Put another way, rather than perceiving reality, we perceive the output of a long chain of noisy translations.

Let’s walk up this chain layer by layer, starting from the bottom (fundamental physics) and ending at the stories we tell. 

Layer 1: We only make measurements

On one common reading of quantum mechanics (part of the deepest description of reality that physicists have a reasonably high degree of confidence in), a fundamental object is the wave function. 

We don’t observe the wave function directly. We make measurements, and those represent properties, such as the position or “spin” of a particle. We can think of this as observing just one realization (or taking one branch) of the deeper thing. The wave function, in a sense, captures all of the realizations we might have observed but didn’t.

That means that at the most basic level, before biology or psychology even enter the picture, there’s already a chasm between us and the fundamental nature of things. 

Rather than reading reality, we sample a thin projection of it. We’re stuck accessing reality only through measurements. But that’s just the first layer of translation.

Layer 2: Measurements turn into signals

Measurements are not something you can directly experience. Your sense organs make the measurements. When light hits your eye, first a chemical reaction occurs, then this chemical reaction kicks off electrical signals – representations of the light (not light itself).

Your brain processes those electrical signals, and out of that, an experience is produced in your mind. Put another way, your brain creates a simulation, and that’s what you experience. For instance, in your brain’s simulation, you experience the vivid sensation of red. But there’s no such thing as red out there in the world – red exists ONLY in the simulations produced by our minds.

Out there in the world, light of certain frequency bands is hitting our eyes. Inside our minds, the experience of red is happening.

The same is true of sound, smell, warmth, and every other quality of experience: they are our brain’s rendering of the measurements made by our sense organs. They are not the measurements themselves, and certainly not the underlying reality.

Three distinct sorts of failures can occur at this layer.

First, the signal itself can be distorted, such as might happen if the optic nerve is damaged or if cataracts tint the light entering our eyes.

Second, the simulation that your brain creates can be unfaithful to reality, misrepresenting what’s there. We see this most clearly with optical illusions. 

The reason we find them interesting is that they lay bare ways our brain’s rendering of reality comes apart from reality itself. 

We can only tell this is happening because we can check our internal rendering against something indisputable to prove a mismatch (e.g., by using a ruler or checking the color of different pixels).

The unsettling implication is that the renderings we can’t easily check are sometimes misleading, too. But we lack the awareness or the right ruler to catch them.

The third distortion at this layer is that our simulations of reality always leave out information. For example, our eyes can’t see ultraviolet or infrared light, so those wavelengths simply never make it into our experience, no matter how carefully we look. Intriguingly, we don’t perceive a gap in the color spectrum. Presumably, that wouldn’t have been useful for our ancient ancestors, so evolution didn’t bother with it. We aren’t even naturally aware that other “colors” (well, really, frequencies) of light are possible. We feel as though we’re seeing the full spectrum (while bees and butterflies enjoy ultraviolet patterns on flowers that are hidden to us).

Every sense is like this. Each provides us with a window of information, which we use to simulate aspects of reality. A lot of information is silently dropped because it lies beyond the window frame. We remain convinced that these narrow portals into reality show the whole thing.

Layer 3: We bucket the simulation

A raw field of colors and sounds may be a partial approximation to how an infant sees the world, as its brain learns furiously how to structure things. But that isn’t yet a world you can act in. To use your experience effectively, your mind has to carve up experience. It has to decide that this region is a table, that one a person, and that other one, the floor.

This chunking happens automatically and below conscious awareness. It’s enormously useful. But it’s another layer of interpretation laid on top of an already-imperfect simulation, and it can distort things in its own ways.

For one thing, the boundaries we draw can simply be mistaken – we can mistake a coat on a chair for a person the moment we enter a room. Or, if you’re me, you can briefly think you see cats in the dark when on vacation because you see cats in the dark when you’re at home.

Our categories take genuinely complex things and force them into a bucket. You may, when walking in a park, stumble on a rare bird – the last of its species, on the brink of extinction. Your brain just says “bird”. 

Moreover, we sometimes get our chunks wrong. You walk by a fresh-faced man with long hair and incorrectly think “woman”. Or, in my case, you see a symbol tattooed on a classmate’s arm and think Swastika. It turned out to be the manji – a sacred Buddhist symbol representing good fortune.

Tremendous variation can hide inside even simple-seeming categories, let alone complex categories like “tree”, consisting of tens of thousands of species.

Buckets produce compression, and compression is what makes the world manageable, but sometimes a lot is lost in the process.

