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Equation 2 · Part 4 · Fine-Tuning Without a Tuner: Selection Effects in Physics

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P(λ∣observed)  ∝  P(λ)×nobs(λ)P(\lambda \mid \text{observed}) \;\propto\; P(\lambda) \times n_{\text{obs}}(\lambda)
∝

What this part means

Proportional to; the scale factor is not shown.

Its job in the formula

Proportional to; the scale factor is not shown.

The passage around this formula

Done correctly, the weak principle is pure statistics: it is a conditioning operation, identical in structure to correcting a biased sample in any other empirical science. A concrete instrument in this article’s own world makes the logic exact rather than analogical. A magneto-optical trap holds a cloud of atoms by continuously discarding the ones moving too fast to be captured by the cooling beams; every atom visible in the trap already survived a velocity cut. Someone who measured only the trapped cloud and concluded “the atoms in this room are unusually cold” would be committing exactly Eddington’s error — the room is not unusually cold, the trap is unusually selective, and the correction…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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