Why Do We Need Faith?

“Why does belief in God require us to have ‘faith’? Why can’t it be just like science?”

I have heard this objection a number of times in various forms. The underlying claim is that science and religious faith require two opposite approaches to truth, and as rational people we should choose the rational approach of science rather than the faith-based approach of religion.

The hiddenness of God is a legitimate problem for the Christian faith (more on that below). However, this objection goes beyond that, implying a dichotomy between the scientific and the religious approach. In doing so, it represents a fundamental misunderstanding of both the scientific method and the process of faith.

First, it is naive to pretend that science does not require some sort of “faith,” a belief in things that have not been definitively proven. Every grade-school student at some point learns that the scientific method begins with a hypothesis—an unproven belief based on prior experience of the world. We then put that hypothesis to the test with a scientific experiment or observation, and based on the results of that test we may or may not reject our hypothesis or its alternatives.

The story of science taught in school usually focuses on instances where this process allows us to reject certain hypotheses with an extremely high degree of confidence. As a result, we say that some alternate hypothesis has been “proven” as a “scientific fact,” and we neglect the error bars as being insignificantly small. The earth is round, atoms are made of subatomic particles, the structure of DNA is a double helix—these are just some of the examples of “scientific facts” that have been discovered through care observation and experimentation.

In the trenches of modern research, however, one soon finds that these sorts of triumphs are the exception rather than the norm. More often, experiments leave us with open questions and uncertainties. Nutritionists still debate whether gluten, eggs, and meat are good for humans to eat. Cosmologists still debate the value of the Hubble parameter. Science exists today precisely because of the vast number of important questions about the physical world that lack a definitive answer.

But if some degree of uncertainty is inherent in both the scientific realm and the religious one, why is the language so different? Why don’t we every talk about the scientist taking “a leap of faith” or “trusting beyond what they can see”? Why is it only in the religious realm that we hear about “a season of doubt” or “wrestling with God”?

The answer lies partly in the semantics. Science and religion have adopted different terminology to emphasize different aspects. A scientist rarely talks about “wrestling” with a textbook or journal article the way a Christian “wrestles” with a passage in the Bible, though their tasks of interpretation, comprehension, and application are quite similar. Similarly, terms like “hypothesis,” “systematic uncertainty,” and “error bars” could easily describe aspects of the religious life, but they sound too rigid and mechanistic to describe an intensely personal and relational experience.

The reason for these differences in semantics is not entirely arbitrary, however. Rather, it points to the different goals of science and religion. The primary goal of science is a comprehensive, intellectual understanding of the physical world. Most of the time, we can separate these from deep, existential questions. Indeed, we can often separate the results of our science from our everyday lives entirely. It would be an enormous shock to my scientific career if someone were to disprove string theory, but in all honesty it would probably have little effect on my life outside the office.

Religion, on the other hand, aims to answer fundamental questions about meaning and purpose—questions that shape every other aspect of our lives. If someone were to disprove Christianity, it would throw every almost aspect of my life into chaos and force me to rethink my community, my career, my morality, and my identity.

Our religious beliefs affect how we live, and in turn, how we live affects what we believe. As a result, there is no way to completely filter out our “subjective” beliefs and approach religious faith from an “objective” lens. If you live like an atheist, eventually you will likely stop believing in God. If you start regularly attending religious services, you will probably start to find that religion more compelling. The terminology of faith emphasizes our active role in shaping our belief systems, and it emphasizes the experiential aspects of a relationship with God.

There is validity to the question of the hiddenness of God: why hasn’t God given us more certainty of his existence? Why leave any room for doubt? The Bible seems to suggest that the close connection between our beliefs and our behaviors is not an accident: God has given us enough evidence to attract those who want to find him, but he has left enough doubt to allow us to ignore him if we choose to do so. Jesus himself spoke in mysterious parables, and when asked why, he responded:

This is why I speak to them in parables:

“Though seeing, they do not see;
    though hearing, they do not hear or understand.

In them is fulfilled the prophecy of Isaiah:

‘You will be ever hearing but never understanding;
    you will be ever seeing but never perceiving.

For this people’s heart has become calloused;
    they hardly hear with their ears,
    and they have closed their eyes.
Otherwise they might see with their eyes,
    hear with their ears,
    understand with their hearts
and turn, and I would heal them.’”

