star trek - Why are there so many 47s?

I have rewatched a number of Star Trek: The Next Generation episodes in quick succession over the past week. One thing I observed that I hadn't before is that the number 47 seems to come up unnaturally often, at least at first glance. I then sampled the episode scripts to produce a list of all occurrences — 203 verbal ones, including variations such as 4-7 and four 7's, as well as appearances within longer numbers (e.g. 247, 0.047).

Examples include:

• "Tin Man" : The Ghorusda incident claims the lives of 47 people.



• "Family" : Picard receives a bottle of the '47 wine from Robert as a gift.


• "The Loss" : The Enterprise-D will arrive at T'lli Beta in 6 days, 13 hours, 47 minutes.


• "In Theory" : The Enterprise-D is 4.7 million km from the edge of a certain nebula.


• "Darmok" : The word "Darmok" appears 47 separate times in the ship's library.


• "The Game" : Nurse Ogawa tells Wesley that she is currently at level 47 of the Ktarian game.


• "Conundrum" : A holodeck program numbered 47C is activated. Later, there are 47 sentries guarding the Lysian Command.


• "I, Borg" : The geometric paradox virus is called "Topological Anomaly 4747" on the display screen.


• "Time's Arrow" : Picard uses phaser setting 0.47 to open the gateway.


• "True Q" : Amanda Rogers is on section 4 of deck 7. Data later remarks that the temperature inside the reaction chamber has increased by 47 percent.


• "Birthright" : The length of time for which Data is unconscious is 47 seconds.



• "Frame of Mind" : Riker is a patient in Ward 47.


• "Timescape" : Data remarks that one of the nacelles has been operating continuously for 47 days.


• "Descent" : Stephen Hawking's hand consists of four 7's, and he subsequently wins the poker game.


• "Parallels" : Starbase 47 is mentioned.


• "Genesis" : The authorization code is Alpha-4-7.

These are only a selection. On top of the many verbal occurrences, I suspect that there are a number of additional non-verbal occurrences where the number 47 flashes on a display screen or PADD, etc. (as in the geometric paradox example above).

I can also recall at least one instance where the number appears in the films: at the beginning of Generations, Scotty is only able to rescue 47 people from one of the El-Aurian refugee ships.

Why does the number 47 appear so frequently in the The Next Generation?

I am looking primarily for an out-of-universe answer. That is, why were the writers fixated on this number? An in-universe answer would of course be interesting, but I don't expect that such an answer exists.

Answer

I have good news: you're not crazy¹.

The number 47 was slipped into Star Trek with alarming regularity, and it all began with TNG writer Joe Menosky. In a 2005 interview with Pomona College Magazine (Menosky's alma mater), he said:

When asked why he started including 47 in episodes, Menosky admits, "After Pomona, Eric [Level, Menosky's freshman RA] and I maintained a correspondence and typically would mention in passing any new sightings. It seemed like placing 47s rather than just spotting them would be a way to continue the reference for any alumni who happened to watch the series."

^{_{Pomona College Magazine Vol. 41, No. 2 "To boldly go where no number has gone before" by Noah Buhayar}}

The number wasn't chosen at random, as that interview hints; "47" has been a campus supersition since at least 1964, where it apparently originated partly in a proof from math professor Donald Bentley that all numbers were equal to each other², and partly from the observation by a few students that the number 47 occurred more often than you'd expect it to. One of these students, Wayne Phillips, discusses the origin in an email archived by the 47 Society:

One of the three had been arguing that his favorite number (not 47) occured more (or was it less?) often than expected in nature. They decided to count occurrences of this number, and as a sort of control, compare it with another number. 47 was picked because it was a large prime number, which, it was assumed, would appear rather infrequently.

Well, as we would now expect, they were astounded to discover that 47 not only won by a wide margin, but also occurred at a phenomenal frequency.

[...]

[T]he fact that Dr. Donald Bentley proved that all numbers are equal to 47 in the summer of 1964 is correct. In fact, as I recall, Dr. Bentley had developed a proof that any number is equal to any other number. Laurie and Bruce had been talking to him about their discovery of 47, and hence, as a corollary, they were able to show that all numbers are equal to 47.

An article in a 2000 issue of Pomona College Magazine discusses the link further:

Perhaps the number [47] reached its final frontier--going where no number has gone before--as part of television and film trivia history, thanks to Joseph Menosky '79. As a writer and co-producer for the television series "Star Trek: The Next Generation," Menosky included the number 47 in almost every episode he wrote. The crew stops at Sub-space Relay Station 47. Data is unconscious for 47 seconds. There are 47 survivors on a planet. The crew discovers element 247.

^{_{Pomona College Magazine Vol. 37, No. 1 "The Mystery of 47" by Sarah Dolinar}}

Over time it seems to have become an in-joke among Star Trek writers, who carried on the tradition presumably for their own amusement (and likely because coming up with arbitrary numbers was more effort than it was worth). They did eventually get tired of it, though, as fellow writer Ronald D. Moore said in a 1997 AOL live chat (archived by Memory Alpha):

Is it my imagination, or have the random occurences of "47" on DS9 been on the decrease?

They've been cut down as we've kinda tired of this particular inside joke.

---

¹ No footnote here; but I had you going, didn't I?

² If you're interested, a former student of Bentley's posted a half-remembered version of the "proof" on Yahoo Groups in 2007. Obviously the claim isn't actually true, but it's a useful exercise for an early course in higher mathematics; as Hans points out in comments, it hinges on some non-intuitive ideas about the nature of infinity, that would fly over the head of most people who haven't done post-secondary calculus.

Conceptually the proof is similar to the common troll proof that π= 4, which has been thoroughly debunked over on Math.SE (in layman and non-layman versions), and YouTube personality Vi Hart made a fascination video about it