What are words?
These black symbols that you’re staring at right now all carry invisible, untouchable, silent meaning. We can translate this meaning through many other patterns, such as español, русский, 中文, العربية, or 01110111 01101111 01110010 01100100 01110011. Or we can translate it into a pattern of sound waves in the air—such as if you read this sentence out loud—or into a pattern of Braille bumps for the blind. Or we can translate it into binary bumps on a DVD, and then use a DVD player to translate it back into sound waves or light waves. Indeed, we can translate it through an unlimited variety of media. But what exactly is that “it” that we are we translating? In all cases, even if we can understand what the words mean, we do not have the slightest clue what the words are.
This same mystery engulfs any and all forms of information. Whether we are talking about semantic information, biological information, quantum information, geological information, etc., scientists remain absolutely stumped as to what it actually is. Although some of our most cherished scientific discoveries—such as those regarding DNA replication, entropy, and quantum mechanics—are all about the flow of data in nature, the nature of that data that we comprehend remains, as Einstein put it, “the eternal mystery of the universe.”
In fact, today, no one even tries to answer the question. In his book, Programming the Universe, MIT physics professor Seth Lloyd tells how he begins his graduate course on information by teasing his twenty-odd students with the question, “What is information?” None of them say a word. He says that although his students can talk all day about how to use information and what a bit of information means, none of them even speculates as to what a bit of information is.
What do my students’ answers, or lack thereof, reveal? That it is far easier to measure a quantity of information than to say what information is. And more broadly, “How much?” is frequently an easier question to answer than “What is . . . ?”[i]
Curiously, Lloyd himself doesn’t try to answer the question either. Nor does Dr. Hans Christian von Baeyer, a professor of physics at the College of William and Mary, in his book titled Information: The New Language of Science (2003). Nor do the authors of a 423-page textbook titled Information Science published in 2006 by Princeton University. Nor does Michio Kaku, a theoretical physics professor at the City College and City University of New York, in his 436-page book The Future of the Mind (2014), in which he says that someday our minds could be downloaded (i.e. as information) into a computer. Nor does Caltech physics professor Sean Carroll in his 480-page book titled The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (2016). The list goes on and on of scientists who avoid the question altogether. It’s a deafening silence.
Yet if we do ask the question we learn a stunning, mesmerizing, glorious fact. Although we don’t know what information is, we do know what it is not: it is not physical. The meaning conveyed by these symbols has no tangible qualities—nothing that can be directly or indirectly seen, heard, felt, tasted or smelled. As John Barrow, professor of mathematical sciences at The University of Cambridge, put it:
A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention except in rather esoterically refined circles: that at the root of the success of 20th century science there lies a deeply “religious” belief—a belief in an unseen and perfect transcendental world that controls us in an unexplained way, yet upon which we seem to exert no influence whatsoever.[ii]
That was nearly 30 years ago. Since then, the establishment has all but swept the mystery under the rug, only occasionally teasing students about it.
So let’s bring it back out in the open and take another look at it. We’ll simply start with this objective, testable, falsifiable, mind-warping scientific fact: the meaning conveyed by these sentences and paragraphs is immaterial, and the same is true for any and all information that we encounter elsewhere in the world, regardless of how subjective or objective the interpretation of that information is, and regardless of how well we are able to understand it. Whether it is the objective information conveyed by the nucleic acid bumps on a DNA molecule (which I personally cannot translate at all), or the objective information carried by stellar light waves (which I only have a vague understanding of), or the both objective and subjective information carried in a wireless download of the Les Misérables song “J’avais rêvé d’une autre vie” (which I can certainly enjoy even though I don’t speak French)—all the information carried by those various media is likewise nonphysical.
But if information is nonphysical, what about the authors of information and the perceivers of information? Could the you that is using your physical brain to process nonphysical information be just as nonphysical as is information itself? That would be a radical conclusion, wouldn’t it? We would be acknowledging that we are acutely aware of an immaterial reality because we ourselves are immaterial—that we have nonphysical/immaterial “souls”. We might realize that there are truly good, rational reasons that 95 percent of the people on the planet embrace some form of classical spirituality. We might even find ourselves agreeing with King David when he said, “The fool has said in his heart, ‘There is no God.'” (Psalm 14:1)
But can we really prove that any and all information is nonphysical? Yes, we can. On the one hand, it might be hard to grasp because it is so incredibly basic. It’s as easy to take for granted as is breathing. To conclude that we’re surrounded by immaterial meaning will be like concluding that fish are surrounded by water.
On the other hand, you’re probably not going to believe it until you see it for yourself. So let’s just take it a step at a time.
This will be a blast.
What Words Are Not
Part of what makes this discussion so tricky is that the question “What are words?” is itself nothing but words. As will be the answer. So where do we begin? Let’s begin with specific, limited, measurable examples of words and information. I’ll give you three examples—a simple one (the word circle), a complex one (The Lord of the Rings movies), and a profound one (a sentence called photosynthesis). I’m using the concept of words here as broadly and exhaustively as possible, such that even a DVD of The Lord of the Rings can be read as a series of the words one and zero (i.e. binary computer language written by rational, creative computer programmers). Although we use computers to translate all that cinematic information that we could not otherwise comprehend, that is no different from using a telescope to see a lot of astronomical information that we could not otherwise see.
EXAMPLE #1: THE WORD CIRCLE
What physical properties do circles have? Are they liquid (such as the ripples in a pond), solid (such as the rings of Saturn), gas (such as smoke rings), or pure light (such as a rainbow)? You can’t say that they are all four at once. Do they have any texture at all? Do they have a particular sound—“circle”, “Kreis”, “κύκλος”, “圈”, or “دائرة”? Do they have any chemical properties? Do they have any force or effect on anything? No, of course not. They have no material properties at all. The circle is an expression of pure meaning that can be translated into any language through an uncountable number of media—as a lead drawing on paper, as circuits in a pen drive, etc.
