I was listening to William Lane Craig’s most recent podcast (Existence of God Part 15) on design and fine-tuning and I recently had William Dembski’s The Design Inference given to me as a gift by a friend (I know, I’m embarrassed I didn’t already own the book). Craig spoke of Dembski’s local and universal small probability calculations and I wanted to make this information available here.[1] The question is at what probability is the probability so small that it could be considered impossible?
10^{80 }x 10^{45 }x 10^{25 }= 10^{150}
The unit 10^{80 }is a number representing the number of elementary particles in the universe. Elementary particles are believed to have no substructure, this would include: quarks, leptons, and bosons.
The unit 10^{45} is measured in hertz, which represents alterations in the states of matter per second. The properties of matter are such that transitions from one physical state to another cannot occur at a rate faster than 10^{45 }times per second. This universal bound on transitions between physical states is based on the Planck time, which constitutes the smallest physically meaningful unit of time.
The unit 10^{25 }is in seconds. This is a generous, upper bound on the number of seconds that the universe can maintain its integrity [before expanding forever or collapsing back in on itself in a “big crunch”]. This number is according to the Standard Model (the big bang).
The product, 10^{150}, is the total number of state changes that all the elementary particles in the universe can undergo throughout its duration. Compare this number to Oxford physicist Roger Penrose’s calculation that the odds of the special low entropy condition having occurred by chance in the absence of any constraining principles is at least one in 10^{10^123}. In other words, that’s how many different ways the universe could appear from it’s initial conditions. To understand how large of a number 10^{10^123 }is, take away the exponents and try writing out the number. If you were to write a one and put a zero on every elementary particle in our universe you could then write out 10^{80}, which only makes up an incredibly tiny portion of Penrose’s probability (twice for Dembski’s universal probability).
[1] For all this information see William Dembski, The Design Inference (New York: Cambridge, 1998), 203-214.