—Matthew 13:13-15

An enduring teaching from the Bible is the idea that people matter more than information. “Knowledge puffs up, but love builds up,” writes Paul in 1 Corinthians 8:1. Ostensibly, God could have given us perfect knowledge of both theological truths and scientific ones. But imperfect knowledge brings people together, generating communities committed to uncovering the mysteries of the universe. In an age where information is easier to find than ever but human interaction is more elusive than ever, the persistence of these communities demonstrates that unanswered questions are not a plague on the human experience, but rather a blessing.

On the Atheistic Basis for Morality

A couple of years ago, I had a debate with an atheistic philosopher named Phil Harper on the podcast Unbelievable. The title of the debate was, “Religion vs. science: is there a conflict?” In practice, however, our discussion focused primarily on questions of morality, the problem of evil, and genocide in the Old Testament.

Frankly, I don’t love these sorts of debates, and I suspect I’ll never do one again. Phil himself was perfectly pleasant and respectful, but debates are inherently designed to be confrontational, and I would much prefer to discuss my own convictions–and doubts–with those who are curious about my beliefs rather than those who want to poke holes in my arguments.

Another issue I have with these sorts of debates is that they require quick thinking rather than slow, deliberate contemplation–they are like the theological equivalent of blitz chess. In general, I do not think that one’s deepest theological and moral convictions should be reasoned on the fly: belief systems require years and years of thoughtful consideration and refinement. Furthermore, in all honesty, I am not very good at thinking on my feet. As a result, I often struggle to find the right response to an atheist’s point, only to have something come to me hours or days later.

This was true of one point in my discussion with Phil. On the topic of morality, I raised the objection that without God, there is no moral judge, and therefore morality is entirely subjective. As a result, there is no way–even in principle–to determine whether our moral beliefs and values are superior to those of ancient cultures who believed in things like human sacrifice and viewed certain classes of people (women, slaves, etc.) as inherently inferior to others.

Phil responded as follows:

“I think we need to be careful not to imagine a false dichotomy between entirely subjective and entirely objective. There can be things that have properties of both.”

Phil gave the example of an exchange rate between different currencies as something that has both objective and subjective properties. He concluded:

“So, I reject the notion that we have to accept that morality has to be perfectly subjective or perfectly objective. What I think we do when we determine laws of morality is we use our judgment, we basically use our, sort of, moral instincts and our moral intuitions and our reason.”

Of course Phil’s analogy between money and morality is not perfect–no analogy ever is. Even if we accept the analogy, however, we find a major issue with Phil’s larger argument. Both man-made money and man-made morality work very well most of the time. Plenty of countries in today’s world have functioning monetary systems as well as functioning legislative and judicial systems. As long as those systems continue to function normally, most people can avoid ever having to ask the deeper questions of where their ultimate power and authority reside. 

But sometimes, those systems break down. All of sudden, it takes a wheelbarrow full of German marks to buy a single loaf of bread, and people realize that the money they had subjectively considered to be valuable has no inherent worth. Similarly, when a fascist dictator convinces an antisemitic majority that Jews are subhuman, it becomes clear that laws, policies, and the views of the majority are insufficient to determine moral value.

The real question at hand is: is there a notion of value that persists regardless of circumstances? In the case of money, the answer is a clear “no”: the value of a bank note is determined by the collective opinion of the masses, and it fluctuates based on how much people are willing to offer in exchange for such a note. If atheism is true, then the same is true for morality: moral values are determined by the masses and dictated by laws and regulations. If the majority decides to take away the rights of the minority, there is no atheistic basis on which to oppose them.

Phil went on to clarify his remarks about moral instincts and intuition: “You know from internal introspection that pain is bad.” 

In response, I would first like to point out that the belief that “pain is bad” was not actually so “intuitive” to many of our ancestors. Ancient philosophers and theologians across many different faith traditions have held nuanced views on pain, often seeing it as the crucible in which perseverance and strength may grow. Even Darwin’s theory views pain as a necessary part of the process of evolution by natural selection.

Ironically, there is another belief that the vast majority of people have inferred via intuition and internal introspection: the existence of a God or gods.

