What is the meaning behind the medium?
These black symbols that you’re staring at right now all carry invisible, untouchable, silent meaning. We can translate that meaning into many other patterns, such as español, русский, 中文, العربية, or 01110111 01101111 01110010 01100100 01110011. Or we could also 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 could 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 could 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.
The nature of information has baffled the brightest minds in science for millennia. Some of our most cherished discoveries—such as those regarding entropy, quantum mechanics, and DNA replication—are all about the flow of data, yet we are totally and completely stumped as to what data actually is.
However, 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. We can actually observe the complete absence of physical qualities in words. In other words, this is an objective, testable, falsifiable fact: sentences and paragraphs are immaterial. 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. Whether we are talking about semantic information, biological information Shannon information, quantum information, geological information, etc.—it is all nonphysical.
Let’s prove it. Let’s prove that we know of an immaterial world. And while we’re at it, let’s prove that we ourselves are immaterial—that we are spiritual beings, that we have nonphysical/immaterial souls. Seriously, let’s prove it scientifically. If it’s true, then it really shouldn’t be that difficult to prove, right? I mean surely there’s a good reason that 95 percent of the people on the planet embrace some form of classical spirituality.
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 Euler’s Identity). 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 understood as a series of the words one and zero (i.e. binary computer language). Although we used computers to translate those words, that is no different from using a telescope to see 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”, “دائرة”, or “圈”? 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 simply an idea, 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, as “a closed curve all of whose points are equal distance from a given point called the center” (I learned that definition in sixth grade), 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 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.) Without trigonometry, which uses π (3.14…), we would have no airplanes, no smart phones, no slushy machines…nothing, at least, which requires a transistor. Furthermore, all of our architecture would be small and clumsy. Now we actually have hundreds of ways of finding π, but the simplest and easiest to understand is, again, by drawing a circle on paper and then dividing its circumference by its diameter. 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?
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 translated. 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 (after a few years of study) to perceive the meaning of geometric shapes and algebraic equations and trigonometric functions and such? Perhaps intelligence is just as immaterial as is the meaning of the word circle/圈/دائرة/κύκλος.
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 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 find a way to save it onto a flash drive. So we have a number of ways to bring the movie into the comfort of home, where we can enjoy it as light waves dancing from a screen and sound waves flying out of speakers. We can store it on:
- 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 it. We could actually translate the electromagnetic waves onto paper as binary—a series of ones and zeros. But that would fill an entire library’s worth of books and probably take a couple of lifetimes to learn to read. Nevertheless, the point is that we can use a variety of media to transport the movie.
Now any such media have several layers of patterns to them. 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. 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 try to figure out the meaning of the dialogue—another, completely different layer. Of course there are so many subtleties of cultural context to the movies (such as Tolkien’s Christian faith, the historical context, 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 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, we definitely would have heard from them 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 DVDs in a time capsule and they were dug up a thousand years later, then people could enjoy the exact same movies.
And that is an astronomically profound fact.
The reason this 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, have no 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 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. 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. J.R.R. 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 (binary for blue)? The meaning of that word is just as immaterial as the meaning of the drama in the movies, yet for some 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 rational, creative muscle for a child to read the book than to stare at a screen.
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.) The easiest way to learn that meaning 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 both of them written as equations. (See James Maxwell’s equations for light on the right.) Believe it or not, vast amounts of research have been done by both neuroscientists and AI scientists in trying to figure out what it even means for us to perceive color. How do we perceive the color blue in a way that a video camera attached to a supercomputer may not necessarily perceive it? We have no idea. However, if we acknowledge that the meaning of words like blue and gray is immaterial, suddenly we realize that neither a movie camera nor a supercomputer nor even the three-pound organ in your skull can “see” it. Whatever comprehends the immaterial meaning behind the material medium must likewise be immaterial.
Granted, it would be extremely difficult for us to learn the meaning of the word blue in any other way but seeing it translated as paint or crayons. To learn the meaning without sight might be as difficult, perhaps, as learning to read the binary version of The Lord of the Rings movies, or as difficult as digging that tunnel through Pluto. However, once we do learn the meaning of colors through paints and crayons, we can then easily understand them translated through different media—such as when reading about Gandalf’s blue hat in The Lord of the Rings.
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 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, paper with 1’s and O’s on it, 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 and look at them 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 have in common?” The plastic discs have no organic gray 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 computer can comprehend. But is the same thing true for any and every bit of information that we perceive in nature? To quote Einstein again, “The eternal mystery of the universe is its comprehensibility.”
EXAMPLE #3: A SENTENCE CALLED EULER’S IDENTITY
In polls mathematicians always say that the most beautiful equation in the world is 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 pi and the imaginary unit, plus one equals zero” (eπi + 1 = 0).
