Imagine a set of revolving concentric circles . . . The relationship between the ever-changing course of Fate and the stable simplicity of Providence is like that between reasoning and understanding, between that which is coming into being and that which is, between time and eternity, or between the moving circle and the still point in the middle . . . For the best way of controlling the universe is if the simplicity immanent in the divine mind produces an unchanging order of causes to govern by its own incommutability . . . – Boethius
As a high school student, I remember being fascinated by the concepts of science. Earth science, biology, chemistry struck me as beautiful. I was never good enough at remembering specific facts to ever be much of a scientist; I had fun being perplexed about the concept of gravity, that the whole earth is trying to prevent my movement with its pull, but that for somewhere between seventy and eighty years, with a bit of good fortune, my will could, to some extent, resist that of the planet’s. There is an inconceivable thrill in recognizing our place in the solar system, this strange gem of blue, brown and white whizzing around a giant ball of fire, itself yet another trinket in the hands of the cosmic juggler. More than memorizing facts, however, there was a part of science which is simply requisite for entering into most parts of the field, especially those which interested me, and it was this part precisely which I found myself entirely incapable of comprehending: mathematics. It should come as no surprise to you that a student of literature suffers with math. So how is it that science could have so much compelling interest for me, and yet that imbedded structure, mathematics, of the scientific conversation was simply beyond me? It doesn’t seem like a simplistic binary, and yet, somehow, they are different.
I am going to present a picture in this chapter which I readily admit to be far too simple, and probably erroneous in some important ways. But it is this relationship, that between math and science, which holds the key to many things, I believe. So, I am going to try and figure out how they relate, a bit of a ridiculous notion considering my ineptitude in both. But I will do my best with the limited insight I have.
Science, let us venture to say, is the study of movement, or of energy, in some sense. Science must test, and test, and test again, before it is willing to say much of anything, because the realm it is attempting to grapple is in some ways fairly chaotic, at least to the unknowing observer. While trees are absorbing sun rays for food, human skin is absorbing those same rays for vitamin D and for skin cancer. At the same moment that a baby is being born, its life just beginning anew, its mother is many more years closer to her death and, in many cases historically, that birth has been the cause of mothers’ deaths. Simultaneously, lions are consuming their prey and black holes are consuming planets, stars and other matter. Fireworks can explode in the same world where snow falls. It is a wondrous place of implacable, dynamic movement, every moment of time and every part of space a flurry with every kind of movement and excitement.
Math is in some sense the photo-negative of this picture. It is, at least in my mind, a static set of abstractions which hold themselves apart, almost coldly, from the world. Oh, yes, I know, science is everywhere infused with math; I’ve already said that above. But if I hold my body at a certain angle or do not, the angle itself does not much care. It stays where it is at, and I come to it, if I lean to the side, and move away from it, as I straighten my back. All numbers, on both side of the zero, are forever those numbers; adding two and two equals four whether or not we can find two apples and two more, or whether we can find two gorillas and two sandwiches to make a group of four. In the realm of science we see a world of constant flux, even if that flux is generally patterned and comprehensible; in the realm of math, every equation imagined by the human mind, and not yet imagined by the human mind, exists in static perfection. It can be found everywhere in the universe; no, more correctly, the universe can be seen everywhere taking shape within math. And yet, how could this be?
Now, has been argued to me that 2 plus 2 does not always equal 4. I am not really familiar with Looking Glass math, as it were, though I am familiar with Lewis Carroll, though I think that he is somehow misunderstood by the mathematicians who try to use him (though I won’t stick to my guns in that regard, not knowing enough regular math to know if some odd magical math works or not). But it seems to me that even if they are right, they have not “changed” the equation of two plus two equals four. Instead, all they have really done is found the equation to have actually been more complex than we once realized. If it is simply the subjective human mind which makes the difference here, than I must ask, what is the value of Looking Glass math? I could simply reject it out of hand and ignore its precepts. On the other hand, if there is something real to math, shouldn’t I allow for Looking Glass math, if it is viable, to impact my conception of mathematics in general? It seems so. Having accepted that, I further hold that mathematical “reality,” unlike scientific reality, is not in flux; it is only the flux of our minds which we are revealing. We have gotten a bit closer to the mathematical truth, if Looking Glass math shows us something we didn’t know about before. After all, we do not think that a child learning algebra for the first time has changed the state of algebra. All he has done is moved his mind towards something which is, indeed, true.
