Where do words occur?

Are you listening?

Excellent News About Your Soul

The heavens declare the glory of God, 

    and the sky above proclaims his handiwork. 

Day to day pours out speech, 

    and night to night reveals knowledge. 

There is no speech, nor are there words, 

    whose voice is not heard. 

Their voice goes out through all the earth, 

    and their words to the end of the world.

                                                (Psalm 19:1-4)

Where do words occur?

The Milky Way still speaks. In fervent, adoring poetry as of a young man in love, so do all the other galaxies and stars and nebulae in the cosmos. Day after day their verse never ceases, night after night their voice never slows as it fills the universe with deep, magnificent utterances. Artists come and go. Politicians change their tunes. Thinkers think and then die, sometimes authoring ideologies that rise and fall and carry nations with them. Even religions dance and sway with the winds of fashion as their merchants seek the most profitable hope in a desperate and maddening world. But the guidance of the stars and the knowledge they pour out—those revelations have endured from civilization to civilization, from generation to generation, from the painful memories of a depraved past to the beautiful promises of a glorious future. If we can just get away from the city lights and find somewhere a clear open sky, we can always look the heavens for a gentle, uplifting, uproarious word.

And the more carefully we listen, the more profound the revelations.

Andromeda as seen with the naked eye.

For example, in the northern hemisphere, on a clear night in the fall, you can start by looking for the Great Square of Pegasus. The left corner of the Square is the star Alpheratz, from which two chains of stars spring, the lower brighter than the upper. If you start with the third star of the lower chain and the move up to the third star of the upper chain (the first star of both chains being Alpheratz), and then keep going the same distance again in a straight line, you’ll find a fuzzy little puff.

Andromeda as seen with a telescope.

Astronomers call it M31 because it’s number 31 on the Messier List, a catalog of 110 astronomical objects. French Astronomer Charles Messier was only interested in hunting for comets, so starting in 1771 he made a list of non-comet objects that frustrated his efforts. And at first M31 may not have seemed that interesting—certainly not as interesting as a comet. But as the years went by, the more astronomers learned about it, the more it captivated them. And the same is true for anyone who finds it: the more you understand, the more you will stare. It’s the Andromeda Galaxy, home to about a trillion stars (well over twice the number in our Milky Way), spanning 220,000 light years across. It’s 2.5 million light years away from us, but on a clear, moonless night in Texas you can see it with the naked eye. And when you can see it not just with your eyes but also with your mind, it will beggar your imagination.

All this spectacular information is brought to us by electromagnetic waves—the same sort of waves we use to listen to the radio or download episodes of Star Trek. They reveal all kinds of messages about superclusters and quasars and a really big bang.

Indeed, if science has taught us anything at all over the past 2000 years, it has taught us that the more carefully we look and listen to the creation, the more amazing and beautiful will be the explanations that we discover. Whether we look through a telescope or through a microscope or just take a walk in the woods, we comprehend rational, creative words that we can translate into English (or العربية, etc.)—such as gravity, special relativity, photosynthesis, DNA replication, the Krebs cycle, the carbon cycle, the water cycle, quantum entanglement, heliocentrism, adaptation, etc. It takes an intelligent, creative person ten or twenty years of study before they can begin to comprehend these explanations. Yet they are simply there, like books sitting on a shelf. As George Washington Carver (1864-1943) put it, “I love to think of nature as an unlimited broadcasting station, through which God speaks to us every hour, if we will only tune in.”

The Book of Nature

Italian astronomer and physicist Galileo Galilei (1564-1642) referred to nature as a book that we are invited by God to study. He said that even hundreds of the keenest minds could study nature for thousands of years and still not tire of learning what God had revealed “in the open book of the heavens,”[i] which was written in the language of mathematics:

Philosophy is written in this grand book the universe, which stands continually open to our gaze.  But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.[ii]

So although the universe might at first appear to be filled with lots of meaningless data, if we listen carefully enough, suddenly all that data can be compressed, brought into focus, and translated into elegant sentences like “Force equals mass times acceleration” and “Energy equals mass times the speed of light squared.” Remember that Einstein called such comprehension miraculous.

But what did Galileo mean by “the language of mathematics”?

MATHEMATICS

Math by itself, apart from its reflection in nature, provides an unending supply of mysteries to be explored. Some equations have taken centuries to solve even after many mathematicians have devoted their careers to finding the solutions. In the past generation alone, we have seen the solutions to two such equations: Fermat’s Last theorem, first posed in the 1630s, and the Poincaré Conjecture, first posed in 1904. In each case there has been a long search for what was assumed to be absolute, objective truth.

