How do you count to 10?

Matthew Connally is a recent graduate of our World Journalism Institute mid-career course, but I first met him in 1992 when he was editor in chief of The Daily Texan, the student newspaper at The University of Texas at Austin. From there he moved on to earn a master’s degree at Trinity Evangelical Divinity School and become a pastor in Princeton, N.J., and a campus chaplain at Princeton University. From 2012 to 2016 he was a teacher and principal in Nanjing, China, and since 2017 has been a pastor at a Houston-area Chinese church.

So let’s review: a Christian on a highly secularized campus newspaper, an evangelical at theologically liberal Princeton and in neo-Maoist China, and (as this essay shows) a critic of Darwinism. Matt is used to being in a minority, and by taking on Darwinism he’s cementing his position as a smart person who doesn’t believe what the smart set still believes—even though discoveries in recent decades about the complexity of cells, the fine-tuning of the universe, and the information coding in and around us have kicked the legs off materialism’s dining room tables.

This is the sixth in an occasional series of essays for our Saturday Series. In the last installment, he asked: What are words? In this one, asks the same question about numbers. —Marvin Olasky

If we couldn’t count to 10, then we couldn’t do algebra, geometry, calculus, physics, chemistry, or biology. We couldn’t put a man on the moon or a slushy machine at the corner trading post. In fact, we would have no technology. But then, if we couldn’t count to 10, the word zero would be meaningless anyway.

Yet this remarkable ability is impossible for your brain to do. You can count to 10, but your brain cannot. You can use your brain to count to 10, in principle, the same way you can use an abacus to add up $10, or use a speedometer to drive 10 mph, or use a thermometer to measure 10 degrees Fahrenheit.

But you are not your brain.

That is the main point of this series, Materialism 101. Perhaps you’ve seen these articles and thought them a bit odd. Indeed, the question, “How do you count to 10?”, almost sounds silly. But I need odd questions to assault a stubborn lie: The modern scientific establishment insists that we are our brains, that we do not have souls, that we are nothing but flesh and bones.

So let me just walk you through one more example of why we know that this is not true. Let’s look at our ability to do arithmetic. It’s easy to take for granted, and the establishment insists that we take it for granted. And yet that is like a fish taking water for granted or a musician taking scales for granted or an astronomer taking telescopes for granted.

Water is a big deal for a fish, scales are a big deal for a musician, telescopes are a big deal for an astronomer, and our ability to count to 10 is a big deal for us. How do we do it?

In pursuing that question, let’s first put the question into context by looking at how Darwinists answer it. One of their strategies is simple obfuscation.

Bury the mystery under philosophical fog

Listen to Harvard professor Steven Pinker explain how we should take our ability to do arithmetic for granted as innate:

Humans … appear to have an innate sense of number, which can be explained by the advantages of reasoning about numerosity during our evolutionary history. (For example, if three bears go into a cave and two come out, is it safe to enter?) But the mere fact that a number faculty evolved does not mean that numbers are hallucinations. According to the Platonist conception of number favored by many mathematicians and philosophers, entities such as numbers and shapes have an existence independent of minds. The number three is not invented out of whole cloth; it has real properties that can be discovered and explored. No rational creature equipped with circuitry to understand the concept “two” and the concept of addition could discover that two plus one equals anything other than three.^[i]

What? What in the world might be the “real properties” of the number three? Does it have size or texture or temperature? Pinker doesn’t say. And if his explanation isn’t confusing enough, we need to recognize that even though he is a zealous materialist—having declared in 2007 that “Scientists have exorcised the ghost [i.e., your soul] from the machine [i.e., your brain]”^[ii]—nevertheless, when he resorts to Platonist philosophy, he is doing a 180-degree turnabout. Plato (428-348 B.C.) taught his followers that the physical world was just a shadowy image of a perfect nonphysical world of ideas—phenomena that philosophers call Platonic forms.

