Quality in a Writer

Recently a Facebook friend¹ posed the question of whether quality still mattered in the publishing market. Considering the number of unremarkable, badly imagined, and badly edited books that have made it into prominence—through both traditional paper publishing and independent epublishing—it’s a good question. My response was and is: “Quality of thought, imagination, and expression is all a writer has to sell.”

The quality of a writer’s thinking is, for me, the most important aspect of what he or she puts on the page. Thinking starts with having access to robust and interesting facts, which shape the essence of the writer’s views and gauge how close he or she comes to describing some kind of truth.

I say “some kind” of truth, because facts and truth both tend to be slippery things. Some facts are concrete and checkable, like who won the World Series in 1938. Get that wrong in an article or story, and it becomes difficult to climb out of the hole your error has dug for you. But many facts represent views of the world and the nature of reality that have not yet been proven or may have no undisputed referent. Every one of us is constantly building mental models of reality covering aspects of life such as human relationships, politics and economics, science and religion, and the various art forms.² We refer to these models when we make decisions about what might be the right or wrong thing to do, what is fair and just, whom we will trust or distrust, whom we love or hate, and what the future will bring.

When a writer uses a fact with a concrete referent—like the Yankees having won the World Series in ’38—he or she had better check and confirm it before publication, because any reader can easily go to sources and check for himself. But when a fact has unclear status—like how much carbon dioxide actually contributes to global warming³—then the writer must choose carefully and buffer his or her statements with qualifying words that acknowledge uncertainty, like “might,” “could,” “probably,” and “possibly.”⁴ The structure of a piece of writing changes with the quality of the facts supporting it.

Having robust, influential facts on hand implies that the writer has read widely, considered deeply, weighed one view of reality against possible others, and made honest, logical, defensible choices. The depth of a writer’s information determines the versatility and viability of his or her writing.

But facts are only the starting point of a writer’s thought; more important is how he or she uses them. Every piece of writing must have an argument—in the older sense of the word, as “a coherent series of reasons, statements, or facts intended to support or establish a point of view.”⁵ The argument depends on linking of those reasons or facts in some logical order. One can argue from the particular to the general, or from the general to the particular, or chronologically, or by order of importance or weight, ascending or descending. The choice of logical structure depends on the nature of the argument being made and how best to overcome the reader’s natural resistance toward, or hesitancy about, the writer’s point of view or the article’s thesis. Without such logical structuring, the writing will be incoherent and the reader will not be persuaded.

These considerations obviously apply to nonfiction, where the whole purpose of the work is to engage the reader in learning something new and interesting, or agreeing with an established viewpoint or proposition, or taking some kind of action. But facts and their logical structure apply equally to fiction. Here the structure is most likely chronological—this happens, then that happens—but the writer must still be aware of how the action comes together. The writer and the characters he or she creates must function in all the tenses: what is happening now, what has happened in the past and is either known or unknown to the character, and what will happen in the future through the character’s hopes, guesses, and expectations. Where cause and effect are not clear, the writer must think through the passage from the reader’s point of view and supply any links or supporting information necessary to making the leap from what the character did or said to what might be the appropriate or expected outcome.

In the best fiction writing—whose practice I strenuously advocate—the writer must not only think like the reader, as he or she follows and absorbs the story, but also think like the character from whose point of view the story is told, as he or she experiences the action, makes decisions about it, and suffers the outcome. In my fiction, I try to stay entirely within one point of view throughout any one scene, even when other characters who have functioned as the viewpoint in other scenes may be present.⁶ This limits the amount and type of information I can reveal through one character’s eyes, ears, and understanding. I have no “omniscient narrator” standing by to explain the action and fill in the blanks concerning what other characters might know and remember. So, for me, fiction writing is a bit like organized schizophrenia: pushing the story forward while being simultaneously mindful of what the reader can absorb and what the viewpoint character can know and think.

The depth of the writer’s understanding and the subtlety with which he or she handles all these variables contribute to the quality of thought. The writer sits in the middle of the writing process and its choices like an airplane pilot sitting in a cockpit full of levers, switches, dials, and gauges. The skill with which he or she manipulates these tools and devices determines the success or failure of the flight … or the writing.