Mathematicians have often discovered such truths long before scientists discovered that the same patterns are written, as Galileo said, in nature. Some of the patterns are simple, such as the curve of a seashell or the branching of a tree, both of which follow what we call the golden ratio, 1.618…, which is an irrational number, like π. (See Cristóbal Vila’s Infinite Patterns.) Other patterns, such as the changes in a quantum wave function, are so complex that they use imaginary numbers, as discovered by physicist Erwin Schrödinger. These equations reveal the profound depth of rationality in the cosmos. As Astronomer Royal Sir Martin Rees, Royal Society Research Professor at Cambridge University, put it, “Science advances by discerning patterns and regularities in nature, so that more and more phenomena can be subsumed into general categories and laws.”[iii]

Rees wrote a book, Just Six Numbers, about how the entire universe depends for its existence upon being finely tuned to six numbers. For example, the number called Ω (omega), represents the amount of matter in the universe. Omega equals 1, and Rees says if it were greater than 1 then the universe would have collapsed long ago, but if it were less than 1 no galaxies would have formed.

A few basic physical laws set the ‘rules’; our emergence from a simple Big Bang was sensitive to six ‘cosmic numbers’. Had these numbers not be ‘well-tuned’, the gradual unfolding of layer upon layer of complexity would have been quenched.[iv]

But what does it mean to say they’re finely tuned? Consider a guitar string: if you turn the nob on it by about a millimeter in either direction, it will be out of tune. Some of the constants of nature appear to be so finely tuned that it would be like saying that if you turned the nob on the string by a trillionth of a millimeter, it would be out of tune. And then there are five other strings that all need to be in tune with each other. And in the universe, technically, according to physicist Sabine Hossenfelder, the number of known constants is not just six.

The currently known laws of nature contain twenty-six constants. We can’t calculate those constants; we just determine their values by measurement. The fine-structure constant (α) sets the strength of the electromagnetic force. Planck’s constant (ħ) tells us when quantum mechanics becomes relevant. Newton’s constant (G) quantifies the strength of gravity. The cosmological constant (Λ) determines the expansion rate of the universe. Then there are the masses of the elementary particles, and so on.[v]

So, you not only have a six-stringed guitar, but add in two violins, a viola, a cello, and a bass all tuned to the same pitch. Throw in just the right amounts of star dust (literally!), balance it all with a finely tuned moon in a finely tuned solar system, and then make it all play not just in tune but in harmony using a notation called DNA, and you get the melody of life, “when the morning stars sang together.” (Job 38:7) (See the Discovery Institute’s List of Fine-Tuning Parameters.)

Even scientists who do not attribute such music and song to God still talk about math as language. As Richard Feynman, another one of the greatest physicists of the twentieth century, put it:

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.[vi]

Nevertheless, when we’re talking about language and using personal pronouns, it becomes rather self-defeating not to attribute the words to a person. As Einstein said, “I have no better expression than the term ‘religious’ for this trust in the rational character of reality and in its being accessible, to some extent, to human reason.”[vii] At the end of the day, one way or another we have to attribute all the intelligent words out there to someone. Your typical 7th-grade science textbook has been translated by scientists, but who wrote it?

That is to say that as engineers don’t create iron but rather discover it and use it creatively, so also scientists don’t create math but rather discover it and use it creatively. It takes rational minds at least ten years of study before they can begin to comprehend some of the sentences. Yet they are simply out there, like a book on shelf.

PHYSICS AND CHEMISTRY

Such patterns are not just written in nature. They form the very background and context for nature—even for space itself. In their book We Have No Idea, Jorge Cham and Daniel Whiteson, professor of experimental particle physics at the University of California, Irvine, talk about how space can only be understood mathematically:

Space is definitely not an empty void, and it is definitely not just a relationship between matter. We know this because we have seen space do things that fit neither of those ideas. We have observed space bend and ripple and expand.[viii]

Space bends and ripples and expands in relation to what? To a nonphysical mathematical grid. The heavens themselves are a medium for profound creative meaning. That’s why so many scientists, such as German Astronomer Johannes Kepler (1571-1630), a friend of Galileo’s, referred to the heavens as a book.

