In a Glass Dome

So let us begin with a classic case of simplifying.

Ptolemy’s planets from the Encyclopaedia Britannica (1st Edition, 1771). Wikipedia

In this diagram of Ptolemy’s universe (developed ca. 150), planets revolve in epicycles around invisible points revolving around a stable earth. This explanation squared with the ancient belief that our earth was the center of the universe. 

Based on Nicolaus Copernicus' De revolutionibus orbium coelestium. Wikipedia

Move the sun to the center as Copernicus did in 1543, and the need for epicycles disappears. Natural philosophers had found Ptolemy’s explanation satisfactory for about 1200 years and resisted Copernicus’s. Beginning in 1609, however, Galileo began making observations with telescopes, producing a series of phenomena that made the geocentric model of the universe harder and harder to defend. However, even Copernicus, for whom the starry dome of the night sky overhead became the “immobile sphere of fixed stars,” did not get it all right.

The accuracy of the sun-centered explanation of the motion of the planets seems obvious to us now, since it is a so much simpler explanation. We often refer to Occam’s razor to explain the scientific preference for the simplest explanation, but William of Occam (1287-1347) was not the first one to formulate this idea; ironically, a much earlier statement of it, “We consider it a good principle to explain the phenomena by the simplest hypothesis possible,” was made by Ptolemy. However, another formulation of Occam’s razor is more precise in its application of simplicity: “Among competing hypotheses, the one with the fewest assumptions should be selected” (Wikipedia). 

The Ptolemaic model required many assumptions, some of which reached far beyond astronomy and were entangled with religious belief so that in the 16th Century, disassembling the world view based on the geocentric universe was hardly a simple act because the heliocentric view of the planets required a whole new view of the world.Religion functioned then as science does now: a universally accepted schema for explaining the world. For us, science predicts the future, tells us what to eat, heals us, speaks the obscure language of mathematics, explicates the stars and planets to us, and understands the mysteries of the invisible quanta, just as medieval Christianity did. If some discovery falsified crucial assumptions of the scientific process—the discovery that, for example, the earth is actually a computer simulation and the code has just been changed so that some conclusions already proven are no longer true—if such a proposition were itself proven, would we all embrace it immediately because it was a simple explanation for why some outcomes defied science? For the 16th Century, heliocentrism was not a simple solution.

Galileo’s proofs of the Copernican universe met with serious push-back, and he died while still in official disgrace, but later, when he was reburied in a place of greater honor, the middle finger of his right hand was removed from his body. Currently on display in a glass dome, it is suitably mounted in a vertical position, perhaps as a warning to those of us too invested in our assumptions to see the simple truth of our situation.

Mystery Lessen

From Hans Jenny. The Soil Resource (1980, Reprinted 2012)

Rainwater falls randomly from the sky into a tree where the rain becomes organized into drip patterns defined by the shape of the leaves, branches, and bark of the tree until, dripping into the soil, the water becomes randomly organized once again. Wendell Berry, in a letter to Wes Jackson (reprinted in Home Economics, 3-5), critiques this description from a scientific book on soil by arguing that randomness is not “a verifiable condition,” but is “a limit of perception.” He asserts that “random” is a misleading word that assumes there is no possible pattern in what is observed; the more proper term is “mystery.” “Random” assumes that there is not possible pattern; “mystery” assumes we just can’t see it.

While Berry emphasizes practicality, he associates mystery with religion and there is danger in letting mystery come trailing that umbilical cord. The earliest uses are theological and often were associated with secret religious rites. The most common and comprehensive theological use of “mystery” today is probably based on this Oxford English Dictionary definition: “A religious truth known or understood only by divine revelation; esp. a doctrine of faith involving difficulties which human reason is incapable of solving.” Defined this way, “mystery” becomes as much of a dead end as “random,” shutting down further exploration with certainty. If we posit a god capable of creating unsolvable mysteries, in a sense the mysteries disappear into God, who embodies the solutions. Why do we die? God does not die. Why are there evil people? God is perfect and entirely good. Why do bad things happen to good people and good things happen to bad people? It will all work out because God is perfectly just. God resolves all mysteries, but if we take God out of the picture, what remains are the mysteries for which there are no facile answers.

