Models are representations, not reality

To make sense of the world, we simplify it.

We draw maps.

We build diagrams.

We write equations.

We classify things into categories.

We collect measurements into datasets.

We construct computer simulations.

We train artificial intelligence models.

All of these activities have something in common:

They create representations of reality rather than reality itself.

This distinction sounds obvious.

A map is clearly not the landscape.

A weather model is clearly not the atmosphere.

A photograph is clearly not the event it records.

Yet when models become complicated, accurate or computationally powerful, it becomes surprisingly easy to forget this distinction.

We begin to treat the output of the model as though it were the world itself.

Understanding why that is dangerous is essential for understanding data, prediction and artificial intelligence.

The map is not the territory

Imagine a map of a city.

The real city contains:

millions of physical objects,
people,
buildings,
trees,
roads,
pipes,
electrical cables,
sounds,
smells,
temperatures,
movements,
conversations,
histories.

A useful road map might contain only:

roads,
road names,
junctions,
directions,
perhaps traffic conditions.

Most of reality has been deliberately removed.

This is not a failure of the map.

It is what makes the map useful.

A map containing every detail of the city would be almost impossible to use.

The map simplifies reality in order to answer a particular set of questions.

For example:

How do I get from here to there?

A geological map of the same city would preserve completely different information.

So would:

a public-transport map,
an electricity-network map,
a flood-risk map,
a property-price map,
an air-quality map.

They all describe the same physical place.

Yet they represent it differently because they have different purposes.

Every model leaves something out

A model is created by deciding what matters.

Suppose we want to model the movement of a car.

A very simple model might include:

position,
speed,
direction.

We might ignore:

the colour of the car,
the driver's name,
the music playing inside,
the number of scratches on the paint.

For predicting where the car will be one second from now, those exclusions are probably sensible.

But perhaps we also ignore:

road conditions,
nearby vehicles,
traffic signals,
driver behaviour.

Now some of the information we excluded might actually matter.

Model design therefore requires judgement.

We must decide which features of reality are relevant to the problem and which can safely be ignored.

That process is called abstraction.

Abstraction makes complexity manageable

The real world is enormously complicated.

Imagine trying to predict the movement of a football.

At the deepest possible physical level, we could attempt to model:

every atom in the ball,
every molecule in the air,
every deformation of the surface,
every microscopic interaction.

That would be absurd for most purposes.

Instead, we might represent the ball using a few variables:

position,
velocity,
mass,
spin.

We have compressed an almost unimaginably complicated physical object into a small mathematical description.

That abstraction allows us to reason about the system.

Good modelling is therefore not about reproducing every detail of reality.

It is about preserving the details that matter for the question being asked.

A useful model is deliberately incomplete

This leads to an important insight:

A model can be useful precisely because it is incomplete.

Consider a public-transport map.

A geographically accurate map of a rail network may be difficult to read because stations and lines are unevenly distributed.

Many transport maps therefore distort:

distances,
directions,
geography.

Yet they make the network structure much clearer.

If the question is:

Which line should I take and where should I change?

the distorted map may actually be more useful than a geographically accurate one.

Accuracy therefore has to be understood relative to purpose.

A model can be inaccurate in one sense while extremely useful in another.

Models answer particular questions

Suppose we build a model of a house.

An architect may care about:

dimensions,
rooms,
materials,
structural loads.

An energy engineer may care about:

insulation,
heating systems,
temperatures,
energy consumption.

A property valuation model may care about:

floor area,
location,
number of bedrooms,
recent sale prices.

All three models describe the same house.

But none is a complete representation of it.

Each model preserves information relevant to a different problem.

This suggests a better question than:

Is this model accurate?

We should also ask:

Accurate for what purpose?

Data is already a model of reality

It is tempting to think that the model only appears after we have collected the data.

But abstraction begins much earlier.

Consider a temperature sensor.

The physical environment around the sensor contains an enormous amount of information.

The sensor produces:

18.4°C

Almost everything else has been discarded.

The instrument itself has reduced reality to a particular measurement.

Similarly, a camera converts the visual world into pixels.

A microphone converts pressure waves into numerical samples.