Indeed, it is quite shocking to me to hear an atheist use “instincts and intuition” as a justification for anything, since typically atheists want to say that virtually all of human experience is an illusion (free will, spiritual reality, etc.), and human intuition cannot be trusted. After all, if atheism is true, our beliefs have been programmed by an impersonal process for survivability rather than truth. Our concept of morality, just like our belief in God, has arisen because it confers some sort of evolutionary advantage. Why trust our intuition about one if not the other?

On theism, we do not need to choose between our intuition and experience on one hand and science and reason on the other: morality exists, free will exists, spiritual experience exists, and science works all for the same reason: God has given us the ability to seek and discover truth about the world around us.

Why Science Proves God

A Brief Reflection on Advent

I always enjoy seeing Christmas trees, lights, and decor in the weeks leading up to Christmas. It’s a reminder of the season, and all the memories that come with it—of family, food, and gifts. 

People debate how early you’re allowed to start celebrating Christmas with Christmas songs and carols. Most people in the US, at least, are OK with Christmas music after Thanksgiving. Some people get upset if they hear carols before then. 

Typically, Christmas itself serves as the culmination of the Christmas season. After that, attention turns to New Year’s. 

In the liturgical calendar, however, the celebration of Christmas is almost the opposite: it last between 12 and 40 days (depending on the tradition) and begins, not ends, on Christmas Day, December 25th.

Furthermore, the time of advent—beginning 22-28 days before Christmas and lasting until Christmas Day—is not a celebration, but rather a time of expectation and longing for the coming of the Messiah, Immanuel, God With Us. 

Traditionally, then, Christmas follows a similar pattern to Easter: one must first pass through the bitterness of pain and longing (advent and Good Friday) in order to get to the hope and joy (of Christmas and Easter).

It’s sad, and telling, that our culture has largely ignored the observation of sadness and darkness that is supposed to come before Christmas. Our culture wants to ignore suffering, pretend it doesn’t exist, and just skip straight to the celebration. In the end, however, it seems like many of us-myself included—tend to feel sad once December 26th rolls around. 

Something I’ve found useful on both Christmas Eve and the Saturday before Easter is to try to put myself in the shoes of a person living before the very first Christmas/Easter. I can’t help but to feel helpless as I reflect on a world without hope, where God seems removed from suffering and death feels like the inevitable end. 

Yet, these reflections on hopelessness make the holidays of Christmas and Easter that much more hopeful. Sometimes, we have to go through the feelings of sadness to truly grasp the joy that God has given us through the incarnation and resurrection. 

If you’re feeling sad this advent season, unable to feel the happiness that everyone else seems to feel, perhaps you’re actually closer to the true Christmas spirit than anyone else. 

And on the other hand, we really ought to bring back the full 20+ day Christmas celebration beginning on Christmas Day. The incarnation is worth more than a single day of celebration. 

Some Quotes from Florence

Earlier this week, I gave a physics seminar for the high-energy theory group at Scuola Normale Superiore in Pisa. The day before, I took a day trip to Florence with my wife–it was my second time there, and her first.

Florence is known as the birthplace of the Renaissance. It holds some of the most magnificent artwork ever created, from people like Leonardo da Vinci, Sandro Botticelli, and Caravaggio.

Yet of all the beautiful works in Florence, there are none more famous and frequently visited than Michaelangelo’s statue of David and Brunelleschi’s dome on top of the Cathedral of Santa Maria del Fiore. With the possible exception of the food, they were my favorite parts of Florence the first time I visited, and they were even more impressive the second time.

I once heard that Brunelleschi’s dome was designed before the architectural methods needed to build it had been invented, so Brunelleschi and his workers essentially had to develop the methods on the fly. Something I’d never heard before, though, was how Brunelleschi was so confident that they’d be able to figure it out. Here’s a Brunelleschi quote I read in Florence, as recorded by his contemporary and biographer Giorgio Visari (Transl. Bondanella & Bondanella 1998, 120):

“If the dome could be rounded, we might employ the technique employed by the Romans when they vaulted the Pantheon in Rome—that is, the Rotunda—but here we must pursue the eight sides, using iron ties and toothing in the stones, which will be an even more difficult feat. But when I remember that this is a church consecrated to God and the Virgin, I am confident that since it is being built in Her honour, She will not fail to instil knowledge where there is none and to provide to whoever may be the architect of such an enterprise the necessary strength, wisdom, and talent.”

The quote is striking because, at least in my experience, the Renaissance is portrayed as the work of enlightened individuals who cast off the straitjacket of religion. Yet it seems that Brunelleschi’s work was inspired by his faith in God.