So how can a devout materialist like Pinker get away with using Platonism? Well, Darwinists do this all the time. Remember when the neuroscientist Christof Koch called himself a “covert Platonist”? Let me repeat a quote that I’ve used before from two world class mathematicians:

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.^[iii]

It is hard to overstate the insanity of this flip-flop. It would be like inviting someone over for dinner every Sunday and then hearing them repeatedly 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 resort to Platonism? In this case, the mystery is in the numbers themselves: What do seven or eight or nine look like or feel like? Contrary to Pinker’s suggestion, they have no tangible qualities that you can touch or see. For that matter, the nonphysical nature of mathematics is an objective, testable, falsifiable fact.

That presents quite a dilemma to our universities. Darwinism requires materialism to be true. There simply cannot be any immaterial phenomena in the universe. Why? If we were to acknowledge that something immaterial existed, that would very quickly lead to the conclusion that we ourselves (the minds that are using our brains) are likewise immaterial. And that is an unacceptable conclusion.

So Pinker buries the mystery under philosophical fog and expects students to take it all for granted. After all, counting is so easy.

Now if obfuscation doesn’t work, then another strategy is to insist that we not ask certain questions.

Just shut up and calculate

Pinker is no neuroscientist—he’s a cognitive psychologist specializing in psycholinguistics—so let’s listen to one of the world’s leading cognitive neuroscientists who specializes in mathematics.

Stanislas Dehaene, a professor at the Collège de France, agrees with Pinker’s assumption that we are our brains. However, Dehaene disagrees with the notion that numbers are Platonic forms existing independently of minds. Why does he disagree? Because he is acutely aware of the dilemma. If numbers really existed outside of our skulls, then there would be no way to explain how the brain perceives them. “If these objects are real but immaterial,” Dehaene asks, “in what extrasensory ways does a mathematician perceive them?”^[iv]

That’s an excellent question. So what’s his solution for maintaining materialism? How does he get past this seeming impasse? By arguing that mathematics only exists in our heads—that our brains literally create it. The title of one of his books is The Number Sense: How the Mind Creates Mathematics.

The evolution of mathematics is a fact. Science historians have recorded its slow rise, through trial and error, to greater efficiency. It may not be necessary, then, to postulate that the universe was designed to conform to mathematical laws. Isn’t it rather our mathematical laws, and the organizing principles of our brain before them, that were selected according to how closely they fit the structure of the universe?^[v]

But if the brain creates mathematics, does that mean that the number three, for example, is a clump of neurons? Is it literally gray and squishy? Surely not. That would be about as coherent as saying, like Pinker, that numbers have “real properties that can be discovered and explored”. We might as well be talking about Lucy in the sky with diamonds, right? If numbers only exist inside our skulls, what exactly are they?

Don’t ask that question! No, seriously, Dehaene insists that we not ask what numbers are: “Providing a univocal formal definition of what we call numbers is essentially impossible: The concept of number is primitive and undefinable.”^[vi] He sees the contradiction but just insists upon ignoring it altogether. Isn’t that rather astonishing?

Now Dehaene is a brilliant scientist and has done fascinating research on the brain. Just as a computer scientist could write a book explaining how your laptop processes mathematical data, so also Dehaene explains the latest scientific understanding on how the brain processes mathematical data. It’s truly dazzling science.

But at the end of the book, in the final chapter, titled “What is a Number?”, he insists that we not ask that question. Because when it comes to explaining how we actually perceive math he says we must simply take it all for granted as intuitive, just like Pinker said we have to take our sense of numerosity for granted as innate, neuroscientist Christof Koch and physicist Sean Carroll said that consciousness is simply intrinsic, and linguist Noam Chomsky said that our ability to perceive words is innate.

It’s much better to leave some things unwritten and unspoken. At all costs, stay away from The-Question-That-Must-Not-Be-Named.

Okay, what reason does Dehaene give for insisting that we not ask some questions? (Is it because otherwise evolutionary theory would die a violent and fiery death? Is it because we cannot, under any circumstances, open the door to spirituality?) It’s because we would be torturing students and practicing poor pedagogy.

