Mathematical Markings

The Y Combinator.jpg
Mark sent this picture in, with this explanation:

I don’t quite have a science tattoo, but I have a math tattoo. That’s close enough, right?

Now, for the explanation. This is a formula called the Y Combinator. It is a fixed-point combinator in the lambda calculus and was discovered by Haskell Curry, a rather prolific mathematician and logician whose work helped start Computer Science.

What this formula does is calculates the fixed point of a function, which in turn allows for recursion by calling on that fixed point; recursion is perhaps the single most important concept in Computer Science. Being a computer scientist and a mathematician, this formula is very important to me and represents the innate beauty of computer science and mathematical logic.

Four more tattoos added to the Flickr set this week, each with its own story. Check them all out.

Update 9/21 8:30 am: Ouch. jwz hints that Mark forgot a parenthesis. Any comment from math folks out there?

Update, 1:50 pm: Mark says his parentheses are all in order, thank you.

0 thoughts on “Mathematical Markings

  1. I got a real kick out of this one, since I’ve finally settled on the Y combinator after trying to think up a Lisp-themed tattoo. I figure it will match the summation I’ve already got nicely. After that, only 22 letters to go, right?

  2. ya, that parans look fine to me too. when i visited jwz’s site they’re counting parans with their fingers. Maybe that should have been a clue in itself. 😉

  3. It isn’t a math tatoo, it’s a computer science tatoo! (You could argue that it’s math too, of course, but it is much more central to CS — for example, it is way more likely to be covered in a typical undergraduate CS curriculum than by a typical undergraduate math curriculum.)

    Real computer science isn’t programming trade skills, big chunks are cool theory like this.

    If you want to mystify people with cool combinator stuff they probably won’t understand, then you should really write fixed-point combinator write in terms of more primitive combinators. For example, you could say Y = S (K (S I I)) (S (S (K S) K) (K (S I I))) using only the classic S, K, and I, or confuse everyone with John Tromp’s shorter fixed-point combinator using only S and K, S S K (S (K (S S (S (S S K)))) K). But my own short and sweet favorite is Y = C’ (B (S I I)) B (S I I)).

    More at .

  4. Oh, the parens are correct. I agonised over my tattoo for several weeks after I got it making sure everything was correct. By the way, I am the canvas.

    Re: Melissa. Well, it’s quite easy and quite correct to say that CS is more a branch of mathematics than anything else. So, yes, it is central to CS which in turn makes it a part of mathematics.

    As far as confusing and hilarious fixed-point combinators, I’m a fan of Jan Klop’s comibinator:
    Y = (L L L L L L L L L L L L L L L L L L L L L L L L L L), where L = λabcdefghijklmnopqstuvwxyzr. (r (t h i s i s a f i x e d p o i n t c o m b i n a t o r))

  5. Re: Martin. You just described the Lisp implementation of a infamous divergent combinator called the omega combinator. If I remember correctly, that is actually what Alonzo Church used in his paper on the Entscheidungsproblem.

  6. Thanks, Mark! I saw that code snippet in a usenet post years ago, and it twisted my brain into a very strange shape by the time I figured it out 🙂 Didn’t know it had a name, or that there was history behind it – will have to go look up the Church paper.

  7. Combinators “eliminate the need for variables”? Can this be an alternative to arrays? I compared a few array-less solutions with typical non-array-less ones, and the array-less solutions were faster (surprisingly). I did this after learning that memory and time are the two basic hindrances. Also, tattoos are dumb.

  8. Kai, presumably the tattoo artist drew it on paper with guides lines first, transferred it over, then traced with the needle. I suppose it’s possible that the original was a printout too.

  9. I just wonder what classes he can’t take because he would be accused of cheating on the final exam. (Yeah, I know, he’s probably *teaching* those classes.)

  10. ruidh: I’d also argue that if he is taking those classes, he almost deserves to get a good grade just because he finds the material so compelling that he was willing to get it inked on him quasi-permanently. (This assumes, of course, that tattoo removal is painful and expensive; if it were cheap and painless one would have to look at this differently.)

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