I was merely thinking God’s thoughts after him. Since we astronomers are priests of the highest God in regard to the book of nature, it benefits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God.[ix]

Kepler believed God wanted us to study and understand these thoughts. “Those laws [of nature] are within the grasp of the human mind; God wanted us to recognize them by creating us after his own image so that we could share in his own thoughts.”[x]

The more scientists have discovered, the deeper and more profound the mathematical discoveries have come. As one of the most famous physicists of the twentieth century, Englishman Paul Durac, put it:

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.[xi]

Along those lines, Anglo-Irish chemist Robert Boyle (1627-1691), considered to be one of the founders of the experimental scientific method, found nature to be a source of divine revelation. He looked at chemistry and saw a book available to be translated:

And when with excellent Microscopes I discern in otherwise invisible Objects the Inimitable Subtlety of Nature’s Curious Workmanship; And when, in a word, by the help of Anatomicall Knives, and the light of Chymicall Furnaces, I study the Book of Nature, and consult the Glosses of Aristotle, Epicurus, Paracelsus, Harvey, Helmont, and other learn’d Expositors of that instructive Volumne; I find my self oftentimes reduc’d to exclaim with the Psalmist, How manifold are thy works, O Lord? In wisdom hast thou made them all.[xii]

Perhaps Boyle’s most famous quote is “Nature abhors a vacuum.” He discovered what chemists call Boyle’s law, which governs the inversely proportional relationship between the volume and pressure of gasses. Like Kepler, he believed that God inspired and invited people to see his work in creation. “If the omniscient author of nature knew that the study of his works tends to make men disbelieve his Being or Attributes, he would not have given them so many invitations to study and contemplate Nature.”[xiii]

As far as physicists can tell, the physical laws and constants of nature are uniform across the universe. If they were not uniform, then perhaps the explanations could be called descriptive of nature rather than prescriptive. That is to say that instead of being governing laws they could simply be called generalized observations. To be sure, many scientists have tried to find exceptions to this uniformity in the universe. But as Richard Muller, professor of physics at the University of California, Berkley, explains, they have always failed.

The equations that we have in physics today—all those that are part of the standard physics, the ones that have been verified experimentally—have the property that they work everywhere. Some people think this is amazing enough that they spend their careers looking for exceptions. They look at things that are very far away, such as distant galaxies or quasars, hoping to find that the laws of physics are a little bit different. So far, no such luck.[xiv]

Implications aside, scientists take it for granted that wherever they look in the cosmos, whether they look through a telescope or through a microscope, they will eventually rational explanations. Consider, for example, the following chart:

To the extent that we know anything at all, to that same extent we know that the sentences on the right are objective, not subjective. That is to say that science rests upon the knowledge (by faith?) that these sentences were true—to the extent that we can say anything is true—long before we perceived them and translated them into English (or Swahili, etc.). Furthermore, we have no context for saying that the sentences on the right are in some way less linguistic than the ones on the left.

From there, it’s easy to extrapolate and declare that rational words saturate the cosmos. Everywhere we find rationality, we find information that can be translated. Indeed, regardless of whether you can keep track of the order of their arrival, and regardless of whether you can even count them, the very hairs on your head are all numbered.

Now we know that some of the natural laws and equations that we use are not perfectly accurate. But that makes them no less objective than government treaties or any other writings that have nuanced translations into other languages. Our translations of the natural laws keep improving and giving us a more accurate understanding of objective natural data, just as our telescopes keep improving and giving us a clearer vision of the objective universe.

And we didn’t need modern science to reveal this to us. As Laozi put it:

Why do you run around looking for the truth? Be still, and there it is—in the mountain, in the pine, in yourself. Do you imagine the universe is agitated? Go into the desert at night and look at the stars. The practice should answer the question.

Similarly, classical Greek philosophers wrote a great deal about how rationality, or logos, filled the cosmos. Furthermore, early Christian apologists found that these teachings resonated deeply with the Hebrew Scriptures. For example, Justin Martyr (100-165 CE), known in his day as Justin the Philosopher, tried to persuade the Roman Emperor, Antoninus, to relent on the persecution of Christian by arguing that the “seeds of Christianity” could be found in the writings of Greek teachers. Historian Justo L. González summarizes Justin’s argument this way:

How, then, can one explain this partial agreement between the philosophers and Christianity? For Justin, the answer is to be found in the doctrine of the Logos. This is a Greek word that means both “word” and “reason.” According to a tradition of long standing in Greek philosophy, the human mind can understand reality because it shares in the Logos or universal reason that undergirds all reality. For instance, if we are able to understand that two and two make four, the reason for this is that both in our minds and in the universe there is a Logos, a reason or order according to which two and two always make four. The Fourth Gospel affirms that in Jesus, the Logos or Word was made flesh. Thus, according to Justin, what has happened in the incarnation is that the underlying reason behind the universe, the Logos or Word of God, has come in the flesh.

