5.5.1 Breakdown & Cheat sheet Notes

IB May 2026 (M26) TOK Essay Title #5 Outline

To what extent do you agree with the claim that “all things are numbers” (Pythagoras)? Discuss with reference to the arts and the human sciences.

The Core Of The Question

1. At first glance, “all things are numbers” sounds hyperbolic or mystical.
2. In Pythagoras’s context, it meant something literal: numbers underpinned music, geometry, and even atoms.
3. In your essay, the task here is to ask when does this claim hold explanatory power, and when does it collapse?

Numbers As Explanatory Power

1. In the arts:
   1. Music theory is inherently numerical (intervals, rhythm, frequency ratios).
   2. Visual arts use proportion, symmetry, and perspective, often expressed numerically (e.g., Fibonacci, golden ratio).
2. In human sciences:
   1. Numbers dominate: survey data, statistics, psychometrics, economics models.
   2. Without quantification, findings are dismissed as anecdotal.

Limits Of Numbers In Arts

1. Numbers can describe structure (beats per minute, pigment ratios), but not meaning or interpretive effect.
2. Some modern art explicitly resists quantification, like abstract expressionism or conceptual art where ambiguity is the point.
3. Here, numbers explain parts of art but fail to capture essence.

Limits Of Numbers In Human Sciences

1. Human behavior changes across time and culture, numerical generalizations are always provisional.
2. This means numbers risk reductionism, making messy human realities appear simpler than they are.
3. This is why qualitative data (oral histories, interviews) is employed, they capture nuance that numbers cannot.

The Spectrum Of Agreement