Plot
One evening on the New York State University campus, a professor records himself lecturing on myth and its place in modern society. A beast slips into the building, climbs to his office, and confronts him. It taunts, "So I think you're pretty smart, don't you," and seizes him.
At the Firehouse, Eduardo Rivera plays a video game, Kylie Griffin studies her Tarot cards, and Garrett Miller lifts weights. Roland Jackson arrives with a book of riddles and tries one out on the group, to silence. Down in the basement, Egon takes a cramp and falls off a ladder. Janine Melnitz suggests he has been overdoing it and that he could trade field work for research, but Egon refuses to admit his age. The alarm rings, with a call from a janitor at the university, and Egon hobbles to the stairs.
Egon drives Ecto-1 erratically to the campus, running a red light and finally bottoming out on the parking spikes. He recalls being fired from the school in 1982, alongside Ray Stantz, for trying to reanimate the dead, and bristles when Garrett points out he was only three years old at the time. Inside the philosophy building, Kylie's PKE Meter spikes fast. Egon insists on showing the team how it was done in the old days, kicking in doors and accidentally firing his thrower into an occupied office. A stronger reading leads them to Professor Barthes, who is found babbling and listless in his chair. Egon orders the team to gather readings and evidence, and Barthes is taken back to the Firehouse for study.
Roland finds that Barthes has no measurable brain activity. Kylie explains that something has wiped out his Theta waves. Egon runs a strange feather and fiber sample through the analyzer and concludes the creature is a composite of several animals: dog hair, lion hair, a snake scale, and a strand from a bird's wing. The clues point to a Griffin, a Basilisk, or a Sphinx. Reaching for his Bestiary, Egon explains that in Greek mythology the Sphinx posed a riddle to everyone it met, and those who answered wrong met disaster. He notes the Sphinx was blamed for wiping out half the population of Thebes, leaving pestilence, plague, and horror behind.
The beast keeps hunting the city for intelligent prey. A trio of intellectuals watching a game show are interrupted when it appears and demands they hear "a simple riddle": "What walks on four legs in the morning, two in the afternoon, and three in the evening?" When they guess wrong, the creature removes its mask, reveals its true form, and drains all three the way it drained Barthes. The Ghostbusters arrive too late, learning from a pizza delivery boy that the Sphinx flew off only minutes earlier. The boy identifies the creature from photos Egon shows him.
A news report describes a wave of unexplained illness striking the city's scientists and educators. The team finds the reading room of the New York City Public Library full of victims, then a classroom of incoherent teachers. At Mensa headquarters they find the membership drained as well. Kylie theorizes the Sphinx is absorbing intellectual energy to make itself ever smarter. When Roland adjusts the power flow on Egon's thrower, Egon snatches it back and removes the Surge Inhibitor to more than double its firepower, brushing off Roland's questions. A news report tips them to a world peace conference at the United Nations, where leading intellectuals from around the world are gathered.
At the U.N., Egon warns everyone to stall and play dumb so the Sphinx will not ask its riddle. After being thrown out by security, the team sneaks in through the loading bay and talks past a guard. Kylie's meter places the Sphinx on the sixth floor. Garrett takes the elevator while the others climb the stairs. Roland, Kylie, and Eduardo find the conference attendees already drained. They open fire, but the creature dodges, and their throwers melt down: the price of pulling the Surge Inhibitors.
Trapped in the stalled elevator with Garrett, Egon finally breaks down, calling Garrett "Ray" and admitting he is old and a has-been who is wearing himself out trying to keep pace with a young team. Garrett reassures him that the team needs his experience, knowledge, and wisdom, not a man playing Rambo. The two pry the doors open. When the Sphinx reappears and offers its riddle, Egon steps up. He works it out and answers, "Man," who crawls on four legs as a baby, walks on two as an adult, and leans on a cane, a third leg, in old age. The Sphinx, stunned that someone finally solved it, begins to come apart, and Garrett blasts it from behind while Kylie throws the trap.