According to the Fourth Gospel, this Logos is “the true light that enlightens” everyone. This means that, even before the incarnation, he is the source of all true knowledge. Paul had already said (1 Corinthians 10:1-4) that the ancient Hebrews’ faith rested on none other than Christ, who had been revealed to them even before the incarnation. Now Justin added that there were also among the pagans those who knew the same Logos, however remotely. Whatever truth there is in the writings of Plato was granted to him by the Logos of God, the same Logos who was incarnate in Jesus. Therefore, in a way, Socrates, Plato, and the other sages of antiquity “were Christians,” for their wisdom came from Christ. This is not to say, however, that the incarnation was not needed, for those philosophers of old knew the Logos “in part,” while those who have seen him in his incarnation know him “fully.”[xv]

Again, regardless of a person’s religious or philosophical upbringing, they must attribute all the rationality in the universe to someone. It can’t be attributed to the ones who discovered it since it was already there before they discovered it.

Are we concluding that rationality saturates the universe? Yes. That is the foundation of science. (Suddenly the Search for Extraterrestrial Intelligence, SETI, sounds terribly ironic.) The one and only reason to deny this conclusion is out of a desperate need to cling to the presuppositions of materialism.

Yet truth comes at us from every direction. So, what can we “in part” know through studying the book of nature?

A SINGLE BOOK WITH MANY CHAPTERS

The mathematical patterns that we discover in nature form a single book. In fact, we can define science simply as the study of patterns in nature and society. Chemists study patterns among the elements, leading to the development of tools such as periodic tables. Biologists study patterns among organisms, resulting in charts such as the one for taxonomic rank: domain, kingdom, phylum, class, order, genus, and species. Astronomers study patterns among stars. Economists study patterns in the production, distribution, and consumption of goods and services. Psychologists study patterns in human behavior. Physicists study patterns in matter and energy, discovering such sentences as “F = MA” and “E = mc2.”

The more carefully we listen, the more amazing the explanations we discover. 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 finally realized that their assumptions were premature. In 2020 three geneticists published an article in a Nature Reviews Genetics’ titled “Overcoming challenges and dogmas to understand the functions of pseudogenes”, in which they said that many of these so-called false genes turn 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.[xvi]

They realized that, for example, just as the patterns of bumps on a DVD can 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. It might be like aliens getting hold of the DVD’s for The Lord of the Rings and, as they translated it, initially thinking that parts of the 88 billion bits of data were merely noise, only later to realize that that “noise” was actually linguistic dialogue that carried the storyline of the whole trilogy.

As Erika Check Hayden, director of the Science Communication Program at the University of California, Santa Cruz, explained it, the complexity of these genetic patterns perpetually stuns scientists:

As sequencing and other new technologies spew forth data, the complexity of biology has seemed to grow by orders of magnitude. Delving into it has been like zooming into a Mandelbrot set — a space that is determined by a simple equation, but that reveals ever more intricate patterns as one peers closer at its boundary.[xvii]

That was a dozen years ago, yet our understanding of complexity of the cell has continued to grow by orders of magnitude. Michael Denton, a senior fellow at the Discovery Institute, says this complexity is without peer:

A cell consists of trillions of atoms, representing the complexity of a jumbo jet and more, packed into a space less than a millionth of the volume of a typical grain of sand. But unlike any jumbo jet, unlike any nano-tech, or indeed unlike even the most advanced human technology of any kind, this wondrous entity can replicate itself.[xviii]

He calls the cell a “third infinity”: “Where the cosmos feels infinitely large and the atomic realm infinitely small, the cell feels infinitely complex.”[xix]

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.

But If You Close Your Eyes and Cover Your Ears…

What do the materialists say about all this? Most will avoid such mysteries like the plagues of Egypt. But occasionally someone will declare that these words and sentences and equations are not “real”—similar to how we read in chapter one about philosophers who say that words are not “real”, or how neuroscientist Anil Seth declared that colors are not “real.” For example, Scientific American ran an article by John Horgan, director of the Center for Science Writings at the Stevens Institute of Technology, declaring that “just because a mathematical formula works does not mean it reflects reality.”

Isn’t that like saying that just because a cake recipe works does not mean you can use it to make a cake? Horgan tries to clarify himself:

Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real, and we shouldn’t confer upon them the status of “truth” or “laws of nature.[xx]

Now part of that statement might make sense if he just changed out the word real (the abstract meaning of which he assumed to be “real”!) for the word physical (though the meaning of that word is also abstract!). However, declaring that general relativity is not a law of nature is like declaring that apples are not a fruit of nature. Horgan went on to praise what he called the “modesty” of this view, and quoted a chemical engineer name Scott Beaver, who teaches online college prep classes for science and math: 

Here’s my simple answer about whether math is real: No. Math is just a way to describe patterns. Patterns are real, but not math. Nonetheless, math is really, really useful stuff![xxi]

What? That’s like saying language isn’t real but is instead just a way of using phonetic patterns to describe ideas—thus making it really useful for confusing students with self-contradictory statements.

