Category Archives: Amateur Philosophy

Boltzmann Brains, Evil Demons, and Why It’s Occasionally a Good Idea to Listen to Philosophers

There’s been a bit of a buzz recently about a paper Sean Carroll posted to the arXiv, “Why Boltzmann Brains Are Bad”. The argument in the paper isn’t new, it’s something Carroll has been arguing for a long time, and the arXiv post was just because he had been invited to contribute a piece to a book on Current Controversies in Philosophy of Science.

(By the way: in our field, invited papers and conference proceedings are almost always reviews of old work, not new results. If you see something on arXiv and want to know whether it’s actually new work, the “Comments:” section will almost always mention this.)

While the argument isn’t new, it is getting new attention. And since I don’t think I’ve said much about my objections to it, now seems like a good time to do so.

Carroll’s argument is based on theoretical beings called Boltzmann brains. The idea is that if you wait a very very long time in a sufficiently random (“high-entropy”) universe, the matter in that universe will arrange itself in pretty much every imaginable way, if only for a moment. In particular, it will eventually form a brain, or enough of a brain to have a conscious experience. Wait long enough, and you can find a momentary brain having any experience you want, with any (fake) memories you want. Long enough, and you can find a brain having the same experience you are having right now.

So, Carroll asks, how do you know you aren’t a Boltzmann brain? If the universe exists for long enough, most of the beings having your current experiences would be Boltzmann brains, not real humans. But if you really are a Boltzmann brain, then you can’t know anything about the universe at all: everything you think are your memories are just random fluctuations with no connection to the real world.

Carroll calls this sort of situation “cognitively unstable”. If you reason scientifically that the universe must be full of Boltzmann brains, then you can’t rule out that you could be a Boltzmann brain, and thus you shouldn’t accept your original reasoning.

The only way out, according to Carroll, is if we live in a universe that will never contain Boltzmann brains, for example one that won’t exist in its current form long enough to create them. So from a general concern about cognitive instability, Carroll argues for specific physics. And if that seems odd…well, it is.

For the purpose of this post, I’m going to take for granted the physics case: that a sufficiently old and random universe would indeed produce Boltzmann brains. That’s far from uncontroversial, and if you’re interested in that side of the argument (and have plenty of patience for tangents and Czech poop jokes) Lubos Motl posted about it recently.

Instead, I’d like to focus on the philosophical side of the argument.

Let’s start with intro philosophy, and talk about Descartes.

Descartes wanted to start philosophy from scratch by questioning everything he thought he knew. In one of his arguments, he asks the reader to imagine an evil demon.


Probably Graz’zt. It’s usually Graz’zt.

Descartes imagines this evil demon exercising all its power to deceive. Perhaps it could confound your senses with illusions, or modify your memories. If such a demon existed, there would be no way to know if anything you believed or reasoned about the world was correct. So, Descartes asked, how do you know you’re not being deceived by an evil demon right now?

Amusingly, like Carroll, Descartes went on to use this uncertainty to argue for specific proposals in physics: in Descartes’ case, everything from the existence of a benevolent god to the idea that gravity was caused by a vortex of fluid around the sun.

Descartes wasn’t the last to propose this kind of uncertainty, and philosophers have asked more sophisticated questions over the years challenging the idea that it makes sense to reason from the past about the future at all.

Carroll is certainly aware of all of this. But I suspect he doesn’t quite appreciate the current opinion philosophers have on these sorts of puzzles.

The impression I’ve gotten from philosophers is that they don’t take this kind of “cognitive instability” very seriously anymore. There are specialists who still work on it, and it’s still of historical interest. But the majority of philosophers have moved on.

How did they move on? How have they dismissed these kinds of arguments?

That varies. Philosophers don’t tend to have the kind of consensus that physicists usually do.

Some reject them on pragmatic grounds: science works, even if we can’t “justify” it. Some use a similar argument to Carroll’s, but take it one step back, arguing that we shouldn’t worry that we could be deceived by an evil demon or be a Boltzmann brain because those worries by themselves are cognitively unstable. Some bite the bullet, that reasoning is impossible, then just ignore it and go on with their lives.

