The Left Brain Speaks, the Right Brain Laughs Page 13

  You touch the stem carefully to avoid the thorns.

  The pattern of “rose-ness” brings together sights, scents, and anticipation of tactile pleasure and displeasure, all activated by a higher-order concept of successful business practices that triggered the “stop and smell the roses” cliché.

  As you pluck the rose, you lean forward and inhale the pleasing scent.

  More binding; all those concepts come together and your entire being knows what to do. Then, as you walk away, you start humming Poison’s “Every Rose Has Its Thorn” and think that your boss may be a thorn, but the paychecks are on time, there’s a nice coffeemaker, and after a few boring meetings, you’ll get a chance to dig into a project that challenges and appeals to you. Now your inner Buddha blasts a message to your hippocampus: “See? Aren’t you glad you stopped to appreciate a little part of the universe? You feel better now, don’t you? And why? Because of me. That’s right, I scored. Stash that away.” Hopefully, the voice of your narcissistic Buddha remains below your conscious boiling point.

  Six days later, you decide to plant a rose garden and can’t remember why.

  Binding is gnarly.

  6.2.2 Reduction of the inconceivable

  Reductionism gets a bad rap because it seems kind of stupid. Why would you take a big, complicated, interrelated system and break it into pieces instead of trying to appreciate the whole thing at once? Because we’re kind of stupid.

  To keep more than one concept handy, we have to pay attention. The word “pay” indicates that it costs something. Attention puts intent, interest, motive, and instinct to work. Since you can only focus on a given kernel of thought for about half a second, and since you can only perform a single operation at a time, when you try to make sense out of complicated situations, you should cut yourself some slack.

  To understand something complicated, we have to break it down and reduce it to its constituents. Then, if we can make sense of the pieces, we have a fighting chance of understanding the whole.

  Let’s build something inconceivable from something simple.

  Stick out a finger, any finger. Okay, even that one, I’m not offended.

  That one finger is one dimension; now stick out your thumb. The space between your finger and thumb, but not above or below, just between, defines two spatial dimensions, a surface. With that finger and your thumb sticking out, curl your other fingers against your palm. They’re in the third spatial dimension. Forward-backward, side-to-side, up-down: three-dimensions.

  You can draw any one-dimensional object. You’re like the Renoir of one-dimensional art. Me too; check out my one-dimensional drawing (figure 14). One spatial dimension is a line. It doesn’t have to be a straight line, but it can’t have any width or thickness, just length.

  Drawing or thinking in one dimension is so easy that it’s hardly worth the bother.

  I try it again in two dimensions (figure 15), advancing an entire order of complexity. While my one-dimensional art is flawless, my two-dimensional art is, well, flawed. Still, even when masters paint, they do so one brushstroke at a time. We conceive great works in all their multidimensional greatness, but when we put them together, whether the act is physical or conceptual, we do so one piece at a time.

  Figure 14: Ransom’s one-dimensional drawing of (a) a bridge over a pond with lily pads (Monet has nothing on me in one dimension), (b) the Moanin’ Liza.

  Figure 15: Ransom’s two-dimensional drawing of (a) a bridge over a pond with lily pads (Monet has something on me in two dimensions), (b) the Moanin’ Liza.

  I can draw a few things in three dimensions. Physicist training includes lots of calculations involving spinning tops (figure 16). Sure, it’s difficult to portray three spatial dimensions on two-dimensional paper, but it’s harder to sculpt something out of three-dimensional rock—even though it’s done one chip at a time.

  Figure 16: A spinning top in three dimensions, including a coordinate system, because I’m the kind of guy who includes coordinate systems.

  The point of this silliness is to convey that the inconceivable can be conceived, and that reduction helps. While it is merely difficult to advance from one dimension to two dimensions to three dimensions, it is impossible to visualize something in four dimensions. Yes, I defy you.

