TOK - Essay Title Five (May 2025)

Summary

In this video, Mr. Darling discusses the essay title for the May 2025 examination series, which explores the claim, 'All models are wrong but some are useful,' attributed to George Box. He breaks down the key concepts of the claim, exploring what it means for models to be 'wrong' and 'useful,' and provides insights from various Areas of Knowledge (AOK) including mathematics, the natural sciences, human sciences, and the arts. Using examples such as statistical models, educational frameworks, and scientific theories, he illustrates how models can be both imperfect yet indispensable tools for understanding complex phenomena.

Takeaways

• 😀 Models can be physical (e.g., architectural designs) or conceptual (e.g., mental models, graphs).
• 😀 The essay question asks to what extent you agree with the statement 'All models are wrong, but some are useful.' The key is to determine the extent of agreement.
• 😀 Models are not perfect representations of reality. They are simplified versions that are often 'wrong' in certain details but still serve a purpose.
• 😀 The word 'wrong' in the context of models refers to their inherent limitations, not necessarily complete inaccuracy.
• 😀 Mathematical models, such as statistical models or graphs, are often 'wrong' in that they are simplified versions of complex real-world phenomena.
• 😀 Despite being wrong, models are useful because they help us predict, simplify, and communicate complex ideas more easily.
• 😀 In the natural sciences, models evolve over time as new theories replace old ones, demonstrating that earlier models were 'wrong.'
• 😀 Examples from economics, like the Laffer curve, show how models can oversimplify reality but still guide important real-world decisions.
• 😀 Bloom's Taxonomy in education is a model that helps guide teaching, despite being critiqued for oversimplifying cognitive development stages.
• 😀 In the arts, models (e.g., anatomical figures for drawing) are useful for helping us understand and replicate reality, even if they are not perfect representations.
• 😀 Historical models, such as 3D reconstructions of Stonehenge, illustrate how models can evolve over time as new methods and theories emerge.

Q & A

What is the central claim made by George Box in the essay title?

George Box claims that 'All models are wrong, but some are useful.' The essay asks students to discuss the extent to which they agree with this statement, considering both the limitations (wrongness) and the utility of models.

What does Mr. Darling mean by 'to what extent' in the essay question?

The phrase 'to what extent' asks students to evaluate the degree to which they agree or disagree with the claim. Students are expected to choose a position (e.g., to a large extent, to a limited extent, or to no extent) and defend it with examples.

What are the two main types of models discussed by Mr. Darling?

Mr. Darling distinguishes between physical models (which can be touched or seen, like architectural models or DNA structures) and conceptual models (which are abstract, like mental models or graphs).

How does Herbert Stovak contribute to the understanding of models?

Herbert Stovak characterizes models by three properties: mapping (models represent something, not the thing itself), reduction (models are simplified versions of reality), and pragmatism (models are useful for understanding and predicting phenomena).

What is the relevance of the 'This is not a pipe' artwork by René Magritte in the context of models?

Magritte's artwork demonstrates the idea that representations (models) are not the actual object. It emphasizes the concept of 'mapping' and 'reduction' in models, where a model is a simplified or abstract version of reality, not reality itself.

Why does Mr. Darling argue that some models are 'useful' despite being 'wrong'?

Models are useful because they simplify complex ideas, make knowledge more accessible, and help predict or understand phenomena. Even though models may not be fully accurate, their utility in conveying ideas and guiding decisions makes them valuable.

How do mathematical models relate to George Box's claim?

Mathematical models are considered 'wrong' because they simplify or abstract real-world patterns into equations or statistical models. However, they are useful for understanding relationships and making predictions, as seen in examples like statistical models and elliptic curves.

What is the role of models in the natural sciences, according to Mr. Darling?

In the natural sciences, models are used to represent complex ideas and theories, such as atomic structures or the solar system. While these models may not be completely accurate (e.g., the size and distances of planets), they provide a framework for understanding and communicating scientific concepts.

How does Mr. Darling relate models to the field of economics?

In economics, models like the Laffer curve are used to represent relationships between tax rates and revenue. Although such models are often criticized for being oversimplified (e.g., the 'napkin theory'), they are useful for guiding policy decisions despite their limitations.

Why does Mr. Darling suggest that Bloom's Taxonomy is an example of a useful model?

Bloom's Taxonomy is a model in education that organizes cognitive skills into a hierarchy, helping educators structure lessons. While it simplifies the complexity of learning, it remains useful for understanding and promoting higher-order thinking, even though it may not capture every aspect of human cognition.