Does an average IQ place a limit on what a person can understand?
In 2017, I asked a provocative question: What kind of ideas is a person with an IQ of 100 unable to grasp? At the time, I was interested in the apparent relationship between intelligence and the difficulty of ideas. If some people can understand highly abstract concepts almost immediately while others struggle with them, is there a point beyond which an average-intelligence person simply cannot go?
Almost a decade later, I think the question needs to be turned around. The more interesting question is not what an average-IQ person cannot understand, but what determines whether an idea becomes understandable in the first place.
An IQ of 100 sits at the statistical mean of the standard IQ scale. It describes neither exceptional intelligence nor intellectual deficiency. Yet the number is often treated as though it were a boundary marker: below a certain level, certain ideas are supposedly inaccessible; above it, they become accessible. Human understanding is unlikely to work that neatly.
Read the original 2017 article: What Kind of Ideas Is a Person with an IQ of 100 Unable to Grasp?
1. An IQ Score Is Not a Map of the Mind
An IQ score summarizes performance on particular kinds of standardized cognitive tasks. It can tell us something meaningful about reasoning and related abilities, but it does not describe every form of intellectual ability a person possesses.
That distinction is easy to lose. When someone says, “His IQ is 100,” it is tempting to translate that into a much broader statement: he has average intelligence, therefore he should have average understanding. But understanding is not a single ability.
A person may be quick at detecting patterns but have little knowledge of a particular subject. Another may process information more slowly but possess a deep conceptual understanding built through years of study. Someone may struggle with formal mathematics while having an exceptional ability to reason about language, people or practical situations.
Even intelligence tests themselves reflect this complexity. Modern cognitive assessment commonly separates different domains rather than treating intelligence as one perfectly uniform mental capacity.
The IQ number is therefore better understood as a measurement of certain cognitive performances under specified conditions, not as a complete description of the mind. If IQ is not the whole mind, how could it define the absolute boundary of what that mind can understand?
2. Understanding Slowly Is Not the Same as Being Unable to Understand
Consider two students encountering the same mathematical idea. The first sees the pattern almost immediately. The second does not. You explain it again, draw a diagram and provide several examples. After an hour, the structure finally becomes clear.
The first student reached the idea quickly. The second reached it slowly. Those are different performances, but they are not necessarily different capacities for understanding.
A fast learner has an obvious advantage. In an examination, research or a competitive environment, reaching a solution quickly can be extremely valuable. Cognitive processing speed and reasoning ability are not irrelevant.
But suppose the second student eventually understands the idea just as well. What exactly has been demonstrated? Perhaps a difference in processing efficiency, prior knowledge, working memory, or simply the way the idea was presented.
The conclusion “therefore, this person cannot understand the idea” requires an additional leap that the evidence does not necessarily justify.
There is a profound difference between “I cannot understand this” and “I cannot understand this yet.”
3. Every Difficult Idea Has an Entry Cost
This becomes clearer when we look at mathematics. A child begins with something concrete:
2 + 3 = 5
Later comes the symbolic:
x + 3 = 5
Then functions, limits, derivatives and differential equations.
To someone encountering differential equations without the preceding structure, the subject can appear almost incomprehensible. But the difficulty is not contained entirely in the final equation. The learner is missing the staircase that leads to it.
Once arithmetic, algebra, functions and calculus have been learned, the same equation occupies a very different place in the mind.
This suggests a useful idea: every complex idea has an entry cost. The entry cost consists partly of the concepts that must already exist before the new concept can make sense.
Education is powerful partly because it constructs the conceptual machinery through which later ideas can be understood. A difficult idea can therefore become easier without the person’s underlying intelligence having changed.
The mind has changed in another sense: it has acquired the map required to navigate the territory.
4. Knowledge Can Make Intelligence Look Different
Imagine giving a physicist a difficult question about a subject they have never studied, such as an unfamiliar branch of classical literature. Now give a literature scholar a problem involving advanced tensor mathematics. Both may struggle.
That does not tell us very much about their general intellectual ability. It tells us that knowledge matters.
Intelligence does not operate in a vacuum. Reasoning works with representations, concepts and information already available to the mind.
A mathematician who has spent twenty years working with abstract structures can manipulate an idea that appears impossibly complicated to someone seeing it for the first time. The difference is not necessarily that one brain can comprehend abstraction and the other cannot. One mind has spent years constructing the necessary abstractions.
This is why expertise can sometimes look like extraordinary intelligence from the outside. The expert is not necessarily solving the problem from nothing. The expert has a vast internal library of patterns, relationships and previously solved problems.