The most expansive non-theological use of the term “mystery” is related to the OED definition, “A hidden or secret thing; something inexplicable or beyond human comprehension; a person or thing evoking awe or wonder but not well known or understood; an enigma.” Despite the use of the word “inexplicable” in the definition, a Google search on “solve a mystery” or “solve the mystery” yields 8.6 M hits, so that for many of us a mystery is something to be solved; it is open-ended, and in that sense calling something a mystery in the non-theological sense is a beginning.

The popular genre of the murder mystery turns on the axis of logical analysis. A satisfying ending generally involves explaining motivations and events with proof that establishes guilt beyond a reasonable doubt, though such stories also allow for the operation of “justice” outside the law. Such an extra-legal conclusion would be unsatisfying, would become a crime in need of solution.

I have argued earlier that not all conflicting dualities can be resolved and that perhaps our best understanding is to accept both and see the world in 3-D. Maybe the better way to describe our response should be to say we can’t ignore dualities. They suggest enigmas, mysteries, in need of deeper exploration, though I suspect that we will discover deeper mysteries that allow us to understand our state more clearly; it will likely be mysteries all the way down.

Science should be done surrounded by mystery. Religion and science could both use more respect for mystery. Perhaps if religions treated God as more mysterious and thought twice before claiming to know what God wants and to speak in God’s behalf, the world might be a more peaceful place.

Science and Arts

At one point, I thought I had figured out the crucial difference between science and the arts: Science could speak with authority only about things in general; it could not say anything about a specific individual. Science draws conclusions about the species acer saccharum; the artist writes about what a specific sugar maple outside the window means to her as a window into the connection between humans and trees.

Sugar Maple planted 

in front of our house 

in Wellsboro, PA

One problem with my tidy conclusion grew out of my work with biologists in our university’s environmental studies program. When I looked at specific trees with them, they saw so much more than I did so they could spot variations that I missed. They seemed better equipped to appreciate individuals than I was.

My brother Tim is a research scientist and a medical doctor who is senior associate dean for clinical and translational research at the University at Buffalo Medical School. So I thought he might have some insight into this paradox; so one day as we were sitting on the patio during a visit to our younger sister, I summarized my theory:

Me: Science can speak only in generalities. Since scientific conclusion must be replicable, it can draw a conclusion about a species but not about one particular tree.

Tim: Actually, your statement ignores the importance of the particular in science because the foundation of science is statements about particular events, each one maintaining its individual characteristics. I run a series of experiments and then look at the outcomes of each instance, and the initial conclusion I draw is that in n% of t cases, when we did x, we obtained a result y in the range between a and b, or whatever. We make a restricted statement about what we observe in the sample we analyzed. Any subsequent generalization we draw is valid only in so far as it connects with what happened in the particular instances in the experiment we performed. If a generalization is insufficiently connected to those original specific incidents, then it is not scientifically valid.

Based on what Tim said—that scientists depend on their ability to observe and distinguish particular individuals to draw their conclusions—I concluded that I needed to revise my neat distinction. And the more I thought about his point, the more I began to question, for example, the role of the specific in literature. After all, Emily Dickinson sits in her room and writes,

The Brain—is wider than the Sky—

For—put them side by side—

The one the other will contain

With ease—and You—beside—



Dickinson packs into four brief lines the insight that a person standing under the sky (contained by it) can also contain the sky in her mind so that each one contains the other. In addition, both the mind can contain “You,” which could mean the reader, who is in the poet’s mind as she writes, or it could be the universal “you,” so that not only does a person’s mind contain the sky that contains it, but the brain also contains the person who contains it. Folding these ideas in on themselves should unbalance us a bit and force us to look with fresh eyes at our place in the world.

