Arthur C. Clark wrote 2001: a Space Odyssey at the same time he was collaborating with Stanley Kubrick on the screenplay to the highly influential movie. They went to great lengths to get the science right in the book and the movie, so it is amazing that a blatant mathematical error in the book seems to have gone unnoticed for almost four decades. This is particularly surprising, since the mistake involves statements in the book that have generated years of comments and discussions.
The statements, in Chapter 31, are about the mysterious monolith found on the moon. “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.”
Over the past four decades, intense discussion about the significance of these ratios has taken place, as well as—inexplicably—heated debates over the fact that 1 is not a prime number, despite the fact that Clark never said “prime numbers.” Stunningly, it seems everyone has missed the fact that 1¼:5:11 is not 1:4:9…it’s 1:4:8.8…!
The fact that Arthur C. Clark could make such a blatant error can be explained (or at least excused) by the fact that he didn’t really care about the actual numbers. What he cared about—the whole point he was trying to make—was the significance of the manufacturing precision: “It was a chastening thought that the entire technology of Earth could not shape even an inert block, of any material, with such a fantastic degree of precision.”
I was led to the error just after I gave a talk at the University of Texas at Austin about Atomically Precise Manufacturing. It was brought to me by the amazingly gifted PhD student Akhila Mallavarapu, who was in the audience. What Akhila and Arthur C. Clarke are saying is that the manufacturing precision achievable by a civilization is equivalent to their level of technological capability. This is why Zyvex Labs is committed to Atomically Precise Manufacturing. We believe that when it is achieved on a large scale, the technological capabilities of our civilization and our quality of life will make a quantum leap.
On a side note, perhaps people’s fascination with mathematical ratios is to blame for missing both the mistake and the important point the author was making. For instance, many interpretations of the significance of these ratios cited in the book have been suggested, including that 9:4 is the ratio of movie screens, 1:4:9 is a particularly good way to construct stable mechanical structures, and (my favorite) that 1:4:9 is the ratio of ingredients to make a fudge bar that the monolith resembles.
Disclaimer: While I can’t be certain that no one else has caught the glaring mathematical error, hours of Googling revealed no reference to it, in spite of many discussions of this passage. This mistake does show up in every edition of the book that I have looked at including one printed in 2016.
Posted by John N. Randall PhD
President Zyvex Labs
I have diligently read and continuously search online for updates and references to every available detail related to the monolith since reading the book circa1998.
I first viewed the film sometime around 1972
I admit to missing this interesting discrepancy, (which I will certainly fact check,) though It’s well known to me that Kubrick changed the enigmas “object’s”, and ultimately arrived at the monolith’ and its many varied proportions during the process, and he made adjustments to suit his cinematic vision. There are still unresolved questions about these dimensional variables so I would not eliminate the potential relevance.
It is likely that the confusion in the book occurred during the extensive selection process and resulted from the many revisions that ultimately led to Clark’s ratio, and that the contradiction described was an understandable consequence of the often difficult process Clarke encountered collaborating with Kubrick while co-writing the book and film script. It was Kubrick’s Studio and his associates intentionally delayed the book’s release, to Clark’s dismay, and as a consequence, very few people actually read the book or understood the film.
I only read the book when I realized it might contain the monoliths specific proportions for “utilitarian reasons related to building blocks and bricks.”
However, the clearly stated proportions 1:4:9 were indisputably arrived at by Clarke, and to my knowledge from online research, the specific ratio 1:4:9 finally occurred very late in the process while both the film and the book were being simultaneously progressed.
I believe, but have never been able to confirm that Clarke had “unique help from an unknown person!”
Clarke is on the record acknowledging Kubrick’s rare mathematical genius, but the extension of the linear ratio to the 3D geometric monolith still puzzles me to this day.
The proportions Clarke stated, in pure theory and applied practice, can only work as the infinite sums of the odd integers, “as the Integers squared.”
The mathematics of the monolithic ratio 1:4:9 is “profound and complex,” the “Riemann hypothesis is implicit.”
I can easily appreciate why Zyvex Labs is committed to Atomically Precise Manufacturing and I agree that when this level of precision is achieved on a large scale, the technological capabilities of our civilization and our quality of life will make a quantum leap. It’s remarkable to note that the Valence shells of an atom follow this inverse square law, as does acceleration due to gravity. http://math.ucr.edu/home/baez/gravitational.html
In truth, and from my practical experience, I think there is much much more yet to be appreciated.
This Facebook album linked below is dated and in need of revision, though I hope it will serve as a modest primer to advance the discussion.
regards
https://www.facebook.com/media/set/?set=a.419059461504139.97482.100002002650029&type=1&l=ebfc60c114
In fact, there is no ‘glaring mathematical error’. Let’s parse the quoted text carefully.
“The monolith was 11 feet high, and 1¼ by 5 feet in cross-section” This is not an exact measurement, these are round numbers for a reader to get a feeling for the rough size.
“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.” (emphasis mine). So in other words, after somebody did a quick measurement with a measuring tape, other people came back and did a precise measurement, and those precise dimensions, which are not quoted in the text, come out with the correct ratio of 1:4:9.
So there is no glaring error. Arthur C. Clarke would know that 9 x 1 1/4 is not going to be 11. Those are just convenient round numbers close to the actual dimensions.
James Owen