On 12-Sep-08 15:36, Phil Cook wrote:
> And lo on Fri, 12 Sep 2008 09:16:07 +0100, Invisible <voi### [at] devnull> did 
> spake, saying:
> 
>>>> Haskell is a small, simple, logical language. C++ is a huge, messy, 
>>>> complex language. I don't see how learning an easy language should 
>>>> enable me to learn a hard language.
>>>  Heh, Haskell looks complicated and hard to learn to me.
>>
>> Well, I guess there are probably people who look at something like
>>
>>    x = (-b +- Sqrt(b^2 - 4ac)/2a
>>
>> and go "OH MY GOD! That looks SO complicated!" But actually, if you 
>> know a little algebra, you discover that this contraption is actually 
>> quite straight forward.
> 
> But look at the knowledge you need for that. We'll assume that the 
> basics are covered = + - x ÷ and that you recognise the x, a, b, and c 
> parts of the equation. First up we get - how can you start with a - 
> symbol, what am I subtracting b from? Next is a ±; okay you hopefully 
> recognise that it's a + and a - combined, but how do I add and subtract 
> at the same time? Then we get a √ um okay the shape of that gives no 
> clue unless you just know it. Then ² which we might know as shorthand 
> for b x b as many times as the number. Then we get an 4ac, is that a new 
> character; you know a-z, aa-az, etc? You have to know that it's 
> shorthand for 4 x a x c. Then finally you get a / or just one big line 
> which you need to recognise as a ÷.
> 
> Spell out all the assumed shorthand plus symbols there and you can see 
> why it could legitimately be considered complicated.
> 

For me the most interesting thing is the ±, that one is quite rare in 
highschool maths. Here, and I assume also elsewhere, it is pronounced as 
'plus or minus'. Where the 'or' apparently means that we have to 
consider one *and* the other. An obvious question is: 'How can it be 
that an equation has more than one answer'? There is also the often 
overlooked complication that formula manipulating normally consists of 
equivalent transformations. Here we have something that isn't, it is 
more of a bifurcation resulting in two separate formulas, neither of 
which is equivalent to the original equation. It is not obvious how to 
run this process in reverse. I think I learned that one later 
separately, without being told the intimate connection to the ± in this 
formula (or more precise the boolean thing hidden in there somewhere).

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