Drake Equation Lab

What is modelled

The Drake equation multiplies seven factors to estimate how many communicating civilisations the galaxy holds now. Several factors are almost completely unknown, so the honest answer is a probability distribution, not a number. Each factor is given a median and a log-normal spread, and the page draws random sets of factors.

Equations

• N = R* fp ne fl fi fc L.
• Taking logarithms turns the product into a sum: log10 N = Σ log10 xi, so with independent log-normal factors log10 N ~ Normal(μ, s2) with μ = Σ μi and s2 = Σ σi2.
• Probability of being alone P(N < 1) = Φ(−μ / s).
• Variance share of factor i is σi2 / s2.

Checks run in the page

• Sample mean and variance of log10 N against mu and s squared.
• Monte Carlo P(N < 1) against the normal law.
• Squared correlation of each factor with log10 N against its variance share.
• Shifting L by one decade shifts every sample by exactly one.

Honest simplifications

The medians and spreads are illustrative, not measured, and the factors are treated as independent. Probabilities are sampled as log-normal values, which can slightly exceed 1; the histogram caps them at 1 while the checks use the uncapped samples and the page reports how many draws were affected. The result shows how uncertainty dominates, not a prediction.

• Press No uncertainty and then Huge uncertainty to see one number turn into a spread of many orders of magnitude.
• Press Rare Earth and Optimistic to move the probability that we are alone from nearly sure to nearly impossible.
• Check the variance shares: life, intelligence and lifetime dominate; the astronomy factors barely matter.