The simple fact is that they can’t do science without math, but they can’t do materialism with math. Therefore, as Brown University mathematics professor, Philip J. Davis, and University of New Mexico mathematics professor, Reuben Hersh, explained in 1981, Darwinists have no other choice but to flat out insist on having it both ways—on having their immaterial cake and eating it, too:

Most writers on the subject seem to agree that the typical working mathematician is a Platonist on weekdays and a formalist on Sundays. That is, when he is doing mathematics, he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that he does not believe in it after all.[xxii]

Now, when you consider the vigorous intellectual discipline that characterizes science, it’s hard to overstate the absurdity of this flip-flop. It would be like inviting someone over for Sunday dinner and hearing them declare that they are a vegetarian even though, Monday through Friday, you have seen them gorging on meat. They have often boasted about their favorite recipes for wild chinook salmon, free-range Cornish hens, and wagyu bavette steaks. Nevertheless, every Sunday they identify as vegetarian and speak passionately about its socio-economic, environmental, and health benefits.

So why do Darwinists preach materialism and then suddenly flip to Platonism? Why “pretend,” as Davis and Hersh put it, and insist on a world of make-believe? Remember that Darwinism is dependent upon the presuppositions of materialism. There simply cannot be any immaterial/nonphysical phenomena in the universe. Therefore, every thought that we use, including numbers and equations, simply must be material. As Noam Chomsky put it, “[Thought] is an aspect of matter, just as electrical properties are an aspect of matter,” he says.[xxiii] Why? Because the alternative—that we are spiritual beings—is simply unacceptable. “Assuming that we’re organic creatures, and not angels, we have certain fixed capacities which yield the range of abilities that we have.”[xxiv]

Notice again the dichotomy: either the presuppositions of materialism are true, or we are spiritual beings. And keep in mind that we know, to the extent that we know anything at all, that the presuppositions are in fact false, leaving them no alternative but to flip-flop into nebulous philosophical babble.

For example, Max Tegmark, a physics professor at The Massachusetts Institute for Technology, starts by saying that we ourselves are, literally, abstract mathematical phenomena. “You’re a pattern in spacetime. A mathematical pattern. Specifically, you’re a braid in spacetime—indeed one of the most elaborate braids known.”[xxv] When he says that we are braids, he is actually talking not only about our minds but also about our physical bodies as mathematical objects. Indeed, he says the entire universe is literally made of math—a theory known as the mathematical universe hypothesis. The Greek mathematician Pythagoras—who had a big influence on Plato—taught the same thing 2,500 years ago with the creed “All things are number.” It’s all very interesting stuff, but I’m just going to skip straight to where Tegmark speculates about consciousness, which he suggests is the way information feels:

I think consciousness is the way information feels when being processed in certain complex ways. Since the different parts of your brain interact with each other, different parts of your reality model can interact with each other, so the model of you can interact with your model of the outside world, giving rise to the subjective sensation of the former perceiving the latter.[xxvi]

We might first think that Tegmark is speaking figuratively here when he calls consciousness a feeling. We might also think that he would not necessarily call himself a materialist, considering his extravagant view of mathematics as the basis of a Platonic reality. However, both hunches would be wrong. He is most assuredly a materialist, but he tries to completely redefine the meaning of the word matter. For in addition to being “the way information feels when being processed in certain complex ways”, he also suggests that consciousness is a “phase of matter.”

My guess is that we’ll one day understand consciousness as yet another phase of matter. I’d expect there to be many types of consciousness just as there are many types of liquids, but in both cases, they share certain characteristic traits that we can aim to understand.[xxvii]

Remember from middle school science class that matter has four phases—solid, liquid, gas, and plasma. Now Tegmark posits that consciousness could be a fifth phase of matter. This phase could come in many varieties that feel different from one another, just as there are many varieties of liquids—such as oil and water—which feel different. So it turns out he wasn’t speaking figuratively at all when he suggested that consciousness is a feeling. “I believe that consciousness is the way information feels when being processed. Since matter can be arranged to process information in numerous ways of vastly varying complexity, this implies a rich variety of levels and types of consciousness.”[xxviii]

So when you and I perceive information—say the information in this sentence—our brains are, literally, feeling it? Yes. “A conscious person is simply food, rearranged.” [xxix] You can taste food and you can feel information?

That’s not just a flip. That’s an Olympic-quality reverse 4 ½ summersault in the pike position.

Am I being unfair? Tegmark has done brilliant work and written fascinating books about physics—especially regarding the study of light—but when it comes to explaining math he is caught between a rock-solid idea and a hardy abstraction. They all are. Remember (from the introduction) how neuroscientist Koch called himself a “covert Platonist”? Naturalists don’t really have any other choice. The only other option is to offer outrageously hypothetical arguments that math is somehow not “real”.

