Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

by Max Tegmark

How far could you rotate the dark-energy knob before the “Oops!” moment? The current setting of the knob, corresponding to the dark-energy density we’ve actually measured, is about 10−27 kilograms per cubic meter, which is almost ridiculously close to zero compared to the available range: the natural maximum value for the dial is a dark-energy density around 1097 kilograms per cubic meter, which is when the quantum fluctuations fill space with tiny black holes, and the minimum value is the same with a minus sign in front. If rotating the dark-energy knob in Figure 6.6 by a full turn would vary the density across the full range, then the actual knob setting for our Universe is about 10−123 of a turn away from the halfway point. That means that if you want to tune the knob to allow galaxies to form, you have to get the angle by which you rotate it right to over 120 decimal places! Although this sounds like an impossible fine-tuning task, some mechanism appears to have done precisely this for our Universe.