  The coordinate system that I couldn’t resist including in my three-dimensional drawing shows a line in one dimension, two perpendicular lines in two dimensions, and three perpendicular lines in three dimensions; so a fourth spatial dimension requires a new line perpendicular to the three axes. Since we live in a three-dimensional world, there’s nowhere to put that fourth perpendicular line; we’ve used up all the perpendicularity available.

  Say you’re out on a sunny day, walking around town and looking fine. You see your shadow on the sidewalk. Your three-dimensional self casts a two-dimensional shadow. You could reconstruct your three-dimensional shape by twirling around and looking at your shadow from many different angles. Similarly, we can imagine how a four-dimensional object would cast a three-dimensional shadow, but I can’t visualize a four-dimensional shape by looking at a bunch of three-dimensional shadows, and neither can you.

  We hit a dead end. Four spatial dimensions are, literally, out of our scope.

  Try to think of nothing; not empty space, nothing. Nothing is a not-place where there are zero dimensions, nowhere to stick out any fingers or imagine lines; nothing, not even space or time. Call me when you sort that out.

  It’s simple enough to write down “nothing” or “four dimensions” and talk about them, but when it comes down to trying to picture them or develop a feel for them, it’s just too hard. We don’t have the wetware required to process that kind of information.

  On the other hand, it’s barely more difficult to do mathematics in four dimensions or five dimensions, or even infinite dimensions, than it is in three dimensions.

  Reducing systems to their simplest components makes it possible to figure them out—how they work, where they fit, what they do— even if we can’t wrap our brains around the whole concept. The magic happens when we start out totally clueless, reduce the system to components, build it back up, and walk away understanding the whole thing.

  Humans come equipped to learn a vast array of skills; the further those skills are from what cave people required for survival, the more difficult they are to acquire. We need tools.

  6.2.3 Words

  Language began with thoughts dying to be articulated. Words emerged as sounds, and then the sounds were mapped into symbols and writing was born. Apparently sounds weren’t in such a hurry to be transcribed, since writing came at least a few hundred millennia later.

  Languages have structure. Some are well ordered and others are quite messy. The structures vary across cultures. All spoken languages use inflection and pitch for emphasis. Tonal languages, including many African and Asian languages, like Mandarin Chinese, implement grammatical rules through use of pitch. Different languages use different combinations of rules and tones for syntax. At one end of the spectrum, if you’re willing to think of software programming languages as languages, like Python or C, tone has no role at all. Sicilian-style Italian sits closer to the middle; it has grammatical rules, but hand gestures and inflections alter meanings.

  In every case, nouns, verbs, adjectives, etc. combine to provide a structure, but perfectly good sentences can be composed that have no meaning. I composed the following sentence using a random number generator and a dictionary with the requirement that it follow the English structure: noun-verb-adjective-noun.

  “Hypocrisy chokes boding trailblazers.”

  There are two reasons that you can dig meaning out of this sentence: First, you’re a pattern-detector and, if you look hard enough, you’ll find patterns whether they exist or not. Second, you’re a metaphor-forager, a meta-forager.

  Consider what that sentence means.

  Done? Okay, my turn. Trailblazers don’t follow the paths of others; they carve their ow
n paths. A boding trailblazer must be one who is closing in on something. But a hypocritical trailblazer claims to carve his own path while actually striding in the well-worn steps of others. And so it is that hypocrisy trips up the boding genius of a would-be trailblazer. In other words, my pattern-detectors found this meaning in the random sentence: Arrogant people betray their own hypocrisy as soon as they believe in their own omniscience. I bet you didn’t get the same pattern that I did.

  Words and grammar are handled by separate processors. Words are assembled in Broca’s area, in front of and about 4 inches (9–10 cm) from your left ear. Wernicke’s area, behind and above your left ear, applies grammatical syntax. Meaning doesn’t require the help of grammatical rules, but they help. You can see the value of syntax in this classic example of comma importance: “Let’s eat grandma!” versus “Let’s eat, grandma!” Still, if we were sitting around the table, and I neglected to pause at the comma, I doubt you’d stick a fork in grandma.