For example, Ulf Danielsson, professor of Theoretical Physics at Uppsala University in Sweden, and a member of the Nobel Prize Committee in Physics, says that it might be theoretically possible for some alien race to do science without math in the way that a soccer player can play soccer without being able to calculate the mass and spin and velocity of the soccer ball. In his book, The World Itself: Consciousness and the Everything of Physics, he says, “There is nothing that basically forbids the existence of extraterrestrial beings who feel just as at home among planets and black holes as the soccer player with the ball.”[xxx]

Is he saying that the velocity of a kicked soccer ball only exists in a scientist’s head? In other words, if an athlete kicks a ball and no one is there to calculate the ball’s velocity, that velocity does not exist? If apples fall from a tree and no one is there to count them, no number of apples fall? (And if they announce the number in English, does that number only exist for English speakers?!)

Danielsson would say yes, for “mathematics arises only in the brain of a poor physicist who tries to understand what is going on.”[xxxi] Furthermore, he says, “Information for itself, without a material manifestation, is nothing. Information without matter simply does not exist. It is matter that matters.”[xxxii]

Still, he can’t help but flip-flop though he is more subtle about it than was Tegmark:

The mathematics we use to model the world in the form of natural laws does not exist in the world itself. The laws of nature manifest themselves and are identical with physical patterns in our brains that reflect phenomena that we observe in the world around us…It exists purely physically in our biological brains and disappears with us and is in that sense a biological construction dependent on our biological nature. The laws of nature exist in our heads and are the tools we use to understand regularities in the surrounding world.[xxxiii]

Regularities in the surrounding world? Like cycles and processes and waves and other regular patterns?!

Another hypothetical argument comes from physicist Sabine Hossenfelder, whom I quoted earlier regarding the constants of nature. She denies that those constants provide evidence for a designer.

The fine-tuning argument comes down to saying, “Based on my prior belief that the constants of nature could have been anything, I am surprised they are what they are.” But this doesn’t mean the universe is fine-tuned for life; it just means you expected something that turned out to not be the case. Big deal.[xxxiv]

We expected to hear a bunch of static and noise, but instead we heard beautiful music. Big deal. We expected a pile of grubs and leaves, but instead we got a feast of rich food, a feast of well-aged wine, of rich food full of marrow—all while the music is playing in the background. Big deal.

So, what does Hossenfelder say about math itself? That although it is very useful for describing the world, we do not need to assume “that the world is math” in the way that Pythagoras and Tegmark (before his summersault routine) did. “Because this additional assumption is unnecessary to explain what we observe, it’s not scientific.”[xxxv] Much to her credit, Hossenfelder does not flip-flop. However, she offers an outrageously hypothetical argument as to why math is not scientifically objective. She says that our discovery of math has simply been way too easy.

It strikes me as presumptuous to think that humans have already discovered the language in which nature speaks, basically on the first try and right after we appeared on the surface of the planet. Who is to say there may not be a better way to understand our universe than mathematics, one that may take us a million years to figure out?…Just because we don’t yet know a better way to describe natural phenomena than mathematics doesn’t mean there isn’t one.[xxxvi]

A million years. Seriously? In a million years we might figure out a way to do science without math; therefore, we should not conclude that math is objective. That’s like Danielsson arguing that, hypothetically, there could be an alien race that does science without doing math. These are the kind of arguments offered, by some of the brightest minds on the planet, in an attempt to deny that rational, creative (literally!) sentences and paragraphs saturate the cosmos.

Who is the Author of it all?

By contrast, the default gut reaction has always been to gaze in wonder at the heavens. As physicist Heinrich Hertz (1857-1894), who in the nineteenth century first proved the existence of electromagnetic waves, put it: “It is impossible to study this wonderful theory without feeling as if the mathematical equations had an independent life and an intelligence of their own, as if they were wiser than ourselves, indeed wiser than their discoverer, as if they gave forth more than he had put into them.”[xxxvii]

Hertz searched for electromagnetic waves based on the predictions of mathematician James Clerk Maxwell (1831-1879). In other words, the equations came first, followed by the discovery of what the equations governed. A devout Christian, Maxwell thought that the equations represented the work of God. “I believe, with the Westminster Divines and their predecessors ad Infinitum that ‘Man’s chief end is to glorify God and to enjoy him forever.’”[xxxviii]

The depth of the mystery of such equations nature continues to amaze scientists. For example, just in the past few years, physicists have proven that the equations governing quantum mechanics depend on what are called imaginary numbers or complex numbers. It was shocking, if not a little disturbing, when they first discovered—a hundred years ago—that imaginary numbers were not just a cool mathematical trick, but were as necessary for modern technology as is π. “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers,” wrote Erwin Schrödinger in 1926 regarding the wave function that he had discovered. “Y [the wave function] is surely fundamentally a real function.”