Now we might usually think of circles when they are translated as geometric shapes, and that’s how we first teach them to children. However, when we use them—and we use them constantly (all the time!) in our technology—we most often translate them as algebraic equations. (The equation of the circle is (x – a)2 + (y – b)2 = r2.) It’s safe to say that without trigonometry, which depends upon π (3.14…), we would have no smart phones, no airplanes, no slushy machines…nothing, at least, which requires a transistor. Furthermore, all of our architecture would be small and clumsy. Although we actually have hundreds of ways of finding π, the simplest and easiest to understand is by drawing a circle on paper and then dividing its circumference by its diameter. But do either the geometric shape or the number π have any physical qualities? Are they composed of lead (from a pencil) or granite (such as in an engraving) or oil paint (such as a Picasso)?
No, of course not. In all cases—regardless of the media and regardless of whether it is translated as a drawing or as an equation—the meaning of the word circle is nonphysical. It cannot be directly or indirectly seen, heard, felt, tasted, or smelled; it can only be comprehended, translated, and used. That might sound a bit silly, so again I will remind you that a video camera cannot see the meaning of a circle any more than a book or a smartphone can understand the algebraic equation of a circle, any more than an abacus understands arithmetic. So why are we, intelligent creatures, able to perceive the meaning of geometric shapes and algebraic equations and trigonometric functions and such? Perhaps intelligence is just as immaterial as is the word circle and the word π and the equation that reads, “The squared difference of variable A from variable X, plus the squared difference of variable B from variable Y, equals variable R squared.”
We know of uncountable other sentences that use words like circle and π. For example, in polls mathematicians always agree that the most beautiful sentence in the world is an equation called Euler’s Identity. It’s discoverer, Swiss mathematician Leonhard Euler (1707-1783), even had it put on his tombstone. It goes like this, “The base of the natural logarithm, raised to the product of π and the imaginary unit, plus one equals zero” (eiπ + 1 = 0). It contains two natural constants, which are numbers that appear everywhere in nature. One of these natural constants is π (3.14…), and the other one is the natural logarithm e (2.71…). A third number, i (the imaginary unit), is the square root of negative one. Mathematicians used to think that the imaginary unit was just a very interesting mathematical enigma, but early in the 20th century physicists discovered that it is woven tightly into quantum mechanics.
Again, scientists and mathematicians discovered these words and sentences, just as if a child found a trigonometry textbook sitting on a shelf—a book available to be read, translated (into English or العربية, etc.) and used to design things like bridges and boats and tractors. Just as we don’t create the iron that we use to build boats and tractors, but instead we discover iron ore and then use it creatively, so also we don’t create the math we use to design things but instead we discover the math and then use it creatively.
The point is that if these words and sentences are objective, then that confirms that they are immaterial. By contrast, if they were something that only existed in our heads, then they would be composed of neurons or some other kind of gray matter. But unlike our physical tools—our cranes and our tractors and our hands and our brains—numbers and equations have no tangible traits at all. Hammers and tractors and brains have lots of physical qualities; circles and triangles and numbers do not. We can feel a hammer as we use it to build, but we cannot feel a trigonometric function as we use it to create the plans for a building. We can measure the force of a tractor as we use it to dig the foundation of a house, but we cannot measure any physical qualities in the trigonometric equations that we use it to build that same house. They are nonphysical.
Are we sure about that? Maybe we’re confusing ourselves. Let’s consider a much larger, more complex bundle of information.
EXAMPLE #2: THE LORD OF THE RINGS MOVIES
We can buy the Lord of the Rings DVD boxed set on Amazon for about $10. Or we can download it wirelessly from iTunes for about $30. In either case we can also save them onto a flash drive. So we have a number of ways to bring the movies into the comfort of homes, where we can enjoy them as light waves soaring from a screen and sound waves flying out of speakers. We can translate the movies as:
- DVDs (plastic discs with dents and bumps on them)
- A wireless stream (electromagnetic waves)
- A flash drive (magnetized alloy)
We could find more ways to record them. We could actually translate the electromagnetic waves onto paper as binary—a series of ones and zeros. Now that would fill an entire library’s worth of books and probably take a few hundred lifetimes to learn to read. (Just as we build cranes in order to lift things that we could not otherwise lift, so also we build computers to read things that we could not otherwise read.) But the point is that we can use a variety of media to transport the movie.
Now just look at DVDs: the movie really is there, right? For example, consider what would happen if aliens from across the galaxy bought the DVDs but forgot to buy a DVD player. Theoretically, if they worked at it long enough, they would eventually be able to translate them—especially if they had some idea what the final product was supposed to look like—a layer at a time. They would start by decompressing the binary patterns—one layer. Then they would translate these into patterns of light waves and sound waves—a cinematic layer. Then they would start the process all over, working to translate the dialogue—another, completely different layer. Of course there are so many subtleties of cultural context to the movies (such as J.R.R. Tolkien’s Christian faith, the historical context of World War I, etc.) that they could never be perfectly translated, and trying to do so would be about as realistic and useful as trying to dig a perfectly straight, perfectly round tunnel from one side of Pluto, through its core, to the other side. But the aliens could eventually get the gist of the movies.
The point is that the information is there on the DVDs, objectively, for intelligent minds to perceive. It doesn’t have to be aliens. Myself, I don’t actually believe there are any aliens in the universe. After all, statistically speaking, if there were intelligent extraterrestrial life then we definitely know it by now. So forget the aliens! I’m just illustrating the fact that each of those three media can contain the entire movie—the colors, the dialogue, the CGI, everything. All of the data is there, like a book sitting on a shelf waiting to be read. The entire cinematic trilogy—the drama, the plot, the characters, the battle scenes, etc.—is on those DVDs. It’s also in the electromagnetic waves. And it’s also in the flash drive. Each of the media contains the entire movie trilogy. If you buried the flash drive in a time capsule and people dug it up a thousand years later, they could enjoy the exact same movies.
And that is an astronomically profound fact.
The reason it is an astronomically profound fact is that even though those three media have exactly the same information in common (i.e. The Lord of the Rings movies), they do not need to have any physical qualities in common. The DVDs, for example, do not need to have any physical qualities in common with the electromagnetic waves. Therefore, whatever those three media do all have in common—the movies—has no physical qualities. That is why we cannot see or hear the movie even though it is there on those DVDs.
