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I've asked about it repeatedly on Wikipedia's talk page for the article about Arthur C. Clarke's novel 2001: A space odyssey, but had no reply (I have also mentioned it on the talk page for the french article, where at least someone chimed in, but it's even less likely to get a conclusive answer there). Is there a known inconsistency in the original text regarding the monolith's measurements, and the peculiar 1 : 4 : 9 ratio that they are supposed to match perfectly ?
I am french, I don't have access to the actual book in original english, but in all the electronic versions of the original I could find there's this sentence : “The monolith was 11 feet high, and 11/4 by 5 feet in cross-section.” Then it goes : “When its dimensions were checked with great care, they were found to be in the exact ratio 1 to 4 to 9.” And yet these measurements do not verify the 1 : 4 : 9 ratio at all ! They would approximately verify it with 11/9 instead of 11/4. The french translation is closer, surprisingly, although not nearly close enough, especially since it mistakenly adds that the measurements given in that sentence are “exact”, whereas only the ratio is said to be exact in the next sentence from the original (which makes sense, as the unit used for measuring lengths is arbitrary, based on historical choices which could have been different and couldn't have been anticipated even by the almighty extraterrestrial intelligence that designed the monolith — especially those weird units used in english speaking countries ! :^p —, whereas the ratio between dimensions is a purely mathematical notion which could indeed have some sort of universal significance).
The french text goes : “The monolith was indeed exactly 3 meters high, by 1.50 meters wide and 35 centimeters of thickness.” That's a ratio of 1.05 : 4.50 : 9.
So, is this a factual error in the novel, or an OCR / transcript mistake ?

As a side note, the english Wikipedia article mentions another inconsistency regarding the monolith(s), but between the novel and the movie : “While it is stated in the book that the ratio of the dimensions of the monolith are supposed to be 1 : 4 : 9 (1² : 2² : 3²), the shape of the actual monolith seen in the movie does not conform to this ratio. A ratio of 1 : 4 : 9 would produce an object that appears thick, wide, and squat. Kubrick wanted something taller and thinner, which he felt would be more imposing. Measurements taken from movie frames show that the movie monolith has dimensions approximately in the ratio 0.65 : 4 : 9 or 1 : 6 : 14.”
That paragraph was flagged as “original research” ; is there a consensus on that matter, and are there quality sources which could properly back up that assertion ?

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    In what chapter does the sentence giving the monolith's measurements appear? I'd like to check this in my copy myself.
    – jwodder
    Commented Feb 22, 2021 at 2:58
  • May be of interest- There is a theory that the movie monolith was altered to be closer to a film screen aspect ratio and the monolith being a symbol for film imagery. See Meaning of the Monolith youtu.be/MSo6s_xrj4c
    – lucasbachmann
    Commented Feb 22, 2021 at 3:16
  • @jwodder It's in chapter 31, “Survival”. Right after HAL has been disconnected and David Bowman heard the message revealing the true nature of the mission.
    – GabrielB
    Commented Feb 22, 2021 at 3:30
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    I expect that's supposed to be 1 1/4 (i.e. 5/4 or 1.25). 1.25 * 4 = 5; 1.25 * 9 = 11.25.
    – DavidW
    Commented Feb 22, 2021 at 4:06
  • @DavidW Indeed, in the mean time I had the confirmation that it was (most likely) an uncorrected OCR error, someone below quoted from the original edition, and I found a PDF version with the same 1¼ value. I made this calculation, which makes the discrepancy less obvious : 5 * 9/11 = 4.09 ; 1.25 * 9/11 = 1.02 ; 11 * 9/11 = 9.
    – GabrielB
    Commented Feb 22, 2021 at 5:07

2 Answers 2

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The passage in question in my 1968 first printing of the novel reads:

The monolith was 11 feet high, and 1¼ by 5 feet in cross-section. When its dimensions were checked with great care, they were found to be in the exact ratio 1 to 4 to 9—the squares of the first three integers.

Note that the depth of the monolith is one and one-quarter, not eleven quarters. These measurements aren't in an exact 1:4:9 ratio either, with the height only being one quarter of a foot away from a perfect match. I suspect the measurements given in the text are meant to be approximations and not the dimensions that one would find when checking them "with great care."

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    The odds that ancient aliens would produce an artifact measuring an even number of any imperial unit in any dimension, is approximately the same as it having an even metric measurement.
    – DavidW
    Commented Feb 22, 2021 at 4:17
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    Semantically, this indeed reads like the numbers are not the "great care" measurements, but rather a spitball, and then a mention of subsequent "great care" measurements (not specified numerically). However, it's counterintuitive that the spitball is at least to within ¼ foot precise on the width, yet lacks the same ¼ foot precision on the height, which suggests a varying degree of accuracy, which leads to questioning the narrator's accuracy on describing whether something is a perfect ratio.
    – Flater
    Commented Feb 22, 2021 at 13:02
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    @Flater Perhaps all measurements were made and reported to the nearest ¼ foot, and both the height and the width happened to be closer to a whole number of feet than to any other quarter-foot number.
    – Sophie Swett
    Commented Feb 22, 2021 at 13:51
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    @Flater Not if it's embedded in sand or the base is covered in millions of years of dust.
    – pipe
    Commented Feb 22, 2021 at 14:55
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    @Flater 16/13, 64/13 and 144/13 feet have the exact ratios and differ from the spitballs by only up to 1/13 foot (they're off by -0.25/13, -1/13 and +1/13 feet, respectively).
    – superb rain
    Commented Feb 22, 2021 at 17:19
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In an interview, Clarke said that he came up with the squares of the first 3 integers thing after he wrote the book, and stuffed it in after the fact. He probably just didn't change the numbers in the rest of the book

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    In which interview?
    – Valorum
    Commented Jul 20 at 15:29
  • It was a written one and it was a very long time ago. I'm pretty sure it was lost worlds of 2001, though it might have been Agel's book.
    – Miss Understands
    Commented Jul 21 at 9:02
  • From Lost Worlds of 2001 - "July 11 (1964). Joined Stanley to discuss plot development, but spent almost all the time arguing about Cantor’s Theory of Transfinite Groups. Stanley tries to refute the “part equals the whole” paradox by arguing that a perfect square is not necessarily identical with the integer of the same value. I decide that he is a latent mathematical genius.
    – Valorum
    Commented Jul 21 at 9:07
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    I think you might be referring to The Making of Kubrick's 2001 (Jérôme Agel) "In the book, the monolith discovered on the Moon has dimensions in the ratio 1 x 4 x 9, the squares of 1, 2, 3, which serve to emphasize the idea of mathematics as a truly universal language. Different-sized monoliths were used in the film. "The 1² x 2² x 3² was my gimmick later," says Clarke."
    – Valorum
    Commented Jul 21 at 9:18
  • @Valorum Write that as an answer so you can get points for it.
    – Miss Understands
    Commented Jul 21 at 10:24

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