26 The legend of Ambalappuzha
26.1 Introduction
This short appendix activity uses the classic “rice on a chessboard” legend (the Ambalappuzha temple story) to build intuition for the sheer speed of exponential/geometric growth. Students use an Excel sheet (and optionally R) to compute the number of grains when each of the 64 squares doubles the previous one, convert the total to a weight, and then relate the doubling process to real population growth and why it cannot continue unchecked.
26.2 Key Concepts
- Doubling is multiplicative: each square is \(2\times\) the previous, so the total over 64 squares is \(2^{64}-1 \approx 1.84\times10^{19}\) grains.
- Scale intuition: at 25 mg/grain that is ~461 gigatonnes — hundreds of times annual global rice production.
- From rice to populations: unchecked doubling is a stand-in for density-independent growth; real populations are limited by survival < 100%, density dependence, carrying capacity, and stochasticity.
26.3 Learning Outcomes
By the end of this exercise, students will be able to: - Use Excel formulae for a simple mathematical model. - Explain the multiplicative nature of exponential/geometric growth. - Articulate why simple doubling is unrealistic for real populations.
26.4 Activity Overview
Suggested Timings:
- 5 minutes: Tell the legend and set up the doubling rule.
- 10 minutes: Students compute grains per square and the total in Excel
(RiceOnAChessboard.xlsx), then convert to kg.
- 5 minutes: Optional R version.
- 10 minutes: Discussion — link doubling to population growth and its limits.
26.5 Instructions for Facilitating
- Have students open
RiceOnAChessboard.xlsxand build the doubling column (each cell = previous cell × 2), then sum all 64 squares. - Convert grains to weight: at 25 mg (0.000025 kg) per grain, the total is ≈ 461,168,601,842,739 kg (~461 Gt).
- Optionally reproduce in R with a simple loop and
sum(). - Pivot to biology: pose the great-tit (“musvit”) thought experiment (~100 breeding pairs, ~6 eggs/female/year, 50:50 sex ratio) — first with 100% survival, then relaxing that assumption.
- Use the discussion prompts to draw out what makes real growth sub-exponential.
26.6 Questions & Model Answers
- How many grains in total, and how much does that weigh?
- \(2^{64}-1 \approx 1.84\times10^{19}\) grains; at 25 mg each, ≈ 461 gigatonnes — far more than the king (or the world) could supply, which is the point of the legend.
- With 100% survival, how many female great tits after 5 years, and what changes when you relax that?
- Under pure doubling the number explodes geometrically; introducing realistic survival < 100%, recruitment, and density dependence dramatically lowers and eventually flattens the trajectory. Exact numbers depend on the assumed rates — the aim is the contrast.
- Why is the simple doubling model unrealistic for real populations?
- Survival is below 100% and is age/stage-specific; resources, territories, disease and predation impose density dependence and a carrying capacity; good and bad years add stochasticity; and dispersal moves individuals in and out. All push growth below the geometric ideal.
26.7 Teaching Tips
- Let the number land: converting grains to gigatonnes (and comparing to world rice production) is what makes exponential growth visceral.
- Bridge to the course: use the great-tit prompt to connect the legend to the population models students have already built.
- Excel technique: this is a natural place to reinforce relative vs absolute cell references and dragging formulae down a column.