3. Our universe is but one member of a gigantic ensemble of universes.

Let me examine very briefly each one of these points and attempt to assess its viability.

Statisticians always dread selection biases. These are distortions of the results, introduced either by the data-collecting tools or by the method of data accumulation. Here are a few simple examples to demonstrate the effect. Imagine that you want to test an investment strategy by examining the performance of a large group of stocks against twenty years’ worth of data. You might be tempted to include in the study only stocks for which you have complete information over the entire twenty-year period. However, eliminating stocks that stopped trading during this period would produce biased results, since these were precisely the stocks that did not survive the market.

During World War II, the Jewish Austro-Hungarian mathematician Abraham Wald demonstrated a remarkable understanding of selection bias. Wald was asked to examine data on the location of enemy fire hits on bodies of returning aircraft, to recommend which parts of the airplanes should be reinforced to improve survivability. To his superiors’ amazement, Wald recommended adding armor to the locations that showed no damage. His unique insight was that the bullet holes that he saw in surviving aircraft indicated places where an airplane could be hit and still endure. He therefore concluded that the planes that had been shot down were probably hit precisely in those places where the persevering planes were lucky enough not to have been hit.

Astronomers are very familiar with the Malmquist bias (named after the Swedish astronomer Gunnar Malmquist, who greatly elaborated upon it in the 1920s). When astronomers survey stars or galaxies, their telescopes are sensitive only down to a certain brightness. However, objects that are intrinsically more luminous can be observed to greater distances. This will create a false trend of increasing average intrinsic brightness with distance, simply because the fainter objects will not be seen.