Edit: I can't find a transcript, so I just transcribed that portion of the interview myself, starting at 13:45:
TG: Now I'll tell you, in preparing for this, I decided, let me Google Google, so I typed in "Google" into the Google search, and I came up with a lot of Google things in the regular search, but in the "Are you feeling lucky?" search, I got nothing.
LP: Well you just got Google itself.
TG: Yeah, I just got Google itself. Oh, I see, Google was giving me itself.
LP: Yeah.
TG: Oh.
LP: In computer science, we call that recursion. [laugh].
TG: Oh, you even have a name for it. [laugh]. I didn't quite get that. I kept thinking it was just repeating itself. I didn't realize it was giving me itself. [laugh].
LP: [laugh]
TG: And what's the name for it?
LP: Uh, recursion. It's... kind of... Sergey is giving me a dirty look.
TG: Why?
LP: It's a loose definition. [laugh]
TG: Lighten up Sergey. [laugh]
LP: It's a loose interpretation of... [laugh]... recursion.
TG: Sergey, what's the more literal interpretation?
SB: The technical term is you got itself back.
TG: Right?
SB: There's not really much beyond that. [laugh]
TG: Okay.
SB: Idempotence. How about that.
TG: Say it again.
SB: Idempotence.
TG: What is it?
SB: That's when you uh... [laugh]... Maybe I should stop while I'm ahead...
TG: ...You're just making this up, aren't you...
SB: ...Before I dig a deeper hole. Idempotence is when you do something and you get the original thing back.
TG: Oh, so that's a real word?
LP: It's a mathematical term.
SB: Yeah, yeah, but it's also just as loose an interpretation as Larry's was of recursion.
I remember listening to that interview way back when and feeling so uncomfortable that I almost turned off the radio. But now, reading that transcript, I just find it satisfying that they said the words recursion and idempotence on Fresh Air. With Terry Gross!
At the same time, I used to do speed dating and too often had to hear the poor guy next to me confuse "what do you do?" with "what exactly do you do day to day in as painstakingly technical detail as possible?" when the other party doesn't even know if they're an astronaut vs full-time dog walker.
By the way, one way to describe idempotence is a function whose range is the fixed points of the function.
Fixed point is very close. Your idea here is that google_search_lucky(search_string), where search_string="google" returns itself. Which would be a fixed point.
The rub is that the function google_search_lucky(search_string) would in all likelihood return the URL of a website if it was to return a string (necessary for even the possibility of a fix point), so the proper fix point would be "https://www.google.com".
If I was trying to map this to mathematical ideas, I'd say the point here is that the function google_search(search_string, is_lucky) with the argument ("google", is_lucky= true) returns the _function_ google_search(search_string, is_lucky) . So it's more like the argument ("google", is_lucky= true) is an identity for the function google_search(search_string, is_lucky).
http://www.npr.org/2003/10/14/167643282/google-founders-larr...
(It does not go very well.)
Edit: I can't find a transcript, so I just transcribed that portion of the interview myself, starting at 13:45:
TG: Now I'll tell you, in preparing for this, I decided, let me Google Google, so I typed in "Google" into the Google search, and I came up with a lot of Google things in the regular search, but in the "Are you feeling lucky?" search, I got nothing.
LP: Well you just got Google itself.
TG: Yeah, I just got Google itself. Oh, I see, Google was giving me itself.
LP: Yeah.
TG: Oh.
LP: In computer science, we call that recursion. [laugh].
TG: Oh, you even have a name for it. [laugh]. I didn't quite get that. I kept thinking it was just repeating itself. I didn't realize it was giving me itself. [laugh].
LP: [laugh]
TG: And what's the name for it?
LP: Uh, recursion. It's... kind of... Sergey is giving me a dirty look.
TG: Why?
LP: It's a loose definition. [laugh]
TG: Lighten up Sergey. [laugh]
LP: It's a loose interpretation of... [laugh]... recursion.
TG: Sergey, what's the more literal interpretation?
SB: The technical term is you got itself back.
TG: Right?
SB: There's not really much beyond that. [laugh]
TG: Okay.
SB: Idempotence. How about that.
TG: Say it again.
SB: Idempotence.
TG: What is it?
SB: That's when you uh... [laugh]... Maybe I should stop while I'm ahead...
TG: ...You're just making this up, aren't you...
SB: ...Before I dig a deeper hole. Idempotence is when you do something and you get the original thing back.
TG: Oh, so that's a real word?
LP: It's a mathematical term.
SB: Yeah, yeah, but it's also just as loose an interpretation as Larry's was of recursion.