I was delighted to hear from John Cramer today. He was on the physics faculty at Wheaton College when I was a Freshman and Sophomore and I hadn't had communication with him since then. He is now emeritus professor of physics at Oglethorpe U in Atlanta.

John offered the following critique of multiverse theories and he gave me permission to post it. I will give all of you time to think it over and comment if you wish. In a day or two I'll submit my response to him and his response to me and perhaps we can keep the conversation going.

**Thesis:** Multiverse theories do not explain the fine tuning of our universe.

**Defense:**

1) Suppose at first that our universe, U_{0}, has only one finely tuned constant, κ. That is, the value of κ in U_{0 }lies in a small range of values, R, that permit intelligent life to exist in U_{0}.

2) Suppose also that U_{0} is only one of many extant universes, U_{i}, in which the values of κ_{i} can range over all real numbers. That is, a multiverse exists.

3) Since the universes of the multiverse are countable, their cardinality is the countable infinity, א_{0}.

4) The upper bound of κ_{i} values in any multiverse is no less than the cardinality of real numbers, א_{1}.

5) As Cantor showed long ago, א_{1 }>> א_{0}.

6) Therefore, a multiverse can never contain all possible values of κ_{i}.

**Discussion: **

Multiverse theories contain, as a standard feature, the implicit assumption that values of κ will be randomly selected from all possible real values and distributed among the universes. The U_{0} value of κ “must” somehow appear in one of the universes. This is an unwarranted belief. The probability that a multiverse contains U_{0} is not 1 but zero (א_{0}/א_{1}, with apologies to mathematical purists).

True enough, א_{0} universes may contain as many as א_{0} values of κ, but it is crucial to specify which values. The set of all integers is a countable infinity but it has א_{0} gaps (ranges like 0 to 1, etc.) in it, each with א_{1} missing values of κ. All multiverse theories necessarily have such gaps. Therefore, to explain the fine tuning of κ, a multiverse theory must be able to show that R is a likely range of values of κ in some universe (which will then be presumed to be U_{0}). Thus, even a countable infinity of universes cannot, by itself, explain the fine tuning of κ.

Additionally, there are many more than one “fine tuned” quantities in U_{0}. Consequently, it is incumbent on proponents of multiverse explanations to show that their choice of multiverse actually generates values of *each* κ in its proper R and that at least one of the universes of the multiverse has all κ values in the proper U_{0} ranges. Although I do not know this cannot be done, I very much doubt it can. Anyone undertaking such a project is to be commended; advancing a serious multiverse theory will be a prodigious undertaking. In fact, multiverse theories need to be theories of everything.