Allow me to neaten up this conversation into two axioms: 1. Abstract truth’s eternal reality is unchanging: One plus one is always two, or the equivalent equation to one plus one equals two, whether known or not, is always true. 2. Absolute energy is total real movement, no atomic structure, simply pure, unrestrained action. Let us demonstrate that, of their own accord, these two “worlds” could never touch each other. Atoms cannot bounce against mathematical formulas and equations cannot alter reality. As V in “V for Vendetta” says, “Ideas are bullet proof.” This works in both directions. No matter how many times 1 is added to 1 to equal 2, two things need never actually manifest in the world of energy. On the other hand, in the world of energy, even if all pairs of things were destroyed, 2 would remain in the world of the abstract. On their own these two worlds could never meet. The brilliant miracle of reality is that some how, in spite of reason, beyond our comprehension, they do meet. Matter can be arranged into numbers, and abstract truth can be illuminated through reality. The possibility of communication between these two worlds depends entirely on the existence of a third power, a power as strange as the world, a power strange enough to tie energy and truth together to form universal law.
Before we come to this power, we must see how math and science begin to become reconciled. What means of truth seeking compromises, on the side of mathematics, towards the direction of science? To me, I hold the answer to be philosophy, especially analytical philosophy. If you question my assertion of the deeply mathematical nature of philosophy, I point you to any textbook on the philosophy of logic, which will probably have an equation which looks something like this: If p, then q.
P. Therefore, q. Let’s fill it in with a likewise stereotypical philosophy example. If Socrates is human, then Socrates is mortal. Socrates is human. Therefore, Socrates is mortal. These sort of constructions are, to be horrifically reductive, the basic job of philosophy. It takes thought and puts them into formulas, and judges whether these formulas are first valid, and then sound. This is not quite math, of course, because the concept of one has nothing but itself there; it is the unit, stripped of all other significance. P and Q look suspiciously like ones, but they are not ones. They are filled with concepts, the humanity and the mortality of Socrates. Now, of course, we can do the same thing with math. We can say that one apple, cut in half, with one half eaten, is now half of an apple. But really, the function of this problem is usually not intended to help us understand apples. We know, without knowing any math, what half of an apple is. But we do not, without the half apple, necessarily conceive of the concept of fraction. Math can certainly be used to help us understand the world, but math is less dependent on what actually happens in the world. After all, if all apples were destroyed on earth, the concept of two apples plus the concept of two apples would still, conceptually, equal two apples.
Philosophy, in a similar way, is untouched by scientific actuality, or if not untouched, it is not wholly dependent on scientific reality. After all, I have argued that philosophy is a sort of compromise between science and math, from the perspective of, let us say, the Cosmic Mathematician. To bring math to the world, one begins to fill it with all sorts of concepts which no longer depend on their numerical reality, but also on the conceivable reality of things, of objects. That is not to say that philosophy can only deal with objects, or that math cannot. But when a math problem integrates objects from the real world (those problems I personally hated, where Sally has a certain variety of coins, gives some to one friend, gets some more from another, and then you are supposed to figure out how many coins Sally has), it edges towards science through philosophy.
In some sense, philosophy retains the metaphysical static nature of math. Unicorns are possible, a philosopher can rightly say, and not only are they possible, they are, in pure metaphysical terms, necessarily and always possible. Much like one plus one equals two, the actual state of the universe can’t do anything to hurt the idea of unicorns, on its own. The actual state of the universe can say, “There are no unicorns about,” but it cannot ever say, “Unicorns are impossible.” Metaphysically, they are absolutely possible; that they do or do not exist does not change this fact. Even so, the concept of the unicorn is bound up in ideas about the actual world, in testimonies of their existence, of fictional stories about their lives, in the actual animals which roam about, sometimes looking an awful lot like unicorns, even if, fundamentally, there simply are none anywhere. So, I hope my point can be seen, that philosophy is a sort of compromise from mathematics, towards science.