A beginner sees a wall. An expert sees a familiar door.
5. The Real Barrier May Be Abstraction
There is another difficulty that has little to do with the IQ number alone: the distance between an idea and ordinary experience.
Gravity is relatively easy to discuss because we experience falling objects. Atoms are harder because we cannot see them directly. Probability becomes more abstract when we begin reasoning about distributions rather than individual events. Higher mathematics moves further still, into objects that may have no intuitive physical counterpart.
At some point, the mind stops being able to rely on direct experience and begins constructing symbolic models. That transition can be difficult.
But difficulty is not the same as impossibility. A good explanation can move an idea down the ladder of abstraction without destroying its essential structure. A diagram can replace a paragraph. An analogy can provide an intuitive foothold. An example can turn an abstract relationship into something the mind can manipulate.
The underlying idea has not changed. The route into the idea has changed.
That distinction is particularly important in teaching.
6. Discovery and Understanding Are Different Achievements
There is another distinction that is often overlooked. Could a person with an average IQ independently discover Einstein’s theory of relativity? That is an extraordinarily demanding question. It involves identifying the problem, possessing enormous background knowledge, developing the mathematics, generating the conceptual insight and pursuing it far enough to formulate a new theory.
But that is not the same as asking whether an average-IQ person can understand the basic idea of relativity once it has been explained. Those are completely different intellectual tasks.
The first involves discovery. The second involves comprehension.
A person does not have to be capable of independently inventing an idea in order to understand it. Most people could not invent calculus, but many can learn to use calculus. Most people could not develop modern computer science from first principles, but millions can understand programming.
Very few people can contribute a new theorem to advanced mathematics. Yet people with no intention of becoming mathematicians can still understand what a theorem means, why it matters and how its underlying idea works.
The ability to create an idea and the ability to reconstruct its meaning are not the same thing.
7. What a Good Teacher Really Does
This is where the subject becomes especially relevant to education. A good teacher does not simply transfer information from one brain to another. A good teacher constructs a path.
Suppose an advanced concept requires five conceptual steps:
A → B → C → D → E
An inexperienced learner may be shown E and told to understand it. Naturally, E appears impossible. A good teacher may instead build the path from A through B, C and D until E becomes accessible.
The destination has not become less sophisticated. The learner has simply been given the road.
This is why a remarkable teacher can make an apparently difficult idea feel almost obvious. The teacher has reduced the entry cost.
And this raises an uncomfortable question about how we sometimes judge intelligence. When a student fails to understand something, are we measuring the student’s cognitive limitation, or the distance between the student’s existing mental model and the way we have presented the idea?
Sometimes it is the former. Sometimes it is the latter. From the outside, the two can look remarkably similar.
8. The Mind Does Not Store Ideas; It Builds Models
There is an even deeper distinction between knowing a statement and understanding an idea.
Suppose I tell someone that a black hole has an event horizon. They can memorize the sentence in seconds. But memorization is not necessarily comprehension.
Understanding begins when the person can do something with the concept. They can explain it in their own words, connect it to gravity, distinguish it from a related concept, understand its consequences, or use it to make sense of another phenomenon.
In other words, understanding is not merely possessing an answer. It is possessing a model that allows the mind to generate consequences.
This may be one reason intelligence and understanding are related but not interchangeable. Intelligence can influence how efficiently we construct and manipulate models, but the model itself also depends on knowledge, experience, language and education.
9. So What Can an Average-IQ Person Actually Understand?
We can now return to the original question. There is no scientifically defensible list of ideas that can simply be labelled “impossible for people with IQ 100.”
That does not mean everyone can understand everything. Human cognitive differences are real. People differ in reasoning ability, memory, processing speed, attention and many other characteristics. Those differences can affect learning and performance.
Some ideas are extraordinarily difficult. Some require years of preparation. Some may remain inaccessible to particular individuals even after extensive effort.
But an IQ score by itself does not tell us where that boundary lies.
The relevant questions are more complicated. What is the person’s existing knowledge? What cognitive operations does the idea require? How abstract is it? How much working memory does it demand? How much time is available? How effectively has it been explained? How much practice has the person had?
And perhaps most importantly: what mental model does the person already possess?
The answers to those questions can change the apparent difficulty of an idea enormously.
10. Cognitive Distance
This leads to what I think is a more useful way of thinking about the problem.
Imagine two people looking at the same idea. For one person, the idea is only a small step beyond what they already know. For the other, it is separated by twenty missing concepts.
The idea is identical. The cognitive distance is not.