Instead, we can only translate it. What are we translating? Pure, nonphysical meaning.
“What?! Wait a second here. You’re telling me that the movies are, literally, nonphysical?” Yes. Consider this: If you’re sitting on the couch watching the movie, and you have a movie camera next to you recording those same light and sound waves, is it comprehending the movie? Can it perceive the drama any better than a paperback book can perceive the plot? Of course not. For what we are perceiving through our eyes and ears is something that no camera can see, something that no recording device can hear, something that no DVD player or computer or robot can understand.
For one thing, we are perceiving the translation of a dramatic story with characters and themes, etc.—things that first began as black symbols on paper (i.e. Tolkien’s original trilogy) but have now been recast through lights and sounds and faces. To say that all of this drama and artistic expression is immaterial might be similar to saying that intelligence, creativity, and morality are immaterial.
But there’s more to it than that, and what is particularly hard to digest—similar, perhaps, to how a tenth-century farmer might have had trouble digesting heliocentrism—is to realize that in addition to the drama, all the rest of the movie’s information is likewise nonphysical. The colors, the music, the facial expressions—all of that is, literally, immaterial. (Just keep reminding yourself that this conclusion could be related to the notion that consciousness itself might be immaterial.) One form of media for carrying that information is through light waves and sound waves in a movie theater. Other forms are electromagnetic waves, DVDs, etc. Thus, for example, when you see the blueness of Gandalf’s hat, that information is just as nonphysical as the gentleness of Gandalf’s character. After all, does the movie camera next to you on the couch have the slightest clue what blueness is, any more than it knows what gentility is? Does the camera comprehend color blue any more than an English book comprehends the word blue or a DVD player comprehends 01100010 01101100 01110101 01100101? The meaning of that word is just as immaterial as the meaning of the drama in the movies, yet for some eternally mysterious reason, we humans can comprehend all of those forms of communication. When we see Gandalf’s blue hat on the TV screen, the blue light waves that our minds translate into meaning (again, something no movie camera or computer can do) are just one of many ways to convey that meaning. Another way to translate it is by reading in the book, “He wore a tall pointed blue hat, a long grey cloak, and a silver scarf.” Of course, as every parent knows, it takes much more creative muscle for a child to read the book than to stare at a screen.
Presumably, this information is also recorded—temporarily at least—as a pattern of neurons in our brains. We could simply add that to the list of media:
- DVDs (plastic discs with dents and bumps on them)
- A wireless stream (electromagnetic waves)
- A flash drive (magnetized alloy)
- A series of 1’s and 0’s printed on paper
- A clump of organic gray matter (a network of neurons in the brain)
Scientists don’t know much about this yet, but it is clear that we use our brains to store information. Regardless, are we really concluding that the meaning of the word blue is immaterial? Yes. (We’re concluding that the meaning behind any and all media is immaterial.) Of course the easiest way to learn the meaning of words like blue and grey is with a box of crayons, just as the easiest way to learn the meaning of the word circle is to see it drawn on paper. Later, with much study, we can comprehend all of these words written as equations. (See James Maxwell’s equations for light to the right.) Granted, it would be extremely difficult for us to learn the meaning of the words like blue or grey in any other way but seeing it translated through paints or crayons. To learn the meaning without sight might be as difficult as single-handedly digging that tunnel through Pluto, or as difficult as learning to read the binary version of the Lord of the Rings movies—not a printed binary version of the English books but a printed binary version of the movie DVDs. After all, it only takes about 11 and a half hours to watch the DVD’s whereas it would surely take at least ten thousand times that long to read through the binary version of them. But once we do learn the meaning, translation becomes relatively easy.
Let’s put this into perspective. The amount of raw data that we take in through our eyes, through roughly 500 million photons per second, can be truly massive as compared to the amount of data that we can take in through a book. The brain has about 100 billion neurons with at least 100 trillion connecting points or synapses, but that’s just the beginning of it all, according to David Eagleman, an adjunct professor in the department of Psychiatry & Behavioral Sciences at Stanford University. He says it’s not just the neurons that are at work, but also chemical processes and protein changes—“quadrillions of interactions between brain cells every second.”[iii] He says that if we wanted to record a high-resolution architecture of a single human brain, we would need a zettabyte of capacity—the same size as all the digital content on planet earth right now. All that processing power is why, just as we can use our fingers to count to ten and use a calculator to do trigonometry and use laptop to do our taxes, so also we can use our brains to process scads of electromagnetic data—the 500 million photons per second.
It’s also why, after our brains take in about 15 quadrillion photons (i.e. when we’re about 2 years old at 12 hours of photons a day) we can learn to identify the colors of the rainbow. And once we learn the meaning of words like blue and red, we can then learn to translate them through different media—such as through black symbols like BLUE and RED. The wonder of language—which we will explore more when we ask “Where do words occur?”—is that we can compress massive amounts of data (such as the data carried by all those photons) into individual words.
And what is true for something as simple as circles and colors is true for every bit of information in the movie. For example, consider the following quote from Chapter 1, “A Long-Expected Party”, of The Fellowship of the Ring: “The wizard’s face remained grave and attentive, and only a flicker in his deep eyes showed that he was startled and indeed alarmed.”
Eventually, I will argue that the rationality, creativity, and morality required to understand the movie—that all those things are immaterial manifestations of an immaterial soul. But for now, let us stay focused on the observation that the digital information that we are perceiving is immaterial. On the one hand, this proof is exceedingly simple: a variety of media (DVDs, electromagnetic waves, flash drives, pages of 1’s and 0’s, etc.) can have exactly the same information in common without needing to have any physical qualities in common. On the other hand, the proof can be exceedingly hard to digest.
Now you might want to argue that what those three media have in common is the physical human brain. In other words, if we ask, “What do the DVD player, the electromagnetic waves, and the flash drive all have in common?” some people might try to answer, “They have the human brain in common.”