Ironically, any 5-year-old has an intimate understanding of those very numbers that the brightest logicians struggle to define. No need for a formal definition. … If I insist so strongly on this point, it is because of its important implications for education in mathematics. If educational psychologists had paid enough attention to the primacy of intuition over formal axioms in the human mind, a breakdown without precedent in the history of mathematics might have been avoided. I am referring to the infamous episode of “modern mathematics,” which has left scars in the minds of many schoolchildren in France, as well as in many other countries.^[vii]

Note that even though he isn’t writing a textbook—so there’s no danger of torturing students—Dehaene still doesn’t want to talk about it. He simply concludes our understanding is intuitive: “The human baby is born with innate mechanisms for individuating objects and for extracting the numerosity of small sets.”^[viii]

Babies can extract the numerosity of small sets? As simple as that sounds, it is a glorious ability! It’s what Einstein called “the eternal mystery of the universe”. And although it is impossible to explain, Darwinists have found all sorts of ways of dancing around the question so that they can cling to the presuppositions of materialism.

Take intelligence for granted

Last spring neuroscientist Jeff Hawkins wrote A Thousand Brains, in which he tried to explain how the brain stores mathematical equations:

For mathematics, the brain must discover useful reference frames in which to store equations and numbers, and it must learn how mathematical behaviors, such as operations and transformations, move to new locations within the reference frames. To a mathematician, equations are familiar objects, similar to how you and I see a smartphone or a bicycle.^[ix]

I can ride a bike while talking on the phone because both are physical objects made of metal. Is Hawkins suggesting that equations are objects with, as Pinker said, “real properties that can be discovered and explored”? He doesn’t say. He just wants to take our perception of math totally and completely for granted.

And the establishment insists not only that circuitry must be able to perceive equations and “understand the concept ‘two’ and the concept of addition”, but also that it makes no difference whether that circuitry is made of neurons (as for us humans) or made of silicon (as for computers). In other words, robots can comprehend math, too.

In his book, How to Create a Mind: The Secret of Human Thought Revealed, Google technologist Ray Kurzweil said, “My own leap of faith is this: Once machines do succeed in being convincing when they speak of their qualia and conscious experiences, they will indeed constitute conscious persons.”^[x] (Qualia here refers to the perception of information—such as the number three—as if it is a quality of matter.)

That is a leap of faith: That if a robot appears to be conscious then it is, literally, a conscious person. That if a machine appears to be able to perceive immaterial numbers, then it does in fact perceive immaterial numbers.

Just let that sink in for a moment. Do we really want to train students to think that way?

That would be like biting into a vegetarian Impossible Whopper and then declaring that because it looks like beef, feels like beef, smells and tastes like beef, it is, literally, beef. Perhaps a mysterious interspecies phase-transition emerged from the intrinsic interplay of some highly differentiated quantum states, causing the soybean cells to transmogrify into cow cells.

Or we could say that it’s an excellent simulation of beef, but that it’s still a plant-based burger. And likewise, no supercomputing, deep-learning, nuclear-powered robot will ever be able to count to 10. Yes, we can use robots and supercomputers to discover information that we could not otherwise discover, but that’s no different from using a telescope to see information that we could not otherwise see, or using an ultra-deepwater, dynamic-positioning, semi-submersible drilling rig to extract information that we could not otherwise extract.

We still have no reason to assume any of those machines perceive arithmetic any more than the internet perceives English or a calculus textbook perceives calculus.

Yet Darwinists insist on assuming it anyway. Circuitry simply must be able to count, and mathematics must have evolved with that circuitry. Michio Kaku, a theoretical physics professor at the City College and City University of New York, argues that even a thermostat can be said to have a degree of consciousness.

The simplest level of consciousness is a thermostat. It automatically turns on an air conditioner or heater to adjust the temperature in a room, without any help. The key is a feedback loop that turns on a switch if the temperature gets too hot or cold.^[xi]

If you wonder why I’m asking odd questions, here is a prime example. Just stop and think: What do feedback loops look, sound, feel, taste or smell like? Do they have any “real properties that can be discovered and explored”? How could any circuitry ever perceive the presence of a feedback loop?

