On the Function of Faith in A Probably-Simulated Universe

What is there to believe in, when you believe only the things that should be believed?

A Summary

People who believe in science and rationality often state that their beliefs are formed from sound foundations of observation, experimentation, and reasoning. They dismiss religion and faith as unscientific forms of thought which cannot lead to knowledge. At the same time, thought experiments like the simulation hypothesis show that there are fundamental limits to what knowledge can be derived from observation and experimentation. I will go further and propose that a form of faith (i.e. unreasonable belief) is necessary to live in and make sense of our world.

This work was carried out as part of a preliminary investigation for the Human Inductive Bias project.

The Argument

It is shocking how much we don’t know about the world. At any moment our senses give us a dismally small picture of our immediate surroundings. I cannot see past the wall a metre or two to my right in the office where I am typing this. I cannot even see under the table where my laptop is sitting unless I really make an effort. The whir of the air conditioning could be blocking out distant screams from a stabbing. For all I know, nuclear war could have started three minutes ago and unless someone thought to send a news alert I would die blissfully ignorant. A new unified theory of physics could have been born five seconds ago, and I would be none the wiser.

But I am not only ignorant about the state of the world. I am also ignorant about its mechanisms. I don’t really know how my phone works. I kind of know how a computer works, but not what’s going on at the processor or OS level. I certainly don’t know how my kidneys work at a chemical level, or how my brain works at any serious level at all. When I try to enumerate everything I am ignorant about, I am stunned by how impossible this task seems. How do plants communicate? Why does my skin suffer from eczema? Why is there war, or suffering, or economic injustice? How do you predict the movements of the stars? How do they make ink pens, combustion engines, headphones, or chocolate bars with embedded wafers? What even is dark matter? The awesome weight of the mysteries of the world crashes down on me and I sit stunned at my chair.

Yet, at the same time, I am not really aware of my ignorance unless I really think very pointedly about everything I don’t know. If you asked me any of those questions above, I’d probably give a vague, high level answer that sounded coherent but had little more than fragments of memorised factoids and ad-hoc speculation to back it up. Any expert in the field of engineering, manufacturing, science, or medicine would have no trouble tearing apart my claims. Even though my day job as a researcher is supposedly to push the limits of what I don’t know, it is only in very specific and bounded domains. When I’m not thinking about AI or the nature of minds or neuroscience I feel confident that I am an informed person whose beliefs about the world are backed by observed facts and collected evidence. This is manifestly untrue.

Still, there must be some reason we don’t spend our lives huddled in our rooms, peeking fearfully at the alien and strange world outside. And it is true that, in many aspects, my life proceeds as if I had a well-grounded grasp on what is true or not. I am not generally harmed by my ignorance of the principles of car manufacturing when I cross the road. I can complete my chores and take a shower despite being ignorant of the mysteries of consciousness. I use my laptop without precise knowledge of the OS-level memory management techniques that enable me to play video games and watch youtube videos at the same time. In short, I suffer limited harm and still achieve my high level goals despite my broad-ranging and almost total ignorance of the fundamental nature of the universe. And I suspect I am not alone.

So how do we get our information? A lot of it is from deferrals to other minds. I do not independently verify the truth of the Fritz-Haber reaction or the existence of gravity, I take it on faith that Newton was not lying to me when he wrote his Principia Mathematica. Some is our sense data. And quite a lot appears to be unspoken assumptions that certain things will transfer: rules like “things that were true in the past will probably be true in the future”, or “the laws of physics are the same everywhere, even in places where nobody has measured them”, “most things have a persistent nature and are not illusions”, and so on. But very little of what we believe is subject to the tiresome and somewhat-inaccurate process of experimental validation, much less replication at different intervals. Don’t judge the conspiracist or the peddler of pseudoscience too harshly: Epistemically speaking, we are all skating on very thin ice.

If we think back through our evolutionary history, it becomes clear that the idea that we derive our knowledge from principled observation and reason is a very new and somewhat silly one. Fish, cows, cats, dogs, and many other animals all manage to gain complex and high-dimensional knowledge about reality and improve their chances of survival despite being manifestly unable to write scientific papers or perform non-trivial reasoning tasks. Your dog is not putting a learned hierarchical Bayesian model of primate psychology into practice when they pant at you in the hopes that you will give them a treat—at least, not consciously.