Quality of imagination is similar to quality of thought in that it reflects the amount of effort the writer has put into obtaining knowledge, reading in an informed manner, and sensing and reflecting on the world around us. Imagination goes beyond the structure of thought and argument to the quality of perception and the structure of dreams.

The writer of nonfiction must live not only in the closed world of his or her reasoned argument but also in the larger universe of opposing viewpoints, negating facts and contrary data, competing choices, and random occurrences. The writer of fiction must live not only within the story he or she wants to tell but also in the larger world where actions and choices by the characters have other possible outcomes, good and bad intentions and consequences, and probable or improbable occurrences. The writer must be aware of and take into consideration these larger worlds, just as every one of us must be aware of and take into consideration the actions of others and the accidents of nature as we go about our daily business. Perception of and allowance for other possibilities give a piece of writing depth and texture.

The fiction writer has special burdens in terms of imagination. With fiction, the writer is creating a “pocket universe”—a complete and functioning world that can fit between the covers of a book, between the two palms of the reader’s hands, and within the finite number of words being used.⁷ And yet the world of the story must suggest so much more than is simply stated on the page. This invented world may or may not conform in shape, color, and size to the world the reader inhabits outside the book. It may either be exactly the historical world we know or an alien planet inhabited by an alien race with subtle and strange customs, thoughts, and assumptions. In either case, the writer must provide enough detail to make this new world come alive in the reader’s mind but without using so much detail that the story bogs down in mere perception and visual, aural, and tactile experience. Oh, and it’s important that any concept or physical detail which the writer describes too lovingly—like the gun in the main character’s pocket—must at some point in the story be made real and used in the action.

The writer following the story’s thread is like a pilot flying a single route. Yet it’s a poor pilot who never takes his eyes off the instruments and the alignment of navigational beacons to see what might lie to left or right outside the canopy. Mountains and their updrafts, thunderheads and their turbulence all will shape the choice of route. The skill with which the pilot perceives these dangers, and with which the writer creates this just-glimpsed world of possibilities, will determine the success or failure of the flight or the writing.

Quality of expression is similar to quality of imagination in that it draws on the writer’s sense of other possibilities from the one he or she has in mind. A writer must use language flexibly, like a fencing master who knows all the possible attacks he or she might use against an opponent, as well as all the possible parries to use against a specific attack, and chooses from among them the appropriate way to start or end the exchange. Varying attacks and parries will keep the fencing match fresh and surprising and keep the opponent just slightly off balance. Similarly, a reader who can see where each dull sentence is coming from and the point it’s plodding toward making will quickly grow bored. The writer must vary the pace of the article or story, the structure and length of its sentences, the speed with which new ideas arise, so as to keep the reader refreshed, engaged, and just slightly off balance—so that the reader keeps guessing at the writer’s ultimate intent and wants to move forward.

The writer weighs each word and phrase for its ability to convey an exact meaning without bogging the reader down with repeated questions or sending him or her on trips to the dictionary. Quality requires the writer to use verbs that paint pictures of action and nouns that make each object glow with its own nimbus of recognition. Economy requires that the writer pare away excess words until those he or she does use vibrate with strength and tension. But mindfulness of a reader’s groping toward understanding sometimes requires the writer to use structures that slow the pace of revelation, so that key thoughts stand out in high relief.

Like the pilot of an airplane, the writer takes off fast, with flaps fully extended and landing gear retracting as soon as it leaves the pavement. And the point of the article or story comes home with precision, like the tiny but definite jolt of impact as the wheels touch down and spin up to speed. A good start and a good ending are worth half the points of the actual trip in both flying and writing.

But none of these qualities—of thought, imagination, or expression—is subject to anything so obvious as a set of rules.⁸ The skilled writer, like the skilled pilot, operates as much by instinct and inner sensibility as by experience of what has worked, or didn’t, in the past. That’s why every writer and every piece of writing is different. That’s why writing is an art, not a science, and never subject to formula.

