Yep, here’s another golden oldie to get stuck into:

Discuss how things go in the comments.

And remember: spoilers abound should you pull back the comment curtain!

**Update:** mic warns in the comments: the answer to 12A is nine letters long, not eight as the clue mistakenly states.

Please note there is a mistake in 12A. I banged my head against the wall for a while with only this clue left, then realised the answer is nine letters, not eight as the clue suggests

I’m assuming people will be crying “bullshit” over 18A, not sure where i stand yet

btw, is 23D a cricket reference?

Found it fairly easy once I’d grasped the theme and era. 20D was the easiest DA clue I’ve seen for a while.

I have no problem with 18A … perhaps “peoples” rather than “people” would have been more precise, but too transparent.

Yes, re 23D. See it for example at http://www.cricinfo.com/ausvpak09/engine/current/match/406206.html

I had no complaint about any clue here, and thought there were several nice ones. Took me a minute to understand 4A, then loved it when I did – very clever and more than fair. 12A’s definition is nicely hidden.

I’m with you AG, it was easier than recent DA’s, but full of stuff to love, especially 4A

the problem with 18A i was anticipating was that the two O’s weren’t adjacent in the answer. and if the OO is supposed to be under the purview of the anagram, then “within” shouldn’t be there

Or you could look at 18A as (soon pointless within lengthy) tussle ?

Yep, Peter – that was my take.

I’m OK with 18 across.

13D is my beef — COTANGENT is not a mathematical function!

On 17D, why BLOODY TIMBER = RAW DEAL? BLOODY = RAW, yes, by TIMBER = DEAL?

And I also didn’t understand how 26A was HOWARD, nor the FEDERAL part of 24A.

And how does 4A work?

Some quality clues there and an enjoyable one overall. 14A was my fave.

AS

13D: it is: cot x = 1 / (tan x)

17D: a deal is a plank of wood

26A: W in HOARD

24A: F (loud) + EDERAL (anagram of leader) + ELECTION (selection – s)

4A: I wouldn’t dare rob you of the joy of working this out. (clue: think laterally)

A very enjoyable crossword. My favourites: 4A (an absolute beauty!), 12A, and 13D. I don’t understand your beef about this last clue, AS. I’m with mic: it’s a trigonometric function. And trigonometry is a branch of mathematics.

Only a few minor quibbles:

18A: ETHNOLOGY. Not quite right on two counts. As AG says, “peoples” would have been more accurate. And I agree with mic that if the OO is supposed to be under the purview of the anagram (as peter and AG have taken it), then “within” is rendered superfluous and misleading.

24A, 25A and 26A: I found the direct defs a bit unsatisfactory (as I often do for &lits).

Cotangent is definitely not a mathematical function. Cotangent is adjacent / opposite sides of a right-angled triangle.

The cotangent can then be used in mathematical functions, for instance cot x = 1 / tan x, but it itself is not a mathematical function.

cot x = 1 / tan x is essentially the equivalent of 2x = 1 / 0.5x, and you would never call 2 or 0.5 a mathematical function.

DEAL = WOOD, who’d a thunk it? I’m always learning the obscurer meanings for quite common words thanks to cryptics.

Now I’m thinking I’m an idiot: I still can’t figure out why IDIOTS is the answer!

cotangent definitely is a function

It is the map x |–> cot x

2 is not a function in the equation 2x = 1 / 0.5x, because there it is one of the two arguments of the multiplcation function, whereas in the mathematical function cot x, x is the argument and cotangent is the function

f(x) = cot x, or y = cot x.

The function of x is all of cot x, not just cot. F(x) = cot or y = cot is nonsensical.

cot x = 1 / tan x is not actually a function anyway, it’s an equation (although I earlier called it a function, which it isn’t). It’s not a function because you can’t map it onto a graph. Instead, it’s an equation or relation.

Your last paragraph is true. i never disputed that

The rest is confused. The notion of a mathematical function is a formal one that came after people became comfortable with writing down arithmetical equations. Familiar arithmetic equations and notation thus become short-hand to are more precise notion of functions, arguments and relations. For example your equation 2x = 1 / 0.5 x could be more canonically written as

* (x) (2) = / (1) (* (0.5) (x))

Here * and / are the relations, and x, 2, 1, and 0.5 are the arguments

This is a piece of algebra, where the x is an unknown (though note that your equation is actually false)

OTOH, in cot x = 1 / tan x, this is NOT a piece of algebra. Here ths x is a variable and it’s expressing a relation between functions

2x = 1 / 0.5x is not false. All it means is that x is equal to 1 and can only equal 1.