A survey converts people's experiences into answers to predefined questions.

A database converts organisations and people into fields and categories.

So the process is not simply:

REALITY → DATA → MODEL

Even the data is already a representation.

A more accurate view is:

REALITY → MEASUREMENT → DATA → MODEL

At every step, information is selected, transformed and discarded.

Categories are models too

Suppose a database contains the field:

Employment status

with possible values:

employed,
unemployed,
student,
retired.

Reality may be much messier.

Someone might:

work part-time,
study part-time,
care for children,
run a small business,
undertake unpaid work,
move between several roles.

The database requires that complexity to fit into predefined categories.

The categories make analysis possible.

But they also impose a particular structure on reality.

This matters because artificial intelligence often learns from exactly these kinds of categories.

If the categories are inadequate, biased or outdated, the model inherits those limitations.

What gets excluded?

Whenever we encounter a model, one of the most useful questions we can ask is:

What has been left out?

Suppose an AI system predicts whether someone will repay a loan.

The model might include:

income,
employment history,
previous repayments,
outstanding debt.

It might not include:

family circumstances,
unexpected illness,
future employment changes,
informal financial support,
personal explanations for previous difficulties.

Some exclusions may be appropriate.

Others may significantly affect the prediction.

The model does not know what it has not been given.

Missing variables can become hidden assumptions

When information is absent, models may rely on other variables instead.

Suppose we are predicting educational performance.

The dataset contains:

previous grades,
attendance,
postcode,
school.

But it does not contain:

household resources,
caring responsibilities,
access to tutoring,
study environment.

The model may discover that postcode is strongly predictive.

Why?

Perhaps postcode indirectly contains information about some of those missing factors.

The model has found a statistical relationship.

But interpreting that relationship requires care.

Prediction does not automatically reveal the underlying cause.

This distinction will become important when we examine correlation, causation and fairness.

Models can succeed for the wrong reason

Imagine an image-recognition model trained to distinguish photographs of wolves from dogs.

Suppose most wolf photographs happen to contain snow, while most dog photographs do not.

The model may appear highly accurate.

But perhaps it has learned:

snow → wolf

rather than learning the characteristics of wolves themselves.

When shown a dog standing in snow, it may confidently make the wrong prediction.

The model has found a pattern in the training data.

It has not necessarily learned the concept we intended.

This illustrates a crucial problem:

A model can make correct predictions while relying on the wrong representation of the problem.

Performance alone does not always tell us what the model has learned.

A model sees what its representation allows it to see

Imagine two models trying to predict traffic congestion.

Model A receives only:

total number of vehicles in the city.

Model B receives:

number of vehicles on each road,
road capacities,
vehicle directions,
current speeds.

Model A may predict total traffic activity reasonably well.

But it cannot know where congestion will occur.

That information simply does not exist in its representation.

The limitation is structural.

No amount of clever optimisation can recover spatial information that was never provided.

This gives us another important principle:

A model cannot use information that its representation has discarded.

Aggregation changes the model

We saw in the previous lesson that spatial aggregation can hide local conditions.

The same principle applies more generally.

Suppose ten people have incomes:

€20k, €22k, €24k, €26k, €28k, €30k, €32k, €34k, €36k, €500k

We could replace these ten values with their average.

That produces one number.

The number is mathematically valid.

But the distribution has disappeared.

A model using only the average cannot distinguish between:

ten people earning similar amounts,
nine moderate incomes and one extremely high income.

Aggregation therefore does not merely simplify the data.

It changes what the model is capable of representing.

Resolution matters

Models operate at particular levels of resolution.

A weather model might represent the atmosphere in geographic cells.

A traffic model might represent individual roads.

An economic model might represent entire industries.

A biological model might represent individual cells.

Changing the resolution changes what the model can see.

At low resolution, local detail disappears.

At very high resolution, computation may become extremely expensive and noise may become more important.

There is rarely one universally correct resolution.

The appropriate level depends on:

the problem,
the available data,
the required accuracy,
computational resources,
the decision being made.

Models contain assumptions

Every model contains assumptions.

Some assumptions are explicit.

For example:

We assume demand grows by 2% each year.

