Which comes first—information or the medium for that information?
Nobody ever accidently goes to the store, buys a bunch of ingredients, brings them home and then says, “Oh look, without even thinking of it I made a large sausage, green pepper, and purple onion pizza and also a Radicchio Caesar Salad with sourdough garlic croutons and, oh wow, here’s a pitcher of blueberry kombucha!” Such things do not happen by accident. For we always precede any dish with some kind of recipe in mind. In similar fashion, a set of rules always precedes any sports game, an architectural blueprint always precedes a building, and a DNA “blueprint” always precedes an organism. So also every rock, every speck of dust—indeed, every single quantum in the cosmos—is preceded by rational words.
This is an objective, testable, falsifiable, massively confirmed fact. Yet this one simple fact, like all the other characteristics of information, completely evaporates the presuppositions of materialism. Therefore, the scientific establishment has no other choice but to categorize this fact as a philosophical conclusion rather than a scientific one and then to try to hide it under a dense fog of relentlessly esoteric philosophical “debate”. But if we just hone in on the observations then the facts will speak for themselves. We’ll start with the mathematical facts and then move to physical laws.
The Nature of Infinity
“It appears to be a universal feature of the mathematics normally believed to underlie the workings of our physical universe that it has a fundamental dependence on the infinite,” writes Sir Roger Penrose, professor of mathematics at Oxford University.[i] Indeed, there is also a massive branch of mathematics, called set theory, that focuses entirely upon infinities, which come in various sizes and forms. The discoverer of set theory, German mathematician George Cantor (1845-1918), saw a deep connection between mathematics and his Christian faith in God, whom he linked with the Absolute Infinite. He believed that God had entrusted him with an understanding of infinities so that he could reveal them to the world.
Of course many mathematicians and philosophers passionately disagreed with Cantor about whether infinities actually exist. Why did they disagree? And why do many philosophers and mathematicians still disagree? It is not for any mathematical reasons at all. Instead, it is precisely because infinities do in fact point directly to spirituality and to an intelligence author. For if they exist then they are not only rational (in the way, for example, that a calculus textbook is rational book written by rational, creative people) but also non-negotiably immaterial.
That is to say that infinities can never be physically represented or imaged in any way. By contrast, for example, the number 5 can be physically imaged by five abacus beads, V knots in a rope, cinco apples, 五 electronic pulses, etc. (Ad infinitum!) But infinity is, by its very nature, 100% unimaginable. Likewise, there are the irrational numbers—the infinite set of irrational numbers—including the constants of nature like π (3.14…), the natural logarithm (2.78…), and the golden ratio (1.61…). Although these numbers can be approximated, they are like infinity in that they can never be fully imaged or represented because they go on eternally. Yet they are absolutely everywhere in nature, just as objective and as useful as if you found them in a textbook.
So what is a good materialist/monist to do? First they change the subject from talking about God to talking about philosophy. (After all, if they’re going to deny spirituality then which god or religion would you be denying the claims of? It’s much easier to find a generic representation of it all.) Then they wax philosophical. So, for example, instead of saying that they don’t believe in spirituality, they say that they don’t believe in a Platonism, which is the philosophy of immaterialism based on the work of the Greek philosopher Plato. He taught that the physical world was a reflection of a nonphysical world of ideals. So naturalists will say that they don’t want to espouse Platonism, and instead they will hold to what’s called Formalism, which focuses on descriptions of the world rather than explanations of it. Or they might also say that they hold to what’s called Intuitionism, which simply says that we know some things to be true intuitively and so do not need an explanation. Intuitive truths are simply part of our DNA, so to speak.
Nevertheless, everyone knows that always looming behind the debate are questions about the author of mathematics and of nature. As former Brown University mathematics professor, Philip J. Davis (1923-2018), and former University of New Mexico mathematics professor, Reuben Hersh (1927-2020), put it:.
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.[ii]
The trouble is that it is terribly difficult to say that you don’t believe infinities exist. It’s on par with saying that you don’t believe that the sky is blue or that the sun will rise tomorrow. (Hence Davis and Hersh use the verb pretend.) For without the use of mathematical infinities we would have precisely zero modern technology. In building a communications satellite, for example, the trigonometry and calculus that engineers use is just as objective and necessary as are the wires and screws and screwdrivers.
But the implications go far deeper: just as a recipe precedes a dish and a blueprint precedes a building and a DNA “blueprint” precedes an organism and a thought precedes a typewritten word, so also mathematical information always precedes its medium. For although infinities—and by implication all of mathematics—exists without any physical representation, the reverse is not true. That is to say that we cannot have any physical phenomenon that are not mediums of mathematical information. For example, no matter how many apples have fallen from a tree—whether 3 or 30 or 33.333—there will most certainly be a particular number of apples under that tree. The information is there, available to be read, like a book on a shelf. If the information were not there, the apples would not be there.