  The way we convey meaning to others models how we convey it to ourselves. Language provides a tool for thinking that transcends rudimentary association and takes us to ever-higher levels of thought, from associating senses to associating thoughts to abstraction of thoughts and so on, until you end up with a philosophical crisis.

  You abstract things all the time by removing an idea from the situation in which it arose, removing its context. Abstraction is a left-brain process. The right brain hangs onto the context and monitors it for consistency, but it is also perfectly happy to find a new context; and so, abstraction allows us to apply one concept to different situations.

  The ability to abstract an idea transforms the beast, and language abstracts reality into words.

  6.2.4 Mental tools—the power of scratch paper

  Once you have the characters on the page, punctuation is bound to follow. You can picture it, right? There’s one in every group: the bozo who demands rules, who must impose order, who desires authority in the form of periods, commas, and question marks. His name was Full Colon, but it was his daughter, Semi O’Colon, who did all the work.

  If we were to insist on absolute syntax consistency and use the rules of that syntax to manipulate word-like things, we’d invent mathematics.

  Just as letters are abstract symbols for sounds, numbers are abstract symbols for quantities. An interesting thing about numbers: Every culture with a written alphabet transcribes the first three numbers in a way that indicates their value. One is a single mark, two is a pair of horizontal lines connected by a line as though I’m too lazy to lift my pen after drawing the first line, and three is three horizontal lines, again with the laziness, but four—what the hell is that? Similarly for the Romans: I, II, III, IV. Once you have numbers, you might as well rule them by laws.

  We’re people; we need tools to accomplish things. The further we advance, the less our tools look like hammers and screwdrivers and the more they look like, well, nothing. Software is essentially nothing: symbols typed into a computer that are converted into voltage levels and currents by the voltages and currents resulting from other symbols previously provided to a computer. It’s bits and bytes, switches and gates, all the way down.

  Mathematics provides a set of rules and many different ways to manipulate symbols. Arithmetic is at the core, but the list of operations goes on and on. Numbers are one level of abstraction. The operations are an abstraction of grammar, so it’s an abstraction of an abstraction.

  Mathematics allows us to begin with a set of statements, that is, assumptions, and then combine, reorder, permute, hammer, and screw those statements into something new. The new thing rests on the assumptions you started with. When you get good at math, it’s like making sausage: You start with some ingredients (for math, the ingredients are assumptions), you turn the mathematical crank, and out come predictions built purely on those ingredients/assumptions. If your assumptions are valid, then the predictions must be accurate too. Far more fun, though, is the opposite case (the corollary, if you will). If you test your prediction and it’s wrong, then at least one of the things you started with, your ingredients, must also be wrong.

  Figure 17: The mathematical crank.

  The reason that most scientific and technological advances of the last 150 years have sprouted from mathematical or computational analysis is that these tools relieve the human brain of the impossible task of holding many different facts, concepts, and assumptions in consciousness at the same time. Math provides step-by-step methods that allow us to work with one thing at a time—which we’re really good at— while making certain that nothing in the conversation is overlooked or forgotten.

  Okay, I can hear you saying, “Whoa, dude. Math is hard for most people because you have to keep all those operations and rules in your brain at once.”

  And I’m all: “Sure, but once you catch the vibe of symbolic manipulation, you don’t have to be conscious of that part of the process, just like Johnny can play music without thinking about notes, and you can talk without thinking about grammar.” Assembling a complicated system by concentrating on one piece at a time might not be the only way that people can understand huge, messy, impossible-to-holistically (whole-istically, gestalt-istically) comprehend systems like climate, fluid flow, how stars work, the Big Bang, or tax forms, but it has the best record of all the other techniques.

  We got nothing without scratch paper, baby. Scratch paper.

  6.3 LATERAL THOUGHT

  Let’s start this section with an example at the crossing point of analysis and creativity. We’ll then follow the scent and try to figure out what enables great creations.