1. Duncan Long, who writes science fiction and is a prolific artist, including book covers. His stuff has quality.

2. Constant readers will note that the latter three are also my favorite blog topics.

3. Everyone would agree CO₂ works as a greenhouse gas, passing incoming full-spectrum solar radiation through the atmosphere but blocking a certain fraction of the outgoing infrared which is radiated from Earth’s surface. However, other gases—chiefly water vapor and methane—also work that way and usually with stronger effect. Given everything else that’s going on with the planet—sunspots and the flux in solar radiation, absorption of CO₂ by green plants, natural cycles and variations based on ocean currents and the mechanics of Earth’s orbit—the exact contribution of human-made CO₂ in relation to global temperatures can only be studied with computer models. Computer models, like the imaginary models we build in our heads, depend on the depth and complexity of the relationships traced and the data that are used as a starting point. Computer models may represent good scientific understanding, but they are by their nature incomplete and arbitrary—otherwise they would have to track every molecule of air and water in real time, which is impossible. A computer model, like my understanding of my relationships with other people, is an educated guess and not a proven or even provable fact.

4. Of course, an intermediate classification of facts exists. It includes approximations, conjectures, and fictitious examples that cannot be checked but “feel right” to the average reader. An example would be the claim “There are eight million stories in the naked city.” Well, maybe 7,990,000 … or perhaps 8,215,000. Populations are fluid and change all the time. The point does not suffer for presenting a rounding error.

5. From my Merriam-Webster Unabridged Dictionary. Curiously, the word “argument” functions similarly in mathematics: “one of the independent variables upon whose value that of a function depends.” Garbage arguments in, garbage value out.

6. By playing off one character’s understanding and perceptions against those of other characters, I can let the reader triangulate on the truth and eventually come to realize what’s actually happening in the story. In my personal view, life is like that: a synthesis of what we know, what we don’t, and what others may know or perceive. It’s a mystery … and a tangle!

7. See A World Between Two Palms from September 8, 2013.

8. See Rules for Writers from October 6, 2013.

Art and Irony

I once heard Alexander Calder’s large, rounded, liquid mobiles criticized as “lacking in irony.” Presumably, the critic felt that Calder wasn’t making enough of a point about large, rounded, liquid shapes and their relationship to society, social justice, political awareness, green conservation, or something else de rigueur. Simply being graceful, serene, and soothing to the soul apparently wasn’t sufficient to qualify as art.

Occasionally, I find what I call “cleavage issues” or “cleavage questions”: notions that, like a diamond cutter finding the fracture plane in a stone, shed important light on facets of the human condition.¹ I believe the question of irony as a basis for art may be one of these.

Art used to be representational. When our earliest ancestors painted bison and horses on the cave walls at Lascaux, they were depicting what they saw. Presumably, they liked and admired these animals and wanted the people looking at the paintings to feel the same way. They may also have been making a propitiatory gesture with the paintings: sending a message in red ochre to some deity somewhere, “These are the things your people need. Please make more of them. Please fill the plains with these animals.”

The representational and propitiatory natures of art came down to us through Classical times to the Renaissance. When the sculptor Phidias made a gigantic statue of Athena for the Parthenon, the message was, “Our city is named for a great and wise goddess who watches over us,” as well as, “Goddess, please remember and protect your people!” When he carved the frieze of the battle between the stone-age Lapiths and the Centaurs, he was portraying a myth known to the viewers. Similarly, when Michelangelo and the rest of the Renaissance sculptors and painters depicted a madonna and child, they were celebrating motherhood and telling a story of the Christ’s humanity that was familiar to the viewers. It was both representational—“Isn’t this a lovely mother?”—as well a propitiatory—“Madonna, watch over us as you watched over your child.”

Even before the Renaissance, western art in the form of illuminated manuscripts and stained glass windows told the story of religion. That was about the only story people had time to hear, and the work was funded by a church with the excess cash with which to pay artists and artisans to tell it. Yes, there were occasional grim warnings—those images of demons tormenting the sinners in the aftermath of Judgment Day or the agonies of saints which proved their blessed nature—but these were meant to be instructive.