Simple. Shattering. Cantor understood well why this haunted the materialists.
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.[iii]
“Just shut up and calculate,” the Formalist and Intuitionist reply. “We own mathematics. Why bother with such vexing questions anyway? We’ve got work to do.”
But Cantor continued to ask such questions with the fervency and zeal of a true pioneer. “In mathematics the art of asking questions is more valuable than solving problems,” he said in his 1867 doctoral thesis. He insisted that mathematicians were explorers of an objective reality, not just the describers of the physical world. And through his explorations he categorized several types of infinities that he discovered. But there were some infinite sets for which, no matter how he tried, he was not able to calculate their size. In 1878 he put forward what is called the Continuum Hypothesis, which is about the possible sizes of infinite sets. But much to his dismay he never proved it, and so the Formalists and Intuitionists said that his inability to prove it justified their denial of the actual existence of infinities. This drove Cantor into deep bouts of depression and he died in a sanatorium in 1918.
But then in 1931, German mathematician Kurt Gödel, who would become one of Einstein’s best buddies, wrote two brief proofs that shook the foundations of both philosophy and mathematics. He proved that Cantor’s Continuum Hypothesis, whether it is true or not, could not actually be proven to be true. For that matter, he showed that we can never actually decide whether any mathematical axiom is true or not. Now that might almost sound like a self-contradictory statement: he mathematically proved that we cannot mathematically prove a statement to be true? He proved that it is impossible to know everything there is to know about mathematics. Although we can know axioms to be useful and consistent for all practical purposes, we do not get to be the authors of their absolute truthfulness. Today, nearly 100 years later, Gödel’s two proofs, which are usually referred to as Gödel’s Incompleteness Theorems, are just as mesmerizing as ever.
In effect, when we know that mathematical axioms are true, we know it by faith. Of course it’s not blind faith in arbitrary statements, but rather reasoned faith in self-evident facts. As Gödel famously put it, “I don’t believe in empirical science. I only believe in a priori truth.” That doesn’t mean that empirical science is not effective and useful; it means that empirical science ultimately rests upon objective, self-evident truths that we cannot wrap our minds around, that we know we will never be able to wrap our minds around. As Galileo had intuitively realized 300 years earlier:
There are such profound secrets and such lofty conceptions that the night labors and the researches of hundreds and yet hundreds of the keenest minds, in investigations extending over thousands of years would not penetrate them, and the delight of the searching and finding endures forever.[iv]
Now, whereas the Formalists and Intuitionists had previously told Cantor that his failure to prove the Continuum Hypothesis revealed the lack of a rational foundation for all of his work on infinities and classical set theory, Gödel showed that the foundations of all of mathematics were likewise unprovable. He said that Cantor’s infinite set theories were just as robust and meaningful as any other consistent branch of mathematics, and that those who still believed that a proof of the Continuum Hypothesis and other such hypotheses was necessary were simply in denial of the facts. To reject set theory because we cannot prove one axiom was no solution at all, for our descriptions of rationality and of nature will always be lacking.
Only someone who (like the Intuitionist) denies that the concepts and axioms of classical set theory have any meaning could be satisfied with such a solution, not someone who believes them to describe some well-determined reality. For in reality Cantor’s conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of reality.[v]
Gödel’s proofs sent shockwaves across the world. Atheist philosopher Bertrand Russell had just a few years earlier finished his massive Principia Mathematica, an ambitious attempt to replace all of religious belief and philosophical belief with mathematical logic. For example, Russell spent several hundred pages laying the foundation for the proof that 1+1=2 because he wanted mankind to be the author of rationality and of axiomatic truth. Then Gödel came along and, in just about 20 very complex pages, proved that whether or not the statement “1+1=2” is true (and of course it is true), we do not get to be the ones who decide that it is true—no matter how badly we wish for it, no matter how hard we try. It remains a self-evident truth that we can only know by reasoned faith. For that matter, we cannot be the authors of any such truth, only the believers and teachers and preachers of it. The math that we use can be reliable enough to run a global economy and to put men on the moon, but it is still something that we do not control any more than we control the tides. As Daniel Andrés Díaz-Pachón, Research Assistant Professor at the Division of Biostatistics at the University of Miami, put it:
The highest we can reach is to assume (which is much weaker than to know) that the system is consistent and to work under such assumption. But we cannot prove it; that is impossible! In the end, the most formal exercise in knowledge is an act of faith. The mathematician is forced to believe, absent all mathematical support, that what he is doing has any meaning whatsoever. The logician is forced to believe, absent all logical support, that what he is doing has any meaning whatsoever… Faith is the most fundamental of the mathematical tools.[vi]
So just as any mathematician or scientist must have faith that infinities are objective realities, Gödel showed that the same was true for all of mathematics: it is objective, not subjective. At the foundation of mathematics is infinite, objective, rational, creative information.