The coherent alternative

Consider the possibility that thermostats are not in fact conscious and, moreover, it is a big deal to be able to read a thermostat. Who designed it and programmed feedback loops into it? For that matter, what is using our eyes to read it? What is directing the nerve cells in our brains?

No matter how far we calculate—to the mercury vessel, to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer. That is, we must always divide the world into two parts, the one being the observed system, the other the observer. In the former we can follow up all the physical processes (in principle at least) arbitrarily precisely. In the latter, this is meaningless.^[xii]

That was written in 1932 by quantum physicist John von Neumann in a textbook that to this day provides the orthodox understanding of quantum mechanics. He and his colleagues concluded that the observer (i.e., the scientist in the laboratory) is not a physical brain but is an “extra-physical” entity: “It is inherently entirely correct that the measurement or the related process of the subjective perception is a new entity relative to the physical environment [i.e., a nonphysical entity] and is not reducible to the latter.”^[xii]

Von Neumann and his colleagues did not set out to overthrow materialism or to understand the mind-over-matter mystery. (Ninety-five percent of his textbook is complex math about wave functions.) They were just following the science. And they concluded that the scientists themselves were extra-physical entities—or souls.

They confirmed what we intuitively know to be true: The reason that we humans are very familiar with immaterial phenomena like numbers and equations is because we have immaterial souls. We extra-physical entities are using our brains in the same way that we use our smartphones and our toaster ovens and our pick-up trucks.

You can flip-flop on the issue or you can try to avoid the questions, but you cannot coherently argue for an alternative. Henry Stapp, a highly published physicist at the Lawrence Berkeley National Laboratory who worked with giants like Werner Heisenberg, Wolfgang Pauli, and J.A. Wheeler, explained it this way in 2017:

Given this recognized major importance of the mind-brain problem, you might think that the most up-to-date, powerful, and appropriate scientific theories would be brought to bear upon it. But just the opposite is true! Most neuro-scientific studies of this problem are based on the precepts of nineteenth century classical physics, which are known to be fundamentally false. Most neuroscientists follow the recommendation of DNA co-discoverer Francis Crick, and steadfastly pursue what philosopher of science Sir Karl Popper called “Promissory Materialism”.^[xiiii]

Thankfully, regardless of where you stand, there is one thing we can all agree on: we were born this way. Remember how Dehaene said that babies can extract the numerosity of small sets? From the mouths of infants and nursing babes comes recognition of the rational, creative power behind not just our own creations—our spaceships and slushy machines—but also all of creation itself.

NOTES:

[i] Steven Pinker, The Blank Slate (New York: Viking, 2002), 192.

[ii] Steven Pinker, “The Brain: The Mystery of Consciousness”, Time magazine Vol 169 No 5. January 29, 2007. http://content.time.com/time/m...,9171,1580394-1,00.html

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

[iv] Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition (New York: Oxford University Press, 2011), 225.

[v] IBID, 232.

[vi] IBID, 222.

[vii] IBID, 223.

[viii] IBID, 227.

[ix] Jeff Hawkins. A Thousand Brains: A New Theory of Intelligence. (New York: Basic Books, 2021) p. 82. Kindle Edition.

[x] Ray Kurzweil. How to Create a Mind: The Secret of Human Though Revealed. Ray Kurzweil. (New York: Penguin Books, 2012.) p. 209-210.

[xi] Michio Kaku, The Future of the Mind: The Scientific Quest to Understand, Enhance, and Empower the Mind (New York: Doubleday, 2014), Kindle edition.

[xii] John von Neumann, Mathematical Foundations of Quantum Mechanics, published 1932, translated from the German edition by Robert T. Beyer in 1949 (Princeton, NJ: Princeton University Press, 1983), 418-419.

[xiii] IBID, 418.

[xiiii] Henry Stapp, Quantum Theory and Free Will (Springer International Publishing, 2017), Kindle Locations 870-874.