The common trait of all of these rejections, though? They don’t rely on physics.

Philosophers don’t argue “evil demons are impossible, therefore we can be sure we’re not deceived by evil demons”. They don’t argue “dreams are never completely realistic, so we can’t just be dreaming right now”.

And they certainly don’t try to argue the reverse: that consistency means there can never be evil demons, or never be realistic dreams.

I was on the debate team in high school. One popular tactic was called the “non-unique”. If your opponent argued that your plan had some negative consequences, you could argue that those consequences would happen regardless of whether you got to enact your plan or not: that the consequences were non-unique.

At this point, philosophers understand that cognitive instability and doubt are “non-unique”. No matter the physics, no matter how the world looks, it’s still possible to argue that reasoning isn’t justified, that even the logic we used to doubt the world in the first place could be flawed.

Carroll’s claim to me seems non-unique. Yes, in a universe that exists for a long time you could be a Boltzmann brain. But even if you don’t live in such a universe, you could still be a brain in a jar or a simulation. You could still be deceived by an “evil demon”.

And so regardless, you need the philosophers. Regardless, you need some argument that reasoning works, that you can ignore doubt. And once you’re happy with that argument, you don’t have to worry about Boltzmann brains.

Science Is a Collection of Projects, Not a Collection of Beliefs

Read a textbook, and you’ll be confronted by a set of beliefs about the world.

(If it’s a half-decent textbook, it will give justifications for those beliefs, and they will be true, putting you well on the way to knowledge.)

The same is true of most science popularization. In either case, you’ll be instructed that a certain set of statements about the world (or about math, or anything else) are true.

If most of your experience with science comes from popularizations and textbooks, you might think that all of science is like this. In particular, you might think of scientific controversies as matters of contrasting beliefs. Some scientists “believe in” supersymmetry, some don’t. Some “believe in” string theory, some don’t. Some “believe in” a multiverse, some don’t.

In practice, though, only settled science takes the form of beliefs. The rest, science as it is actually practiced, is better understood as a collection of projects.

Scientists spend most of their time working on projects. (Well, or procrastinating in my case.) Those projects, not our beliefs about the world, are how we influence other scientists, because projects build off each other. Any time we successfully do a calculation or make a measurement, we’re opening up new calculations and measurements for others to do. We all need to keep working and publishing, so anything that gives people something concrete to do is going to be influential.

The beliefs that matter come later. They come once projects have been so successful, and so widespread, that their success itself is evidence for beliefs. They’re the beliefs that serve as foundational assumptions for future projects. If you’re going to worry that some scientists are behaving unscientifically, these are the sorts of beliefs you want to worry about. Even then, things are often constrained by viable projects: in many fields, you can’t have a textbook without problem sets.

Far too many people seem to miss this distinction. I’ve seen philosophers focus on scientists’ public statements instead of their projects when trying to understand the implications of their science. I’ve seen bloggers and journalists who mostly describe conflicts of beliefs, what scientists expect and hope to be true rather than what they actually work on.

Do scientists have beliefs about controversial topics? Absolutely. Do those beliefs influence what they work on? Sure. But only so far as there’s actually something there to work on.

That’s why you see quite a few high-profile physicists endorsing some form of multiverse, but barely any actual journal articles about it. The belief in a multiverse may or may not be true, but regardless, there just isn’t much that one can do with the idea right now, and it’s what scientists are doing, not what they believe, that constitutes the health of science.

Different fields seem to understand this to different extents. I’m reminded of a story I heard in grad school, of two dueling psychologists. One of them believed that conversation was inherently cooperative, and showed that, unless unusually stressed or busy, people would put in the effort to understand the other person’s perspective. The other believed that conversation was inherently egocentric, and showed that, the more you stressed or busy people are, the more they assume that everyone else has the same perspective they do.

Strip off the “beliefs”, and these two worked on the exact same thing, with the same results. With their beliefs included, though, they were bitter rivals who bristled if their grad students so much as mentioned the other scientist.

We need to avoid this kind of mistake. The skills we have, the kind of work we do, these are important, these are part of science. The way we talk about it to reporters, the ideas we champion when we debate, those are sidelines. They have some influence, dragging people one way or another. But they’re not what science is, because on the front lines, science is about projects, not beliefs.