Michaelangelo is quite plausibly the 2nd most famous artist of all time, after da Vinci. His sculptures are second to none, and his statue of David draws a 2-3 hour-long line of tourists on a daily basis. Yet near the end of his life, Michaelangelo wrote this poem, which is now displayed in Florence’s Museum of the Works of the Cathedral:

“The course of my life has now brought me
through a stormy sea, in a frail ship,
to the common port where, landing,
we account for every deed, wretched or holy.

So that now I clearly see
how wrong the fond illusion was
that made art my idol and my king
leading me to want what harmed me.

My amorous fancies, once foolish and happy:
what sense have they, now that I approach two deaths-
the first of which I know is sure, the second threatening.

Let neither painting nor carving any longer calm
my soul turned to that divine love
that to embrace us opened his arms upon the cross.”

It’s humbling to think that one of most accomplished humans who ever lived would look back on his life’s work as nothing but an idol. Yet Michaelangelo understood that even his most outstanding works paled in comparison to the divine love offered him through Christ.

Bayes’ Theorem VIII: The Hiddenness of God

The hiddenness of God is, in my opinion, one of the most troubling objections to the Christian faith. As we saw last time in our discussion of the absence of evidence, the question on which everything hinges is this: if God exists, should we have seen more evidence of his existence?

The reason why the hiddenness of God bothers me is because it is very easy to envision scenarios in which God does give us clearer proof of his existence. God could speak to us audibly, or appear to us visibly, on a regular basis. God could shower us with miracles. One can easily imagine a world in which debates over the existence of God don’t even exist.1

On the other hand, just because one can envision such a world, it doesn’t necessarily mean that such a world is more likely on theism. Perhaps God might have reasons for not revealing himself to us in such an obvious way.

My personal view is that it is a bit hard to see why an abstract, hypothetical God would remain hidden. But I can see reasons why the Christian God, in particular, would remain hidden within the particular Christian story.

The first reason is the imperfect nature of our relationship with God. We live in a broken world, and the Bible connects this brokenness to the brokenness of our relationship with God. In a perfect world, God’s presence would manifest clearly in the world around us. Before the Fall, for instance, Adam and Eve seem to speak regularly with God. But in our world of evil and suffering, God is distant from us.

One could imagine a world in which evil and suffering exist but God is not hidden from us: he speaks to us audibly on a regular basis and gives us clearer instructions as to our meaning and purpose in life. But it is not clear (at least to me) that such a world is more likely under theism than a world with suffering and a hidden God. In other words, it seems hard to argue that the conditional probability of a hidden God given theism and a broken world is smaller than the probability of a clearly evident God given theism and a broken world. If so, this already cuts the probabilistic gain for atheism over theism from the hiddenness of God to no more than a factor of 2, since P(hiddenness of God | theism + evil) ~ 1/2, P(hiddenness of God | atheism + evil) ~ 1.

But within the Christian context, this factor can perhaps be cut down even more, because the God revealed to us in Jesus is a God who intentionally remains hidden to us. Jesus spoke in mysterious parables and when his disciples asked him why, he replied,

“To those who listen to my teaching, more understanding will be given, and they will have an abundance of knowledge. But for those who are not listening, even what little understanding they have will be taken away from them.That is why I use these parables, For they look, but they don’t really see. They hear, but they don’t really listen or understand.” (Matthew 13:12-13)

Jesus could have spoken more clearly, but he deliberately chose to speak to his followers in a way that confused those who sought to trap him while imparting wisdom to those who truly sought to understand. Jesus spoke in riddles, and if we believe God is revealed to us in Jesus, it is perhaps not so surprising that God speaks to us in riddles as well.

But why does God do such a thing? Jesus’s answer suggests that God hides from us in order that we might hide from him, as Adam and Eve did in the Garden of Eden after their disobedience. Indeed, when people came to Jesus demanding to see a sign, Jesus responded, “Only an evil, adulterous generation would demand a miraculous sign, but the only sign I will give them is the sign of the prophet Jonah.” Jesus did plenty of signs—healing the sick, feeding the hungry, casting out demons, raising the dead—but when people come to him to test him, he refuses. Jesus consistently used his miraculous powers to help people who came to him in desperation, but he kept those powers hidden from those who came only to test him.