Others are embedded in the structure of the model.

For example:

We assume these variables are sufficient to predict the outcome.

Or:

We assume relationships learned from historical data will continue into the future.

Or:

We assume observations are independent.

Or:

We assume this geographic boundary is the appropriate unit of analysis.

These assumptions may be reasonable.

But they are still assumptions.

When circumstances change, they can become wrong.

The model creates a possible world

One useful way to think about a model is as a small artificial world.

Inside the model:

certain variables exist,
certain relationships exist,
certain actions are possible,
certain outcomes can occur.

Everything outside that representation is absent.

Consider a chess-playing AI.

The model of the world is exceptionally constrained.

It contains:

a board,
pieces,
legal moves,
an objective.

It does not need to model weather, politics or the price of electricity.

That narrow representation makes extraordinary performance possible.

The challenge becomes much greater when AI operates in the real world, because the real world is open-ended.

Closed worlds and open worlds

Some problems have well-defined boundaries.

Chess is a relatively closed world.

We know:

the board,
the pieces,
the rules,
the possible legal actions.

The real world is much more open.

An autonomous vehicle may encounter:

roadworks,
unusual vehicles,
animals,
damaged traffic signals,
unexpected human behaviour,
weather conditions,
objects that were rare or absent from training data.

It is impossible to enumerate every possible situation in advance.

This is one reason moving AI from controlled environments into society and the physical world is so challenging.

Simulation is not reality

Computer simulations allow us to experiment with models.

We can ask:

What happens if we change this?

This is extraordinarily useful.

An engineer can test a bridge design before building it.

A climate scientist can explore possible future scenarios.

A robot can learn behaviours in a simulated environment.

An electricity planner can test different generation portfolios.

But simulation results are conditional on the model.

If the model omits an important feature, the simulation omits it too.

A beautifully detailed simulation can therefore produce misleading results if its underlying assumptions are wrong.

Computational sophistication does not remove modelling assumptions.

Digital twins are still models

The term digital twin is sometimes used for highly detailed digital representations of physical systems.

A digital twin might continuously receive measurements from:

a factory,
a wind turbine,
a building,
a power network,
a vehicle.

The digital representation updates as new data arrives.

This can create an extremely useful representation of the physical system.

But the digital twin is still not the physical system.

Sensors may be wrong.

Some variables may not be measured.

The mathematical representation may be imperfect.

Unexpected behaviour may occur.

The twin can become a very good model of reality.

It cannot become reality itself.

Artificial intelligence models are representations too

The same principle applies to artificial intelligence.

A language model does not contain the world.

It contains a learned representation derived from patterns in training data.

A computer-vision system does not directly experience objects.

It learns representations derived from images.

A recommendation model does not directly know a person.

It represents aspects of their behaviour through data such as:

clicks,
purchases,
viewing history,
ratings,
interactions.

These representations can be extraordinarily powerful.

But they remain abstractions.

Representations inside AI

Modern AI systems often create internal numerical representations of information.

Words, images, sounds and other inputs can be transformed into vectors: collections of numbers that encode useful relationships.

For example, a model may learn representations in which concepts with related meanings occupy related regions of a mathematical space.

The original object has been transformed.

A word is no longer represented merely as a sequence of letters.

An image is no longer merely a grid of pixels.

The model constructs internal features that are useful for its task.

This process of learning representations is one of the key reasons modern AI has become so powerful.

But once again:

The representation is not the thing being represented.

Compressing reality

Another way to understand modelling is as compression.

The world contains enormous complexity.

A model tries to preserve useful structure using a much smaller representation.

We can think of the process as:

COMPLEX REALITY

↓

SELECTED OBSERVATIONS

↓

COMPRESSED REPRESENTATION

↓

USEFUL INFERENCE

Good models preserve information that helps answer the question.

Poor models discard information that later turns out to matter.

The challenge is knowing the difference.

More detail is not always better

It may seem that the solution is simply to include everything.

But that creates its own problems.

More variables can mean:

more data collection,
greater computational cost,
more noise,
more opportunities for spurious relationships,
more privacy intrusion,
more difficult interpretation.

