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FiveThirtyEight

Last Thursday, FXX began its “Every Simpsons Ever” promotion. The network’s airing “The Simpsons” — all 552 episodes — over 12 consecutive days, and Season 11’s “Missionary: Impossible,” at 10 a.m. Tuesday, marked the end of hour No. 120.

As with any ludicrous television marathon — especially with a show as popular as “The Simpsons” — there are going to be a few ambitious individuals who try to watch as long as they can. I’d bet that some writer somewhere is working on a stunt piece titled “I Tried To Watch Every Simpsons Ever And Here’s What Happened.”

So, what’s happening to these poor souls? I reached out to my friend Olivia Walch, a mathematics doctoral student at the University of Michigan. Walch made the sleep-repair app Entrain, so she sent us a pile of sleep deprivation studies so we could find out what people trying to mainline “The Simpsons” are going through.

The impairment brought on by sleep deprivation in the early couple of days is often compared to impairment from alcohol consumption. Essentially, for the first few hours of sleep deprivation, the watcher would feel as if they’d thrown back a couple of Duff beers. A 1997 study with 40 participants published in the journal Nature (find links to all mentioned studies at the end of this piece) calculated that “each hour of wakefulness between 10 and 26 hours was equivalent to the performance decrement observed with a 0.004% rise in blood alcohol concentration” (BAC).

So, after 17 hours of wakefulness — right as Bart gives blood to Mr. Burns in the Season 2 finale, “Blood Feud” — you’d be functioning at the level of someone with a 0.05 percent BAC. After 24 hours — as Season 3’s classic “Lisa the Greek” airs — you’d have a performance deficit of someone with a BAC of 0.10 percent.

At hour 49.5 — just as the Season 5 classic “Sweet Seymour Skinner’s Baadasssss Song” would hit the airwaves — we have data about how people’s sense of humor changes with sleep deprivation. The authors of a 2006 study, published in the journal Sleep, kept people awake and then gave them a humor appreciation test. The researchers found that people having gone without sleep tend not to find things as funny as they normally would. “The means for both verbal and visual humor” of people kept awake for 49.5 hours without stimulants was a full standard deviation below normally wakeful people.

And after a certain amount of time, the sleep-deprived start to see stuff.

In “Responses to Sleep Deprivation,” a 1962 study published in the Annals of New York Academy of Sciences, most of the 12 subjects grew increasingly paranoid at about the 100-hour mark; they developed “systematized delusions.” In “Simpsons” terms, that means systematized delusions onset shortly after Season 9’s Emmy-winning “Trash of the Titans,” in which Homer becomes Springfield’s sanitation commissioner.

Having just made it past the 120-hour benchmark early Tuesday, our hypothetical marathoners are, perhaps surprisingly, feeling pretty good.

“Around hour 120 is when you see the ‘fifth day turning point,’ ” Walch said. “A lot of older papers observe this — basically, people get a temporary second wind and feel better about the whole no-sleep thing. But at the same time, this is when the psychotic symptoms really start to manifest. So, it’s possible that the ‘second wind’ is actually just a sign that you’re really losing it.”

Essentially, it’s about to get weird.

Walch here referred to several papers discussing that turning point. A 1962 study ominously titled “The Psychosis of Sleep Deprivation” (also in the Annals of New York Academy of Sciences) observed that “gross disturbances of reality testing are seen to persist for increasing periods of time” around the fifth night of sleep deprivation, with hallucinatory experiences becoming more vivid and paranoia increasing.

So, what’s coming next?

The further back in time, the weirder — and less rigorous — the papers get. A 1933 study in the Archives of Neurology & Psychiatry monitored a volunteer who thought that sleep wasn’t really necessary. The individual (“Z”) stayed up for nine-and-a-half days with only eight brief incidents of intermittent accidental sleep. (This study would probably not be ethically or scientifically sound in contemporary sleep research.)

“On the ninth day he was able to think only in fragments and had reminiscences,” the authors reported. Each day, Z was asked to stare into a crystal orb and report what he saw. “He saw several soap dishes, but he looked away most of the time.” In “Simpsons” time, this would put fragmented thinking just after Season 20’s “Lisa the Drama Queen,” the final episode broadcast in standard definition. The last episode that Z would have stayed up to watch was Season 21’s “American History X-cellent,” the 458th episode. On this day, the authors said, Z “was unable to report a single thought or image.”

And after that? That’s when we really start running out of even anecdotal academic data. If the pattern holds, the more recent you get in the run of “The Simpsons,” the more incoherent and prone to passing out you get.

Which, I suppose, we already knew.

Here are the links to the studies. They make for outstanding reading.

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