So, in conclusion, I claim that P(hiddenness of God | Christianity + evil) is actually rather close to 1, so while atheism gets a probabilistic boost over Christianity from the hiddenness of God, it isn’t a very big one. Of course, this raises the question of why there is evil and suffering in the first place. That is a conversation for another day, but if the problem of the hiddenness of God is simply a corollary of the problem and evil and suffering, that’s already a big win for theism: two of the most serious objections to the existence of God have been reduced to a single one.

  1. That said, it’s also easy to imagine a world in which there is less evidence for God, such as a world where there are no intelligent observers to even ponder the existence of God. This usually gets classified under the fine-tuning argument. ↩︎

Physics, Evolution, and Atheism: Pick Two

Einstein once wrote,1 “The eternal mystery of the world is its comprehensibility…The fact that it is comprehensible is a miracle.”

It is astounding that physics works at all: it is astounding that the world around us follows mathematical equations with such regularity and uniformity.

At the same time, it is perhaps even more astounding that we as a species are able to make sense of the laws of nature. We are able to perform the calculations and experiments needed for science to progress. We are able to learn and acquire true beliefs about the world around us.

Consciousness is incredible. Beliefs are incredible. True beliefs are even more incredible. Where did this all come from?

Well, it depends on whom you ask.

Part I: The Evolutionary Biologist’s Tale

The evolutionary biologist (or the evolutionary psychologist, to be more specific) has a ready answer to this question. Consciousness, according to the evolutionary psychologist, emerged through the process of natural selection, conferring an evolutionary advantage upon its beneficiary. Similarly, since organisms with false beliefs and defective cognitive faculties are more likely to make foolish/dangerous decisions and get themselves killed, the organisms that survive to pass on their genes will tend to be more intelligent and more capable of forming true beliefs, and thus reliable cognitive faculties are preferred by natural selection.

This story can be summarized by the following feedback loop: 

True beliefs (e.g. that type of berry is poisonous) lead to beneficial behaviors (e.g. eating some nuts instead of berries), and in turn the process of random mutations+natural selection ensures that more intelligent organisms, who are better able to form true beliefs, are more likely to survive. This tale nicely explains why true beliefs are more likely to emerge: they share a symbiotic relationship with beneficial behaviors and increased survivability.

There’s just one problem with this tale: it contradicts the physicist’s tale.

Part II: The Physicist’s Tale

According to the physicist, macroscopic phenomena emerge from the classical limit of the underlying quantum theory of our universe. Biology is just a special branch of organic chemistry, chemistry is special subfield of solid state physics, and solid state physics is simply the application of particle physics to systems with large numbers of microscopic degrees of freedom. Indeed, there are plenty of examples in which an observed phenomenon in each of these fields can be understood or even derived through a more fundamental field (see e.g. the entire field of statistical mechanics).

Furthermore, the underlying quantum theory of our universe is—depending on your interpretation of quantum mechanics—either (a) completely deterministic, following from unitary evolution of the Wavefunction, or else (b) deterministic up to some random quantum mechanical fluctuations. Even in case (b), however, these random quantum fluctuations are largely irrelevant for most processes of interest to us, including e.g. the evolutionary process. (When biologists say that mutations are random, they mean that they occur without preference for the survival of the organism and/or they cannot be predicted accurately in light of our ignorance of the full quantum microstate of the system, not that they are fundamentally random in a quantum mechanical sense.)

Thus, according to the physicist’s tale, all of our behaviors are determined exclusively by the laws of physics. Free will is an illusion: our future actions are determined by deterministic evolution of the current state of the universe combined with random fluctuations that are out of our control (and are not really important for neurobiology, anyway).

The physicist’s tale can be summarized with the following picture: 

Now, here’s the main point: if behaviors are determined exclusively by the laws of nature, then the link between behaviors and beliefs that was so crucial to the evolutionary biologist’s story is severed. If (Libertarian) free will is just an illusion, then our beliefs have no impact whatsoever on our actions, which in turn means that there can be no evolutionary advantage gained by having true beliefs. The fact that our beliefs seem to accurately correspond to reality—or even the fact that we have beliefs at all, that we as a species have gained consciousness—cannot be attributed to natural selection. Whatever ultimately explains consciousness is a mystery, and it remains an enormous coincidence that our beliefs match our external reality at all.