Now, granted, science uses math all of the time. We must admit that these things exist, in some way, in the same stuff of the universe, somehow, or they could never come together. After all, in chemistry there is the concept of the mole, a unit of measurement which I never really grasped, to be perfectly honest. Nonetheless it is measurement, and measurements are the watchword of scientific inquiry. So science has necessarily admitted math into its questioning of the empirical world. But science has found its best friend on the opposite spectrum of question making, as I have attempted to demonstrate. So what is the compromise made by science, towards math? I think that the answer is history. History is the study of events, a story about how events happened, which is precisely what science tries to find. Now, science has some things in view which are properly historical, in that it has actually seen them. Scientific inquiry has actually seen the sun, the planet earth, the growth of trees, and so forth. Science has not seen, however, the circumstances by which life began, the behavior of every population of species which it seeks to study, or the movement all of the chemicals and atoms which it hopes to quantify. I do mean here, of course, human science specifically. If science is defined as a method which forms beliefs based upon a catalog of events, what we are saying is, in other words, that science is the process of creating history out of data. When we are told about the process of a tree making food out of nutrients of the sun and of soil, we are being told the collective story of actual trees which have been looked at across the planet. The fluctuating data of the empirical world is captured, photographed, as it were, to hold it still in one’s mind, so that a scientific premise can be made. By freezing empirical data in this way, by weaving it into a scientific history, the scientist can then look for the mathematics holding it all together.
History, of course, does not primarily attempt to study natural science. However, history does attempt to be as scientific as possible; or at least, modern history does. History is built from a great deal of fragmented evidence, fragments of poetry and bad attempts at history of earlier human beings, which are then rummaged through for plausible explanations of what happened. The historian looks for a variety of empirical data, including anthropological data, like clay pots, burial remains and building remnants, combined with whatever written testimonies may accompany them. We may not be able to attest that a battle happened because Geoffrey of Monmouth wrote that it did, but we can attest that someone, namely, Geoffrey, did write about the battle, and that he thought, for some reason, it was important to do so. This evidence is pointing at something, even if it is not that the battle in question actually happened. With these glaring fractures in the evidence, historians must play the part of philosophers, sifting through theories and looking for the most plausible evidence, and also must consider what science tells us is actually part of reality, and thus be a bit suspicious when William Butler Yeats compiles the history of fairies in Ireland.
But our whole soul need not be suspicious of the fairytales, for it means something that humans thought to write them, though that writing may not be apparent, as with the battles of Geoffrey of Monmouth mentioned above. The philosopher and the historian must come together in this, then: they must have imagination. When presented with artifacts which only tell part of the story, testimony which gives a no doubt skewed vision of the story, and philosophical doubts as to that vision, the historian must then use his imagination to think up ways of explaining the evidence at hand. This does not mean, of course, that scientists or mathematicians are not imaginative. I believe that they are, and that the imagination is greatly involved in what they do. As I said, the picture I am building is just too simple. But I hope what I am showing will get the gist across. For you can see, I hope, that as history is a compromise from science to get at help from math, so imagination is employed by the historian to get at the help philosophy offers. Imagination, poetic expression, is the space between philosophy and history, and both must look to it to perform their function on a routine basis.
It will be rightly asserted that I am biased. I am a literary scholar who studies poetry for a living, and so putting the imagination at the center of knowledge will sound like a glib advertisement for my services to the cynical reader. But that is not my intention, and I can only hope that I am taken at my word. I do not mean to say that imagination is necessarily more important than any other means of intellectual discovery, but I do think it is, in a sense, the crux of the function of mind. Evidence, whether mathematical or scientific, all amounts to little more than a bunch of noise, if there is not some means of bringing them together to create a coherent structure. Reason is certainly useful, but reason only helps to explain that which has already been, to some degree, apprehended by the mind. But all other kinds of knowledge are simply having an effect on the mind; science, history, philosophy, and math are all things which the mind studies. Poetry, on the other hand, is the response of the mind to those things which it studies. Poetry is the mind feeling all of this information, and creating a single, if complex and not always consistent, experience of it. When we are told about science, our imagination looks at our sensory knowledge, and can make the leap necessary to belief, even when we do not wholly see the thing for ourselves. I said this was not a book about faith, and it is not, but here is where it does bear mentioning. Scientists give us information which, from our end, is incomplete. We cannot see all that they see, but our imaginations are able to stretch and accommodate the wild things they say with a combination of empirical and rational experiences we have of the world on our own. If there is any faculty which I would attribute faith to, I suppose it would be this one, that of imagination. The scientist has painted a picture of hydrogen and oxygen molecules working together to create water; I consider it logically and see no contradiction there, and then I bring these two experiences together imaginatively to create the belief that water is, in fact, dihydrogen monoxide, as odd as that claim sounds.