Sometime after the Protestant Reformation, a sense of edginess and wise-guy humor came into religious painting. Pieter Brueghel the Elder painted village scenes and landscapes, but he also painted and drew comic allegories such as The Fight Between Carnival and Lent and Fight of the Money Bags and Strong Boxes. He was using satire to comment on social values. After that, you might still get artists whose work was sincerely representational—many of the French Impressionists come to mind here—but the art world would start to call them “naïve.”

Satire is an old literary device, going back at least to the Greeks and Romans. The playwright or poet will focus on some vice or supposed virtue or other human tendency and expose it to ridicule, often with a sense of suggesting how to avoid or correct it. Satire uses laughter to bring home the point. Irony is a closely related device, again drawn from literature. In Plato’s Dialogues, Socrates would feign ignorance of some question or proposition—using “Socratic irony”—in order to get his conversational foils to commit to a position and then examine it through questioning. In literature, irony means “the thing not being what it seems.” When Oliver Hardy tells Stan Laurel, “Isn’t this a nice kettle of fish,” he means the exact opposite. The juxtaposition of words saying one thing and meaning another invokes the suddenly perceived incongruity, the dissonance, the unexpected lurch which is the basis of all jokes and most humor.

As I said above, this is a literary device, played out in words. As applied to the visual art forms, irony becomes trickier. Think of Rodin’s She Who Was the Helmet Maker’s Once-Beautiful Wife. The sculpture shows an old woman borne down with age, tired, and presumably near death. Rodin is making a comment on the transitoriness of beauty by showing the viewer something ugly. Through her we confront the passage of time and our own mortality. He does something similar with The Fallen Caryatid, showing a strong young woman crushed by her burdens. These are superficially ugly images that, underneath and with reflection, show something noble and enduring in the human spirit. That’s the work of a master.

Somewhere along the road from Pieter Brueghel to modern art, the gentle, sober, and astounding irony of Auguste Rodin subsided into rude satire and ugly mocking. I remember seeing an exhibition of student artwork when I was an undergraduate at Penn State. To me, one of the most memorable pictures—and not for its beauty—showed a life-size, seated nude wearing a surgical mask and a look of pure agony in her eyes because she was stuck all over with pins. What stayed with me about the painting was that I had no idea what the artist was trying to represent or even comment on. “Does that hurt?” comes to mind as possible meaning. “Isn’t this just awful?” is a close second. But the difference between this image and, say, the martyrdom of an early saint is that the agony being portrayed had no justification, related to no historical precedent, was not the result of any kind of social injustice, war, or overt malevolence—other than the artist’s own hatred of the subject—and was not apparently meant to be instructive. What did the artist want me to do? I turned away in confusion.

Much of modern art—not all, but a depressingly large amount—has this same vague or intentional bitterness. It’s not meant ironically but is simply mean-spirited. “Doesn’t life suck?” It doesn’t seem to mean anything except, “I dare you to look away. You’re a coward, a bourgeois, a naïf, a child if you look away.” If there’s an underlying message, it’s not ironic but simply rude. Think of the Andres Serrano photograph Piss Christ, showing a crucifix dipped in urine. The artist may be making a statement about Christianity—in which case he’s resorting to infantile gestures. The deepest meaning of the work seems to be “I can offend you—and you’re a fool who’s not in on my joke if you get offended.”

Too much of the kind of art that’s meant to be ironic seems to me just belittling, snide, intentionally offensive, and cruel, with no deeper meaning than “I can laugh at you, and you out there can’t do a thing about it.”

I’d like to be charitable and see this kind of artwork as a psychological cry for help on the artist’s part. I’m afraid, however, that the artist who could conceive of these works would find my pity offensive. And who am I to impose my values on another who is so sure of him- or herself as to commit such atrocities to film, canvas, or clay?

I’m content to see artistic “irony” as simply a fracture plane. On the one side is the artist who photographs, paints, or sculpts because he or she has found something beautiful, interesting, strikingly instructive, transcendent, or even merely whimsical and, like the voice in The Book of Revelation, calls to us, “Come and see!” On the other side are people with an artistic bent but not much vision, who don’t much like their life or the world they were born into, and who can only comment, “Doesn’t life suck?”