Part III: The Problem

If it really is true that free will and consciousness are illusions that emerge from the laws of nature, it’s incredible how much of a role they play in our lives. Indeed, as you are reading this, you are wasting precious time thinking about consciousness that could be spent on your Darwinian duties of hunting, gathering, and reproducing. Yet, the physicist of the aforementioned tale would have us believe that somehow, at eternity past, the Wavefunction foresaw a species that would while away their days bickering about free will and consciousness. And it just so happens that we would not only engage in these activities, but we would also (by some miracle) develop subjective experiences and the illusion of free will, so that somehow we come to believe that our thoughts are causally impacting our actions when in fact they are not. Oh, and also, our beliefs somehow actually match our external reality, allowing us to make sense of the world in the first place.

To put it another way, the problem is this: the evolutionary biologist wants to say that consciousness and beliefs are correlated through the process of natural selection. But the physicist says that ultimately, even natural selection is merely an illusion—it is an effective description of something that admits a more fundamental description as a collective phenomenon of zillions of molecules evolving according to the laws of nature. And the problem is that, in this more fundamental description, there is no room for “beliefs” to have a causal impact on the rest of the system.

Incidentally, this also means that the physicist will not buy into the biologist’s understanding of animal consciousness and suffering. The biologist observes a dog whimpering from hunger or a cat noticing its own reflection in a mirror and concludes that these creatures must be self-aware. How else could you explain such human-like behaviors?

Yet the physicist responds that he does have an alternate explanation for such behaviors: they result from the laws of physics applied to many-body systems, without any need to appeal to concepts like consciousness or self-awareness. To the physicist, there is no clear way to leap from observations of behavior to inferences of subjective experience. Of course, the physicist may observe that these two are miraculously linked in the case of his own subjective experience, but the idea that this miraculous link extends to other entities—especially nonhuman ones—is an assumption that is highly questionable on the physicist’s view that behavior cannot be used to infer consciousness.

At this point, you might be tempted to dismiss the coldhearted physicist, who cannot who explain the miraculous coincidence between external reality and subjective experience, who attributes all of human behavior to the motion of molecules, who hears a hungry dog whimper and dispassionately reminds himself that this doesn’t prove that the dog is really conscious, who rejects the idea that right and wrong exist in any objective sense.

The problem is that you cannot dismiss the physicist’s view of reality without committing to a tremendous amount of ontology beyond the laws of nature themselves. You must believe that something fits into the question mark box of the figure above, which not only explains consciousness and beliefs, but also fits perfectly with the laws of physics, thus enabling the biologist’s feedback loop between belief and behavior. You must reject reductionism. And you  should believe that free will exists in a libertarian sense, such that the free choices of creatures actually have a causal impact on their behaviors, and thus on the physical motion of matter and energy. If you want to believe in right and wrong, then you must further assume that moral values exist, and these too just happen to fit perfectly with our beliefs, our experiences, and the laws of physics.

What we need, then, is a paradigm that makes sense of all of these coincidences, which unifies behavior, belief, morality, and physics into a single coherent framework.

This is what theism is all about.

Part IV: The Theist’s Tale

Forget your Santa-like caricature of God as an old bearded man who grants wishes: theism is not about magic, invisible entities wandering around in our universe. Rather, it is a framework centered about the question of why the world is the way that it is, as opposed to some other way.

On theism, our universe should be understood—at its most fundamental—to be not merely a quantum state in some high-dimensional Hilbert space, but rather a world, or if you like, a story. This means that it is designed to have free moral agents—characters in the story, if you will—who face moral decisions and must act accordingly. For this to work, the characters must be able to make sense of the world around them, which means that their cognitive faculties must be at least somewhat reliable, their beliefs and behaviors must agree, and the world around them must be a rational place. To the theist, evolution is not (or at least, should not be) an alternative to design, but rather it is simply one of many instances in which our thirst for truth is satisfied by a deeper understanding of the world around us—in this case, a deeper understanding of our origins as a species.

The theist’s tale can be roughly summarized by the following diagram: 

Note that the theist need not reject physics or biology; theism does not replace the laws of physics or the process of evolution, but rather it places them within a larger framework that explains why they are correlated. On theism, the remarkable agreement between our beliefs, our experiences, our behaviors, and the laws of physics is not a coincidence: it is a necessary feature for the story of our world to make any sense at all.