But I would advise you to go back and take another look. It might help to actually put a DVD and a flash drive and a laptop on the table in front of you as you ask, “Are the movies really here on these DVD’s and on this flash drive—the colors, the music, everything?” and, ”What do these different media have in common?” The plastic discs have no organic grey matter on them. (Gross.) And when we shoot the electromagnetic waves across the planet, those waves are not composed of neurons. (Okay, really gross.) So they don’t have brains in common any more than they have livers or lungs in common. Yes, they do all come from human authors. They do all have the same sources. But keep in mind that the word brain is concrete while the words source and author are both abstract. What exactly are sources and authors?
We’ll come back to that later. For now, we want to stick with the examination of raw information. Are we sure that any and all communication has no physical qualities? Well, we might be able to at least conclude that the Lord of the Rings movies have no physical qualities, right? Perhaps that means that when we watch them, we comprehend things that no supercomputer can comprehend. But is the same thing true for any and every bit of information that we perceive in nature?
EXAMPLE #3: A SENTENCE CALLED PHOTOSYNTHESIS
Students begin learning to comprehend photosynthesis in middle school. It is the process by which a plant converts solar energy into chemical energy, and it goes like this: “Six molecules of carbon dioxide plus six molecules of water plus sunlight yields one molecule of sugar and six molecules of oxygen” (6CO2 + 6H2O + sunlight —> C6H1206 + 602). The explanation for that sentences takes up about a chapter in a seventh-grade science textbook. As students grow and learn more about chemistry and biology, the explanation for photosynthesis also grows. We could compare this education to the process of learning that George Washington was the first president of the United States, and then over the years learning more and more of the historical and political context to that fact.
Now students also learn that photosynthesis has been going on for many millions of years. Therefore, a student could ask: “Who wrote my biology textbook? Who wrote, for example, this chapter on photosynthesis? We know that biologists discovered the explanation for photosynthesis and then translated it into English (and Spanish, etc.), but who wrote it? After all, if it was true 10,000 years ago, long before we had a clue about the periodic table, was not the truth of this rational information just sitting there in the plants, available to be comprehended—just as surely as my textbook sits on my desk, available to be comprehended? Who wrote it?!”
That might sound like a philosophical question, but it doesn’t need to be. All we have to do is remember that the instructions for photosynthesis are encoded in every plant’s DNA. And as Rice University Chemistry Professor James Tour explains, the information in the deoxyribonucleic acid code is primary for life, but the medium for that information is secondary, just the medium for our own creative ideas is secondary.
What is the code? Even if you had the nucleic acids and even if you could hook them up, what’s the code?… So I have an idea and then I transcribe this onto a piece of paper, and now its on the paper. And then I type this onto my computer and it goes into DRAM and then when I hit save it goes into flash memory. And then when I upload it to the web, that same information now is going through an RF wave into a box on the wall. And then from that box on the wall its going through a wire to some server farm some place where it goes right back down into transistor-based flash memory. That same information which was [in my brain], in my hand, to the paper, in my computer in several different forms, in an RF wave—same information, different medium. The information is primary. The medium can change all the time.[iv]
So the meaning of the DNA code—and thus of photosynthesis—is primary; the medium for it is secondary. It’s first medium is nucleic acid bumps on DNA molecules, and then as molecular interactions on a plant. Then scientists discovered it and translated it into black symbols on paper for little Susie’s textbook. Thus, to the extent that we know anything at all, we know that the rational, creative explanation for photosynthesis was written long ago and just sat there, like a book on a shelf. Furthermore, we know that the textbooks themselves cannot comprehend the explanations written in them, nor do DVDs or DNA molecules or apple seeds. Only rational, creative minds can comprehend them.
Wait, wait, wait, wait a second, you say: photosynthesis only actually happens in plant leaves and such. When we talk about it in textbooks, we’re only giving students descriptions—very precise, detailed descriptions—of what is happening. But you say that we cannot fully “translate” it into black symbols on paper.
Actually, we can. However, you’re making an excellent point: there is more to this world than just rational information. For example, although we can translate an apple tree’s DNA (including the plan for photosynthesis) into black symbols on paper, and although we can translate all the information about an apple into black symbols, we still cannot not translate the apple itself—the fruit of that DNA—into black symbols on paper, any more than we could translate Rembrandt’s Starry Night to a blind person or translate Beethoven’s Ninth Symphony to a deaf person. The mediums for such expressions expresses more than just coherent patterns.
So…where does that leave us? It leaves us with the realization that rational information is not an end in itself. Just as the sentence “I love you” conveys more than just data—regardless of what medium is used to express it—so also an apple tree might convey more than just rational chemical equations encoded in deoxyribonucleic acid. It might also convey other things like…goodness, beauty, even joy.
Speaking of joy, Beethoven’s Ninth Symphony actually can, technically speaking, be translated into black symbols on paper. In fact, that’s how the author himself first recorded it—when he was almost deaf! But he did that for a greater purpose. He directed an orchestra to translate it from a pattern of black symbols on paper into a pattern of sound waves. But now who has the time or the money to go listen to that?! We need those sound waves translated into bumps on a DVD or into a pattern of electromagnetic waves. So, again, what exactly is being translated from black symbols into sound waves and then into electromagnetic waves? Whatever it is, it is more than just a rational pattern.
Similarly, photosynthesis might be more than just data. Nevertheless, it is rational data, and that data can be translated and used. (Scientists are using artificial photosynthesis to create all kinds of interesting stuff.) Furthermore, to get back to our main point: to the extent that we know that all those rational, creative words and sentences are objective, to that same extent we also know that they immaterial. (Of course we could also say that things like love, beauty, and joy are also immaterial.)
Or perhaps I’m tricking you with some rhetorical sleight-of-hand? (I’m not.) Let’s slow down, step back, and examine this more carefully. We are zeroing in on the rationality that permeates nature. Although these other aspects of life, like beauty and joy, are certainly intriguing, we won’t go there. Instead, we’ll just look at the creative information that precedes them.
What All Information Has in Common
We’ve looked at some magnificent evidence for what information appears not to be—it appears not to be physical—but we still aren’t saying what information actually is. The trouble is that we could just keep begging the question. If we say information is data, then we’ll have to ask what is data. If we say that data is a series of bits, then we’ll have to ask what are bits. Because, again, the question “What is information?” is itself pure information. As will be the answer.
