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With Futurama premiering a new season later this month, let’s revisit 10 of the most clever science and math references in the series… up to now. The writers of Futurama often hold advanced degrees in fields like physics, mathematics, and computer science. This expertise allows them to weave intricate jokes into the show that only resonate with viewers well-versed in complex topics. Now, you can also discover something new and laugh at jokes you might have missed earlier.
10. The Life Cycle of Salmon
Season 7, Episode 13, titled “Naturama,” showcases the characters in a three-part nature documentary named “Mutuals of Omicron’s Wild Universe.” Departing from the show’s usual focus on quantum physics, this episode delves into ecological themes, such as the salmon life cycle, tortoise mating behaviors, and the social hierarchies of elephant seals. While not as intellectually intense as other Futurama episodes, “Naturama” would have been a lifesaver for me during my 6th-grade biology quiz.
The segment titled “Part 1: The Salmon” starts in a chilly freshwater stream where salmon eggs hatch in the gravel. Although not explored in depth, the animation highlights the initial stages of a salmon’s life. The newly hatched alevins, small fish still attached to their yolk sacs, eventually consume the yolk and emerge as juvenile fry. Much like Fry the character, these fry embark on their journey from the river to the ocean.
Before long, he encounters and starts wooing a stunning fish named Leela, who pledges herself to him once they reach the right age for mating. After a series of underwater rendezvous, Fry, Leela, and their peers complete their maturation process and start their journey back to their ancestral spawning grounds. Sadly, nature separates Fry and Leela when they realize they hail from neighboring streams. Thanks to a heroic act and a bear with a critical eye, the pair is reunited. Leela deposits her eggs, Fry fertilizes them, and the two pass away together.
To our knowledge, salmon don’t experience romantic love or go on charming dates. In reality, their courtship and spawning rituals only commence once they’ve returned to their native freshwater habitats. Despite some creative liberties, Futurama crafted a both accurate and engaging depiction of the salmon life cycle.
9. Delta Brain Waves
In the episode “Roswell That Ends Well,” the Planet Express team finds themselves in 1947 New Mexico. After a chain of mishaps and questionable decisions, Fry ends up sleeping with his grandmother, effectively becoming his own grandfather. This anomaly leaves him with a distinct brain pattern devoid of delta brainwaves. On multiple occasions, Fry’s lack of delta brainwaves enables him to resist various malevolent, mind-controlling forces.
For instance, in “Into the Wild Green Yonder,” the “Dark Ones,” a telepathic species bent on universal domination, are introduced. Fry’s absence of delta brainwaves makes him immune to the Dark Ones, allowing him to shield his thoughts and save the universe undetected.
Interestingly, before researching for this list, I believed the delta brainwave was another fictional concept created by Futurama to advance the plot and add complexity to Fry’s persona. In truth, delta brainwaves are a genuine phenomenon, though they remain poorly understood.
Delta waves, the slowest brainwaves observed in humans, play a crucial role in deep relaxation and restorative sleep. Linked to subconscious activity, they are a plausible target for brain hackers. Furthermore, studies have shown an inverse relationship between delta wave activity and spiritual intelligence, implying that Fry’s lack of delta waves might indicate high spiritual intelligence, enabling him to resist the universe’s dark forces.
8. BASIC
BASIC, a programming language designed for beginners, was created in 1964 by John G. Kemeny and Thomas E. Kurtz. As highlighted in the episode “I, Robot,” this language remains technologically relevant even a millennium into the future. When Fry moves in with Bender, he encounters a sign displaying “10 HOME, 20 SWEET, 30 GO TO 10,” which translates to “Home Sweet Home” for those unfamiliar with BASIC.
7. The Birth of Our Universe
In Season 6, Episode 7, titled “The Late Phillip J Fry,” the series explores one of its most intriguing concepts about time’s cyclical nature, offering viewers profound insights into the origins of our universe. While hurrying to meet Leela for dinner, Fry is convinced by Professor Farnsworth to assist in testing his latest invention: a forward time machine. Accompanied by Bender, the trio enters the machine, expecting to travel just one minute into the future. However, a mishap causes the machine to accelerate uncontrollably through spacetime.
When the professor finally halts the machine, they find themselves in the year AD 10,000. Choosing to journey further into the future, they witness the universe’s transformation into nothingness. Remarkably, this apparent end triggers a colossal explosion, which Farnsworth identifies as the Big Bang. According to the Big Bang Theory, the universe originated from an infinitely hot and dense point that rapidly expanded. After observing this pivotal event, Farnsworth deduces they are in a universe identical to the previous one. By continuing forward in time, the group—comprising two men and a robot—can eventually return to their lives in New New York.