By “real” Schrödinger meant that the function surely must represent something we could picture, in the way that 2 + 2 = 4 can be pictured with four apples, or in the way that Isaac Newton’s 2nd equation, “Force equals mass times acceleration” (F = MA) can be pictured in the movement of a train or a cannonball, etc. But how could imaginary/complex numbers represent something in the physical world? We can sort of even picture what π represents or what infinity represents. But imaginary numbers are based on the square root of negative one! How do you picture that?

Put simply, imaginary numbers represent something non-physical—pure meaning. As such, the wave function that Schrödinger discovered was not just another example of an exquisitely rational nonphysical reality, but an example of how such a nonphysical reality is intimately linked to every quantum of the physical world.

Why was that so unpleasant and objectional to him? Well, he wasn’t just an atheist—he wanted to keep any notion of God as far away from himself as possible. Although he was married, he had many affairs and kept a diary of his sexual exploitations, in which he justified his “predilection for teenage girls on the grounds that their innocence was the ideal match for his natural genius.”[xxxix] In 2021 the Irish Times ran an article (Schrödinger had fled Germany in 1933 and eventually settled in Ireland, where he became a naturalized Irish citizen in 1948) that said he demonstrated “behaviour [that] fitted the profile of a paedophile in the widely understood sense of that term.”[xl]

For one reason or another, he and many others tried to do quantum mechanics without imaginary/complex numbers—calling the revised version “real quantum theory” as opposed to “complex quantum theory.” But the revised version simply doesn’t work. And in 2020, three scientists finally managed to prove that it doesn’t work. Marc-Olivier Renou, a theoretical physicist at the Inria Saclay Center in Paris, Antonio Acín, who leads the quantum information theory group at the Institute of Photonic Sciences in Castelldefels, Spain, and Miguel Navascués, a junior group leader at the Institute for Quantum Optics and Quantum Information in Vienna, devised an experiment comparing the two theories. “The experiment, repeated many times, will produce statistics that are compatible only with the predictions of complex quantum theory, not with real quantum theory.”[xli] Several other teams around the world soon confirmed their findings. “We now know that neither classical [materialistic theory] nor real quantum theory can explain certain phenomena, so what comes next?”[xlii]

What logically comes next is to acknowledge the existence of an immaterial reality that is just as “real” as is arithmetic or technology or chemistry or color or the meaning of the word real. For if science has taught us anything at all over the past 2000 years, it has taught us to have faith that if we study nature carefully enough, if we look and listen long enough, we will always be able to discover and decipher rational explanations. We will discover information that narrates the unfolding of the creation.

Now if the Author of life were to write “Made by God” somewhere, what medium do you think he would use? Pen and paper? Engraving on stone? Electromagnetic waves? Would he put his name on his creations like Louis Chevrolet or Henry Ford or Levi Strauss did? What language would we expect him to use? Ancient עִברִית? Modern, simplified 中文? Or something else?


[i] As stated by William H. Hobbs, “The Making of Scientific Theories,” Address of the president of Michigan Academy of Science at the Annual Meeting, Ann Arbor (28 Mar 1917) in Science (11 May 1917), N.S. 45, No. 1167, 443.

[ii] Galileo Galilei, The Assayer, (1623).

[iii] Martin Rees, Just Six Numbers: The Deep Forces That Shape the Universe (New York: Basic Books, 2000), 1.

[iv] Martin Rees, Just Six Numbers: The Deep Forces That Shape the Universe (New York: Basic Books, 2000), 178-179.

[v] Sabine Hossenfelder, Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. (New York: Viking, 2022) p. 152-153.

[vi] Richard Feynman, The Character of Physical Law, Modern Library; Modern Library ed. 1994, chap. 2.

[vii] Albert Einstein, quoted in Maurice Solovine, Albert Einstein: Lettres à Maurice Solovine (Gauthier-Villars, Paris, 1956). This quote is reproduced in Arthur Fine, The Shaky Game: Einstein, Realism and the Quantum Theory, 2nd edition (University of Chicago Press, Chicago, 1986), p. 110. I got it from Quatnum Reality by Jim Baggott (Oxford: Oxford University Press, 2020), Kindle edition.

[viii] Jorge Cham and Daniel Whiteson, We Have No Idea (New York: Riverhead Books, 2017), 98.

[ix] https://www.newworldencyclopedia.org/entry/Johannes_Kepler

[x] “Letter (9/10 Apr 1599) to the Bavarian chancellor Herwart von Hohenburg.” Collected by Carola Baumgardt and Jamie Callan in Johannes Kepler Life and Letters (1953), 50.