So what kind of knowledge are we producing, if we are not using the clean hypothesis-confirming model of the Scientific Method? Here the new science of artificial neural networks (NNs or ANNs) offers us some clues—ANNs do not necessarily “grasp the meaning” or “understand the mechanisms” of the data they are presented with. In fact, many would argue that they cannot understand or grasp much of anything, since they aren’t conscious or sentient. Instead, they learn a series of transformations that turn input data into ideal outputs that minimise some loss function. Sometimes these transformations are largely stateless, as in the case with arithmetic: the answer to 20*5 is not dependent on the answer to 4+3. Sometimes the transformations require some information transfer from moment to moment, as with an RNN or transformer learning to predict text sequences. Still, nothing here demands that they “get”, on some deep level, why what they’re doing works. Does a transformer need to know the true nature of New York to internalise that the phrase “the American city of New” is usually followed by the token “York”? Probably not.

The same is true of our evolutionary ancestors: a nematode does not need to understand the intricacies of the ATP metabolic cycle to seek out food in its native habitat. A cat does not need to understand mouse neuroscience to catch mice. I further argue that the same is true for humans. We do not need to know how a combustion engine works to learn how to drive a car, or what toxins are in a mushroom to know that it is toxic. Effectively, what we learn are a series of transformations based on environmental cues, which we then take on faith will reproduce similar outcomes to what worked in the past¹. We turn moments of sense data into input-output cause and effect pairs. We effectively engage in black-box learning for just about everything we touch, treating it as a mysterious box where certain inputs produce certain outputs. Science and reason augment this black-box process by giving us deeper sensitivity to the connections between particular input and output cues, and therefore greater predictive power. They might also give us access to new sense-data generated by experiments with which to draw causal inferences. Over time we develop models of the machines and living entities around us, which we carry forward to make more and more deep and confident predictions. Still, we never leave the regime of tying together moments of sensory data into input-output transformations, because ultimately that is the only way we receive any information about the outside world at all.

Still, nothing of this requires faith, right? If not for our limited brains and lifespans surely we would be able to catalogue everything, understand every truth, reason out every principle? Or the other way around—surely we will find the underlying principles of the universe, and with time deduce all relevant facts from axioms alone? So we come to the issue of the simulation hypothesis, i.e. the Evil Demon or Plato’s Cave problem. The problem is that we cannot verify that our senses are not deceiving us purely on the basis of our senses. It can always be the case that every piece of sense data we received was part of a meticulous Matrix whose sole purpose was to deceive us into inferring false relationships between the mass of an object and its energy content. Your eyes and ears cannot determine whether your eyes and ears are lying to you.

Ultimately, the problem we have when talking about whether our universe is simulated is the same one as that which motivated Gödel's incompleteness theorems. In short, we cannot use a set of information gathering techniques (whether based on sensory inputs or formal proofs) to prove the consistency and truth of those information gathering techniques in toto. We always need to depend on something beyond those techniques which acts as a guarantor that our techniques are built on solid foundations. And if we take our techniques plus that guarantor as our new information gathering system, a new Gödel statement can be formulated which proves this joint system inadequate, et cetera unto infinity. In other words, we must have an unreasonable belief in something that cannot be sensed or proven by observation and experiment with our senses. That something must act as a guarantor that our senses are not feeding us false information.

What happens if we deny the existence of this guarantor? Well, the problem with living in the Matrix is that the laws of physics can in fact change at any moment. Since all we are receiving is fabricated information, it becomes trivial to summon dragons, flip the world upside down, or turn day into night. At any time our hard-earned world model of transformations can be entirely broken down and twisted into lies. You, armed with all your science and rationality, may one day find yourself with no mouth and unable to scream. There is a reason why people who believe in the simulation hypothesis often fall prey to nihilism, bleak terror, or attain a view that there is no meaning in life. For what is faith? Faith is trust in some future eventuality despite uncertainty. And what is prediction? Trust in some future eventuality despite uncertainty.

This is not a statement of truth or fact. In fact, according to scientific principles what I am saying is categorically unprovable. But I argue that this faith in “something out there” is necessary to live in our world without giving into the nihilism of “everything can turn to ash in an instant”. However, this something is also emphatically not like the gods we have seen in our myths, religions, and fictions. Beings you can see and touch, who can rain fire from the sky or open chasms in the earth, are automatically disqualified from being the guarantor, which exists outside the realm of sense data entirely. What it is, unfortunately, I cannot say or describe. It appears to be codified best as an implicit promise that time will continue to operate as we understand it, that the rules of physics will hold true in one instant as they have in another, that cause and effect will be obeyed. In short, the inductive biases upon which we build our linkages of sensory data. But the fact that it has held true up to now, of course, is no inductive evidence for it holding true in the future. Induction tells us that the turkey was safest the day before it was slaughtered.

1. This is why we are so surprised when someone we know no longer responds reliably to e.g. their favourite joke, or their most detested foodstuff. It’s not that we think it is impossible for a human to change, but that most of our knowledge is predicated on things staying mostly the same.