To be sure, theism does not necessarily explain how these different aspects of our universe fit together. I have no idea how consciousness or free will have come to exist (nor, I suspect, does anyone else), and I do not understand how these fit into the laws of physics that I know and love. There is plenty of unresolved mystery in the story above, even once we bring God into it.

But from a probabilistic perspective, there is a big difference between a mystery and a coincidence. Even the best scientific theories raise new questions and leave some things unexplained. For instance, the standard model of particle physics fits the LHC data incredibly well, even if it leaves unresolved the question of what is dark matter. Evolution explains the diversity of species very well, even if it doesn’t address the question of where life came from in the first place. In science, we often have to live with some amount of mystery.

But when we see a coincidence—something that is enormously improbable given a certain theory or framework—it tells us that we need a new framework altogether. In Newtonian gravity, for instance, it is a huge coincidence that an object’s gravitational mass and its inertial mass are exactly the same. This coincidence points us toward a more fundamental framework—general relativity—that explains this coincidence.

And just as we do not completely toss out Newtonian gravity once we have the more fundamental framework of general relativity (after all, Newtonian gravity works quite well for most practical purposes), we should not toss out physics or biology once we have theism—after all, both the physicist’s laws and the biologist’s evolutionary account work quite well within their respective domains of validity. Rather, the problem comes when we try to make the physicist’s story the Story (capital S) that explains everything else. This is where naturalism fails, and a new paradigm is needed to tie all the pieces together.

Much more could be said about theism, of course, but let me conclude by pointing out that if the theist’s tale is true, then love, beauty, hope, and joy are not merely convenient names for “hormones gone haywire” (as an atheist friend of mine once described it), but rather they are central to what our world is all about. We can, of course, glean some insight into the mind of our Creator by gazing at the stars through a telescope or peering into the inner workings of a blood cell through a microscope, but ultimately none of these reveal God’s mind as well as the minds of our fellow created beings do. It is through loving relationships with others that we may truly begin to see the face of God, and most of all it is through a relationship with Christ that we may know not only the mind of God, but his heart as well.

  1. Franklin Institute Journal, March 1936 ‘Physics and Reality.’ ↩︎

Bayes’ Theorem VII: Is Absence of Evidence Evidence of Absence?

Is absence of evidence evidence of absence?

It depends.

If I tell you that there is an elephant in your backyard, and you look out your kitchen window and don’t see an elephant, then you have very good evidence that I was lying. In this case, absence of evidence is good evidence of absence.

But if I tell you that there are inchworms all over your backyard, and you look out your window and don’t see an inchworm, it is not good evidence that I was lying. Here, absence of evidence is not very good evidence of absence.

The key difference is that, in the first case, you would have expected to see the elephant if it were there, while in the second case, you likely would not have seen an inchworm even if it were there.

This difference can be easily quantified from the perspective of Bayes’ theorem. Recall from previous posts that the probability of a given hypothesis H updates in light of new evidence E according to the size of the ratio

r = P(E | H) / P(E | !H), 

where P(E | H) is the probability of the evidence given that H is true and P(E | !H) is the probability of the evidence given that H is false.

If r is larger than 1, then E gives evidence in favor of H, whereas if r is smaller than 1, then E gives evidence against H. More generally, larger the ratio r, the more it favors H. 

To analyze the case of the elephant above, we set E = “you don’t see an elephant in your backyard” and H = “there is an elephant in your backyard.” Here, P(E | !H) is equal to 1 for all practical purposes, since there is no way you will see an elephant in your backyard if there isn’t one there. Additionally, P(E | H) is quite close to zero, since if there were an elephant in your backyard, you really ought to see it. Therefore, r is very close to zero in this case, indicating that the absence of evidence for the elephant is very strong evidence against the presence of an elephant in your backyard.

On the other hand, suppose we set E = “you don’t see an inchworm in your backyard” and H = “there is an inchworm in your backyard.” Once again, P(E | !H) is equal to 1 for all practical purposes, since there is no way you will see an inchworm in your backyard if there isn’t one there. However, in this case, P(E | H) is also rather close to 1, since it’s quite likely that you wouldn’t be able to see an inchworm from you kitchen window, even if there is one in your backyard. As a result, r in this case will be only slightly smaller than 1: the absence of evidence for the inchworm gives only weak evidence against the presence of the inchworm.