The animation depicting the birth of our universe is both visually stunning and educational. Farnsworth, Fry, and Bender observe gravity pulling matter together to form the first stars and galaxies. They witness Earth emerging from swirling dust and gas, followed by a massive collision that created the moon. This event, known as the “moon-forming impact,” vaporized rock and metal from Earth and the colliding object, eventually forming the moon. The trio also observes early evolution, the arrival of the first colonizers, and other significant milestones in natural and human history before finally returning home.
6. The Problem of Relativity
Characters in Futurama frequently travel faster than the speed of light to navigate intergalactic space quickly—a narrative device that defies the laws of physics. This scientific inaccuracy is not an oversight but a deliberate choice by executive producers David Cohen and Matt Groening, who prioritized entertainment over scientific accuracy.
In a discussion with the American Physical Society, Cohen describes how he and the writing team creatively manipulate scientific rules to entertain scientists, even if the concepts are fictional. The writers humorously address the impossibility of faster-than-light travel in the episode “A Clone of My Own.” During a scene where Professor Farnsworth showcases his inventions to his clone, Cubert, he mentions that his “dark-matter engines… can traverse galaxies in just hours.” Cubert counters that this is impossible, as nothing can exceed the speed of light. Farnsworth casually responds that scientists resolved this issue by increasing the speed of light in 2208.
Einstein’s special relativity equation, E=mc², where c represents the speed of light, states that an object nearing the speed of light gains infinite mass. Consequently, the energy required to propel such an object becomes infinitely large, making faster-than-light travel unattainable. Instead of inventing technology capable of generating infinite energy, the Futurama writers sidestepped this issue by humorously raising the speed of light, allowing objects to move at extraordinary speeds without approaching the theoretical limit c.
5. Heisenberg’s Uncertainty Principle
In Season 3, Episode 4, “Luck of the Fryrish,” Professor Farnsworth mentions the Observer Effect after a frustrating loss at the race track. In 1927, Werner Heisenberg, a German physicist and Nobel laureate, proposed that it’s impossible to simultaneously determine a particle’s exact speed and position. Due to its wave-like properties, a particle doesn’t occupy a single precise location but exists across a range of positions. To measure a wave’s position accurately, one would need to collapse it into a single point, resulting in an indefinite wavelength and speed.
Similarly, a particle consists of wave groups that represent a range of momentum. A wave with perfectly measurable momentum would oscillate infinitely across space, making its position indefinite. The Uncertainty Principle isn’t a limitation of measurement but an inherent characteristic of quantum particles. However, its semiclassical interpretation highlights challenges in quantum mechanical measurements. For example, researchers must use photons to determine an electron’s position. These photons transfer their momentum to the electron, inevitably altering the system.
Farnsworth wagered on a horse race that ended in a tie. To his frustration, the judges employed an electron microscope to declare a quantum winner. The professor objected, exclaiming, “No fair! You altered the outcome by measuring it.” This remark not only reflects Farnsworth’s disappointment at losing but also highlights a key implication of the Uncertainty Principle. Since the principle is an intrinsic property of quantum particles, even advanced measurement techniques cannot prevent the system from being altered when one quantum variable is measured.
4. Schrodinger’s Cat
During a conversation with Albert Einstein in 1935, Erwin Schrodinger conceived one of physics’ most famous thought experiments. The two physicists were exploring the quantum principle that, due to wave-like properties, a quantum object exists in a state of superposition.
Schrodinger’s cat demonstrates this idea through a hypothetical scenario: a cat is placed in a sealed box with a radioactive substance that has a 50% chance of decaying. If decay occurs, it releases poison, killing the cat. Without opening the box, the cat is considered both alive and dead simultaneously until observed.
In Season 6, Episode 16, “Law and Oracle,” a reckless Erwin Schrodinger evades Fry, a newly appointed NNYPD officer, and his partner URL. Upon capturing the physicist, Fry inquires about the mysterious box in Schrodinger’s car. In a thick German accent, Schrodinger explains it contains “a cat, some poison, und a cesium atom.” When Fry asks if the cat is dead, Schrodinger replies, “It’s a superposition of both states until you open it and collapse the wave function.” Skeptical, Fry opens the box and is attacked by the very much alive cat.
3. The Futurama Theorem
The episode “The Prisoner of Benda” (7ACV10), penned by Ken Keeler, who holds a Ph.D. in applied mathematics from Harvard University, features the only mathematical proof ever created exclusively for a TV show. Known as “The Futurama Theorem,” it asserts that any permutation of n objects can be resolved through a series of non-repeating swaps, requiring no more than two extra objects. In the episode, the theorem is formulated by Bubblegum, Sweet Clyde, and Express of the Harlem Globetrotters to fix a chaotic situation caused by Professor Farnsworth, Amy, and their “Mind-Switcher” invention.