Nevertheless, we still need a coherent way to put everything in context. What do all forms of information have in common?
- Semantic information: language and vocabulary.
- Digital information: flash drives, DVD’s, electromagnetic waves, etc.
- Biological information: DNA (which is actually also digital information).
- Financial information: what businessmen and economists study (Okay, this is also digital.)
- Meteorological information: what weather-forecasters study (…and then digitize!)
- etc., etc., etc.
What all information has in common is that it can be digitized because it forms a mathematical pattern. Now to call a pattern mathematical is redundant, like calling a rainbow colorful. But I want to use that redundancy to help make the point that any and all languages—English, Chinese, C++, Java, etc.—are also mathematical because they form patterns. With languages, we convey meaning through patterns in sound and symbol. Therefore, if we could not do math, then we could not do language, for the two are one-and-the-same.
Consider, for example, two of the key ingredients for language—grammar and vocabulary. Let’s look at how language and mathematics are one-and-the-same phenomenon in regard to these ingredients.
GRAMMAR IS MATHEMATICAL AND MATH IS GRAMMATICAL
Grammar is so mathematical that laptop computers today have excellent editing and translation programs. For we are actually doing simple forms of math when we discriminate between singular and plural; between right and left (as if translating a graph); amongst comparatives and superlatives (for example: “terrible, tolerable, okay, good, very good, excellent” could be roughly translated as, “On a scale of 1 to 7”); amongst past, present, future, future perfect, pluperfect, etc. (simple translations of a timeline); etc., etc., etc.
Going the other direction, a mathematical equation is simply a sentence whose main verb is “equal”. Math is made of up nouns (numbers, shapes, angles, integrals, etc.), verbs (multiply, add, subtract, divide, differentiate, etc.), adjectives (negative, greater than, raised, etc.), adverbs (when, where, etc.), conjunctions (“as x approaches infinity…”), pronouns (variables), prepositions (plus, minus, etc.), etc. This isn’t philosophy, but rather fact: there is nothing more or less to math than grammar rules and vocabulary—rules and vocabulary that a laptop computer can follow translate patterns of English symbols into русский symbols, etc. As a couple of ivy league mathematicians put it:
Changeux: Mathematical language is plainly an authentic language. But is it therefore the only authentic language?
Connes: It is unquestionably the only universal language.[v]
The universal language Professor Connes refers to there is something linguists theorized about for decades. Linguist Noam Chomsky first proposed that all humans have a genetic component in their brains that allows them to communicate according to universal rules (or patterns) which he called a universal grammar. Thus, for example, even though Chinese verbs have no tense—meaning that a Chinese speaker uses the exact same verb form regardless of whether they are expressing past, present, or future action (leading to clumsy translations like “long time no see” 好久不见)—they nevertheless still have very effective ways to communicate a mathematical timeline. After all, bilingual speakers can provide excellent translations between Chinese and English. Okay, so what is the universal grammar or universal pattern that both Chinese and English speakers—and any other language speaker—can understand? As Connes observes, its math.
Now let us consider vocabulary.
VOCABULARY IS MATHEMATICAL AND MATH IS SEMANTICAL
The reason we can use computers (i.e. binary) to store entire libraries is that numbers are nothing more than words. For that matter, just as there are different types of numbers, so also there are the equivalent types of linguistic vocabulary. For example, two primary types of numbers are rational numbers and irrational numbers and these are perfectly synonymous with two primary types of vocabulary—concrete words and abstract words. Rational numbers are the ones that can be fully, concretely represented—at least in theory. Technically speaking, they are numbers that can be written as fractions. You can have 7 apples (or 7/1 apples), 35 and 1/3 pieces of pizza, 10.6578 inches of pipe, etc. Similarly, concrete vocabulary refers to things that can be fully represented—things that can be seen, heard, tasted, smelled, or touched—such as apples, pizzas, and pipes.
By contrast, both irrational numbers and abstract words communicate meaning that cannot be fully represented. Technically speaking, irrational numbers cannot be written as fractions. The most well-known irrational number is π (3.14159…), which goes on infinitely. So although you could have 3.1 pieces of apple pie, and perhaps with the use of a good laboratory scale you could have 3.14 pieces of apple pie, you could never have π pieces of apple pie because you cannot cut the pie with infinite precision (for the same reason that you cannot have an infinitely small piece of apple). Similarly, just as irrational numbers can only be understood/translated and never fully represented, so also the other main type of linguistic vocabulary—abstract words—can only be understood/translated and never be fully imaged. Consider, for example, the abstract word peace. You could have a very peaceful, beautiful island, and yet there could always be room for just a little more peace, just a fraction more unity-in-diversity. You could never have a 100% perfectly peaceful island any more than you could ever have exactly π pieces of apple pie.
All that is to illustrate how numbers are words—nothing more, nothing less.
But it goes much deeper than that, for linguistic vocabulary is dimensional in exactly the same way that math is dimensional (as in three dimensions). Linguistic vocabulary may not often be as precise as mathematical vocabulary, but we can still get an idea of how words nuance each other. Consider, for example, the abstract word freedom. You can’t really begin to define or understand that word unless you also define the word slavery—just like you can’t define the word hot without also defining cold, or up without down, or three without four and five and 500, etc. And just like you can put hot and cold on a number line to define a thermometer, you could also plot freedom and slavery on a number line to show the spectrum of meaning that the words convey.
However, this is just a one-dimensional understanding of freedom, and we still need more context in order to effectively communicate. After all, if you lived in the dark then you wouldn’t have much freedom would you, even if you were not enslaved to someone else. The light of truth and education increases our freedom. So if we want to express ourselves more precisely and clearly, we will need more words. We could start by plotting another number line with knowledge defining one end and ignorance the other:
Now the words freedom and knowledge are not synonyms, nor are the words slavery and ignorance. So these concepts would not run parallel to each other, but instead, intersect each other:
If we want even more clarity, we could add a third line that is defined by the words determinism and randomness.