I’ll spend my money on the former kind of artwork. More importantly, I’ll spend my time trying to understand the underlying revelation. But for the latter, not one penny!

The Labor Theory of Value

For the past year or two, I’ve been trying to define why I’m so bothered by much of the economic thinking on the leftward side of the aisle. In particular, I revolt at the concept of the economy as simply a great pie—that is, if my slice is bigger, then yours must necessarily be smaller. For a while now, I have championed the concept that an economy is more like an ecology. Activity begets activity, creates more niches and opportunities, and expands the base of wealth, in the same way that the canopy of a rain forest is more productive—creates a bigger pie—than the sandy floor of a desert.¹

The driver of the rain forest—the foundation for all biological activity, there and in the desert as well—is sunlight, which is captured through photosynthesis in green plants as carbohydrates and then spread throughout the ecology as food energy. In this analogy, the driver of the economy is human energy, which is captured both as the direct effort of making products and offering services, as well as through subtler channels such as delayed gratification and future mindfulness. By delaying the immediate spend of his or her earned energy, a person may invest for greater productivity in the future, or make loans through savings accounts, bond purchases, and other instruments to share in the productivity of others. As carbohydrates are the solid form of captured sunlight, so money is the solidified form of human energy.

However, this treads awfully close to the “labor theory of value,” most often attributed to Marx. The theory says that the value of a commodity can only be objectively measured by the number of hours of human labor needed to produce it. If shoes take twice as long to make as gloves, then shoes are more valuable than gloves. This aspect of the analogy to a rain forest troubles me.

Shoes and gloves aside, the labor theory of value is easy enough to refute on the face of it. Let’s say our village has two cobblers. One is skilled and can make a pair of shoes in about three hours, with precise cuts and strong stitches. One is less skilled and needs six hours to make a pair of shoes, with sloppy cuts and weak stitches. The first cobbler's shoes will last you several years. The second's will fall apart in six months. But according to the labor theory of value, the second cobbler's shoes should be worth twice as much as the first's. Uh-huh!

A Marxist might reply that I’m confusing the particular with the general, that on the whole, or on average, or by some other leveling device, we should look at the output of cobblers as a class and not the skill, effort, and manual inputs of individual cobblers. This is certainly the claim of a unionized labor force, that only time in the job classification—which is supposed to equate to greater experience and skill—has any meaning, and that in all other respects one worker’s output is equivalent to any other’s of the same classification.

But I adhere to market principles. The value of a commodity or service is related, not to what the provider put into it, but what the consumer appreciates about it. In a free market, if people like what they’re buying—for any reason, frivolous or not—they will pay more for it. The reason can be based on real perception, like shoes with good cuts and tight stitching, or on imagined qualities, like the cachet that comes with a stylish brand or label. If they don’t like what they’re buying—for any reason, such as wrong fit, wrong function, wrong color … wrong smell—they will pay less, or only pay the asking price under duress, or refuse to buy at all.²

In dealing with commodities that cannot be as easily differentiated by individual elements of style and quality as shoes or gloves—here we’re talking about graded and fungible commodities like oil or wheat³—or commodities that people must have to survive, then issues of supply and demand dictate value. If a large supply of oil or wheat comes on the market, no matter its quality as a particular product, the people will value it less and the price will go down, even if they desperately need it. If oil or wheat is scarce in the market, then people will value it more and the price will go up, even if they complain that they’re paying too much.

This is not just a nice theory about economics, created by a wise man sitting in a cozy library, but simply the way human beings in large masses with no reason to love or trust one another actually work. What you can get for your effort in making a pair of shoes—or gloves, or finding oil, or growing wheat … or writing a novel—depends on the needs and wants of the consumer. In the transaction, it’s irrelevant how hard you worked on getting or making the product, or in offering the service, except in your willingness to let it go and do the work at the market price. If your needs as a producer cannot be met at that price, then there is no sale, you take your wares and go home. You cannot force the consumer to pay more for your labor.⁴

So, does the rain forest analogy still stand up? I believe it does.