  In trying to understand how something works or where it’s going or what will happen to it (it can be an atom, a brain, an economy, a piece of oak floating in a glass of scotch, but probably not a tawdry love affair), scientists and mathematicians assemble relationships between the pieces of the system and then try to determine the underlying principles that govern how the pieces fit together. The process amounts to writing down the relationships between components in mathematical sentences called differential equations—sentences in the sense that the symbols are abstractions for words and the relationships are abstractions of grammar. Erwin Schrödinger used this sort of analysis to create quantum mechanics.

  Okay, maybe you’ve never heard of differential equations, maybe you were told that there wouldn’t be any math in this class, but I have an all-important point to make, and DEs are a perfect example (yeah, like everyone else, mathematicians like to use acronyms to make sure no one else knows what they’re talking about, as though “differential equation” would give it away).

  Solving a differential equation amounts to finding the common theme, the trajectory of the system, a single predictive description of how the system it describes behaves through time and space. The problem with differential equations is that they’re notoriously difficult to solve; there is no step-by-step method. Only a few simple classes can be solved by turning the crank, so most of these analyses reach a point that demands pure, raw creativity.

  I bet you’ve been in a class where an instructor performed an example. You follow the example, but it still doesn’t help with the more relevant question: “How did you know to do that?”

  Professor Pedagogue says, “You just have to keep trying different things—sometimes you have to pull a rabbit out of your hat—until you find something that works.”

  In this context, trying something is sort of like trying different ingredients in a recipe. If it tastes good, it works. If it solves the differential equation, it works, and how you found the solution doesn’t matter. Practice teaches you what things go together, where to look for the rabbit in your hat.

  But what if you have a recipe that simply doesn’t work? This is the situation at the edge of scientific discovery: a known situation without a description. General relativity and quantum mechanics have sat at this point for almost a century. Both theories rest on vast legacies of confirmation, but when you
bring the two together, they don’t work. By “don’t work,” I literally mean that putting Einstein’s modification of Newton’s theory of gravity into quantum mechanics doesn’t add up; you get absurd predictions.

  Trying different things means letting more ideas boil up. As new ideas surface, your top-down consciousness sends instructions to your parallel processors telling them what to look for. Trying different things calls on your right brain to look far and wide, to figuratively see something that’s not right in front of you, where your left brain is focused, trying different contexts, different scenarios, and taking pieces from way over there and trying them over here—combining lateral thoughts.

  Where do we find the missing piece?

  Where does the magic bullet of an idea—the coherent concept that unites a bunch of facts, the missing piece to a plot, the riff that joins the melody and lyrics, the rhythm that conveys the right feeling to a poem, the perfect metaphor to illustrate lateral thought—come from?

  Sometimes we find what we’re looking for where we look for it, that is, through analysis, that concerted, focused, figurative banging of one’s head against a pile of thoughts hoping to find the missing piece of the puzzle. The problem with analysis by head-banging is that feeding data into the same set of nearby circuits usually leads to the same or similar results over and over again. Genuine insight usually occurs when we turn away from a problem, take a shower, walk through a forest, or even sit at a bar.

  Just as the river carves a canyon to find its way to the sea, we search for new ideas along the paths, tributaries, brooks, and creeks where we found old ideas. But what started out as a trickle has formed a rut, an efficient rut, to be sure, but when we get set in our ways, we have to scale the canyon walls to look across the horizon for a better way, a new idea.

  When you walk away from a problem and do something else, the details and data unbind from your consciousness, but they don’t go away. Your bottom-up parallel processors remain tuned in to the task and keep plugging away without interference from your top-down autocrat. The context-seekers in your right brain propose increasingly different, weirder, wider contexts, anything to string the pieces together as the less sophisticated, less certain, less critical, lower-paid unconscious processors in both hemispheres bring a broad range of associations to bear. You cast a wider neural net that accesses patterns far from the narrow focus of conscious analysis, off the by-now thoroughly beaten path.