Importantly, the more you pay attention to a type of thing and the more you understand about it, the more refined and subtle your buckets are likely to become. That’s not just a tree. It’s a Sycamore tree. And it’s not just a Sycamore tree; it’s Platanus wrightii – an Arizona Sycamore. 

Layer 4: We ignore almost everything

Even with the compression achieved by this chunking up of reality, there’s far too much information for us to process, so our brain uses another heuristic: if something doesn’t draw our attention, it’s ignored.

When we’re told to carefully count how many times people pass a basketball, we can, with remarkable ease, miss the person in a gorilla suit that’s walking between them.

Or, if you’re having a conversation with me, and you ask me to close my eyes, then you ask me to recall what you were wearing, I’ll be clueless, despite having been looking at you moments ago. Heck, with my eyes closed, I may not even be able to tell you what I’M wearing. 

On the other hand, if you try the same thing with a person who works in fashion, they’ll not only be able to describe what you are wearing, but also make a guess about the brand.

We notice what we find interesting, important, or surprising, as well as what we’ve trained ourselves or been trained to notice. And we are unaware of most of the rest. This (in part) explains why eyewitness testimony has proven to be much more fallible than a lot of people assume. 

You didn’t know that person was about to rob the store you’re in, so even though they walked right in front of you, you have no recollection of what they look like. 

Even when you realized that they were robbing the store, your attention was drawn to the knife in their hand or the exit door, rather than the contour of their brow, lips, and nose.

Our limited attention acts as yet another filter on what makes it into our experience. But one layer remains.

Layer 5: We turn noticed chunks into meaningful ones

Even once you’ve chunked the world into objects and categories, and we’re actually paying attention to some of them, the process of perceiving isn’t complete. Your brain still has to decide what it all means. 

A Sycamore tree to Bob has no special significance, whereas to Sally it’s where she had her first kiss, and to Elio, it’s what his grandfather died under. To me, it was a phrase served to me in an ad when I was looking for a type of tree to use in this example.

Once we’ve chunked a scene, it gets woven into a story. Our reflective minds run on such stories.

The stories tell us what’s important, what’s threatening, and what’s good. But this final layer of interpretation is steered heavily by things that have nothing to do with the scene itself: our identities, our motivations, our worldviews, our past experiences, our anticipations, and our social groups.

This is why two people can look at an identical event – even identical data represented in a chart – and walk away with opposite understandings. They are running the same visual input through different meaning-making machinery constructed within different lives.

Of course, that’s not how this all feels. The meaning we make feels like it’s obviously the way things are – the one true story – or, not even a story – just reality itself.

We, of course, don’t think of the wave function that we collapsed (or took a branch of) with our measurements. Or the electrical signals that flow through the retina. Or even the bucketing we did to compress the information. We don’t, of course, pay attention to what we failed to pay attention to. And we rarely consider alternative stories our brains could have told us (but didn’t) about what we did pay attention to.

This may sound grim, but it’s not a complete epistemic disaster. Despite all this, we know a lot about how to get reality to do things for us. Science often works to discover new truths. Bridges rarely fall. Some stories are accurate, even if they aren’t complete.

The practical upshot of it all is epistemic humility. 

It helps to remember, from time to time, that what we’re experiencing is a model, a series of translations removed from whatever is actually out there. And to aim to make our estimates and opinions at least somewhat more uncertain as a result.

Doing so has a happy effect: it makes it easier to consider alternative perspectives that contradict our own. That’s useful societally, where there’s an overabundance of perspectives that are rigidly held. But it’s also helpful in relationships, friendships, and our work.

We can’t see reality directly – it’s not actually the sort of thing that’s capable of being seen. But we can, at least, stop mistaking the top of the stack for the bottom.

This piece was first written on June 30, 2026, and first appeared on my website on July 23, 2026.

The oddest part is that despite a heroic attempt to do so, the study authors failed to explain why the different research teams reached such different conclusions:

“More than 95% of the total variance in numerical results remains unexplained even after qualitative coding of all identifiable decisions in each team’s workflow. This reveals a universe of uncertainty that remains hidden when considering a single study in isolation.”

The hypothesis they were trying to test was whether greater immigration reduces support for social policies (such as for government-provided healthcare).

The study included data from 31 countries at up to five time periods each.

If all of the countries and time points were independent data points, that would be an effective sample size of at most 5*31 = 155.

However, the data points from one country at different points in time are highly correlated.

So, in practice, this might be equivalent to more like 75 (independent) data points.

