# What is always increasing and decreasing at the same time?

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 613616.  Wed Sep 16, 2009 3:01 am Stephen: And now fingers on the buzzer please, for the General Ignorance round. What is always increasing and decreasing at the same time? Alan (presses buzzer): Nothing. Stephen: Ohhh...! Klaxons sound. The word "NOTHING" flashes on the screen.Stephen: Oh Alan, that is so not right at all! Alan: Yes it is! Cos if something's both increasing and decreasing at the same time, it would be a contradiction in terms. Stephen: No it wouldn't. There is something which is always increasing and decreasing at the same time. It's a mathematical entity. It's called a constant function. Alan: Wow. Ben: Sorry, but did you just say constant function? Stephen: Yes. Ben: Well, no. In mathematics, a constant function is, basically, what its name implies, i.e. constant. It neither increases nor decreases. Stephen: Ohhh...! Klaxons sound. The screen flashes: "A CONSTANT FUNCTION NEITHER INCREASES NOR DECREASES"Stephen: Oh no, Mr Miller. We thought you might say that so we laid that trap just for you. Ben: But it's true! Stephen: It's not. You see, when mathematicians talk about increasing and decreasing, say increasing, they distinguish between strictly increasing and monotone increasing. Ben: Oh. Alan: So what's the difference between strictly increasing and what's that? Ringtone increasing? Stephen: Monotone. If a function is strictly increasing, it increases steadily, that is to say, without staying constant. A monotone increasing function, on the other hand, is increasing, but is allowed intervals where it stays constant. Decreasing is the same, only in the opposite direction. Alan: Ben, do you understand what he's saying? Ben: Yes. And I understand now. A constant function is both monotone increasing and monotone decreasing. What I meant just now was that a constant function is neither strictly increasing nor strictly decreasing. I didn't specifically say the word "strictly" so Stephen took me to mean the other one, that sly old bastard. Stephen: I say! What's that you just called me? Ben: Oh nothing, nothing. In any case, you called me horse-faced the other time, didn't you? Stephen (shrugs): Well, I suppose I did (though I could have sworn it was actually Rob Brydon). Never mind. Fingers on the buzzer now for the next question. What can be both open and closed closed at the same time? Alan (presses buzzer): A door that's ajar? Stephen: Nope, that would be neither open nor closed. But what can be simultaneously open and closed? Alan: Is it another mathematical, like, thing? Stephen: Yes it is. Ben: Oh! [presses buzzer] A topological space! Topology! In a topological space, you have a set and a topology consisting of subsets of that set, including the empty set and that set itself, such that the union of any collection of subsets and the intersection of any finite collection of subsets are also in the topology. Some of the sets in the topology are open, some are closed, some are neither open nor closed, but there are some that can be both open and closed! Is that the answer? Stephen: Well, I'm most impressed! It certainly is the answer. My word, that was so impressive that I really ought to award you a million points. But, in view of the names you called me a few moments ago, Ben, I'm not giving you any points. Anyway, next question. Fingers on the buzzers. What can be both real and imaginary at the same time? Ben (presses buzzer): The number 0 considered as a complex number. Or, if you like, the origin of the complex plane. It is the intersection between the real axis and the imaginary axis on an Argand diagram. Stephen: No, Ben, that's wrong! The answer is, nothing can be both real and imaginary at the same time, because that would be a contradiction in terms! Minus a million points for Ben! Ben: Don't worry Stephen. I'll get you back one day.

 617239.  Thu Sep 24, 2009 12:16 pm Is not Ben's last answer correct?

 617245.  Thu Sep 24, 2009 12:28 pm Is this from the show or did you write it ChristopherRobin? It's fantastic :)

 617462.  Fri Sep 25, 2009 1:17 am I always thought QI was scripted - here's the proof!!

619396.  Tue Sep 29, 2009 8:36 am

 gruff5 wrote: Is not Ben's last answer correct?

It is, but I think Stephen is just being tongue in cheek at the end.

 619411.  Tue Sep 29, 2009 9:47 am Very nice, CR - fantasy QI.

 619700.  Tue Sep 29, 2009 5:51 pm As long as it doesn't become slash fiction.

 619746.  Tue Sep 29, 2009 7:07 pm Aaarghhh! I can't say that this surprised me overmuch, but I discover that the notion of Stephen Fry slash Alan Davies has already occurred to a few people on the Interwebs. Does anyone here admit to being alan_stephen, who runs a LiveJournal site based on that very premise?

620272.  Wed Sep 30, 2009 5:47 pm

 suze wrote: a few people

You're underestimating the Internet. Being a LJ-ite, I've seen that sort of thing crop up not uncommonly before, in many different places. Even more distressing, perhaps IMO, is the small contingent of people who write fic about S and his real-life partner. One wonders if there is a dearth of acceptable hobbies. I've looked up alan_stephen and see that it's an LJ community, not a single user, and therefore anyone who is a member (of which there seem to be 98) can read and post to it, and I doubt any of those people would admit here to being an adherent!

At least no one (as far as I know, Suze) is writing fanfic about you; someone I know discovered that he is not so lucky.

 620305.  Wed Sep 30, 2009 6:10 pm Ooh, is RV another of your celebrity acquaintances? As for suze fanfic, I don't know or really want to know whether any exists or not. (EDIT of a heavily coded suggestion as to who might have written some - it's served its purpose).Last edited by suze on Thu Oct 01, 2009 11:30 am; edited 1 time in total

620317.  Wed Sep 30, 2009 6:23 pm

 suze wrote: another of your celebrity acquaintances?

"Another", as though they're collectible and I'm racking them up! (Hint: I'm not.)

I'll write Suzefic just to compensate for the lack of it in the world. Feel free to suggest your intended(s). Man, I could even do it in the form of a transcript for extra sizzle.

Suze [sotto voce]
Shall we go up?

Forfeit: Klaxons sound. Viewscreens flash the words "ONE OF US IS ALREADY UP".

 620321.  Wed Sep 30, 2009 6:31 pm Ah. I'd got the first three words, then got all stuck.

620340.  Wed Sep 30, 2009 7:01 pm

 MinervaMoon wrote: I'll write Suzefic just to compensate for the lack of it in the world. Feel free to suggest your intended(s). Man, I could even do it in the form of a transcript for extra sizzle.

As I suggested above - in an heavily coded sort of a way that I'm hoping only you will understand - I think there may possibly already be some.

But if there is to be canonical suzefic, let's see. Bill Clinton was always the obvious candidate - and let's face it, it wouldn't be massively out of character for him - but I guess John and the guys might struggle to book him for an episode of QI.

I'm certainly not going to name here the (very minor) celebrity who, quite a few years ago, introduced me to cocaine and then introduced himself, as it were, to me. For one thing, he's married (although I don't believe that he was then); for another, no one here would ever have heard of him. But not him please; not especially impressive.

 620457.  Thu Oct 01, 2009 7:32 am *blush* ........ do you mean ....you know...... not the guy with the coke but the possible author.... is it do you think.....??

 709044.  Thu May 13, 2010 4:30 pm During arousal - Blood flow to the Bell end and blood flow to the brain.

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