And again, that foundation is also non-negotiably immaterial, for infinity can never be physically represented and remains unimaginable. But now if you can have rational information without a physical medium—and yet the reverse is not true—then the implication is that information precedes its medium. And that is exactly what physicists have concluded.
The Preeminence of the Laws of Physics
Physicist John Archibald Wheeler (1911-2008), a member of the Manhattan Project and a professor of physics at Princeton University, famously coined the phrase “it from bit” in 1989 to explain how information precedes every quantum of the cosmos. For scientists had discovered, starting with the double-slit experiment back in 1801, that the questions that they asked in the laboratory didn’t just lead to the discovery of answers, but also actually prompted the physical creation of answers. By contrast, what they had been used to was finding that answers were simply waiting to be discovered in nature, like books sitting on a shelf. For example, if they asked, “How does a plant turn solar energy into chemical energy?” they could eventually discover the objective equation for photosynthesis. But with the advent of quantum mechanics, they learned that answers literally did not exist until after they asked the questions.
I, like other searchers, attempt formulation after formulation of the central issues and here present a wider overview, taking for working hypothesis the most effective one that has survived this winnowing: It from Bit. Otherwise put, every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes or no questions, binary choices, bits.
It from Bit symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most instances—an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this is a participatory universe.”[vii]
From at least the early 20th century, physicists realized that their experiments contradicted the presuppositions of materialism. Not only that, they realized that it directly indicated the presence of free will in the scientists themselves. So from beginning to end this discovery has led to endless speculations about the divine Author of quantum mechanics in particular and of nature in general. Thus Wheeler and his wife, for example, were founding members of the Unitarian Church of Princeton. But of course other scientists have persisted in arguing that the evidence does not point to God. For example, listen to physicist Lawrence Krauss, professor of physics and cosmology at Arizona State University:
In quantum gravity, universes can, and indeed always will, spontaneously appear from nothing. Such universes need not be empty, but can have matter and radiation in them, as long as the total energy, including the negative energy associated with gravity [balancing the positive energy of matter], is zero…The lesson is clear: quantum gravity not only appears to allow universes to be created from nothing—meaning, in this case, I emphasize, the absence of space and time—it may require them. ‘Nothing’—in this case no space, no time, no anything!—is unstable.[viii]
What in the world, you ask, could it possibly mean for “nothing” to be unstable and hence lead to the existence of “something”? Stephen Hawking (1942-2018) said very much the same thing:
Because there is a law such as gravity, the universe can and will create itself from nothing…Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.[ix]
Okay, these are profoundly bold assertions to make, so let’s look at them very carefully. When both Krauss and Hawking said that the universe could be created from “nothing”, what they meant by the word “nothing” was “nothing…material or physical”. But they also meant that in the absence of anything physical there is still something: there are still verbal laws such as for quantum gravity. And so not only are they acknowledging that these laws, these sentences, are immaterial/nonphysical, but they are also saying that it is entirely coherent to believe that these sentences preceded the universe. So where exactly would such sentences come from? If it takes a rational, creative person decades of study before they can begin to understand these laws—and that only after dozens of generations of mathematicians and scientists dedicated their lives to deciphering them—then how can we possibly assume that the laws just wrote themselves?
I do not question the brilliance of these scientists. I’m sure they understand all these laws 10,000 times better than I ever could. But I do want to point out just how very much they are taking for granted. Keep in mind that the laws are only coherent in the context of exceedingly complex systems of mathematics, physics, and chemistry. For example, the sentence “Energy equals mass times the speed of light squared” combines high levels of mathematics with a chemist’s understanding of mass and energy and a physicist’s understanding of light. And yet Krauss and Hawking want us to believe that these sentences simply existed prior to the existence of mass or energy or light?
Again, I actually have no problem believing that the sentences could come first. I just have trouble seeing how this does not point directly to rational, creative author. Have we ever known of such laws apart from rational authors? How could they possibly declare that nature is inevitable? As the editors at Evolution News and Science Today put it:
None of this splendor and precision is “inevitable,” any more than a Shakespearean sonnet or the Sistine ceiling are inevitable. The mathematical subtlety of physics is the work of a living Mind of inexpressible grace and power.