If the (effective) sample size was equivalent to only about n=75, the 95th percentile confidence interval on a correlation could be pretty large (e.g., it could be +- 0.20), suggesting that false negatives would be very common (unless the relationship in question is pretty strong).

In view of this, I think it’s possible that this study was doomed from the start.

Why? Unless we’d expect a reasonably strong effect, maybe there just wasn’t enough data to answer the question at hand.

Some of the teams may have come to this conclusion as well. Of the 73 research teams involved in the study, one of them conducted preliminary measurement scaling tests and concluded that the hypothesis could not be reliably tested. Another team’s preregistered models failed to converge, and so that team also had no numerical results. Some teams reached more than one conclusion, and across the 89 team conclusions reached, 12 of those conclusions (13.5%) were that the hypothesis was not testable with the data provided.

Then, of course, there is the possibility of confounding variables – other factors that could be linked to both immigration and inflation that make the true relationship seem bigger or smaller than it really is.

Here’s a link to the paper if you’re interested: “Observing many researchers using the same data and hypothesis reveals a hidden universe of uncertainty.”

A big thanks to Cameron Colby Thomson for pointing me to this study!

This piece was first written on November 30, 2022, and first appeared on this site on September 29, 2023.

Can a chosen definition be “wrong”? No. If you choose a definition, then you can define a sound or series of characters to mean whatever you want them to mean. For instance, if you wanted, you could declare that whenever you say “phloop,” you mean one of those little paper umbrellas that are sometimes found in Piña coladas. That would be weird, but it wouldn’t be “wrong.” But we suggest that there are at least seven ways a definition can be “lousy.” 

By understanding what makes a good definition and what makes a lousy one, you can better formulate your ideas, and you can better spot mistakes in other people’s arguments. For instance, you might be in a situation where you’re trying to define the essence of an idea you came up with or characterize the unique career role that you’ve designed for yourself. Alternatively, you might be struggling to understand a definition that someone else is using, and you want to diagnose why exactly you’re finding it confusing. The words we use are crucial to the success of the interactions we have, and it is very handy to be able to pinpoint when a particular word is making a conversation more confusing than it needs to be. So, here are the things that we think make for lousy definitions! 

1. Miscommunication

If you decide the word “dog” refers to cats, people are going to be very confused.

Similarly, if you’re talking to someone who uses the word “racism” to mean X (say, “an explicitly held and endorsed belief that some racial groups are inferior to others”), and you use it to mean Y (say, “any form of negative generalization or attitude to a racial group, whether it’s implicit or explicit”), your conversation is probably not going to go as well as you would like until you identify that difference in usage. For these reasons, good definitions shouldn’t reuse terms that people are already familiar with or have multiple meanings associated with them. A good way to avoid the latter is to clarify upfront what you mean when you’re using a particular definition if the other person might not know what you mean when using that word.

2. Irrelevance

If you define a “dooooog” to be a dog with more than five legs, you’re not going to find it to be useful for much of anything. Dogs like that probably do exist, but they are not something almost anyone ever needs to refer to. We want our definitions to aim toward the things we are likely to want to reference.

For instance, someone bothered to define the word “Rasceta” to mean the crease commonly found going across a person’s wrist. Presumably, there is some subculture where that is a useful word, but very few people will ever need to know that definition. 

3. Unnaturalness

If you define “dogephant” to include all dogs smaller than 10 pounds AND all elephants more than 8000 pounds, you have not “carved reality at the joints.” Because of mixing things that aren’t clearly alike, using this definition makes communicating more muddled than it needs to be.

Another instance of this phenomenon is our use of the word “selfish.” Sometimes people define the word “selfish” in such a way that it includes both “stealing money from someone” and “sacrificing your own life to save the life of ten others because you feel such a strong emotion of compassion for those people;” it’s about doing things that make you feel “good.” An alternate reading of “selfish” might be much more negative: it’s about taking actions which benefit you at the cost of other peoples’ wellbeing.

4. Opinionatedness

If you define “dogmor” to be “those dog-loving morons who somehow are convinced that dogs are better than cats,” then the definition imports both a debatable opinion and an emotional slant into its meaning, causing usage of this word to be infected with either or both of these things.

For example, the word “sissy” not only suggests that someone — usually a boy or man — embodies feminine qualities but carries with it a negative, insulting connotation. If your aim is to make certain people feel bad, then this might be a good strategy to take, though you might be being a jerk, and that approach doesn’t make for clear, unbiased communication.

5. Ambiguity

If by “dogdog” you mean anything that a dog can like, then your word is (1) hard to use and (2) hard to think about; dogs like a large range of things, and individual dogs also have distinct preferences!