In the forest canopy, not all carbohydrates are created equal. Some plants put intense effort into creating fruits with interesting flavors and high sugar content, which then attract birds and animals that will eat the fruit, consume the seeds, and spread them far and wide. On the other hand, some plants don’t taste very good and will only be eaten in extreme need or by voracious and unpicky eaters.⁵ But the effort the plant puts into manufacturing the flavorful sugar is not the driver of the transaction; the bird or animal must be genuinely attracted. The value placed upon the carbohydrate comes from the consumer, not the producer. And in fashion similar to a free market, if it’s been a good year, with much sun and rain bringing forth lots of berries, the birds will be picky about which ones they eat, taking only the fattest and juiciest. If it’s been a poor year, they will eat even the smallest, most shriveled fruits. Value is related to scarcity as much as to taste, but still not to the production cost.

Value, utility, and necessity—like beauty—are in the eye of the beholder and consumer. And this is so in terms of both the ecology and the economy.

1. See The Economy as an Ecology from November 14, 2011.

2. I once met a man who had spent twenty years writing an epic poem about the Spanish conquest of Latin America. It was 700 pages of iambic quadrameter rhyming couplets. “For they had come upon this shore/To see what fate had put in store.” All those years of labor had not made his great poem either readable or publishable.

3. “Fungible” is a fancy word for “all the same and nothing to choose from.” When a commodity or service is fungible, you don’t care which quart of oil out of a barrel, peck of wheat out of a bushel, kilowatthour out of a generator—or fry cook at McDonald’s out of a low-skill labor force—you get in the transaction. One’s as good as another.

4. Well, not at the point of sale anyway. Of course, producers can work on people’s needs, wants, and desires through their belief systems. This is branding, and it can make a Louis Vuitton handbag worth, not just a few dollars but hundreds or thousands more than a bag of similar capacity made with similar materials. The same goes for cars and other luxury goods, and even for products as ephemeral as food prepared by a famous chef or at a popular restaurant. But the underlying quality must still exist in some measure. If a Louis Vuitton handbag had sloppy seams and smelled like rotting fish, it still wouldn’t sell.

5. Like the deer in your garden.

Fun with (Negative) Numbers

Disclaimer: In high school I took math up through algebra and geometry, thereby missing trigonometry, analytical geometry, and calculus. I’m an English major by training and predilection, not a mathematician. I was, however, trained in logic and remain fiercely loyal to clear and open reasoning. Over the years I have worked as a technical writer alongside engineers and scientists, as well as written novels of “hard” science fiction—all of which required me to go back and learn mathematical principles and gain some facility with manipulating numbers. I just don’t always like them very much.¹

Mathematics is an intellectual exercise, carried out in the human brain. It is a species of logical reasoning. While we all subscribe to the belief—at least since the Greeks of ancient times, and more recently with the Enlightenment of the 17th century and beyond—that the universe and the physical world around us are defined and best described by mathematics, this remains a matter of conviction and belief. It is based on the fact that mathematics is the dominant way in which we have come to perceive and study this part of reality. Because math has worked in describing many of the phenomena that we can see, we now believe it’s the best way. Still, that does not preclude some other means of achieving a deeper understanding.

Just as it’s possible to write nonsense in perfectly grammatical English sentences, it is possible to write equations with perfectly valid mathematical operations that do not represent actual relationships. For example, I can represent the speed of an automobile in miles traveled per hour, and the rate of my metabolism in calories burned per hour. I can then equate the hours and compare calories burned per miles traveled. That doesn’t mean the one has anything to do with the other.

That’s a ludicrous example, of course. It’s logical inconsistency would be obvious to a child. But many scientific calculations—especially those in modern physics—extend to dozens if not hundreds of computations involving abstractions that are supposed to reference real situations. The logic is not always easy to follow and check. Great minds may work over these calculations and agree about what’s going on. But logical fallacies and incautious comparisons are sometimes difficult to trace and discover at this level of theorizing. Many great minds may take the same wrong turn together and follow each other out the window.²

One obvious rip in the fabric of mathematical logic that makes me uneasy has to do with the extension of the number system into both positive and negative territory. There it becomes difficult to keep track of the difference between what’s mathematically possible and what’s going on in the real world.

