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

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