The word “problematic” (when used without clarification) is another (problematic) example of a definition: the problem being referred to could be of many different types and could range from quite objective to just the idiosyncratic, subjective opinion of the writer.

6. Inefficiency 

If you define “doglegs” to be anything with the legs of a dog, and “dogface” to be anything with the face of a dog, etc., then you can talk about walking your dog by saying, “I just got back from walking a creature with doglegs, dogface, dogfur, dogheart, …” But this is a ridiculously inefficient way to talk about your dog! Some definitions make communication substantially more efficient since they compress lots of information you commonly want to express into a small package.

Consider a different instance of this: it is possible to talk about calculus without having a word that means “the derivative” (e.g., by always referring to “limits of functions”), but this is going to be a painful and inefficient way to think and communicate. The word derivative makes ideas in calculus much easier to talk about. 

7. Lack of precision

If you define “floofster” to be any animal with fur, then you will not be communicating very precisely when you say, “I pet my floofster this morning.” You may be saying something true (and rather adorable), but someone will not know if you were petting a dog, a cat, or something more exotic like a lizard wearing a fur coat! Ideally, we want our definitions to focus on just those items or concepts we are trying to communicate.

Similarly, if you say to your friend, “I’m feeling bad,” the ambiguity of the word “bad” makes it harder for them to understand what you’re going through. If you say, “I have a headache,” then it will be easier for your friend to help you. Even better, if true, would be to say, “I have a migraine.” 

So, no chosen definition can be “wrong,” but plenty of definitions are “lousy.” To prevent lousy definitions, you should choose definitions that:

(1) allow clear communication, 

(2) refer specifically to the things of interest, 

(3) carve reality at the joints, 

(4) don’t sneak in debatable opinions/slants, 

(5) are relatively unambiguous, 

(6) express more information in fewer words, and 

(7) allow us to be more exact and specific with our words. 

We hope you found this helpful!

This piece first appeared on the Clearer Thinking blog on March 2, 2021, and was published on this site on December 16, 2022.

I know of 8 approaches to interpreting the U.S. Constitution (and its amendments). None is obviously correct; some are more popular than others, but all are, in some unsatisfying sense, an arbitrary choice we could make:

(1) What the authors believed their words were literally saying (for instance, by studying what is known about how James Madison interpreted his writing). Because that tells us what the documents were intended to say.

(2) What the authors were trying to achieve on behalf of our country by writing those words (for instance, by studying what is known about why Alexander Hamilton thought certain things should be in the Constitution). Because this takes into account the spirit, rather than just the letter, of the law.

(3) What did the ratifiers / those who voted to approve the amendments interpret the words as meaning? Because that takes into account the reasons why the documents were actually accepted as law.

(4) What those who first enforced each of the different terms of these documents interpreted them to mean. Because that tells us what the documents first actually meant in practice.

(5) What decisions in our courts most recently interpreted the words to mean? Because that represents the current theoretical state of the law (even though it sometimes changes). There are, of course, good reasons to think we should implement the law as court decisions indicate. What I’m referring to here is something different, namely, when one says that the “correct” interpretations of the Constitution are automatically what the courts have most recently decided they are.

(6) What most people today would interpret the words to mean, if the words are taken at their face value in modern English. Because this is what those words actually mean to us when we read them.

(7) Whichever method of interpretation listed above causes an interpretation most like what we wish the documents said, accompanied by us then arguing that this is always the correct approach to interpretation. This one is especially popular.

(8) Decide what we think the Constitution should have said, then try to find some interpretation of the words that at least sort of makes it sound like it’s saying those things.

—

It would be nice if the Constitution told us which of these methods to use to interpret its pages (though I imagine we’d end up just debating what THOSE words mean too).

It would be even better if we could decide which of these methods would actually produce better outcomes for our society. That’s unfortunately very hard to do.

To some extent, the choice for how to interpret the Constitution hinges on how much we value stability of interpretation (which makes the law more understandable and consistent) vs. achieving certain outcomes we desire (e.g., making sure there are strong protections for things that society feels should be protected). But this dichotomy is not sufficient to allow us to choose between all the different interpretative methods, in my opinion.

Usually, we either seem to treat the Constitution as though it is not ambiguous (a theory that’s unfortunately been falsified) or as though one of these approaches is the “right” way to do it, as though there could be such a thing as one “right” way to interpret an ambiguous document.

This piece was first written on March 20, 2018, and first appeared on my website on September 4, 2025.