The Metaphysics of Card Games

I tend to be skeptical of attempts to apply metaphysics to physics. In particular, I get leery when someone tries to describe physics in terms of which fundamental things exist, and which things are made up of other things.

Now, I’m not the sort of physicist who thinks metaphysics is useless in general. I’ve seen some impressive uses of supervenience, for example.

But I think that, in physics, talk of “things” is almost always premature. As physicists, we describe the world mathematically. It’s the most precise way we have access to of describing the universe. The trouble is, slightly different mathematics can imply the existence of vastly different “things”.

To give a slightly unusual example, let’s talk about card games.


To defeat metaphysics, we must best it at a children’s card game!

Magic: The Gathering is a collectible card game in which players play powerful spellcasters who fight by casting spells and summoning creatures. Those spells and creatures are represented by cards.

If you wanted to find which “things” exist in Magic: The Gathering, you’d probably start with the cards. And indeed, cards are pretty good candidates for fundamental “things”. As a player, you have a hand of cards, a discard pile (“graveyard”) and a deck (“library”), and all of these are indeed filled with cards.

However, not every “thing” in the game is a card. That’s because the game is in some sense limited: it needs to represent a broad set of concepts while still using physical, purchasable cards.

Suppose you have a card that represents a general. Every turn, the general recruits a soldier. You could represent the soldiers with actual cards, but they’d have to come from somewhere, and over many turns you might quickly run out.

Instead, Magic represents these soldiers with “tokens”. A token is not a card: you can’t shuffle a token into your deck or return it to your hand, and if you try to it just ceases to exist. But otherwise, the tokens behave just like other creatures: they’re both the same type of “thing”, something Magic calls a “permanent”. Permanents live in an area between players called the “battlefield”.

And it gets even more complicated! Some creatures have special abilities. When those abilities are activated, they’re treated like spells in many ways: you can cast spells in response, and even counter them with the right cards. However, they’re not spells, because they’re not cards: like tokens, you can’t shuffle them into your deck. Instead, both they and spells that have just been cast live in another area, the “stack”.

So while Magic might look like it just has one type of “thing”, cards, in fact it has three: cards, permanents, and objects on the stack.

We can contrast this with another card game, Hearthstone.


Hearthstone is much like Magic. You are a spellcaster, you cast spells, you summon creatures, and those spells and creatures are represented by cards.

The difference is, Hearthstone is purely electronic. You can’t go out and buy the cards in a store, they’re simulated in the online game. And this means that Hearthstone’s metaphysics can be a whole lot simpler.

In Hearthstone, if you have a general who recruits a soldier every turn, the soldiers can be cards just like the general. You can return them to your hand, or shuffle them into your deck, just like a normal card. Your computer can keep track of them, and make sure they go away properly at the end of the game.

This means that Hearthstone doesn’t need a concept of “permanents”: everything on its “battlefield” is just a card, which can have some strange consequences. If you return a creature to your hand, and you have room, it will just go there. But if your hand is full, and the creature has nowhere to go, it will “die”, in exactly the same way it would have died in the game if another creature killed it. From the game’s perspective, the creature was always a card, and the card “died”, so the creature died.

These small differences in implementation, in the “mathematics” of the game, change the metaphysics completely. Magic has three types of “things”, Hearthstone has only one.

And card games are a special case, because in some sense they’re built to make metaphysics easy. Cards are intuitive, everyday objects, and both Magic and Hearthstone are built off of our intuitions about them, which is why I can talk about “things” in either game.

Physics doesn’t have to be built that way. Physics is meant to capture our observations, and help us make predictions. It doesn’t have to sort itself neatly into “things”. Even if it does, I hope I’ve convinced you that small changes in physics could lead to large changes in which “things” exist. Unless you’re convinced that you understand the physics of something completely, you might want to skip the metaphysics. A minor mathematical detail could sweep it all away.

Thought Experiments, Minus the Thought

My second-favorite Newton fact is that, despite inventing calculus, he refused to use it for his most famous work of physics, the Principia. Instead, he used geometrical proofs, tweaked to smuggle in calculus without admitting it.