The design of nature is not “inevitable.” Creation is from purpose, not decay. Those select scientists who are privileged to see and understand the intricate mathematical beauty of nature owe its Author a citation.[x]
Nothing doing, says Dr. Michael Shermer, founder of The Skeptics Society and a former columnist for Scientific American. He says that if people want to believe that all these observations provide evidence of God, that only begs the question and avoids the real issue.
Theists retort that God is that which does not need to be created. But why can’t the universe be in the same ontological and epistemological category as God, wherein we could simply say that the universe is that which does not need to be created? Theists counter that the universe had a Big Bang beginning and everything that begins to exist has a cause. But not everything in the universe is strictly causal, such as some quantum effects, and even though our universe in its current state can be traced back to a Big Bang beginning that doesn’t mean there was not a previous universe that gave birth to our universe through the Big Bang. Theists also note that that the universe is a thing, whereas God is an agent or being. But don’t things and beings all need a causal explanation? Why should God be exempt from such causal reasoning? Because, rejoins the theist, God is supernatural—outside of space, time, and matter—whereas everything in the universe, and the universe itself, is natural—made up of space, time, and matter, so God and the universe are ontologically different.[xi]
No doubt “Where did the Creator come from?” is an inevitable question. Regardless, here is what we know: rational, creative, immaterial information saturates the cosmos, and we cannot know where it came from. That is effectively what Gödel discovered—that the question “Where did mathematics come from?” is unanswerable. In fact, the sense of awe that Gödel’s equations stir in a mathematician might be somewhat comparable to the sense of awe you can feel in asking God where he came from. But that is still zero reason to deny the fact that all of nature is a medium for rational, creative information. Shermer is a zealous materialist and so he, like all the others, simply wants to take rationality for granted even though none of them can acknowledge that it is immaterial and that by the word “nothing” they still need the presence of something—words and sentences and paragraphs, enough to at least fill a few dozen textbooks.
Now, just to be clear, the discoveries of quantum mechanics are massively confirmed. Scientists are not tell us what we do not know, but rather what we do know. Which is actually very little. For example, as chemist Wolfram Research cofounder Theodore Gray put it, we have no idea what electricity actually is:
The force that holds compounds together and drives all of chemistry is the electrostatic force. It’s the same force that holds a balloon to the wall after you rub it on your shirt or makes your hair stand on end when you shuffle on the right kind of carpet.
It’s easy to start describing this force. Any material can carry an electric charge, which can be either positive or negative. If two things have charges of the same sign, then they repel each other. If they have charges of the opposite sign, then they attract each other. (It’s a bit like with magnets, where two north poles or two south poles repel each other, but a north pole and a south pole attract.)
We know a lot about how this force works—how strong it is, how quickly it weakens with distance, how fast it can be transmitted through space, and so on. These details can be described with great precision and mathematical sophistication. But what the electrostatic force actually is remains a complete and utter mystery.[xi]
For that matter, the part of the universe that we are familiar with—the part composed of electrons, protons, and neutrons—only accounts for five percent of the universe. Jorge Cham, who earned a PhD in robotics at Stanford, and Daniel Whiteson, professor of experimental particle physics at the University of California, Irvine, wrote a wonderful book titled We Have No Idea: A Guide to the Unknown Universe. The talk about many of the mysteries scientists are trying to figure out. For example, they explain how a proton is made up of 3 quantum particles called quarks. The mass of the 3 quarks combined is only 1% the mass of the proton. The other 99% is binding energy. But we have no idea why. It seems entirely arbitrary. And where did all that energy come from anyway? Furthermore, those 3 quark particles only account for 1% of the mass after they have been bound together. Prior to binding they actually have no mass at all.
Particles—in our current theory—are actually indivisible points in space. That means that in theory they take up zero volume and they are located at exactly one infinitesimal location in three-dimensional space. There’s actually no size to them at all. And since you’re made of particles, that means you’re not mostly empty space, you are entirely empty space!…
We like to think of particles as tiny little balls of stuff. That works for lots of thought experiments even though particles aren’t little balls. Not even a little bit. According to quantum mechanics, they are superbizarre little fluctuations in fields that permeate the entire universe.[xii]
Could that be any more bizarre? On the one hand, we can define physical stuff as that which can be directly or indirectly seen, heard, felt, tasted, smelled, or measured in some way. Thus the words physical and nonphysical are entirely coherent. There is a clear distinction between the medium of information and the meaning of information. And yet all of these scientists are concluding that physical mediums spring from nothing? As Cham and Whiteson ask it:
How does it make sense for a particle to have zero mass? For example, the photon has exactly zero mass. If it has no mass, then it’s a particle of what? If you demand that mas is equal to stuff, then you have to conclude that a massles particle literally has nothing to it. Instead of thinking about a particle’s mass as how much stuff is crammed into a supertiny ball, just think of it as a label that we apply to an infinitesimal quantum object.”[xiii]
A label? As in a word? I didn’t say that. They said it, and they’re the scientists. But I will also point at that waves are, strictly speaking, immaterial. For waves are nothing but patterns. You cannot describe any physical qualities for a wave any more than you can describe, as we concluded previously, the physical qualities of a circle. Is a wave solid, liquid, or gas? It can’t be all three at the same time.