Dickinson exploits both her insight into experience and the elasticity of language to point to a universal experience. She draws a conclusion based on an insight; when that conclusion is (finally) published, we get to see whether it resonates with others so that, as in science, the particular is the foundation for the general. The experiment in this case is the work of literature, and where v is value, p is the number of people who read it, and t is the time over which people continue to read it, we decide whether something is a great piece of literature based on v = pt. If the poem contains an effective combination of particular and general experience, then the value is high.

For a while I had a shiny new theory about the difference between science and art, not one based on general vs. particular, but one based on unambiguous vs. ambiguous or single statements vs. double statements of truth. The goal of science is a statement so restricted in its meaning and scope that there is no difference in understanding between speaker and listener, or that difference approaches zero. Thus, scientists can communicate (ideally) without ambiguity,

In previous posts I have argued for the complexity and ambiguity inherent in questions, in metaphors, in creative non-fiction, in art, in humor, and in the concept of truth, and have asserted that the ability of artistic and humanistic expression to embody and help us understand the ambiguity inherent in our worlds is its great strength. So, here is another tidy distinction.

Schrodinger’s Cat By Dhatfield  

[CC BY-SA 3.0 viaWikimedia Commons]

But then, of course, there is quantum mechanics, with its wave-particle duality and the Heisenberg Uncertainty Principle. Erwin Schrödinger, by creating a thought experiment—a metaphor of sorts—tried to point out the absurdity of positing that the quantum state of an electron should be measured using probability. In his experiment, a cat in a sealed box has an equal probability of being alive or dead. Using probability, quantum theory would assert that the cat was partly alive and partly dead, a patently ridiculous idea. Unfortunately for Schrödinger, his opponents embraced his experiment as an explanation, stating that opening the box and observing the state of the cat collapses the superimposed states and resolves the conflict. Unobserved, however, the cat is both alive and dead, just as an electron can be in more than one state.

I do not pretend to understand what is going on with quantum theory yet, but out at the edge, where theoretical physics is operating, we are dealing with ideas where opposites must be held in tension, the kinds of ideas that have long been formulated in the language of art and literature. I don’t know what we will discover when we are finally able to open the quantum mechanics box and look inside, but right now the unopened box seems to be half art and half science.

So ultimately, science and art both contain ambiguities and set side by side are contained in a larger ambiguity, which also includes all of us.

The Metaphorist in the Metaphorest

[The last paragraph of the original version of this post has been revised: The last paragraph has been split in two, and some hard-to-follow leaps of thought have been clarified (he said, confidently)]

The same mental predisposition that attracts us to the satisfying uncertainty of open-ended questions may explain the essential power of metaphor as a tool for expressing the balance and tension that characterizes experience. In another place, in answering the question “Is the Self an Illusion?” I suggested that metaphors are a way to clarify irreducibly complex ideas because metaphors combine resolution and ambiguity.

Metaphor is normally introduced in school in contrast to simile, which is “a comparison using like or as.” Metaphor then becomes a comparison that does not use like or as. This approach is so unhelpful since it underestimates the complexity of the difference. For one thing a simile advertises that it is a comparison and makes clear that what is being compared maintain separate identities. T. S. Eliot begins his poem “The Love Song of J. Alfred Proofrock,”

Let us go then, you and I,

When the evening is spread out against the sky

Like a patient etherized upon a table;

And a little further on, he speaks of,

Streets that follow like a tedious argument

Of insidious intent

These comparisons (with their wonderful evocative language) make a clear distinction between the two things being compared and they communicate across the like. The sky and the patient share characteristics, perhaps a different one for each person: a sense of time suspended before some great event—night and an operation—a sense of blankness or clouds like the white hospital gown. The same is true of the image of the back streets and the tedious argument.

Later in the same poem are these lines:

And I have known the eyes already, known them all—

The eyes that fix you in a formulated phrase,

And when I am formulated, sprawling on a pin,

When I am pinned and wriggling on the wall,

Then how should I begin

To spit out all the butt-ends of my days and ways?