Essentially, these proofs were thought experiments. Newton would start with a standard geometry argument, one that would have been acceptable to mathematicians centuries earlier. Then, he’d imagine taking it further, pushing a line or angle to some infinite point. He’d argue that, if the proof worked for every finite choice, then it should work in the infinite limit as well.

These thought experiments let Newton argue on the basis of something that looked more rigorous than calculus. However, they also held science back. At the time, only a few people in the world could understand what Newton was doing. It was only later, when Newton’s laws were reformulated in calculus terms, that a wider group of researchers could start doing serious physics.

What changed? If Newton could describe his physics with geometrical thought experiments, why couldn’t everyone else?

The trouble with thought experiments is that they require careful setup, setup that has to be thought through for each new thought experiment. Calculus took Newton’s geometrical thought experiments, and took out the need for thought: the setup was automatically a part of calculus, and each new researcher could build on their predecessors without having to set everything up again.

This sort of thing happens a lot in science. An example from my field is the scattering matrix, or S-matrix.

The S-matrix, deep down, is a thought experiment. Take some particles, and put them infinitely far away from each other, off in the infinite past. Then, let them approach, close enough to collide. If they do, new particles can form, and these new particles will travel out again, infinite far away in the infinite future. The S-matrix then is a metaphorical matrix that tells you, for each possible set of incoming particles, what the probability is to get each possible set of outgoing particles.

In a real collider, the particles don’t come from infinitely far away, and they don’t travel infinitely far before they’re stopped. But the distances are long enough, compared to the sizes relevant for particle physics, that the S-matrix is the right idea for the job.

Like calculus, the S-matrix is a thought experiment minus the thought. When we want to calculate the probability of particles scattering, we don’t need to set up the whole thought experiment all over again. Instead, we can start by calculating, and over time we’ve gotten very good at it.

In general, sub-fields in physics can be divided into those that have found their S-matrices, their thought experiments minus thought, and those that have not. When a topic has to rely on thought experiments, progress is much slower: people argue over the details of each setup, and it’s difficult to build something that can last. It’s only when a field turns the corner, removing the thought from its thought experiments, that people can start making real collaborative progress.

What Does It Mean to Know the Answer?

My sub-field isn’t big on philosophical debates. We don’t tend to get hung up on how to measure an infinite universe, or in arguing about how to interpret quantum mechanics. Instead, we develop new calculation techniques, which tends to nicely sidestep all of that.

If there’s anything we do get philosophical about, though, any question with a little bit of ambiguity, it’s this: What counts as an analytic result?

“Analytic” here is in contrast to “numerical”. If all we need is a number and we don’t care if it’s slightly off, we can use numerical methods. We have a computer use some estimation trick, repeating steps over and over again until we have approximately the right answer.

“Analytic”, then, refers to everything else. When you want an analytic result, you want something exact. Most of the time, you don’t just want a single number: you want a function, one that can give you numbers for whichever situation you’re interested in.

It might sound like there’s no ambiguity there. If it’s a function, with sines and cosines and the like, then it’s clearly analytic. If you can only get numbers out through some approximation, it’s numerical. But as the following example shows, things can get a bit more complicated.

Suppose you’re trying to calculate something, and you find the answer is some messy integral. Still, you’ve simplified the integral enough that you can do numerical integration and get some approximate numbers out. What’s more, you can express the integral as an infinite series, so that any finite number of terms will get close to the correct result. Maybe you even know a few special cases, situations where you plug specific numbers in and you do get an exact answer.

It might sound like you only know the answer numerically. As it turns out, though, this is roughly how your computer handles sines and cosines.

When your computer tries to calculate a sine or a cosine, it doesn’t have access to the exact solution all of the time. It does have some special cases, but the rest of the time it’s using an infinite series, or some other numerical trick. Type in a random sine into your calculator and it will be just as approximate as if you did a numerical integration.

So what’s the real difference?

Rather than how we get numbers out, think about what else we know. We know how to take derivatives of sines, and how to integrate them. We know how to take limits, and series expansions. And we know their relations to other functions, including how to express them in terms of other things.