Now speaking of labels, consider a truck driving down the road. If you study it, you will find some information written on it. It has a 7.3-liter V-8 gas engine and runs on a four-wheel drive chassis. If you look inside the car, you’ll find a book that gives more detailed information about it—the precise amount of fuel, oil, and other fluids that it holds, the specifications for tuning it, etc. If you go to an auto-parts store, you can get a much larger book with even more detailed information about the engine and transmission. And if you go to the factory, you can find the actual blue prints for every cubic millimeter of the truck. However, you don’t need to comprehend any of that information in order to grasp its authorship: “[Made by] Ford or Chevrolet or Toyota”.
In like manner, what if we found “Made by God” written in nature. What language would we expect him to write it in—ancient Hebrew, modern simplified Chinese, or Java? Whatever language he used, it preceded nature. As Isaac Newton put it in 1713 in “General Scholium”, which was an essay appended to Philosophiæ Naturalis Principia Mathematica, one of the most important books in the history of science:
Though these bodies may indeed continue in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws. Thus, this most beautiful system of the sun, planets, and comets, could only proceed from the council and dominion of an intelligent and powerful Being.
Gödel believed the same thing and worked for many years on a mathematical proof for the existence of God, but he didn’t show it to anyone until he was on his death bed. He described his own faith as “baptized Lutheran (but not member of any religious congregation)”.[xiv] Although he seldom joined in any public worship his wife, Adele, said, “Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning.”[xv] Perhaps the reason he never showed anyone his mathematical proof was because he knew it was a moot point, since the belief in the rationality of mathematics demands that it has an Author. As Díaz-Pachón put it:
In order for faith and reason to have a foundation, not merely from an epistemological viewpoint but also from an ontological one, there must be something that sustains it —a First Sustainer undergirding them all. There is no logic without a Logos. Faith’s only task is to accept that such a Logos does exist. The opposite is despair, meaninglessness.[xiv]
[i] Roger Penrose, The Road to Reality (New York: Alfred A. Knopf, 2005), 357.
[ii] Philip J. Davis and Reuben Hersh, The Mathematical Experience (Boston: Birkhäuser, 1981), 362.
[iii] Georg Cantor, Gesammelte Abhandlungen [Collected Essays], eds. A. Fraenkel and E. Zermelo (Berlin: Springer-Verlag, 1932), 374. As quoted in Infinity and the Mind by Rudy Rucker.
[iv] Galileo Galilei, 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.
[v] Kurt Gödel, Collected Works: Volume II: Publications 1938-1974, edited by S. Feferman et al (Oxford: Oxford University Press, 2001), 181.
[vii] John Archibald Wheeler, “Information, Physics, Quantum: The Search for Links” in the Japanese journal Proceedings of the 3rd International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, 1989 (309-336). https://philpapers.org/archive/WHEIPQ.pdf
[viii] Lawrence M. Krauss. A Universe From Nothing: Why There Is Something Rather Than Nothing. (New York: Free Press, 2012) 169-170.
[ix] Stephen Hawking and Leonard Mlodinow, The Grand Design (New York: Bantam, 2010), p. 180.
[xi] Michael Shermer, “Why is There Something Rather Than Nothing?”, Skeptic Magazine, Vol 23 No 4, 2018. https://www.skeptic.com/reading_room/why-is-there-something-rather-than-nothing/#note02
[xi] Theodore Gray, Molecules: The Elements and the Architecture of Everything (New York: Black Dog & Leventhal Publishers, 2014), 12.
[xii] Jorge Cham and Daniel Whiteson, We Have No Idea (New York: Riverhead Books, 2017), 66-67.
[xiii] Jorge Cham and Daniel Whiteson, We Have No Idea (New York: Riverhead Books, 2017), 67.
[xiv] Hao Wang, Reflections on Kurt Gödel, (Mass: MIT Press, Cambridge, MA, 1987.
[xv] Hao Wang, A Logical Journey: From Gödel to Philosophy. A Bradford Book, 1997. Print. p.316.