After experimenting with the device and enjoying life in each other’s bodies, Farnsworth and Amy attempt to switch back. However, they soon discover that the machine prohibits the same pair from using it more than once. “Oh no! Can we restore everyone to their original bodies using four or more people?” The chaos escalates as more individuals (and even wash buckets) become entangled in the mind-switching debacle.
Thanks to “The Futurama Theorem,” all minds are eventually returned to their proper bodies by the episode’s conclusion. I’ve outlined a simplified version of the mind-switching scenario based on Cheryl Grood’s explanation from the Philadelphia Math Teacher’s Circle. Bubblegum and Sweet Clyde serve as the additional participants required by the theorem.
To resolve the situation, divide everyone into groups based on the body they need to occupy. Arrange these groups in a sequence, with each person facing the body they are destined to inhabit.
Group 1: Professor(Leela) → L(Hermes) → H(Amy) → A(Washbucket) → W(Emperor Nikolai) → EN(Bender) → B(P)
Group 2: Zoidberg in Fry’s body (F(Z)) and Fry in Zoidberg’s body (Z(F))
First, swap the mind of the person at the front of any line with the first helper (Sweet Clyde). Next, have the second helper (Bubblegum) switch minds with everyone else, starting from the end of the line and moving forward.
Group 1: B(P) ↔ SC(SC) = B(SC) & SC(P) BG(BG) ↔ P(L) = BG(L) & P(BG) BG(L) ↔ L(H) = L(L)! BG(H) ↔ H(A) = H(H)! BG(A) ↔ A(W) = A(A)! BG(W) ↔ W(EN) = W(W)! BG(EN) ↔ EN(B) = EN (EN) BG(B) ↔ B(SC) = BG(SC) & B(B)! BG(SC) ↔ P(BG) = BG(BG)! & P(SC) P(SC) ↔ SC(P) = P(P) & SC(SC)!
Group 2: SC(Z) and F(SC) BG(BG) ↔Z**(F) = BG(F) & Z(BG) SC(Z) ↔Z(BG) = Z(Z)! BG(F) ↔ F(SC) = F(F)! BG(SC) ↔ SC(BG) = SC(SC)! & BG(BG)!
2. The Banach-Tarski Paradox
In the episode “Benderama,” Professor Farnsworth unveils his latest invention, the “Banach-Tarski Dupla-Shrinker.” The Banach-Tarski paradox, which deals with infinite cloning, demonstrates that it’s mathematically feasible to divide a three-dimensional sphere into parts and reassemble them into two exact replicas of the original. Moreover, a sphere can be reconstructed into a sphere of any size. This paradox relies on manipulating countably and uncountably infinite sets, the intricate details of which I’ll spare you. For those curious, I recommend reading the QuantaMagazine article on the subject.
Farnsworth, an elderly and shrinking man, creates a device to produce smaller duplicates of his sweaters, which he assigns Bender to fold. To avoid the task, Bender installs the machine in his chest and generates two clones at 60% size to do his work. These clones, in turn, create smaller versions of themselves, leading to an infinite proliferation of Benders. By the episode’s end, the countless Benders unite to form a colossal version of themselves, helping the original Bender defeat a giant. While the Banach-Tarski Dupla-Shrinker doesn’t perfectly align with its mathematical inspiration, the episode cleverly references the paradox.
1. Möbius Strip
Did your high school math teacher ever give you a strip of paper, instruct you to twist it halfway, and tape the ends together? If so, you’ve created one of mathematics’ most artistic discoveries: the Möbius strip. This non-orientable surface blurs the distinction between clockwise and counter-clockwise turns. As a single-sided, two-dimensional object existing in our three-dimensional world, tracing its entire surface requires no lifting of your finger or crossing any boundaries.
In the episode “Möbius Dick” (6ACV15), Futurama introduces its first Möbius strip pun. While navigating the Bermuda Tetrahedron, the Planet Express crew encounters a four-dimensional space whale, which Leela dubs Möbius Dick. This clever nod to Herman Melville’s novel is fitting, as a Möbius strip can be seamlessly embedded in four-dimensional space, making it an ideal name for such a creature.
The second mention of this abstract surface occurs in “2-D Blacktop” (7ACV15), where Leela and Professor Farnsworth compete on the Möbius Dragstrip. As they race “once around both same sides of the half twist, and back to the start and the finish line,” their vehicles collide at relativistic speeds, catapulting them into a two-dimensional universe. Fortunately, they manage to return safely to the third dimension.