More generally, absence of evidence for some hypothesis will typically provide some evidence of absence, but as in the case of the inchworm, this evidence may be very, very weak. Another good example of this is my field of string theory, which famously has no real experimental evidence in its favor. However, this is due to the fact that the energies required to test string theory lie well beyond our technological capabilities, so the absence of evidence for string theory gives only very weak evidence against string theory.

So, when it comes to the existence of God, one might reasonably ask: does absence of evidence give evidence of absence?

As in the cases of the elephant and the inchworm, the key to answering this question is to compute the ratio r, which brings us to the key question: if God does in fact exist, should we have seen more evidence of his existence?

I’ll return to this question soon.

Bayes’ Theorem VI: Does Theism Bear the Burden of Proof?

There’s a strange line of thinking out there that stipulates that theism is a “positive truth claim” while atheism is a “negative truth claim,” and therefore theism “bears the burden of proof.”

As Scott Church explains nicely in this blog post, any intellectually honest denial of theism must include a fully developed philosophy of naturalism, which brings its own positive truth claims (e.g. the universe is a brute fact, causality is an illusion, free will is an illusion, etc.). Naturalism makes positive truth claims about the nature of reality, just as theism does.

But even apart from this objection, there is a more general question raised by this strange line of thinking: do positive truth claims bear a higher burden of proof than negative truth claims? And what does the “burden of proof” even mean in the first place?

From a Bayesian perspective, the “burden of proof” lies simply on the side with a lower prior probability; if some hypothesis A is more likely true that false a priori, then the proponent of A has to provide more evidence than the opponent of A.

It is clearly not true that the prior probability of a positive truth claim is inherently lower than that of a negative truth claim. If my roommate tells me that he picked up some toilet paper at the store, I don’t feel the need to go into the bathroom to confirm. Unless my roommate is a pathological liar, the prior probability to support his “positive truth claim” that he went to the store and bought toilet paper is much larger than the prior probability of the negative truth claim that he did not buy any toilet paper. And in fact, there really isn’t even a very good distinction between “negative” and “positive” truth claims, as we saw in the last post.

Does theism have a lower prior probability than naturalism? Aron Wall makes a good point in his blog post about fundamental reality: the remarkable effectiveness of mathematics in describing the world around us strongly suggests that the fundamental reality behind all that exists is either something like a mathematical equation or something like a mathematician. The former possibility is (a form of) naturalism, and the latter is theism. Before considering any of the other arguments for/against the existence of God, (e.g. fine-tuning, the problem of evil and suffering, etc.) there doesn’t seem to be an especially good reason to favor one or the other, so in my view the prior probabilities of theism and naturalism are both pretty close to 50%. From a Bayesian perspective, neither the theist nor the atheist bears any more of a burden of proof than the other.

But there is another, more practical sense in which the term “burden of proof” could be used, aside from the theoretical question of which hypothesis is more likely. In criminal law, for instance, we declare that a defendant is innocent unless proven guilty. Here, the burden proof is placed on the prosecution not because the prior probability of the defendant’s innocence is more likely than their guilt, but rather because we as a society have decided that it is better to let a guilty man walk free than it is to punish an innocent man. More generally, given the possibility of both a false positive or a false negative, we tend to place the burden of proof on whichever error will prove more costly.

So, from this more practical perspective, does theism or naturalism bear the burden of proof? Here, Pascal’s wager comes in, and it points heavily toward the latter; from a practical perspective, the expected value of putting one’s faith in God is far larger than the expected value of putting one’s faith in naturalism. I have written about Pascal’s wager previously, and defer further discussion on the subject to that post.

In conclusion, Bayes’ theorem gives us no strong grounds to place a higher burden of proof on theism than naturalism, and more generally it does not necessarily favor negative truth claims over positive ones. From a practical perspective, atheism bears a higher burden of proof than theism; a drowning man must give a very good reason before rejecting his best possible lifeline.

My Book Is Now Available!

My first book, a memoir called Chasing Proof, Finding Faith, is now available for purchase on AmazonChristianBookTyndale, or Target. The book tells the story of my journey to faith as a college student, and the road of science and faith that I’ve traversed since then.

Many thanks to my friend and fellow Christian physicist Aron Wall for his excellent foreword, and to the folks at Tyndale House Publishers for making this book a reality.