If you can do that with your integral, then you’ve probably got an analytic result. If you can’t, then you don’t.

What if you have only some of the requirements, but not the others? What if you can take derivatives, but don’t know all of the identities between your functions? What if you can do series expansions, but only in some limits? What if you can do all the above, but can’t get numbers out without a supercomputer?

That’s where the ambiguity sets in.

In the end, whether or not we have the full analytic answer is a matter of degree. The closer we can get to functions that mathematicians have studied and understood, the better grasp we have of our answer and the more “analytic” it is. In practice, we end up with a very pragmatic approach to knowledge: whether we know the answer depends entirely on what we can do with it.

In Defense of Lord Kelvin, Michelson, and the Physics of Decimals

William Thompson, Lord Kelvin, was a towering genius of 19th century physics. He is often quoted as saying,

There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.


Certainly sounds like something I would say!

As it happens, he never actually said this. It’s a paraphrase of a quote from Albert Michelson, of the Michelson-Morley Experiment:

While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance — where quantitative work is more to be desired than qualitative work. An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals.


Now that’s more like it!

In hindsight, this quote looks pretty silly. When Michelson said that “it seems probable that most of the grand underlying principles have been firmly established” he was leaving out special relativity, general relativity, and quantum mechanics. From our perspective, the grandest underlying principles had yet to be discovered!

And yet, I think we should give Michelson some slack.

Someone asked me on twitter recently what I would choose if given the opportunity to unravel one of the secrets of the universe. At the time, I went for the wishing-for-more-wishes answer: I’d ask for a procedure to discover all of the other secrets.

I was cheating, to some extent. But I do think that the biggest and most important mystery isn’t black holes or the big bang, isn’t asking what will replace space-time or what determines the constants in the Standard Model. The most critical, most important question in physics, rather, is to find the consequences of the principles we actually know!

We know our world is described fairly well by quantum field theory. We’ve tested it, not just to the sixth decimal place, but to the tenth. And while we suspect it’s not the full story, it should still describe the vast majority of our everyday world.

If we knew not just the underlying principles, but the full consequences of quantum field theory, we’d understand almost everything we care about. But we don’t. Instead, we’re forced to calculate with approximations. When those approximations break down, we fall back on experiment, trying to propose models that describe the data without precisely explaining it. This is true even for something as “simple” as the distribution of quarks inside a proton. Once you start trying to describe materials, or chemistry or biology, all bets are off.

This is what the vast majority of physics is about. Even more, it’s what the vast majority of science is about. And that’s true even back to Michelson’s day. Quantum mechanics and relativity were revelations…but there are still large corners of physics in which neither matters very much, and even larger parts of the more nebulous “physical science”.

New fundamental principles get a lot of press, but you shouldn’t discount the physics of “the sixth place of decimals”. Most of the big mysteries don’t ask us to challenge our fundamental paradigm: rather, they’re challenges to calculate or measure better, to get more precision out of rules we already know. If a genie gave me the solution to any of physics’ mysteries I’d choose to understand the full consequences of quantum field theory, or even of the physics of Michelson’s day, long before I’d look for the answer to a trendy question like quantum gravity.

Who Needs Non-Empirical Confirmation?

I’ve figured out what was bugging me about Dawid’s workshop on non-empirical theory confirmation.

It’s not the concept itself that bothers me. While you might think of science as entirely based on observations of the real world, in practice we can’t test everything. Inevitably, we have to add in other sorts of evidence: judgments based on precedent, philosophical considerations, or sociological factors.

It’s Dawid’s examples that annoy me: string theory, inflation, and the multiverse. Misleading popularizations aside, none of these ideas involve non-empirical confirmation. In particular, string theory doesn’t need non-empirical confirmation, inflation doesn’t want it, and the multiverse, as of yet, doesn’t merit it.

In order for non-empirical confirmation to matter, it needs to affect how people do science. Public statements aren’t very relevant from a philosophy of science perspective; they ebb and flow based on how people promote themselves. Rather, we should care about what scientists assume in the course of their work. If people are basing new work on assumptions that haven’t been established experimentally, then we need to make sure their confidence isn’t misplaced.

