in modern science to use anthropic reasoning. Prior to knowledge of the Big Bang Boltzmann's thermodynamic concepts painted a picture of a universe that had inexplicably low entropy. Boltzmann suggested several explanations, one of which relied on fluctuations that could produce pockets of low entropy or Boltzmann universes. While most of the universe is featureless in this model, to Boltzmann, it is unremarkable that humanity happens to inhabit a Boltzmann universe, as that is the only place where intelligent life could be. Variants Weak anthropic principle (WAP) (Carter): "... our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers." Note that for Carter, "location" refers to our location in time as well as space. Strong anthropic principle (SAP) (Carter): "[T]he universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage. To paraphrase Descartes, cogito ergo mundus talis est."The Latin tag ("I think, therefore the world is such [as it is]") makes it clear that "must" indicates a deduction from the fact of our existence; the statement is thus a truism. In their 1986 book, The Anthropic Cosmological Principle, John Barrow and Frank Tipler depart from Carter and define the WAP and SAP as follows: Weak anthropic principle (WAP) (Barrow and Tipler): "The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirements that the universe be old enough for it to have already done so."Unlike Carter they restrict the principle to carbon-based life, rather than just "observers". A more important difference is that they apply the WAP to the fundamental physical constants, such as the fine-structure constant, the number of spacetime dimensions, and the cosmological constant—topics that fall under Carter's SAP. Strong anthropic principle (SAP) (Barrow and Tipler): "The Universe must have those properties which allow life to develop within it at some stage in its history."This looks very similar to Carter's SAP, but unlike the case with Carter's SAP, the "must" is an imperative, as shown by the following three possible elaborations of the SAP, each proposed by Barrow and Tipler: "There exists one possible Universe 'designed' with the goal of generating and sustaining 'observers'." This can be seen as simply