A model containing every available variable may perform worse than a carefully designed simpler model.

Abstraction is therefore unavoidable.

The goal is not to eliminate abstraction.

It is to choose it intelligently.

All models have boundaries

Imagine drawing a box around the system we want to model.

Inside the box are things the model represents.

Outside the box are things we treat as external.

For a building-energy model, the box might include:

the building,
heating system,
occupants,
weather.

But perhaps electricity prices are treated as external.

For an electricity-market model, electricity prices might be inside the model, while global fuel markets remain outside.

For an economic model, global fuel markets might become part of the system.

Every analysis draws its boundary somewhere.

Moving the boundary changes the model.

External factors become disturbances

Systems are continually affected by things outside their modelled boundary.

Engineers often call these disturbances.

A robot may experience:

wind,
bumps,
someone pushing it.

An electricity system may experience:

generator failures,
sudden weather changes,
unexpected demand.

A business may experience:

political events,
competitor actions,
supply disruptions.

Models can sometimes represent disturbances probabilistically.

But unexpected disturbances remind us that the model does not contain the entire world.

Models can change the thing they model

There is another complication.

Models are not always passive observers.

Imagine a navigation model predicts that Road A is the fastest route.

Thousands of people receive the same prediction.

They all choose Road A.

The traffic state changes.

The prediction helped alter the reality it was modelling.

Recommendation systems can do the same.

If a platform predicts that people will engage with certain content and therefore shows them more of it, the model influences what people see.

Their future behaviour becomes partly shaped by the previous model.

That behaviour then becomes new training data.

A feedback loop emerges.

When predictions become interventions

Consider a bank using a model to decide who receives credit.

The model predicts:

Applicant A is high risk.

The bank refuses the loan.

Because the applicant never receives the loan, we never observe whether they would actually have repaid it.

The decision has changed the future data available to us.

Similarly:

MODEL → PREDICTION → DECISION → ACTION

changes:

WHAT HAPPENS NEXT

which changes:

WHAT DATA EXISTS LATER

This is an extremely important idea.

Models do not merely learn from society.

Once deployed, they can begin to shape society.

The feedback loop

We can now introduce the framework that will run throughout this course:

PAST → DATA → MODEL → PREDICTION → DECISION → ACTION → FUTURE

Let us examine each step.

Past

Events occur.

Data

Some aspects of those events are observed, measured and recorded.

Model

We build a representation that attempts to capture useful relationships in that data.

Prediction

The model is used to infer something unknown or something that may happen next.

Decision

The prediction informs a choice.

Action

The decision is implemented.

Future

The world changes.

But the process does not stop there.

The future eventually becomes the present.

Then the past.

It can be observed.

And it generates new data.

So the process is actually a loop:

PAST → DATA → MODEL → PREDICTION → DECISION → ACTION → FUTURE

↑ ↓

← ← ← ← ← ← ← NEW OBSERVATIONS ← ← ← ← ← ← ←

The output of today's system can become the input to tomorrow's system.

Models can therefore reshape their own training data

This feedback loop creates some remarkable possibilities.

Imagine a recommendation system.

It learns from what people watched in the past.

It predicts what people will watch next.

It recommends those items.

People watch some of the recommendations.

Those viewing choices become new data.

The system trains on that data.

So:

PAST BEHAVIOUR

↓

MODEL

↓

RECOMMENDATIONS

↓

FUTURE BEHAVIOUR

↓

NEW TRAINING DATA

The model is now partly learning from a world that its previous decisions helped create.

Feedback can amplify bias

Suppose historical data contains a bias.

The model learns that pattern.

The model's decisions reproduce the pattern.

Those decisions generate new data.

The new data appears to confirm the original relationship.

The loop becomes:

HISTORICAL BIAS

↓

DATA

↓

MODEL

↓

BIASED DECISION

↓

BIASED OUTCOME

↓

NEW DATA

↓

MODEL

This can create self-reinforcing feedback.

The model may appear increasingly certain because the world it observes increasingly reflects its own previous decisions.

This is one reason fairness cannot be understood by examining a model in isolation.

We need to examine the entire system around it.

