In mathematics, Zeno’s paradox is used to illustrate that “contrary to the evidence of one’s senses, motion is nothing but an illusion” (Zeno’s Paradoxes). The paradox goes as follows: Achilles and a tortoise are in a race together. Knowing that the tortoise is slower than Achilles, the tortoise is given a head start. The race begins once the tortoise reaches one hundred feet. Achilles eventually reaches the point that the tortoise originally was when given the head start, but in that time, the tortoise moved further in the race. Now ten feet ahead of him, Achilles sprints to catch up to the tortoise’s most recent position. In that time, however, the tortoise moved one foot further in the race. Forced to catch up to the tortoise, Achilles sprints to where the tortoise was yet again. This process keeps happening over and over again, with Achilles continuously sprinting to catch up to the tortoise and the tortoise slowly inching forward. Whenever Achilles reaches a position in the race where the tortoise has been, he still has to run even farther to catch up with the tortoise. The distance between the two runners gets infinitely small, but not finite (Huggett). So does Achilles ever catch up with the tortoise? This is Zeno’s paradox. Obviously, he must catch up to the tortoise at some point. In the real world, Achilles would pass the tortoise and win the race. However, according to the paradox, traveling from his current position in the race to where the tortoise previously was—or from any location to any other location for that matter—would take Achilles an infinite amount of time. Mathematicians must suspend any disbelief in this idea in order to make sense of the concept in real life. Math concepts often make sense on paper or in a theoretical world that is not our own, but not in the real, physical world.
Another mathematical concept that involves the suspension of disbelief involves irrational numbers applied to distances. Imagine a sandbox that is shaped like an isosceles right triangle whose two legs are one meter in length. Instead of using a measuring tape to find the length of the hypotenuse, or the longest side of the triangle across from the right angle in the triangle, one could use the Pythagorean Theorem. The theorem states that “the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides” (Morris). Expressed as an equation, this is equivalent to a2+b2=c2, where c is the hypotenuse and a and b are the other two sides of the triangle. When plugging in the values for the two sides of the triangle into the equation, one would get 12+12=c2, and simplifying the equation to get the value for c would result in c=?2 meters. However, ?2 is an irrational number, meaning that the number cannot be expressed as a ratio between two integers. It also means that the number expressed in decimal form would contain numbers that continue on infinitely. In the real world, distances are always finite with a definite end to it’s numerical value. But how could the sandbox have a side that is not necessarily infinitely long, but be of a length that cannot be expressed as a finite number. Again, mathematicians must put their mathematical approaches to the side to accept that although the math works on paper—in fact, there are many proofs that using the Pythagorean Theorems to find the length of an unknown side of a right triangle works—it just might not work in real life. We must sacrifice our disbelief in reality even if this results in a conclusion that might not be entirely realistic or logical. It is for these reasons that I believe suspension of disbelief is an essential feature in the area of knowledge of mathematics.
The second area of knowledge that I will be exploring is the natural sciences, which I will closely tie to the arts; film specifically. Science fiction films often push the boundaries of what is possible in the real world. The 1979 Ridley Scott movie Alien, for instance, depicts the crew of the starship Nostromo encountering an alien ship with a nest eggs of an unknown species. They soon come face to face with the Xenomorph, a fictional extraterrestrial life form that murders most of the crew. Of course, it is generally shared knowledge that aliens do not exist; no concrete evidence has been discovered that validate their existence. This is not to say that aliens don’t exist anywhere in the universe. However, both moviegoers and scientists alike must suspend their belief in the non-existence of aliens in order to enjoy the film—sort of the opposite of suspending one’s disbelief. This idea can be applied to the natural sciences as a whole, as anything we don’t physically see or perceive through sense perception doesn’t necessarily imply that they don’t exist, but in order to truly believe that they do or did, we must sacrifice our disbelief in reality.
Although suspension of disbelief can be more or less essential in certain areas of knowledge, it is still fundamental feature in the identity of those areas. In mathematics and the natural sciences in particular, we must “suspend our critical faculties and believe the unbelievable.” Or in other words, we must put our mathematical and scientific mindsets aside in order to apply theoretical and/or hypothetical concepts to the real world.

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