But the physicists say that beyond a certain degree of accuracy, we cannot determine precisely where these particles are, and what momentum they possess; they say that one cannot distinguish two particles that have the same properties. And furthermore, most of them say that this is more than a limitation of our knowledge, but a fact of nature. Is that true?"
Michael thought about this for a moment before answering cautiously, "Quantum mechanics tends to oversimplify. But by human standards it is a rich and beautiful theory."
"You mean that nature is actually stranger than that?"
"I don't know about strange; it is what God has made it to be."
"That still does not answer my question," I said recklessly. "Supposing you wanted to move one particular photon, how would you do it?"
"I have never tried. Nothing important depends upon my being able to move one photon rather than another just like it. Which photon do you want me to move?"
"Any one you like." I said; and then realized that this was in fact the nub of the problem. How could we distinguish one from another, if there is no practical method for telling them apart? If one could tack a serial number onto a photon's back or monitor its precise trajectory, one would be able to identify it and direct its future course. But at this point the Schrodinger equation and the uncertainty principle take over. We have only a probability distribution for location and momentum, and the resolution of either is inversely proportional to the other. If we knew where it was, we would not know its momentum, and hence could not direct its movement with precision. But without knowing where it is, how can we know for certain which it is?
"But this is impossible." I exclaimed. "Surely a photon has its own existence independently of whether we can identify it or determine its location. Surely to claim that nature is limited by our limitations is to claim to be like God. Quantum mechanics makes the whole universe look subjective."
We had come to a corner, and Michael asked, in a tone that was more like a statement, if that was my stop for the street car. There was an island in the middle of the road where passengers could board the car. We crossed to the middle and waited. Presently Michael said,
"Catherine, how do you know that you exist?"
"I just know it," I replied. "I remember my past. I just assume that there is something, someone, that remains through all the changes, from one day to the next."
"You are right about that, and your soul, to which you refer, will persist through greater changes even than those occurring in biological life. But notice that to exist as a person is not to exist blindly. You are an observer of your own being.
"The subjectivity that you fear so much in quantum mechanics is simply another instance of a general law, that awareness, in the broadest sense, is part of the nature of things You cannot divide the world into blind doers and detached observers, since each one of us is both.
"But as you can see, the greater the degree of action, the greater the capacity for self-awareness. Animals, for instance, are more aware of themselves than plants, that can only grow without feeling. Something like a post is incapable of growth, but at least it has enough self-presence to occupy a location. It has an identity of sorts, which is why you can use it as a marker for the bus route. But subatomic particles are not capable of acting as their own observers except in the most limited sense. In a way, they can only be reckoned as events when they interact with something more complex, like a detector, that completes for them what is absent."
"But surely the photons must be somewhere," I put in. "I can accept that we may only know their location up to a probability distribution, and even that that is all you can know, but God must know where they are. How can he control the universe if it contains things whose behaviour cannot be determined? Or is even God surprised by their outcomes?"
"Never say that, Catherine; never say that," the archangel replied. "There is nothing whatever in the universe that is not subject to God's Providence, and nothing falls beyond his knowledge. But I wonder if you are not turning geometry into the eye of the Almighty. It is true that nothing exists outside his gaze; but you seem to be saying that nothing can exist that is not composed of individual material units, and that nothing can be known that lacks a set of geometric, spatial co-ordinates of mathematical precision. 'In mathematics, the world lives and moves and has its being!' The space-time grid is the fixed point against which you measure the existence of all moving things. But how could that possibly be the case? Geometry is a concept, not a place; and there is only one fixed, eternal and immobile place in existence, namely the mind of God.
"God knows the particles, and he knows what they are doing. They exist because he knows them and has made them. But he knows them for the kind of entities that they are, indeterminacies and all."
During these exchanges, I saw the street-car appear out of the sunset, and lumber down the road from stop to stop. The stops were close together here, and all along the street one could see little groups of people waiting on their concrete islands. One could indeed solve most of the world's problems while waiting for the Queen Street car. Progressing down the street, the car would stop, blocking the traffic behind it, white the passengers heaved themselves inside, parcels first. Then, as soon as they were safely inside, and the doors closed behind them, the traffic light would turn red, and the car would have another few minutes to wait before gliding up to the next stop. The car reached the last stop before ours. Time is measured by the motions that concern us, and distance by the events we can affect.
Michael was also following the approach of the street car. Then he turned to me again.
"Prayer is the location of the rational soul," he said, "After all, space does not contain me, and yet God knows where I am."
The car reached the stop where we were standing and Michael handed me inside. I found a token, paid and sat down. Suddenly I realized that he was no longer beside me. I hurried to the back of the car and saw him standing by the side of the road as we lurched forward. I reached for the bell to stop the car, and then retracted the gesture. It was ridiculous and useless. He would join me if he wanted to.
The blue figure was still there, but more distant than space can measure. It waved and disappeared. I settled back in the seat at the rear of the car and rested my feet on the radiator, looking forward, thinking of nothing I was too tired for that. Some high quality of attention that had sustained me during the appearance of the archangel now ebbed and left me vacant in my seat. For once my own internal voice was still; assessment, judgement, resolution ceased.
The car moved forward down the street, from stop to stop. I sat very still, one arm thrown around my parcel, the other resting on my lap. I listened to the sounds of the traffic. I heard the wheels running in the tracks, the bell to signal the driver, the passengers, and beyond these, the sounds of other cars. Then even these sounds proved too focused for my dissolving attention, and I thought I heard something else, something lower and more persistent running through the higher moments of determined sound. It was like a thousand clear and rustling voices, calling out of the centre of the world and singing the praises of their Creator as proclaimed in Scripture.
The car reached Yonge Street. I got off and descended into the Subway.
This book is reproduced with the author's permission.
Copyright © Catherine Dalzell 1995, 2009
All rights reserved
Illustrations Copyright © Gordon Gillick 1995
Version: 1st December 2009