A collection of universes is called a multiverse. If there are enough universes in a multiverse, can almost anything happen? No. Common models of the universe aren’t big enough.

The argument that anything can happen in a multiverse is nicely presented in a 2011 scene in the sitcom The Big Bang Theory (2007–2019) involving consummate nerd Sheldon Cooper and Penny, the girl next door (here).

Penny: Morning, Sheldon! Come dance with me!

Sheldon: No.

Penny: Why not?

Sheldon: While I subscribe to the Many Worlds theory, which posits the existence of an infinite number of Sheldons in an infinite number of universes, I assure you that in none of them I am dancing.

Penny: Are you fun in any of them?

Sheldon: The math would suggest that in a few I’m a clown made of candy. But I don’t dance.

Renowned physicist Max Tegmark has made a similar statement with a greater degree of seriousness in Scientific American (2003):

Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on.¹

There are many theories of the multiverse, positing various flavors.² Many physicists champion the idea. Others are skeptical.³ Some scientists even contend that “studying the multiverse doesn’t count as science.”⁴

A commonly quoted upper bound on the number of possible universes in the multiverse is the enormous number⁵, 10¹⁰⁰⁰. That’s a 1 followed by a thousand zeros. A 1 followed by 12 zeros, or 10¹² is a trillion. A stack of one trillion dollar bills is 67,866 miles high. That is more than twice the circumference of the earth. Say “a trillion, trillion, trillion…” eighty three times and it’s still short of 10¹⁰⁰⁰.

At first glance, it looks as if there is nothing that we cannot do in such an enormous space. A closer look shows that this is not the case. Here’s why not:

If there is a universe where you read this article and one where you don’t, two universes are needed. Suppose, in addition, that in one universe you are bald and in another you have hair. That takes four universes:

1. You are bald and read this article
2. You have hair and read this article
3. You are bald and don’t read this article
4. You’re hairy and don’t.

Let’s add one more difference. In one universe, you have at least 10 toes and in another you have more than 10 toes. Now eight universes are needed to handle this additional case. Every new contingency we add doubles the size of the required number of universes.

What if a contingency is added that offers three possibilities? An example of such a triple is that you have one, two, or more than two eyes. The number of universes now multiplies by three. The necessary size of the number of universes is seen to grow exponentially with respect to the number of these contingencies.

We can work backwards, starting with the proposed number of universes. If there are 10¹⁰⁰⁰ universes in the multiverse, how many binary (only two choices) contingencies can we have?

Only 3,322.

This means that if a count is doubled 3,323 times, the result will be more than 10¹⁰⁰⁰. Get out paper and pencil and try it. Write, 2, 4, 8, 16, 32 and on and on. On the 3,323^rd entry, the count will be over 10¹⁰⁰⁰.

3,222 contingencies is nothing! You or I can easily make a list this long and quickly exhaust the multiverse. Here’s a portion of my list:

1.You read this article, you don’t.

2.You are bald. You have hair.

3.You have at least 10 toes. You have more than 10 toes.

…

3321.You never had an appendix. You have or had an appendix.

3322.Your blood is red. Your blood is green (like Mr. Spock’s)

So the multiverse of 10¹⁰⁰⁰ universes isn’t big enough to let a lot happen.

But some multiverse models predict bigger numbers of component universes. One extreme model estimates the number of universes to be 1 followed by 10^10,000,000 zeros.⁶ That’s some multiverse! A lot can happen here and no list of contingencies can be made. The list would be too long to write one contingency on each of the roughly 10⁸⁰ atoms in our universe.

But, some claim, there is an infinite number of universes in the multiverse. That is ludicrous because there are no infinities in the physical world. Even if there were, Cantor’s theory of the infinite shows that, if there were an infinite number of contingencies, not all contingency combinations could be accounted for by an infinite number of universes.

Therefore, even if there is an infinite number of universes with an infinite number of contingencies, then—among an infinite number of Sheldons—it’s possible that none of the Sheldons dance. ⁷

Note: Much of the content in this article is borrowed from: Marks, Robert J. Diversity Inadequacies of Parallel Universes: When the Multiverse Becomes Insufficient to Account for Conflicting Contradistinctions.  Perspectives on Science and Christian Faith  71, no. 3 (2019): 146-153.

¹ Max Tegmark, “Parallel Universes,” Scientific American 288, no. 5 (2003): 40–51.
² Max Tegmark “Parallel Universes,” in Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity, ed. Barrow, Davies, and Harper.
³ Jim Baggott, Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth (New York: Pegasus Books, 2014); George F. R. Ellis, “Does the Multiverse Really Exist?”, Scientific American 305, no. 2 (2011): 38-43; George Ellis and Joe Silk, “Scientific Method: Defend the Integrity of Physics,” Nature News 516, no. 7531 (2014): 321; Anna Ijjas, Paul J. Steinhardt, and Abraham Loeb, “Cosmic Inflation Theory Faces Challenges,” Scientific American 316, no. 2 (2017): 32–39; and Sarah Scoles, “Can Physics Ever Prove the Multiverse Is Real?,” Smithsonian.com (April 19, 2016).
⁴ Tom Siegfried, “Making Sense of Many Universes,” Knowable Magazine (April 26, 2018).
⁵ Andrei Linde and Vitaly Vanchurin, “How Many Universes Are in the Multiverse?”, Physical Review D 81, no. 8 (2010): 083525.
⁶ Ibid.
⁷ The explanation of this point gets mathy, so I refer my fellow nerds in search of deeper truth to take a look at my more detailed paper.