Now, it could be granted that this image of knowledge-making, with the imagination reaching to the right towards math and philosophy and to the left towards history and science, is simply a product of one human’s fancy. To some extent, that’s true; it’s the product of my experiences, biases, and prejudices. But where, precisely, do you get off board with me? To reject my picture, will you destroy the field of science, or of math? You must find some other way of accounting for the relationship between science and math, and I have heard none which satisfy me any better. It may be, indeed, that in reality these things hook up in different ways. But even if that is the case, in reality the mathematical, philosophical, imaginative, historical and scientific truths do still hook up; if we think they don’t, we must scrap them. If we do scrap them, we are lost in subjectivity, and theism and atheism are equally impossible. But if we think of these five kinds of knowing are true, then they are all true together, and they were true at the very origin of the universe. I imagine a celestial rail-road, with one track being math, the other science, with the imagination the ties which are welded or nailed to each side of the track with philosophy and history, respectively. It is a total rail-road, existing throughout all time and space; it stood there at the origin of the universe, and upon it moves the engine of the entire universe.
This is, of course, a rather crummy analogy. A more beautiful one would be of the conductor of an orchestra, with each means of knowing being a sort of musical instrument. But musical productions, like rail-roads, work because they are put together properly. They are conceived and structured with care and varying degrees of precision, usually the more beautiful for the amount of both. The rail-road, too, can only function if its elements are properly aligned. Without philosophy or history, imagination will become detached from science and philosophy and begin, in our minds, creating all sorts of monstrous fancies. Science which has lost its sense of history will begin to make claims about humanity which are reductive (it already has, I believe), and similarly, math, without its philosophical connection to the rest of the search of truth, will reduce the world to lifeless formula. To perform the proper function of belief-making, all these means of inquiry must be brought into balance with one another. And it is this assumption, that at some point they do come into perfect harmony, or perfect symphony, with each other which makes the pursuit of knowledge possible at all. We must think that in the universe, the truths of these five realms come together in proper balance, for if we assume their discord, then all of them lose their potency.
I have argued that the origin of the universe must be, can only be, a thing of interdisciplinary reality. I have defended myself against the complaints of subjectivity on the grounds that subjectivity stems from actual things in the world and that there could be no other means of learning, and that our subjective minds have, generally, drawn up beliefs from these five means of knowing. We must assume that if the universe contains mathematical truth, that truth was present when it all began. If it contains imaginative truth, and scientific truth, the same must also be true. Aristotle says that insofar as X may produce Y, if nothing else helped X to produce Y, then X must contain within itself everything which Y possesses. In the same way, if the universe is a place which has the abstract truth of math and philosophy and the motive truth of science and history, and the mental faculty of imagination which brings them together, then these things, too, must have been present before the universe began. If these pieces are removed, we lose the whole picture; but everybody loses, atheists as well as theists. Having assumed what I have said to be correct, for the moment, permit me to explore some of the ramifications which result.
It seems to me that the highest and fullest reality must be a complete union of truth and energy. We could imagine there being two “worlds,” one of the abstract and the other of the motive. Neither is superior to the other, for without motion the abstract can never obtain and without the abstract the motive is mere chaos. In the world we see, we tend towards the motive, since it is easier to perceive. But the motive aspects of the world are apparently inseparable from the abstract, to our ordinary perception. In the ultimate, both worlds are one being and where all abstract and all motive truth join, God is. A pure abstract could be posited to exist, and a pure motive (or world of energy), whether one never touches the other, could also be imagined to exist. What brings about the existence of these worlds, whether one precedes the other, is a question I cannot answer. But in God, and in God alone, can both fully obtain.
Somehow, there was in the universe the power to reconcile the motive and the abstract. This power, Divinity, is the First Imagination. This is the error of Intelligent Design: They start with God as a being of analytical truth. On the other hand, the anthropomorphist makes God so human his creative nature becomes incredible. But it must be understood that Divinity is the highest imagination, for matter and the abstract apart could never depict God, and bringing them together is an act more holy than we can conceive. That we do it every moment we think does not make it less miraculous. The joining of two essentially opposed realities could take only a stroke of omniscient genius, for a mind composed of both worlds could never be God.
Composition of matter and formula can only create; the possibility of that composition must exist prior to its being effected. Imagination must precede the joining of the worlds though imagination, and so Imagination, by marrying these things, these “worlds,” becomes the first cause. God is, therefore, the total reconciliation of energy and mind, destiny and ratio, inside the verdant vacuum of imagination. The mind of God is manifested in this celestial rail-road, the divine symphony, in operation behind every human effort to learn about the cosmos.