It contains two natural constants, which are irrational numbers that appear everywhere in nature. One of these natural constants is π (3.14…), and the other one is the natural logarithm (2.71…). A third number, called the imaginary unit, is the square root of negative one. Scientists used to think that it was just a very interesting mathematical enigma, but early in the 20th century physicists discovered that the equations of quantum mechanics included it. That is to say that all these numbers, and this sentence that we call Euler’s Identity, had been there all along. Like a trigonometry textbook sitting on a shelf, they were available to be comprehended, translated (into English or العربية, etc.) and used. And, again, just as the cranes and tractors that we use are objective, so also is the math. We don’t create the metal in the tools that we use; instead, we discover the metal ore and then use it creatively. Likewise, we don’t create the math we use to design things; instead, we discover the math and then use it creatively.
The point of all of this is that if an equation like Euler’s Identity is objective, then it is immaterial. If it were something that only existed in our heads, then it would be composed of neurons or some other kind of gray matter. But unlike our physical tools—cranes and tractors—numbers and equations have no tangible traits at all. As with any and all information, they are immaterial words and sentences, pure meaning. Hammers and tractors and protractors 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.
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. After all, this one simple observation—that the meaning behind any medium is immaterial—dramatically changes every branch of science. So we need to be careful.
What All Information Has in Common
We’ve looked at some intriguingly magnificent evidence for what information appears not to be—it appears not to be physical—but we aren’t saying what information actually is. The trouble now 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 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 (your basic flash drive or DVD or electromagnetic wave)
- biological information (such as is in DNA, etc.)
- Shannon information (the measurement physicists use for information, and where we get the term bit)
- financial information (what businessmen and economists study)
- meteorological information (your basic weather report)
What these all have in common is that they form a mathematical pattern. Electromagnetic waves form a mathematical pattern. The magnetized alloy on a flash drive forms a mathematical pattern. Computer bytes and bits convey information in the context of a mathematical pattern called binary. Another way to understand this is to say that all of these different forms of information can be stored on a DVD because they can be digitized. So that will be my working definition of information: that which can be digitized.
Now at this point, some people may want to stop and argue that I’m confusing information with the concepts of interpretation or meaning. But such distinctions are irrelevant to my point, which is that it is all nonphysical/immaterial, so debating and protesting about these definitions is a red herring. It would be like someone was trying to show you how to make a great batch of fajitas, but you protested and left the room because their recipe didn’t fit your particular definition of the word fajitas. Instead, you can stay and learn to cook a great meal and worry about what to call it later.
I invite you to stay and enjoy this incredible mystery about that which is objective yet nonphysical.
Again, 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 actually a redundant repetition, 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—again, like the pattern of black symbols that you’re staring at right now. Therefore, if we could not do math, then we could not do language, for the two are virtually one and the same. In other words, describing language as mathematical would also be a redundant repetition.
Consider, for example, two of the key ingredients for language—grammar and vocabulary. Let’s look at how language and mathematics are virtually 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 we can use a laptop computer to translate into English, Swahili, 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.
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.
So that’s a brief summary of the grammatical equivalencies in math and other languages. 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 (3.14159…), which goes on to infinity. 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 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 pieces of apple pie.
All that is to illustrate how numbers are words—nothing more, nothing less.
But it gets even better, 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.
slavery <——————————> freedom
However, this is just a one-dimensional understanding of freedom, and we still need more context in order to really communicate the meaning of the word. 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:
ignorance <——————————> knowledge
Now 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:
Now we want even more clarity, we could add a third line that is defined by the words determinism and randomness.
randomness <——————————> determinism
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.
All that is to say that 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, all I am pointing out is that words nuance each other in complex, multi-dimensional ways. We’re just talking about how language works. So although you could have all kinds of interesting discussions about the causes and effects of various types of slavery—whether political, economic, cultural, or religious slavery—we’re not going there now. We’re just talking about how words function in sentences.
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 in linguistics.
So as deep as all this is, we’re just making observations about how words and sentences work. We’re just observing patterns in meaning. 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 colors: 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.
Again, this isn’t philosophy; it’s just semantics. These are just the literal facts.
Sticking to the Facts
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. But the only thing their philosophizing will really accomplish is to fill the room with fog. Instead of clarifying the facts, they will just be mixing the facts with a bunch of speculations about speculations about speculations. But 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, planetary orbits, 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 gravity. 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 “Energy equals mass times the speed of light squared” and “Force equals mass times acceleration”.
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 the way a single strand of DNA has folded matters tremendously. They discovered 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 astronomically 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
Take, for example, the very simple pattern of a circle—any circle. What physical properties does it have? Does it have color or texture or size? Does it have a particular sound—“circle”, “Kreis”, “κύκλος”, “دائرة”, or “圈”? Does it have any chemical properties? Does it have any force or effect on anything? No, of course not. It has no material properties at all. It is simply an idea, 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, as “a closed curve all of whose points are equal distance from a given point called the center” (I learned that definition in sixth grade), etc. Now we might usually think of circles when they translated as geometric shapes, and that’s how we first teach them to children. However, when we use them—such as in calculations—we most often translate them as algebraic equations. The equation of the circle is (x – a)2 + (y – b)2 = r2.
Regardless, in all cases—whether they’re translated as drawings or as equations—the meaning of the word circle is nonphysical. It cannot be directly or indirectly seen, heard, felt, tasted, or smelled; it can only be translated. 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 (after a few years of study) to perceive the meaning of geometric shapes and algebraic equations and trigonometric functions and such? Perhaps intelligence is just as immaterial as is the meaning of the word circle/圈/دائرة/κύκλος.