By the laws of mathematics, you can add or subtract positive and negative numbers to get a positive or negative result. So, if I start with five apples and subtract two apples (i.e., add -2 apples), I have three apples. Or, if I start with five apples and subtract seven apples (i.e., add -7 apples), I end up with two apples less than none. Weird but logical. In this case, I owe somebody—probably the person who took all seven apples—two more apples than I started with.

Of course, without positing some such obligation as “I owe you two apples,” the negatives of a real object are difficult to identify. One cannot point to the space where two apples might exist and say “there are -2 apples.” You can’t point to holes in the air to find missing quantities. Of course, you can imagine an apple crate or some other framework with two empty slots and say “those empty holes are where two more apples would probably fit.” That’s somewhat like working with a negative number. But without such a framework or crate, the whole remains abstract. “See the two apples that I just don’t have!”

But when it comes to multiplication and division, the result is not even so intuitive. The rule says that when multiplying or dividing numbers of the same sign (i.e., +2 times +2, or -2 times -2), the result is always positive. But when multiplying or dividing numbers of different signs (i.e., +2 times -2), the result is always negative. This may make a tidy rule and easy for a mathematician to remember, but what does it have to do with representations in the real world? Multiplying or dividing with negatives does not seem to have any corollary with what you can do with physical objects.³

This leads to problems within the intellectual structure of mathematics itself.

Take, for example, “imaginary numbers.” These are numbers whose square root (i.e., the number multiplied by itself) is a negative number. So, by the above rules, the square of -5 is easy to understand: -5 times -5 equals +25, just as +5 times +5 equals +25. But while we can imagine that a negative number like -25 might have a square root (i.e., the number which, multiplied by itself, equals -25) we can’t validly calculate it, because the only way to get -25 as a square is to multiply +5 times -5—which is not multiplying the same number by itself. The square root of +25 is may be either +5 or -5, but the square root of -25 is, according to the laws of mathematics, gibberish.

But let’s close our eyes to the mystery of imaginary numbers. Back to just dealing with positives and negatives …

What becomes nonsense with apples makes perfect sense in the relationship of apples or money to the activities that we call commerce and finance. If you have contracted to sell me five apples and yet have only produced three apples, I will take your three apples and agree that you owe me, sometime in the future, a further two apples. You have acquired an obligation to provide me with more two apples. These are not apple-holes-in-the-air but apples-yet-to-be-produced.

The notion that two apples exist to be provided is an intellectual construct. You may obtain the apples which you owe me through purchase from another apple supplier, or we may agree to discharge your debt through payment of money. But the transaction is carried in our heads and communicated through our speech and perhaps in written form. Negative apples do not exist in the real world. If you obtain them from a supplier, he still has to grow and make them real before they can be traded.

In similar fashion, we can make a difficult fit of negative numbers to notions of time. Suppose that at one o’clock you promise to deliver something to me by a deadline of two o’clock—or one hour’s time into the future. I wait. You do not arrive on time. And then you show up at 2:15—or 15 minutes after the deadline. I can say, “You should have been here 15 minutes ago.” That’s a perfectly valid grammatical construct. It’s also valid mathematically: 2 hours 15 minutes plus -15 minutes equals 2 hours. But the concept of “15 minutes ago” is physically impossible. You cannot take back those minutes and arrive on time.

Our experience of time, like our experience of physical apples, only works with positive numbers. We can play with negative time as an intellectual exercise and as a form of reproach,⁴ just as we can contract for a debt of apples-to-be-delivered. But we cannot directly experience either.

This is why I am leery about much of today’s physics, which is so heavily dependent upon mathematics. In particular, string theory seems to be based entirely on mathematical reasoning absent concrete observations.