We could therefore think of understanding conceptually as:
Difficulty ≈ Complexity of Idea − Existing Mental Structure
This is not a scientific equation. It is a conceptual one. Its purpose is to make us notice something that the IQ number tends to hide: the difficulty of an idea is partly a relationship between the idea and the mind encountering it.
A highly trained mathematician can find an advanced mathematical concept easier than an elementary probability problem involving unfamiliar intuition. A historian may immediately understand a complicated historical development that leaves a physicist confused. A mechanic may understand the behaviour of an engine better than someone with a much higher measured IQ but no mechanical experience.
The mind is not a single ladder. It is a landscape.
10A. Can Cognitive Ability Be Changed?
There is evidence that at least some aspects of cognitive performance can be changed through intensive training. This is important because it challenges a simplistic picture in which a person’s measured cognitive ability is treated as completely fixed.
A U.S. Navy Brain Fitness Training program explicitly sought to test whether domain-general cognitive skills—including working memory and fluid intelligence—could be substantially increased. The Navy’s research topic called for testing whether mean ability could be moved by about one standard deviation, using less than 40 hours of training. This was a research objective, not proof that every participant would achieve such a gain.
A separate three-year research and development effort funded by the U.S. Navy and Marine Corps reported that a software program improved participating sailors’ reading comprehension by about two grade levels after 40 hours of study. This illustrates how training can produce substantial improvement in a specific cognitive skill without establishing that general IQ has risen by the same amount.
There is also a frequently cited 30-point IQ gain from a different three-year intervention involving young autistic children. The original Lovaas research reported a mean IQ gain 30 points higher than controls after two to three years of intensive intervention. However, the study was small and had methodological limitations, including non-random assignment, so this should not be generalized into a claim that anyone can permanently raise IQ by 30 points through training.
The important point for our question is narrower and more useful: cognitive performance is not necessarily a completely fixed quantity. Training, education, experience and the acquisition of mental structures can change what a person is able to do—and therefore change the apparent distance between a person and a difficult idea.
Research references: U.S. Navy Brain Fitness Training SBIR award · Navy cognitive-training research topic · Office of Naval Research: sailors’ reading improvement · Review discussing the Lovaas intervention
11. Perhaps IQ Measures the Traveller, Not the Entire Journey
This brings us back to the original question from 2017. Perhaps we were asking the wrong thing.
We asked: What ideas can a person with an IQ of 100 not understand?
But perhaps the more revealing question is: How far can a person travel from their starting point with the right knowledge, education and intellectual tools?
IQ matters. It can tell us something about cognitive differences between people. But it does not tell the entire story of intellectual development.
One person may reach a conclusion quickly. Another may take much longer. One may require diagrams. Another may need equations. One may understand through examples. Another through abstraction.
Sometimes the person who takes the longer route develops a more detailed map of the terrain.
That is not an argument against intelligence testing. It is an argument against asking one number to carry more meaning than it was designed to carry.
12. The Question Behind the Question
The original question was about IQ. But underneath it was a much more interesting question:
Are there limits to human understanding?
Of course there are. Every human being has finite time, finite memory, finite attention and finite cognitive resources. No individual can understand everything.
But the location of the boundary is not determined by IQ alone.
A person may encounter an idea today and find it incomprehensible. After a year of learning, the same idea may seem obvious. What changed? Not necessarily the person’s IQ.
The map changed.
The prerequisites were acquired. The abstractions became familiar. The pieces began connecting.
And once the connections exist, an idea that previously appeared impossibly distant can suddenly become almost ordinary.
That may be one of the most important facts about learning: the mind does not merely become better at solving problems; it changes the space in which problems can be understood.
13. Conclusion: IQ 100 Is Not a Wall
An average IQ of 100 does not define an intellectual boundary. It tells us something about performance on standardized measures of cognitive ability, but it does not tell us which ideas a particular person can eventually understand.
There are genuine differences in cognitive ability. There are genuinely difficult ideas. Some forms of reasoning demand abilities that not everyone possesses to the same degree.
But between “difficult” and “impossible” lies an enormous territory called learning.
Knowledge reduces distance. Education builds structure. Experience supplies patterns. Language provides representation. Good teaching builds bridges. Curiosity keeps us moving. Intelligence influences how efficiently we travel.
So perhaps the question should no longer be:
What ideas can a person with an average IQ of 100 understand?
Perhaps the better question is:
How much of the intellectual world becomes accessible once the right mental map has been built?
That is a much harder question.
And, perhaps, a much more interesting one.
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