Again, this line would not run parallel to the line defined by freedom and slavery, for randomness is not a synonym for freedom, nor is determinism a synonym for slavery. Just consider, for example, the laws of gravity. They are textbook examples of determinism, but we would not say that we are slaves to the laws of gravity. Rather than enslaving us, do they not instead free us, so that we can walk around on a planet that orbits the sun? In a similar fashion, traffic laws and police officers don’t inhibit our freedom; instead, they instead provide the order necessary for moving about freely.
So if the freedom/slavery line and the randomness/determinism line don’t run parallel, then we can consider how they intersect one another:
Then we can also consider how the knowledge/ignorance line and the determinism/randomness line intersect one another:
So to get a richer sense of the semantics of how these six words nuance each other’s meaning we could combine them into a 3-dimensional graph, like this:
This isn’t philosophy, but rather semantics. Although these observations might provide fertile ground for a lot of fruitful philosophical discussion, we aren’t doing that here. We are simply observing how words nuance each other in complex, multi-dimensional ways. We are just making observations about how words and sentences work. Although our linguistic semantics are often not as precise and exact as our mathematical semantics, we can nevertheless see how any and all semantics is dimensional. The above six words will nuance each other in a virtually infinite variety of ways, just as the colors red, blue, and green can mix to form an unlimited variety of colors. (By the way, in case you don’t know your physics: even though blue and yellow paint mix to make green paint, it is red and green light waves that mix to form yellow light.) And the purpose of all these illustrations is to show that mathematics and language are one-and-the-same. If we could not do one, then we could not do the other. As mathematician A. Alfred Adler put it:
Mathematics is pure language—the language of science. It is unique among languages in its ability to provide a precise expression for every thought or concept that can be formulated in its terms. (In a spoken language, there exist words, like “happiness”, that defy definition.) It is also an art—the most intellectual and classical of the arts.[vi]
Again, this isn’t philosophy; it’s just semantics. These are just literal facts. Literally. Now, of course, a person doesn’t need to understand any of this in order to be able to use language effectively. Someone could be completely illiterate and not know the difference between a noun and a verb, and yet that same person might be able to communicate more fluently and poetically and with greater mathematical precision than another person who has Ph.D.’s in both mathematics and literature.
Sticking to the Facts
Nevertheless, by this point many people might start giving things philosophical names and then insisting that we’re talking about philosophy. They might start pontificating about your basic epistemologies and ontologies and existentialities, and you’re going to have to beat them back with a stick. Again, as I suggested on the home page, imagine that you’re trying to see the Andromeda Galaxy when they come running up with their flashlights and spotlights. Or, to use another analogy, it may be that the only thing all their philosophizing accomplishes is to fill the room with fog. Instead of clarifying the facts, they might just be mixing the facts with a bunch of speculations about interpretations of pontifications. Yet if we just hone in on the observations and let the facts speak for themselves, the fog will evaporate. We can leave all the interpretations and speculations for some other time.
The facts are:
- Information flows in patterns. Whether it is biological information (such as DNA), semantic information (such as an English dictionary), mathematical information, digital information, chemical data, sheet music, sound waves, light waves, etc., etc., etc.—it all flows in patterns. That’s what any and all information has in common.
- Numbers are simply words. Although there might be more to them than that, there is not less. So we don’t need to say anything else about them. The word “=” is a verb and equations are sentences.
- Since language and math both convey all of their meaning through patterns, language and math go hand in hand. They are one and the same, and we could not do one unless we could also do the other. If semicolons and definite articles and pronouns and verbs are linguistic, then so are the words “multiply” and “divide” and the phrases “carry the one” and “find the slope of the tangent line to the function at a point”. If dictionaries and grammar books are linguistic, then so are trigonometry exams and calculus textbooks.
- Any and all information is immaterial. It has no tangible qualities that we can see, hear, taste, touch, or smell. We can only translate it, but whatever that “it” is that we are translating has no physical qualities.
Those are facts, even self-evident truths. And the implications of them are astonishingly profound. For if language and math are interchangeable, that means that any and all patterns are linguistic. That is to say that any time you find a pattern, you have found meaning that can be translated—whether it’s simple meaning, like the word three, or wonderfully complex meaning, like the word photosynthesis. Indeed, if science has taught us anything at all over the past two thousand years, it has taught us that if we study nature carefully enough, we will eventually find rational explanations that we can translate into English (or into العربية, etc.). At first glance, for example, there appeared to be vast amounts of relatively meaningless data (i.e. random patterns) out in space. Yet we later learned that if we listen carefully enough, suddenly all that data can be compressed, brought into focus, and translated into elegant English sentences like “Force equals mass times acceleration” and “Energy equals mass times the speed of light squared”.
Similarly, just as outer space conveys intelligent sentences, so also your average rock will translate into volumes of rational understanding about geology, chemistry, and subatomic physics. And of course, this also goes without saying for living things—again, so long as we listen rather than dictate. For many years, biologists thought that much of our DNA was meaningless junk because that’s how it appeared at first glance—a lot of random patterns. But they continued to listen carefully and realized that their assumptions were premature. In 2020 three geneticists published an article in a Nature Reviews Genetics’ article titled “Overcoming challenges and dogmas to understand the functions of pseudogenes”, in which they said that many of these so-called pseudogenes turns out to have stabilizing, mediating, and regulating functions.
Although often presumed to lack function, growing numbers of pseudogenes are being found to play important biological roles…We posit that pseudogenes have been classified on a scientifically unsubstantiated basis. We reflect that a broad misunderstanding of pseudogenes, perpetuated in part by the pejorative inference of the ‘pseudogene’ label, has led to their frequent dismissal from functional assessment and exclusion from genomic analyses.[vii]
They are discovering that just as the dents on a DVD carry several layers of meaning—a binary layer, a cinematic layer, a linguistic layer (i.e. the dialogue), etc.—so also the nucleic acid bumps on a DNA molecule carry astonishingly deep layers of meaning, revealing patterns incredibly more complex than they first thought. And so they press on with the quest to understand and then translate them so that students can have fun reading about it all in their textbooks.