Back at the Firehouse, Egon considers dyeing his gray hair, but Janine tells him he looks distinguished. He decides that age brings wisdom and that it is all right to grow older. Slimer, who spent the episode chasing a fad exercise routine, throws away his self-help book.
The Sphinx
The Sphinx of this episode is a Class 6 composite entity that combines traits of multiple animals: dog, lion, bird, and snake, all concealed behind a humanoid mask. It targets the intellectually gifted out of contempt for human arrogance about knowledge. Its method is to present its riddle; if the victim answers wrong, it removes the mask and extends a long green tentacle from its true face, draining all theta waves from the victim's brain and leaving them in a vegetative state. The power cannot be used unless the victim has been given the riddle; and if the victim answers correctly, the Sphinx begins to molt uncontrollably, a fact Garrett exploits to expose it for a clear shot.
The design was created by character designer Fil Barlow, drawing partly from sketches faxed to him by illustrator Everett Peck. The hidden creature beneath the mask was based on a sketch by executive producer Richard Raynis. Barlow incorporated his personal interest in masks into the overall shape, using the mask itself to suggest the historical Greek tradition of the Sphinx being female, while the tentacle-like headdress nods to Egyptian iconography. Peck's original sketches were distinctly male. Barlow's earliest designs were more monstrous, but he was directed toward a more traditional approach before the final design was settled.
The Sphinx has since appeared in IDW Publishing's comics in non-canon cameos: its depiction from the in-universe Bestiary appears on page 6 of Ghostbusters Volume 2 Issue #11, and it appears on the subscription cover of Ghostbusters Volume 2 Issue #18.
Production
In terms of continuity, Egon's midlife crisis was intended to occur right after the team formed in "Darkness at Noon, Part 2."1 Although "The Sphinx" aired last in many markets, it was actually the first script to enter production; its first production supervisor was called back to work on "Jumanji," and the episode languished and was finished much later than the others.1
Notes and references
The episode is dense with real-world references. The first victim, Professor Barthes of the Department of Philosophy, appears to nod to the 20th-century philosopher Roland Barthes. Roland mentions wanting to transfer to New York State University someday. When the Ghostbusters study the composite fibers, Eduardo references Barnum & Bailey's in his comparison.
The trio of intellectuals is watching "Jeopardy!" when the Sphinx attacks, with the Four Horsemen of the Apocalypse appearing as a clue on the show; those same Horsemen were defeated by the original Ghostbusters in The Real Ghostbusters episode "Apocalypse -- What, Now?" When the team investigates that scene, the television appears to have shifted to "Wheel of Fortune," with a contestant asking Pat Sajak to buy a vowel. The building where the trio was attacked is visually consistent with 550 Central Park West, identifiable by the adjacent church resembling Holy Trinity Church, the same building stepped on by the Stay Puft Marshmallow Man in the first film. During the montage of Sphinx attacks, the Mass-Energy Equivalence equation (E=mc²) appears above one of the affected professors on a chalkboard. Eduardo picks up a Rubik's Cube from a drained Mensa member.
When Egon shows the pizza delivery boy photos of ghosts to jog his memory, Tempus appears at the top of the stack. Garrett name-checks the Egyptian Sphinx and the 1981 film "Clash of the Titans." Egon mentions he was once a Mensa member, kicked out after being disbarred by the American Science Association, and within the story he claims no one knows the riddle of the Sphinx, even though the "man" riddle is famously the one Oedipus answered to become king of Thebes. Egon puts his own age at 39.
While in the stalled elevator, Egon accidentally calls Garrett "Ray." Garrett was three years old in 1982 when Egon and Ray were fired from New York State University, placing his birth year at approximately 1979 given the series is set in 1997.
References
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Shannon Muir, "Production Supervisor Tidbits," Ghostbusters HQ, archived at web.archive.org (May 17, 2008).