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TOK ESSAY TITLE-5

To what extent do you agree with the claim “all models are wrong, but some are useful” (attributed to George Box)? Discuss with reference to mathematics and one other area of knowledge.

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MODELS

AND

MEANING

While beginning this exploration, here’s a foundational idea to keep in mind-What makes a model “wrong,” and why do we still rely on them?

Models are simplified representations of complex realities.

No model can perfectly capture the full intricacies of a phenomenon.

Yet some models are powerful tools

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All models are wrong” highlights their simplification and incompleteness.
“But some are useful” reflects their real-world value and predictive power.
Models are tools — not truths — used to interpret and explore complex realities.
Mathematical models: equations, graphs, and statistical patterns.
Scientific models: atomic structures, climate simulations. Other examples: economic theories, psychological frameworks, historical narratives.

FLAWED

YET

FUNCTIONAL

“All models are wrong, but some are useful.” — George Box

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MODELS IN MATHEMATICS

Understanding Usefulness Through Limitations

SIR model for COVID-19: helpful but relies on assumptions like uniform mixing.
Newtonian mechanics: effective in daily life but replaced by Einstein’s theory at extreme speeds.
Models can’t mirror reality exactly — but they offer predictions, test hypotheses, and shape real-world decisions.

Applied math uses models like exponential growth and probability to represent real-world situations.
Pure math relies on axiomatic models (e.g., Euclidean geometry) within a logical system.
Mathematical models are “wrong” when applied simplistically to complex conditions.
Yet, within defined rules, models are internally consistent and precise.

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WHY DO SCIENTISTS USE MODELS?

To simplify and test hypotheses about complex natural phenomena.
Examples include atomic models, climate models, and evolutionary models.

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SCIENTIFIC MODELS ARE TOOLS — NOT TRUTHS. THEIR VALUE LIES IN APPROXIMATION, NOT PERFECTION.

How do models help us understand, even when they're wrong?

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In both mathematics and science, models act as mental tools that simplify the complex world around us.

While they may leave out details or contain flaws, their strength lies in their ability to reveal patterns, make predictions, and guide decisions.

Whether it's a graph showing exponential growth or a theory explaining atomic structure, a “wrong” model can still lead us to powerful insights — if we use it with care and awareness.

A model doesn’t mirror reality. It helps us explore it more meaningfully.

MODELS HELP US THINK — NOT DEFINE TRUTH

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A model might look mathematical or scientific, but it also includes context, simplifications, and interpretations.

Whether you're modeling disease spread, planetary motion, or economic behavior, you're also making judgments about what to include and what to ignore.

Usefulness doesn't mean perfection — it means how effectively a model helps us understand, act, or decide.

A MODEL IS MORE THAN JUST A FORMULA.

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“Wrong” answers the question

“How accurate?”

— about the limitations of a model.

“Useful” answers the question

“How effective?”

— about the purpose of a model.

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99%

of global climate models simplify real-world data

— yet they remain critical in shaping environmental policy.

Many rely on models for answers — without questioning their assumptions.

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Here are some common factors that can make models “wrong” in Theory of Knowledge.

Recognizing these helps us use models more critically and effectively.

Awareness of assumptions is the first step to using models responsibly.

UNDERSTANDING MODEL LIMITATIONS

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ON DIVERSITY, BELONGING, AND KNOWLEDGE CONSTRUCTION)

While assembling a diverse group of knowers is crucial to broadening the scope of perspectives in knowledge production, it is only the beginning. True epistemic progress is made not merely by inclusion, but by ensuring that all voices are valued, understood, and critically engaged with. For example, in the human sciences, incorporating participants from varied cultural and socioeconomic backgrounds enhances the reliability of data. However, if those voices are dismissed or only superficially acknowledged, the process reinforces epistemic injustice rather than mitigates it. This raises important questions: To what extent does the presence of diverse voices in a community of knowers actually influence the knowledge produced? and How does the feeling of belonging affect the confidence with which individuals share their knowledge? In Areas of Knowledge such as history and the arts, marginalized narratives are often rediscovered only when institutions commit to listening and re-evaluating existing paradigms. Hence, diversity is a structural start, but inclusion and meaningful engagement are what shape more balanced and ethical knowledge systems.

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Knowledge is shaped by who contributes to it.

Diverse, inclusive teams challenge assumptions.

Inclusion ensures all voices are valued.

Group knowledge improves when biases are addressed.

Shared knowledge in virtual settings requires effort.

THE BOTTOMLINE