And they are also immaterial. But now, of course, calling patterns immaterial is just as redundant as calling them mathematical. For, again, we can observe the complete absence of any physical qualities in any pattern.
Testing the Immaterial Nature of Information
We can test these observations simply by translating any sentence or equation—or any other piece of information—into a variety of (physical) media. Whenever we find that various different media do not need to have any of the same physical qualities in order to convey the same piece of information, then we can conclude that that piece of information must have no physical qualities. Thus we could also falsify this claim—the claim that information is immaterial—if we were able to identify any physical quality in any single piece of or collection of data. It makes no difference whether that data is large and complex, such as the Lord of the Rings movies, or a very small and simple, such as the number 11.
Consider, for example, eleven apples sitting on a table—large, red, juicy, sweet, crisp apples. Now one of the apples has eleven small bites taken out of it, and so eleven fruit flies are doing the Macarena on it—a dance with eleven steps. That’s four different ways of conveying the meaning of the word eleven. Yet we can look right at each one of them and observe the absence of any physical qualities in that number.
“Seriously?!” you say. “It can’t possibly be this simple, can it? Surely we’re missing something. Surely we’ve wandered off into a labyrinth of quagmires. Are we actually concluding that the entire universe is, literally, saturated with immaterial language?”
Yes, that’s exactly what we’re concluding. And no, we haven’t wandered off into a labyrinth of quagmires. We are on very stable, solid, high ground here. It really, truly is, just that simple. By comparison, here is something else that once sounded outrageous (actually, it still sounds outrageous): a small bag of mud has enough energy in it to power New York City for a month. Dr. Richard Muller, professor of physics at the University of California, Berkeley, says that the implications of Einstein’s theories of mass-energy equivalence still boggle the mind. “In the United States, the average cost of electricity is 10 cents per kilowatt-hour. So one pound of anything converted to electric energy would be worth over a billion dollars.”[viii] If there is so much power in a bag of mud, why should we be reluctant to recognize that there is an equivalent amount of rational, creative information in that same bag of mud? No one has been able to put a dent into Einstein’s theories. Likewise, no one can refute these conclusions about the immaterial nature of information.
But now if you still want to try to refute them, then you’ll probably need to do a couple of things:
- Avoid any engagement with the observations. In particular, avoid the fact that several different media can have exactly the same information in common, regardless of how simple or complex that information is.
- Try to label it all as philosophy—amateurish philosophy—rather than fact, and then trivialize it with foggy language. “Both Plato and Laozi pointed to all this more than two thousand years ago. This is nothing new! You’re just using their profound insights to create an absurd game of smoke and mirrors. You want us to tell you what the number eleven is?!?! No, you want us to chase red herrings down a rabbit hole and then you declare victory when we can’t catch them!” A person saying such things is clinging blindly to their presupposition of materialism and is incapable of questioning it, much less of asking questions without it.
- Perhaps wax philosophical yourself and argue that our “ontology of facts” is wrong because concepts like infinity and π are in some vague way not “real”—at least not as “real” as the meaning of the abstract word real is “real”. (Using the word real that way is the real game of smoke and mirrors.) Try to say that instead of being “real”, concepts like infinity and π are “human constructs” and therefore not legitimate examples of natural phenomena, and that reality is actually…very philosophical.
Otherwise, keep an open mind and stay focused on this main observation: information (a set of data, a unit of meaning, a word or sentence or a paragraph) has no physical qualities. It is immaterial. Perhaps someone can offer a dozen reasons why this should not be true, but they cannot give a single reason that it is not true.
So What Are We Observing the Presence Of?
But if we can observe the complete absence of physical qualities in a piece of data, then what are we observing the presence of? What is it that has no physical qualities? Am I suggesting that circles and numbers are spiritual? Not necessarily. However, the rationality that perceives and uses them—that might be spiritual.
After all, look at those three media again—the DVDs, the electromagnetic waves, and the flash drive. There is something else besides The Lord of the Rings that they all have in common. They also have authors in common—hundreds of human authors, starting with Tolkien but now also including the movies’ director, Peter Jackson, as well as the actors, the CGI specialists, the costume designers, etc. All of those authors contributed to the final product—the cinematic telling of the story.
So what is an author? We don’t know. We do know that all authors use their brains even as we use our livers and our lungs and our laptops. But what is the “it” that is using my brain to do math just as it is using my fingers to type words?
Even if we authors did try to speculate that we are one-and-the-same with our physical bodies, we would have a lot of trouble authoring a coherent argument, says Rice Chemistry Professor James Tour. For he says that every molecule in our bodies—including even in our teeth—is constantly changing in its atomic make-up.
We are dynamic structures, constantly changing. What is the real me? I don’t know what the real me is. If you want to say the matter is the real me, then you’ve got a big problem because its constantly changing…What is the real me?[ix]
What is an author? It would appear to be just as immaterial as is information itself. That is to say that to the extent that we have evidence that information is nonphysical, to that same extent we have evidence that the authors of information are likewise nonphysical—that we are immaterial souls using our brains the same way that we use our coffee mugs and our movie cameras. Why? Because several different media can not only have the same information in common but also the same authors in common.
Seriously? Absolutely. But are we certain about this? Is there any counterargument at this point? No, none.
Now that doesn’t mean that many scientists won’t just assume that there must surely be good a counterargument. Indeed, some will arbitrarily declare that information is physical. However, when you look at their explanations you will find that what they are actually saying is that all physical things convey information. For example, in 1999 world-renowned Physicist Rolf Landauer, who did research both at NASA and IBM, published an often-cited paper titled, Information is a Physical Entity. “Information is not an abstract entity but exists only through a physical representation,” Landauer explained, “thus tying it to all the restrictions and possibilities of our real physical universe.”[x]
What exactly does he mean by that? First of all, what is an “entity”? (Could my soul be an “entity”?) That’s a terribly abstract word to use for something that you say is not abstract. Second of all, what is the “it” that is tied to all the restrictions and possibilities of our physical universe? If “it” is a physical “entity”, then what are its physical qualities? Is it soft or shiny or fluid or…? And finally of all, we actually know and use a massive amount of information that is provably not tied to our physical universe. We’ll explore this more later, but for now I’ll cite an example given by Dr. Muller at Berkley. He explains how we can prove that the square root of 2 is irrational, meaning that it goes on infinitely (1.41421…) just like the numbers π (3.14159…) and e (2.71828…). Because such numbers go on infinitely, we can only approximate them with physical things. You can have 2 apples or, with a good laboratory scale you could have 2.71 apples, but you could never have the number of apples equaling the square root of 2. Yet to the extent that mathematicians know anything at all—to the extent, for example, that they know that the statement “1 + 1 = 2” is true—to that same extent they also know that this piece of information (the square root of 2) is irrational.