I don’t doubt much of what I said is confused. The last time I learnt maths formally was about ten years ago during my uni days.

Nevertheless, looking at the dictionary, it says that a function in maths is “A variable so related to another that for each value assumed by one there is a value determined for the other.”

My point: cot by itself can’t be a function because it has nothing to do with variables. Cot x = y is a function, but that’s only because x and y, variables thus related to each other, have been introduced.

Ps. I’m more than willing to accept that the dictionary definition is not precise or expansive enough for how the term is used in mathematical circles, but as it stands in the dictionary, I still claim cot can’t be a function.

Well, it means x = 1 or -1

While you seem to have a good grasp of doing mathematics, I think you are slightly mistaken about the terminology. The dictionary definition is slightly misleading because it tries to avoid the necessary supporting mathematical jargon

http://en.wikipedia.org/wiki/Trigonometric_functions

I don’t know where you’re coming from on this, AS. It could be that you are making some really fine distinction here, but it’s completely evading me! Both my dictionaries, and Google too, say cotangent is a function. See Wikipedia link:

http://en.wikipedia.org/wiki/Trigonometric_functions#Reciprocal_functions

And, when I did Maths at school and uni, degree, sine, cosine, tangent, and their reciprocals were all called “functions”. OK, that was well over 40yrs ago and I may have changed a lot, but “cotangent” hasn’t!

BTW, your equation 2x = 1 / 0.5x does have another solution, namely x = -1

Now on to more interesting things: AS are you still puzzled by 4A? mic’s hint to “think laterally” should be taken literally! i.e. look sideways! Can I hear the sound of you kicking yourself yet?

An extra word crept in there! Ignore the word “degree” in the line after the wikipedia link.

My definition of function, which coincides with ordinary dictionary definition: equation that can be plotted on a graph.

My problem with COTANGENT: y = cot is nonsensical and cannot be plotted on a graph. y = cot (x) can be plotted, but not y = cot.

My claim: COTANGENT alone can’t be called a function, although COTANGENT (X), for instance, can.

mic reckons my definition of function is not all that accurate in mathematical circles. I reckon he’s right (I’m assuming mic means him).

As for IDIOTS, I really need help. I’ve looked sideways, I’ve looked askance — I’ve got nothing.

OK, so you’re drawing a distinction between “cotangent” and “cotangent x”. And you’ve looked up “function” in the dictionary to support your argument. Trouble is that if you look up “cotangent” it will say it’s a trigonometric function!

Now for IDIOTS. Look at the clue; move along to the very end; what do you see there?

Awesomeness!

Fantastic!

Modesty forbids detail, but I’ll nominate myself as extremely well qualified in both maths and English to offer my opinion on the COT issue. AS is right in the most narrow and precise mathematician’s sense, but only to that extent. f(x) is a function. But where f is a simple one-term relation like cotangent, to call that a function for short is commonplace. I like to nitpick definitions (see flag/exhaust this week), but to object to COT on that distinction is over the top IMO. If anyone asked me “Is cotangent a trigonometric function?”, I’d say “Of course it is.”

Glad you finally saw the dots, AS. A beautifully disguised ripper, isn’t it? I was halfway through compiling a complaint about it on Saturday when it suddenly dawned on me and graduated from confusion to clue of the week! As I posted at the time, brilliant and scrupulously fair.

The dots is ridiculously good. Very happy about discovering that one, if not solving it right out.

The discussion about COT reminded me somewhat of the discussion about the 66% clue of a while ago now: a lot of nitpicking over something that was essentially not that big of a deal. But of course, this is what the site is about and what I have again and again demonstrated a fondness for.

And I also had another thought: i² is also a possible solution to 2x = 1 / 0.5x.

Although i² is no different to any other expression that equals -1 or 1, for instance 5 – 4 or 6^0, so calling i² a solution is cheating.

I enjoyed this one and even remembered a couple of them (but only after I had got them out)!. Back to the future.