The Fault in “The Fault in Our Stars”

By: Isaac Brown                                                                                                              

Illustrated by: Carla Cieza Espinoza                                                                                                          

            On Feb. 23, the Math Club hosted Assistant Professor of Mathematics Dr. Tom Shifley to discuss infinity and its relation to John Green’s romance novel “The Fault in Our Stars.”            

            In the “Fault in Our Stars,” Green makes a few claims about infinity; some of these claims Shifley allowed, while others he said were “heresy.” First, Green writes that “[t]here are infinite numbers between 0 and 1”; Shifley agreed. Green continued, “[s]ome infinities are bigger than other infinities”; Shifley again agreed, but with more caution, and said that when talking about infinity, one has to be clear about what they mean by “bigger.” Then Green writes that “there is a bigger infinite set of numbers between 0 and 2 [than there are between 0 and 1].” Dr. Shifley negates this. He said this is a “beautiful” sentiment, since one could argue that life is made up of an infinite amount of moments, but that Green is not presenting a nuanced view of infinity. “There are,” Shifley said, “infinitely many different infinities,” some of which are in fact bigger than others. Nonetheless, Green was incorrect about which infinite sets are bigger.

            Shifley said two infinite sets are equal if they have a “one-to-one cardinality”; that is, if you can match each number in one infinite set to a number in the infinite set of natural numbers, then the sets are equal. How Shifley proves that one infinite set matches another is beyond the scope of this article, but he concluded that there is a one-to-one correspondence in the set of decimal numbers (0.1, 0.01, etc.) between 0 and 1 and the set of decimal numbers between 0 and 2. Nonetheless, there are an infinite amount of sets of numbers, and an infinite amount of these sets are larger than the set of numbers between any two integers. 

            Though it may be difficult for even math majors to understand Shifley’s set theory proofs, he summarized some more accessible points. Most importantly, one should always approach a romance novelist’s view of an advanced mathematical topic skeptically. Despite the nuances of infinity, Shifley also said that certain claims about infinity “have no effect on math.” For instance, there are a pair of sets, each containing an infinite amount of numbers, which cannot be proven to be equal; and either way you assume, it doesn’t have an effect on how math operates.

        Shifley also said the study of infinity is a cause for “wonder.” For instance, if you were to make an (infinitely large) dartboard of all possible numbers, there would be a 0% chance of hitting a natural number (ie, a positive integer) with your dart, because the infinity of the sum of all other number is so much greater. Perhaps Green should have consulted Shifley for this piece in “The Fault in Our Stars.”

            Theology major and self-described “infinity enthusiast,” Brayden Tibbets, said that when philosophers make major claims about infinity, he doesn’t make much of it; but when a mathematician makes the same claim, it is “cause to pay attention.” 

        The Math Club meets every Wednesday at 4:30 pm in Hoover 207, where they have similar guest lectures and other hands-on activities.

Illustrated by Carla Cieza Espinoza.