String theory hasn’t been established experimentally…but it fails the other side of this test: almost no-one is assuming string theory is true.

I’ve talked before about theorists who study theories that aren’t true. String theory isn’t quite in that category, it’s still quite possible that it describes the real world. Nonetheless, for most string theorists, the distinction is irrelevant: string theory is a way to relate different quantum field theories together, and to formulate novel ones with interesting properties. That sort of research doesn’t rely on string theory being true, often it doesn’t directly involve strings at all. Rather, it relies on string theory’s mathematical abundance, its versatility and power as a lens to look at the world.

There are string theorists who are more directly interested in describing the world with string theory, though they’re a minority. They’re called String Phenomenologists. By itself, “phenomenologist” refers to particle physicists who try to propose theories that can be tested in the real world. “String phenomenology” is actually a bit misleading, since most string phenomenologists aren’t actually in the business of creating new testable theories. Rather, they try to reproduce some of the more common proposals of phenomenologists, like the MSSM, from within the framework of string theory. While string theory can reproduce many possible descriptions of the world (10^500 by some estimates), that doesn’t mean it covers every possible theory; making sure it can cover realistic options is an important, ongoing technical challenge. Beyond that, a minority within a minority of string phenomenologists actually try to make testable predictions, though often these are controversial.

None of these people need non-empirical confirmation. For the majority of string theorists, string theory doesn’t need to be “confirmed” at all. And for the minority who work on string phenomenology, empirical confirmation is still the order of the day, either directly from experiment or indirectly from the particle phenomenologists struggling to describe it.

What about inflation?

Cosmic inflation was proposed to solve an empirical problem, the surprising uniformity of the observed universe. Look through a few papers in the field, and you’ll notice that most are dedicated to finding empirical confirmation: they’re proposing observable effects on the cosmic microwave background, or on the distribution of large-scale structures in the universe. Cosmologists who study inflation aren’t claiming to be certain, and they aren’t rejecting experiment: overall, they don’t actually want non-empirical confirmation.

To be honest, though, I’m being a little unfair to Dawid here. The reason that string theory and inflation are in the name of his workshop aren’t because he thinks they independently use non-empirical confirmation. Rather, it’s because, if you view both as confirmed (and make a few other assumptions), then you’ve got a multiverse.

In this case, it’s again important to compare what people are doing in their actual work to what they’re saying in public. While a lot of people have made public claims about the existence of a multiverse, very few of them actually work on it. In fact, the two sets of people seem to be almost entirely disjoint.

People who make public statements about the multiverse tend to be older prominent physicists, often ones who’ve worked on supersymmetry as a solution to the naturalness problem. For them, the multiverse is essentially an excuse. Naturalness predicted new particles, we didn’t find new particles, so we need an excuse to have an “unnatural” universe, and for many people the multiverse is that excuse. As I’ve argued before, though, this excuse doesn’t have much of an impact on research. These people aren’t discouraged from coming up with new ideas because they believe in the multiverse, rather, they’re talking about the multiverse because they’re currently out of new ideas. Nima Arkani-Hamed is a pretty clear case of someone who has supported the multiverse in pieces like Particle Fever, but who also gets thoroughly excited about new ideas to rescue naturalness.

By contrast, there are many fewer people who actually work on the multiverse itself, and they’re usually less prominent. For the most part, they actually seem concerned with empirical confirmation, trying to hone tricks like anthropic reasoning to the point where they can actually make predictions about future experiments. It’s unclear whether this tiny group of people are on the right track…but what they’re doing definitely doesn’t seem like something that merits non-empirical confirmation, at least at this point.

It’s a shame that Dawid chose the focus he did for his workshop. Non-empirical theory confirmation is an interesting idea (albeit one almost certainly known to philosophy long before Dawid), and there are plenty of places in physics where it could use some examination. We seem to have come to our current interpretation of renormalization non-empirically, and while string theory itself doesn’t rely on non-empirical conformation many of its arguments with loop quantum gravity seem to rely on non-empirical considerations, in particular arguments about what is actually required for a proper theory of quantum gravity. But string theory, inflation, and the multiverse aren’t the examples he’s looking for.