Speaking of intelligence, circles have proven to be one of the most valuable tools in technological history. We use them constantly. If you take the circumference of a circle and divide it by its diameter, that’s one way to get π. We actually have hundreds of other ways to find that number—most of them by use of algebraic equations—but using the geometric drawing of a circle is one of the simplest and best known. To date, π has been calculated to over thirteen trillion digits, but we know it goes on infinitely.
And infinity, like all irrational numbers, can never be physically represented or imaged in any way. For example, the number 5 can be physically represented by 5 abacus beads, five apples, five electronic pulses, etc. (Ad infinitum!) By contrast, infinity can never be physically represented. It is, by its very nature, 100% pure abstraction. Yet we use infinity (via calculus) along with irrational numbers like (via trigonometry) in the development of almost any piece of modern technology. Without such tools, we would have no smartphones, no jet airplanes, no slushy machines—nothing, at least, that requires a transistor. Furthermore, our architecture would all be relatively small and clumsy. Because as tools, circles and triangles, and infinity—they are all just as essential as our machine shops, our forges, and our cranes and tractors.
And just as the cranes and tractors that we use are objective, so also is the math. We don’t create the metal in the tools that we use; instead, we discover the metal ore and then use it creatively. Likewise, we don’t create the math we use to design things; instead, we discover the math and then use it creatively.
The point of all of this is that mathematics is objective. It is not something that only exists in our heads. (We will explore this more in the next chapter.) But unlike our physical tools—cranes and tractors, etc.—numbers and equations have no tangible traits at all. As with any and all information, they are simply immaterial words and sentences, pure meaning. Hammers and tractors and protractors have lots of physical qualities; circles and triangles and integrals 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.
That is to say, we can actually observe the complete absence of physical qualities in the math that we use. We can test this observation simply by translating any number or equation—or any other piece of information—into a variety of (physical) media. And 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. And so 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 3.
Or 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? 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 sound outrageous): a bag of mud has enough energy in it to power New York City months. According to Einstein’s theories, that bag of mud contains about a billion dollars’ worth of energy. Dr. Richard Muller, professor of physics at the University of California, Berkeley, says that the implications of his elegant equations 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.”
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 my “ontology of facts” is wrong because concepts like infinity and 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 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 some 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 of course with J.R.R. Tolkien, but now also including the movies’ director, Peter Jackson, as well as the actors, the CGI specialists, the costume designers, etc., etc., etc. All of these 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? 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.
Are we sure about this? Is there any counterargument at this point? No, none. Okay, some people might try to declare that the information only exists in our brains, that the data on those DVDs is not objective and does not exist outside of our skulls, and that trigonometry and calculus are, again, “human constructs”. But such arguments disintegrate in about ten seconds—as the next two chapters will show. 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? Or are you saying information is, literally, one and the same with neurons?” It’s a completely hopeless argument.
But are we really sure about all this? Aside from pretending that it’s all irrelevant by labeling it “philosophy”, is there really no counterargument?
No, there is no counterargument. The only option for the naturalist is to back up to the beginning, presuppose materialism, and just take information for granted. 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 links 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 Clerk Maxwell realized this in 1867, and we have wrestled to understand it ever since. It’s one of a couple of ways that physicists articulate the mind-over-matter mystery: how does knowledge lead to power? And is knowledge equivalent to power, similar to how Einstein in 1905 discovered that energy is equivalent to mass with the equation E = MC2? 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 power is a physical thing.
But the point is that 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 information conveyed by these black symbols that you’re staring at right now? The meaning of these words is immaterial, right? I’m not asking you what these words mean in their definitions; rather, I’m asking you what they are in their substance.
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. This is an observable, testable, falsifiable fact. To the extent that we know anything at all (which, by the way, could be translated “as ℵ approaches infinity…”), to that same extent we know this to be true: these units/bits/quanta of immaterial meaning, these things that we call words, are immaterial.
It really, truly is that simple. A materialistic world would be utterly meaningless, not just in a deep, moralistic way—as in saying, “Life has no purpose, no meaning!”—but also in a blunt, practical way such that the meaning of the words like three and blue would not exist either. Literally! In chapter 5 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 the life is meaningless since the word “meaningless” has meaning.)
But the excellent news is that this is a self-evident truth: (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.
Illustrations from Pixabay
Waves Designed by Creative_hat / Freepik: https://www.freepik.com/free-vector/abstract-blue-wave-flowing-background_5600651.htm#page=1&query=waves&position=29
 J.P. Changeux, A. Connes, Conversations on Mind, Matter and Mathematics. Princeton University Press. 1995. (pp. 10).
 A. Adler. “Mathematics and Creativity”, in The World Treasury of Physics, Astronomy and Mathematics. (T. Ferris, ed). Little, Brown and Co. 1991. (pp. 435).
 Muller, Richard A. Now: The Physics of Time (Kindle Locations 533-534). W. W. Norton & Company. Kindle Edition. 2016.