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

1. Agree: Numbers capture patterns and structures, giving knowledge stability.
2. Disagree: “All” is too sweeping. In both arts and human sciences, meaning, interpretation, and subjectivity exceed quantification.
3. Middle ground: Numbers are part of the story, powerful tools, but not the essence of everything.

Structuring Your Essay

1. Keep every paragraph tied to “extent.”
2. Examiners expect explicit evaluative language (“to a moderate extent,” “to a limited extent”).

Yes/No Structure (Easier)

1. Yes: Music theory and statistical models show knowledge built on numbers.
2. Yes: Numerical tools lend reliability and authority in both AOKs.
3. No: Arts involve irreducible subjective meaning.
4. No: Human sciences deal with context-dependent, shifting behavior that numbers alone can’t capture.

Nuanced Spectrum (Harder To Get Right, Higher Scoring)

1. Considerable extent: In both AOKs, numbers give structure and legitimacy.
2. Moderate extent: Numbers describe form but fail to capture intent or effect in the arts.
3. Limited extent: In human sciences, numbers help but oversimplify, qualitative dimensions remain central.
4. Overall: Numbers matter deeply, but cannot account for “all things.”

Conclusion

1. Reject the absolute claim: “all things” are not numbers.
2. Argue instead that numbers are foundational but not exhaustive.
3. Numbers explain patterns, structures, and measurements, but not meaning, value, or subjective experience.