Purdue Cooperative Extension

Here is the comparison without like or as, and we are in the middle of the comparison before we even know it has started. Not until “sprawling on a pin” do we realize that we cannot take what is being said literally. Because there is no clear signal that a comparison is being made, the writer depends on the reader not only to interpret the comparison but even to know it is happening. So we can see the speaker as an insect, mounted and labeled in some collection, pinned in place while still alive, at the same as being subjected to the judgmental eyes of those attending a social gathering. The two parts of the comparison remain separate and blur together at the same time. The metaphor of the bug is then displaced by the metaphor of how talking at such an event involves people merely spitting out the conclusions they have drawn, a shift which brings us back to the social event. Each of the metaphors involved in the example requires at least two frames of reference present at the same time, frames of reference that must still coexist after the metaphor is deployed: the eyes fixing and the pin fixing.

This preservation of the frames of reference is the key to metaphor’s power. Deciding what to do within a frame of reference—which vegetable to plant first, which book to read next—involves comparing conventionally similar objects, but deciding whether to plant a vegetable or read a book requires a larger frame of reference so that planting and reading also become two instances of the same thing--two self-nurturing activities for example. Looking for a logical solution requires the platform of a single frame of reference. Because most complex and interesting problems do involve different frames of reference, that preliminary step means the subsequent solution is always simpler, flatter, than the formulation of the original problem.

Thus some complex problems will not be solvable in a single frame of reference. Thinking metaphorically may be the only way to understand such problems, since a metaphor creates a comparison in two frames of reference at once, a relationship that is both true and untrue at the same time: you are pinned to the wall and not pinned to the wall. 

The Irreconcilable Difference

Often movies begin well—lay out an intriguing conflict, create tension among interesting characters, complicate a promising situation; however, once they have completed constructing the problem, they deteriorate into a facile resolution. That may be because problems are more satisfying than solutions, or maybe more believable. Since everything, in being alive, is connected and temporary, every resolution of a problem requires a frame of reference, literally something that surrounds problem and crops off all the messy complications. At the end of the classic romantic comedy, in which the boy and girl connect and get married, the assumption is that they will live happily ever after, but such living will take place outside the story’s frame.

C. E. Brock Illustration for 1895 

edition of Pride and Prejudice 

(public domain)

After Elizabeth Bennet and Darcy have been happily united and professed their mutual love, Elizabeth risks opening up the plot that brought them together and look at the clockwork inside. He was attracted to her, she tells him, because, unlike all other women, she did not faun all over him; her behavior had been “bordering on the uncivil.” She notes, “To be sure, you knew no actual good of me -- but nobody thinks of that when they fall in love." But that daring move by both Elizabeth and Jane Austen is a clue to why Pride and Prejudice works so well.

Such deconstruction is consistent with what Austen has done throughout the novel (for example, of all the marriages that Jane and Elizabeth can look to, only one is a happy one), and it is also consistent with Elizabeth’s character. And while Austen implies that their suitability means that Elizabeth and Darcy will live happily together, in the last chapter Austen also makes clear that all the other disagreeable characters in their lives will remain consistently disagreeable, though manageable. Austen steps outside the frame of reference of the happy couple to remind us of some of the open questions, but Austen frames the story’s resolution in terms of family and relationships; she excludes those real threats that could destroy the frame itself: disease, death in childbirth, murder, and, of course, zombies.

Life’s problems usually involve more than one frame of reference, perhaps even overlapping frames of reference that like a carpet of Venn diagrams stretch to the horizon. Even if we go to stories for escape, we must find the resolution convincing. The willing suspension of disbelief can hold off the disruptions of daily life for only so long before they flood our minds again. Perhaps questions are more convincing than answers because they stand up better when hit with a bucket of cold water. It should not surprise us that the interlocked complexity of questions creates a stronger tool for dealing with problems than an answer useful only so long as we don’t move.