Most of you will never have heard of Solomon W. Golomb. But he invented some of the technology used in the image compression algorithms aboard our rovers, among other fundamental contributions. (To things like, you know, cell phones.)

In college I was for a while obsessed with Golomb rulers -- his idea, of course. You can think of these as a kind of game: make the shortest ruler you can that measures the most (integer) distances using only a given number of marks.

For example, the best four-mark ruler has a length of 6; its marks are at positions 0, 1, 4, and 6. It's obvious how you measure lengths 1, 4, and 6, but the others are also easy. If you want to measure the distance 2, you do it between the 4 and 6 marks; to measure 3, you use the 1 and 4 marks; and 5 is between the 1 and 6 marks. (This particular ruler is both

*optimal* and

*perfect* -- that is, no shorter ruler measures all of these distances, and all distances up to the ruler's length can be measured -- but it's the longest one that is. No optimal ruler with five or more marks is also perfect, mainly because the universe is out to get us.)

Golomb rulers are hugely useful in, for example, phased-array radars, where you get more information the more distances the ruler can measure but (a) the marks are expensive (because every one is a radar dish), and (b) you also want to keep the ruler's overall length short (because that way you can buy less land).

Thanks for many late nights writing ruler-hunting software and watching it work, Dr. Golomb. Also for the pretty Mars rover pictures, and, oh, yeah, for a bunch of stuff in my cell phone.

More information about Golomb rulers is here:

https://en.wikipedia.org/wiki/Golomb_ruler. Also here:

http://mathworld.wolfram.com/GolombRuler.html.