Why did Frank Drake choose these math equations for the Voyager Golden Record?

Question

Not sure this belongs in this or some other community, but one of the images on the golden record is a brief snapshot of our decimal system and then a few math examples. Here is the image in question:

http://webodysseum.com/wp-content/uploads/2012/06/Voyager-Golden-Record-Pictures-03.gif

Is there a reason he chose these values to show how we do arithmetic? Does is introduce concepts that other equations would lack? Just curious... also I might get a tattoo of this so I'd like to know more about the background of it first. Thank you!

Answer 1

At a guess, $2+3=5$ is the simplest non-confusing sum: $2+2=4$ is confusable with multiplication. $1+2=3$ is confusable with an ordering, as is $1+1=2$. It looks like all of the digits are used in the calculations, too.

Answer 2

Part of the answer can be found in this passage from Drake's chapter, "The Foundations of the Voyager Record," in Murmurs of Earth, a popular book edited by Carl Sagan which came out at around the time of the Voyager launchings:

"About this time [1961] Lingua Cosmica, a book on interstellar codes, was published by Hans Freudenthal, a Yale mathematician. It contained an ingenious method to construct a language by utilizing simple mathematics to establish simple rules and concepts. For example, an equation such as $2+3=5$ and another equation such as $4+5=9$ can be used to establish the meaning of the plus sign and the equal sign.... Freudenthal showed that by using such mathematical equations one could develop quite a sophisticated language -- in fact even an ability in the end to express emotion."

The book by Freudenthal that Drakes cites is actually titled Lincos: Design of a Language for Cosmic Intercourse Part I. ("Lincos" is a contraction of "Lingua Cosmica.") Freudenthal's book is in the tradition of Russell and Whitehead's Principia Mathematica, with pages and pages of logical impenetralia. There is no Part II.

Incidentally, there is a fun 1961 essay, Extraterrestrial Linguistics, by Solomon Golomb of polyomino fame. Here's an excerpt (with an interpolated "[more]" to make sense of one of the sentences):

"[I]t is probably rank terrestrial provincialism to expect others to attach the same importance to pi that we do. Even in our own mathematics, such constants as e and log 2 are considered [more] important, and the exaggerated role of pi stems largely from the Greeks' undue efforts attempting to square the circle....

"My own recommendation is the prime sequence $2, 3, 5, 7, 11, 13, 17, 19, 23,\ldots$, with a long period to prove the non-accidental nature of the signal. It isn't so much that I'm sure these Extra-terrestrials would recognize the primes; but if they don't, they must be dull fellows, and I would just as soon uot [sic] get acquainted."