[xi] Paul Dirac, “The Evolution of the Physicist’s Picture of Nature.” (May 1963). Scientific American. Retrieved 4 April 2013.

[xii] Robert Boyle, Some Motives and Incentives to the Love of God (1659), 56-7.

[xiii] Robert Boyle, “Some considerations touching the usefulness of experimental philosophy” (1663). Quoted by Peter Gay in The Enlightenment (1977), 140.

[xiv] Richard A. Muller, Now: The Physics of Time. (New York: W. W. Norton & Company, 2016). Kindle Locations 4653-4657.

[xv] Justo L. González, The Story of Christianity: Volume 1: The Early Church to the Dawn of the Reformation (New York: HarperCollins, 2010), 65-66. Kindle Edition.

[xvi] 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

[xvii] Erika Check Hayden, “Human genome at ten: Life is complicated” (Nature Vol 464, April, 2010) 664–667. https://doi.org/10.1038/464664a

[xviii] https://mindmatters.ai/2020/10/new-book-our-bodies-cells-are-a-third-infinity-of-information/

[xix] Michael Denton, The Miracle of the Cell (Seattle, WA: Discovery Institute, 2020) 16.

[xx] John Horgan, “Is the Schrödinger Equation True?” (Scientific American: January 7, 2021) https://www.scientificamerican.com/article/is-the-schroedinger-equation-true1/

[xxi] IBID

[xxii] Philip J. Davis and Reuben Hersh, The Mathematical Experience (Boston: Birkhäuser, 1981), 362.

[xxiii] Tiger Web, “Noam Chomsky on the unsolved mysteries of language and the brain.” (ABC: March, 2016) https://www.abc.net.au/radionational/programs/philosopherszone/noam-chomsky-galileo-challenge-origin-of-language/7284178

[xxiv] Tiger Web, “Noam Chomsky on the unsolved mysteries of language and the brain.” (ABC: March, 2016) https://www.abc.net.au/radionational/programs/philosopherszone/noam-chomsky-galileo-challenge-origin-of-language/7284178

[xxv] Max Tegmark, Our Mathematical Universe (New York: Vintage Books, 2014), 283.

[xxvi] IBID 290.

[xxvii] IBID 295.

[xxviii] IBID 382.

[xxix] Max Tegmark. Life 3.0: Being Human in the Age of Artificial Intelligence. (New York: Alfred A. Knopf, 2017), 284-285.

[xxx] Ulf Danielsson, The World Itself: Consciousness and the Everything of Physics (New York: Bellevue Literary Press, 2020) Kindle Edition, p. 58.

[xxxi] Ulf Danielsson, The World Itself (New York: Bellevue Literary Press, 2020) Kindle Edition, p. 58.

[xxxii] Ulf Danielsson, The World Itself (New York: Bellevue Literary Press, 2020) Kindle Edition, p. 72.

[xxxiii] Ulf Danielsson, The World Itself (New York: Bellevue Literary Press, 2020) Kindle Edition, p. 72.

[xxxiv] Sabine Hossenfelder, Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. (New York, NY: Viking, 2022) p. 158.

[xxxv] Sabine Hossenfelder, Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. (New York, NY: Viking, 2022) p. 20.

[xxxvi] Sabine Hossenfelder, Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. (New York, NY: Viking, 2022) p. 21-22.

[xxxvii] Heinrich Hertz, “This Wonderful Theory,” Miscellaneous Papers, p. 318; quoted from George Musser, Spooky Action at a Distance (New York: Scientific American/Farrar, Straus and Giroux, 2015. Kindle Edition.

[xxxviii] James Clerk Maxwell, “Letter to Lewis Campbell (9 November 1851)” in Ch. 6: Undergraduate Life At Cambridge October 1850 to January 1854 — ÆT. 19-22, p. 158.

[xxxix] Humphreys, Joe (11 December 2021). “How Erwin Schrödinger indulged his ‘Lolita complex’ in Ireland.” The Irish Times. Retrieved 25 January 2022.

[xl] Humphreys, Joe (11 December 2021). “How Erwin Schrödinger indulged his ‘Lolita complex’ in Ireland.” The Irish Times. Retrieved 25 January 2022.

[xli] Marc-Olivier Renou, Antonio Acín and Miguel Navascués, “Imaginary Universe.” Scientific American, volume 328, No. 4, April 2023, pp. 62-67.

[xlii] Marc-Olivier Renou, Antonio Acín and Miguel Navascués, “Imaginary Universe.” Scientific American, volume 328, No. 4, April 2023, pp. 62-67.

First image (Andromeda with the naked eye) by Sojan Janso from Pixabay

Second image (Andromeda with a telescope) by Guillermo Ferla on Unsplash

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