What is a Joke? A Dialogue (part 2 - part 1 can be found here)
(Note: this blog contains an extremely distasteful and offensive comment - I say 'comment' because whether or not it qualifies as a joke is the reason for its inclusion. Obviously I don't endorse said comment, etc.)

Dear Neil,
At the risk of appearing rather churlish in the face of interest from an actual member of the public, I’m not convinced by the equation. For one thing, I’m not sure what difference, if any, holds between ‘+’ and ‘*’. For another, although a joke will often feature all three elements, it seems possible to find jokes that don’t. A simple pun such as ‘Why was six scared of seven? Because seven eight nine’ works almost completely independently of any mood, and its subject matter appears to be nothing other than the potential for double meanings with which the English language, particularly when spoken aloud, is so blessed.
But the more general point about mood is well made. Here’s a very similar joke to the previous effort: ‘What did Freud think came between fear and sex? Funf’ There’s a bit more to this joke, for a few reasons – for one thing, the punning is between different languages. But it also involves a shift in what might be termed register, and which is at least close to what you refer to as ‘mood’: what appeared to be psychoanalytic totems are revealed as mere placeholders for wordplay. There’s a change in attitude which isn’t brought about by argument or derision, but by slyer and arguably more effective means. It’s a lot more subtle than the manipulation of mood Frankie Boyle is so good at, but it’s still there.
I think your suggestion of constants in the equation, i.e., elements present in every joke or ever good joke, is very interesting. I’m loath to speculate as to what these might be – that way lies the elephant’s graveyard of Theories of Humour – but I’m not so loath that I won’t throw around a couple of ideas for the sake of a blog post. One contender is probably wit (more or less the extra level of cleverness you mention). But witty things are not always funny, as the plays of Oscar Wilde so epigrammatically demonstrate, and not all funny jokes are clever (although interestingly, the best examples I can think of are probably from slapstick).
Another possibility is incongruity or the confounding of expectations, which was a criterion I suggested in my original article. Interestingly, I came across a possible counterexample to this recently, in Jim Holt's charming little volume Stop Me if You've Heard This Before. It's one of the few jokes, or attempted jokes, to have impacted on a national level - it cost then US Secretary of Agriculture Earl Butz his job when he was overheard making it on a flight from the Republican National Convention in 1976. It is, undoubtedly, quite something:
“I’ll tell you what the coloreds want. It’s three things: first, a tight pussy; second, loose shoes; and third, a warm place to shit”[i]
Obviously, this is a truly feeble attempt at humour. Holt comments:
“What is striking about the Butz joke, apart from its ugliness, is its dismal lack of art. It contains no paralogical twist, makes no unexpected conceptual links; it is merely a clumsy enumeration of racist stereotypes. (Indeed, it is recognisable as an intended joke only by dint of its formal observance of the Rule of Three.)”
I’m inclined to suggest that Butz’s comment is not a joke at all. In saying this, I’m not appealing to its crudely offensive nature. Many jokes are crudely offensive; indeed, revolting examples are only a couple of clicks away from this page. But this particular clumsy enumeration of stereotypes lacks the element of surprise, of the reader or audience having to draw a connection themselves, that seems to me to distinguish jokes from brute insults or offensive remarks.[ii] In short, there is no joke to get here. If there’s anything that characterises jokes, it’s that they can be ‘got’, much as commands can be obeyed or questions answered.

[i] Interestingly, in each of the slightly different wordings I’ve read – this one is from Time – Butz is said to have used ‘coloreds’ rather than another well-known term for black people. Although one doubts he chose to phrase his point this way to avoid causing offence.
[ii] These can, unlike Bautz’s effort, themselves be witty: for instance (to continue the theme of 70s politics) Denis Healey’s famous remark that being criticised by Geoffrey Howe was like being savaged by a dead sheep. Nevertheless, I wouldn’t say that Healey had in this instance made a joke.




What is the Joke? A Dialogue

Dissecting the Frog reader and comic presence in his own right, Neil Wates, writes:

Interested to read your deconstruction of the Joke - something a lot of people (including myself) have been trying to get their heads round. I like your approach very much, particularly the point about subverting audience expectations, which reminds me of this masterful, masterful effort from Plum Wodehouse: 

 "Mr. Wooster, how would you support a wife?"

"Well, I suppose it depends on who's wife it was. A little gentle pressure beneath the elbow while crossing a busy street usually fits the bill."

The point I am interested in is what I am loosely terming the 'mood' of a joke (for now). Some of Frankie Boyle's worst stuff uses exactly the same linguistic and comedic conventions as the above, but the darker subject matter makes it a) seem like a different beast altogether and b) slightly funnier/less funny, dependant on your point of view. I guess what I am loosely grabbing at is that in the subjective world of jokes, there seems to be an equation going on where X = effectiveness of wordplay (into which we incorporate subversion of expectation, maybe), Y = subject matter, Z= Mood (or attitude toward subject matter). So, X+(Y*Z) = Joke, perhaps? Does that work?

I've been thinking about the linguistic value of some forms of comedy, not because I want to come up with some breakthrough theory or anything - just because it tends to ameliorate the joke if there is an evaluated extra level of cleverness (is this part of what we call ‘wit’?), though this is often one of the intangible/abstract reasons why one joke is supposedly 'better' than another. This is often completely separate from subject matter, which is noteworthy. I am not ignoring the completely wonderful subjectivity involved in all this, in fact I am trying to work out why linguistic layout effects jokes precisely because different people find different things funny. A fool’s errand it may be, but I have often wondered if there are one or two constants in the equation alongside the subjective variables of sense of humour, recipient's mood, context, experience etc etc.

It also hasn't escaped my notice that true to beautiful ironic absurdity there is some kind of Heisenberg uncertainty principle effect: The more the linguistic tricks are appreciated the less obvious humour therein (for most except the nerdiest of nerds like you and I). Heisenberg's unfunny principle? Who knows. 
Neil Wates runs Monster Comedy, which has disappointingly little to do with monsters.