What makes this result so fascinating is that it never could have been discovered through the science of physics. No measurement could demonstrate that the square root of two is irrational. The fact that the square root of two is irrational is a truth that is beyond physical measurement; it exists only in the minds of humans. It is nonphysics knowledge.[xi]
Thus Landauer was simply wrong to declare that information is restricted by our physical universe—at least by what he calls the “real” physical universe.
Now some people might try to declare that such information is not objective but rather subjective—that it only exists in our brains and that it is, again, a “human construct”. But such arguments disintegrate in about ten seconds, as we will discover when we ask “Where do words occur?” and “When do words occur?”. Furthermore, keep in mind that such a discussion would actually be completely irrelevant to the fact that information is immaterial. That is to say that even if information did only exist in our skulls, we would still be stumped by the question, “How does the brain perceive—much less create—something that is immaterial?” Would anyone say that saying information is, literally, one and the same with the organic gray matter inside our skulls? It’s a completely hopeless argument.
But are we really sure about all this? Aside from labeling it all a bunch of “philosophy” and pretending that it’s not scientific, is there really no counterargument?
No, there is no counterargument. The only option for the naturalist is to go back to the beginning, presuppose materialism, take information for granted, and then fill the room with philosophical fog. For example, here is an argument that some scientists will offer as to why we should assume that information is physical: knowledge is power. We all might be familiar with how knowledge is power in a political and economic sense. As Gordon Gekko said in the movie Wall Street, “The most valuable commodity I know of is information.” After all, if you were to know what is going to be reported in The Wall Street Journal tomorrow before everyone else was to know it, then you could make a whole lot of money. The same is true if you know where to dig for gold or drill for oil: information can bring the opportunity for wealth and power. And in a similar fashion, physicists can prove that knowledge leads to power in the laboratory, though physicists use the word power in a different, more precise and measurable way than businessmen like Gordon Gekko. The physicist’s standard metric unit of power is the watt (as in a 75-watt light bulb) and they can prove that, just as insider business knowledge can lead to economic and political power, so also insider physical knowledge can lead, in a measurable, testable way, to physical power. A physicist named James Maxwell realized this in 1867, and we have wrestled to understand it ever since. It’s one of the ways that physicists articulate the mind-over-matter mystery: how does knowledge lead to power? And is knowledge equivalent to power? Or, instead, does knowledge simply provide the opportunity to use power—even to harness that billion dollars-worth of power in a bag of mud? If the former were true, if knowledge were, in fact, equivalent to power (if knowledge = power) then knowledge would be a physical thing since energy is a physical thing.
Yet this question itself continues to take information for granted. It simply replaces the mystery of the nature of information with the mystery of the nature of knowledge. After all, if we ask the question “What do we mean by the word knowledge?” or “What is the information that we know?”, then any answer that we author will always, only beg the question. (If you don’t believe me, give it a try.) How do we “know” any information at all? How do you know, for example, the immaterial meaning being conveyed by these black symbols that you’re staring at right now?
If we can answer that question, then we might also answer the questions “What is knowledge?” and “What are authors?” But the fact remains that, in all cases, although we do not know what words are, or what knowledge is, we still do know what they all are not. They are not physical. For words and sentences, numbers and equations, bits and bytes of data—they have no physical qualities. To the extent that we know anything at all (which, by the way, could be translated “as x approaches infinity…”), to that same extent we know this to be true: these units/bits/quanta of meaning, these things that we call words, are immaterial. And the fact that both the question “What is information?” and its answer are, at the end of the day, nothing but words—that fact indicates that we are dealing with objective, self-evident truth.
It really, truly is that simple. A materialistic world would be utterly meaningless not just in a deep, moralistic way—as in saying, “My life has no meaning!”—but also in a blunt, practical way such that the meaning of the words like three and four and blue and grey would not exist either. Literally! Later we will hear about some philosophers who, in their zeal for intellectual honesty, take this possibility very seriously. (Of course, they can’t actually say that life is meaningless since the word meaningless is meaningful.)
But the excellent news is that (immaterial) meaning exists. The mind-over-matter mystery, though more awesome and enigmatic than ever, also remains more certain than ever. And here is a good initial working definition for the word soul: a rational, creative author.
[i] Seth Lloyd, Programming the Universe (New York: Knopf Doubleday, 2006), 17
[ii] John D. Barrow, Pi in the Sky: Counting, Thinking, and Being (New York: Oxford University Press, 1992), 3.
[iii] David Eagleman, The Brain (New York: Pantheon Books, 2017), 201.
[v] J.P. Changeux, A. Connes, Conversations on Mind, Matter and Mathematics. Princeton University Press. 1995. (pp. 10).
[vi] A. Adler. “Mathematics and Creativity”, in The World Treasury of Physics, Astronomy and Mathematics. (T. Ferris, ed). Little, Brown and Co. 1991. (pp. 435).
[vii] S.W. Cheetham, G.J. Faulkner, and M.E. Dinger, “Overcoming challenges and dogmas to understand the functions of pseudogenes”. Nat Rev Genet21, 191–201 (2020). https://doi.org/10.1038/s41576-019-0196-1
[viii] Muller, Richard A. Now: The Physics of Time (Kindle Locations 533-534). W. W. Norton & Company. Kindle Edition. 2016.
[x] Rolf Landauer, “Information is a Physical Entity”, IBM Thomas J. Watson Research Center, Yorktown Heights, NY. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.192.2928&rep=rep1&type=pdf
[xi] Muller, location 4715.
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