The model is part of the system

This gives us a deeper way of thinking about artificial intelligence.

Instead of asking only:

How accurate is the AI model?

we should ask:

What system is this model part of?

We need to consider:

what generates the data,
what the model represents,
what it predicts,
who uses the prediction,
what decisions follow,
what actions those decisions create,
who experiences the consequences,
what new data those consequences generate.

The AI model is only one component in a much larger feedback system.

Model error and system error are different

A model can be statistically accurate while the overall system produces poor outcomes.

Imagine an AI system that predicts which customers are most likely to spend money if shown an advertisement.

The prediction may be excellent.

But if the broader objective is to improve people's wellbeing, maximising advertising engagement may not be the right goal.

The model has solved the task it was given.

The system designer may have chosen the wrong task.

This distinction is crucial:

A good model does not guarantee a good system.

Better models do not solve bad objectives

Suppose an optimisation system has the objective:

maximise engagement

A more accurate predictive model may become exceptionally good at identifying content that keeps users engaged.

But perhaps the result is:

greater distraction,
more outrage,
more polarisation,
poorer mental wellbeing.

Improving the model may actually make the undesirable system behaviour stronger.

The question is therefore not only:

How do we build better models?

It is also:

What are those models being used to achieve?

We will return to this when we study optimisation, service design and fairness.

Reality remains the final test

No matter how sophisticated a model becomes, reality remains outside it.

A model can predict that a bridge is safe.

The bridge still has to stand.

A model can predict that a patient is healthy.

The patient's actual condition matters more.

A model can predict that a power system is secure.

The physical network still has to operate.

A model can predict that a robot's path is clear.

The robot still has to move through the real environment.

Ultimately:

The world does not have to obey the model.

The model must continually be tested against the world.

Learning requires comparison with reality

When predictions eventually become observable, we can compare:

WHAT THE MODEL PREDICTED

with:

WHAT ACTUALLY HAPPENED

The difference provides information.

If predictions are consistently wrong, something may need to change:

the data,
the representation,
the assumptions,
the parameters,
perhaps the model itself.

This process of comparing predictions with observations is fundamental to learning.

The model is updated because reality provides new evidence.

The loop becomes learning

Our course framework can therefore be expanded:

PAST

↓

DATA

↓

MODEL

↓

PREDICTION

↓

DECISION

↓

ACTION

↓

FUTURE

↓

OBSERVATION

↓

NEW DATA

↓

UPDATE MODEL

The system can learn over time.

This loop lies behind many forms of machine intelligence.

And as machines increasingly make decisions and take actions themselves, the loop becomes faster and more consequential.

A model should help us think, not replace thinking

Models are powerful because they allow us to reason about systems too complicated to hold entirely in our minds.

But their outputs should not automatically be treated as truth.

When using a model, useful questions include:

What is being represented?
What is being excluded?
What assumptions have been made?
What data created the model?
At what time and spatial scale does it operate?
What uncertainty exists?
Where might the model fail?
What happens if people act on its prediction?
Who is affected by the resulting decisions?

These questions become more important, not less important, as models become more powerful.

The central idea

Reality is extraordinarily complicated.

To reason about it, we build representations.

Those representations deliberately simplify the world.

They preserve some information and discard other information.

That is what makes modelling possible.

But it also creates limitations.

The map is not the territory. The dataset is not the event. The model is not the world. The prediction is not the future.

These distinctions form the foundation for everything that follows.

We can now see the complete conceptual loop introduced in this module:

PAST → DATA → MODEL → PREDICTION → DECISION → ACTION → FUTURE

And then:

FUTURE → OBSERVATION → NEW DATA → UPDATED MODEL

This is not merely a description of artificial intelligence.

It is a description of how intelligent systems interact with time.

The past provides evidence.

Data records part of that evidence.

Models create representations from it.

Predictions describe possible futures.

Decisions select actions.

Actions change the world.

And the changed world becomes the evidence from which the next generation of models learns.

This feedback loop will appear again and again throughout the course.

In the next module, we move deeper into the first major component of that loop:

data itself — how the world becomes information, what gets measured, what gets missed, and what happens before an AI model ever sees a single example.