Quantum mechanics may find a mathematical relationship between a proposed particle like the Higgs boson—which is too heavy to exist in our spacetime and may only ever have existed at some micro-instant following the Big Bang—and the proposed field conditions which this boson would generate, were it to exist. Without the Higgs, all the other particles in the Standard Model of quarks, leptons, gluons, and the rest would not have mass, and so the measurable quantity—although indefinable quality—of gravity would not exist in the universe. I’m still trying to wrap my head around a field that exists in nature without an actual particle being present to create it. It sounds like experiencing electric or magnetic fields without the actuality of a moving photon. Would just the possibility of the photon create a measurable field? I think not.⁵

String theorists have an elegant proposition all worked out, where every particle we can see and measure in the Standard Model is actually a tiny bit of energy, drawn out in a tiny loop like a bit of … string vibrating at a particular wavelength. This doesn’t actually work in the three dimensions which we can actually see and experience: x, y, and z, or “side-to-side,” “up-and-down,” and “in-and-out.” But if you propose a universe infested with a kind of spacetime that adds eight more dimensions at microscopic levels which we can’t see or detect, it all works out fine. Uh-huh.

These theories are all valid mathematically. For the rest of us, to whom the proposed situation makes no sense, or who suspect a possibly missing step that might hide a logical trap, we are told that’s just because we don’t understand the mathematics involved. But, for my money, it’s also possible that the tightly knit community of particle physicists is spinning a shared fantasy of elegant, complex equations that just might be equating calories burned to miles traveled.

I’m not anti-science. I love science. I believe that the scientific method and scientific reasoning have given us a quality of life and an outlook on reality that have never before been shared by human beings. But that doesn’t mean I automatically accept whatever a scientist says. And when what a group of scientists says seems to defy logic and common sense, or violate observed reality somewhere else, I become cautious.

Science and mathematics are still human endeavors. Even when pursued with the most fine-grained instruments and powerful computers, I remember also that these machines are still products of the human mind. While two heads may be better than one, people in pairs and groups are still susceptible to hopes, dreams, illusions, misinterpretations, and stubborn folies à deux—and sometimes folies à plus.

I want to see test results that can be shown concretely, without invoking negative apples and holes in the air.

1. For two similar entries on this theme, see: Fun With Numbers (I) and Fun With Numbers (II) from 2010.

2. In this context, I’m drawn back to Stephen Hawking’s explanation about why the universe does not abound in micro black holes. See If You Can Believe … from February 17, 2013.

3. For that matter, multiplication and division appear to be simple shorthand techniques applied to addition and subtraction. If I want to give each of three people five apples apiece, I can add five apples three times, or I can simply multiply five times three. Similarly, if I want to determine how many apples each of three people gets when I have fifteen apples and want to distribute them fairly, I can divide fifteen by three.
       Signs and negative numbers don’t seem to come into it, except in the abstract sense that 15 actual apples divided among three people who aren’t there would be -5 apples, while giving five apples that don’t exist to each of three living people is likewise -15 apples. Somewhere apples are owed that do not exist, and so the debt is canceled.
       That’s a case of multiplying or dividing a negative by a positive. But the rule doesn’t make any more sense when multiplying or dividing a negative by a negative. If two people less than nobody each take three apples less than none, the mathematical result becomes six real, positive apples. Huh? Is that like the double negative in English, where “I won’t never go to the store again” grammatically comes out meaning “I will always go to the store”? But, of course, the ungrammatical person using the double negative still means “no, not ever.”

4. Of course, we can’t even deal with positive expressions of time except in our imagination. I might imagine that I will be somewhere else in the next two hours, but until those hours pass and that instant of time becomes my reality, it’s all just make-believe. This is why I classify science fiction novels involving time travel, including my own recent The Children of Possibility, as a kind of science fantasy. Fascinating to think about, impossible to do.

5. Oh, yes. The people at CERN’s Large Hadron Collider just “discovered” the Higgs boson. From what I understand, they did no such thing. They smashed together two protons moving near the speed of light and got a flash of energy and detected a shower of particles. They traced back the decay lines of at least two of those particles to a common origin—which means they started out as something much bigger that briefly appeared and immediately disintegrated—and came up with a mass of ~125 GeV (billion electron volts), which correlates to the theoretically proposed mass of the Higgs. Clearly, they did this more than once and came up with answers each time that satisfied everyone all around. But that’s not like they put the thing in a bottle.