On 11/16/09 10:33, Invisible wrote:
>> sin x^-1 vs sin^-1 x
>>
>> where the two "^-1" mean entirely different operations.
>
> The first one, at least, is unambiguous. But the second one? Now do you
> suppose that's the arcsine of x? Or the reciprocol of the sine of x?

	I think you'd be hard pressed to find someone who has used it to mean 
the reciprocal of the sine. Perhaps that's why they defined the cosecant?

> And then of course, people will write "log x". Wanna take a guess which
> base that is? Now, sometimes it actually doesn't matter which base. And
> if it does, it *probably* means the natural logarithm. Probably...

	Go back far enough, and it always meant base e. I wonder when ln(x) 
notation cropped up.

	If it doesn't matter what base it is, then it'd be "obvious" from the 
context.

> Speaking of which, the base of natural logarithms is "e". And sometimes
> "e" means 1 + 1/1 + 1/2 + 1/3 + 1/4... And sometimes "e" is just another
> variable.

	You're missing some exclamation symbols.


-- 
Friends help you move. Real friends help you move bodies.

Post a reply to this message

On 11/16/09 16:22, andrel wrote:
>> I've also seen pi used more than once as a general variable, rather
>> than a function name or a mathematical constant. This is why you see
>> phrases like "e^(i x) where e is the base of natural logarithms and i
>> is the imaginary unit". Because otherwise it's horrifyingly ambiguous.
>
> I am working in an environment where the imaginary unit is j (because i
> is for current). I have trouble adapting.

	Damn them electrical engineers.<G>

	When I was an undergrad, I worked at a math tutoring institute. A 
number of tutors were EE majors. I once caught one of them trying to 
help a student, and he kept writing stuff with j. It was really 
confusing her till I pointed out to the tutor that just about everyone 
else uses "i". I've met a bunch of guys who didn't know that.

-- 
Friends help you move. Real friends help you move bodies.

Post a reply to this message

On 11/16/09 08:59, scott wrote:
> You'd be surprised how many industries require specialist knowledge :-)
> For example, I suspect the structural engineer that designed your
> building did plenty of calculations using calculus to estimate stresses
> based on the loading (simple cases can be looked up in tables, but
> anything unusual needs to be worked out manually). Ditto for an
> electrical engineer who designed the power supply for your computer, the
> DCDC converter in your mobile phone and numerous other circuits -
> without an understanding of calculus you're going to be totally lost.

	I somewhat doubt it.

	Often, calculus is used in developing the theory. Then the rest is 
simply approximations or computers.

	When I was taking a statics course, the professor taught us how to 
calculate the center of mass by taking the shape, splitting up into 
triangles, calculating the center of mass of each (formula for 
triangles), and taking the weighted average.

	He never once mentioned the generic integral formulation. I asked him 
why. He said, "That's good stuff to know if you're going to grad 
school/academia, but in the real world, you almost never have the actual 
function to integrate."

	Which is mostly true. Of course, it's a stretch to say no one in 
industry uses calculus, but it's a tiny tiny minority.

> Of course computers can simulate and calculate stuff for you, but you're
> going to look a right idiot if you need to run ten 12 hour simulations
> to decide the correct structure or capacitor size when your colleague
> can work it out exactly in a few minutes with a piece of paper.

	If your colleague can work it out quickly on paper, it shouldn't take 
long to do it on a computer (Maple, Mathematica, etc). Just because it's 
computers doesn't mean it has to be a finite element  or Monte Carlo 
calculation. Additionally, if it's routine enough, there are handbooks...

-- 
Friends help you move. Real friends help you move bodies.

Post a reply to this message

On 11/16/09 16:36, andrel wrote:
>> None of these seem to require knowledge of calculus. In fact, jobs
>> that *do* require such knowledge are seemingly so absurdly rare that I
>> almost find it difficult to believe they exist.
>
> So I don't exist? Nor do many of my collegues?
> I think I disagree.

	I think your job _is_ fairly rare. Even among people in technical fields.

	Does it require a PhD?

	There you go.

	Perhaps he exaggerated a bit, but to be honest, it *is* fairly hard to 
get a job outside of academia that requires calculus knowledge, and 
doesn't require a graduate degree (at least in the US).

	It's kind of like people who know advanced CS, and are depressed to 
find almost all jobs for programmers are for code monkeys. Although I'm 
sure there are some good jobs that don't require a graduate degree in CS...

-- 
Friends help you move. Real friends help you move bodies.

Post a reply to this message

On 11/16/09 10:09, Darren New wrote:
> Invisible wrote:
>> What the hell is the derivative of f(f(x))?
>
> LMATFY

	You really shouldn't start any acronym with LMA... It was quite 
anticlimactic.


-- 
Friends help you move. Real friends help you move bodies.

Post a reply to this message

Neeum Zawan <m.n### [at] ieeeorg> wrote:
> On 11/16/09 10:21, Darren New wrote:
> > Invisible wrote:
> >> Just for giggles: how many meanings can you find for "normal"?
> >
> > Sure. But even differences between things like
> >
> > sin x^-1 vs sin^-1 x
> >
> > where the two "^-1" mean entirely different operations. [/snip]

It's actually the same operation, you are just inverting different objects with
respect to different operations. In the first case you are inverting a number
(x) with respect to multiplication, in the second case you are inverting a
function (sin) with respect to composition.
It's similar to how sin and sin(x) are not the same thing. sin is a function and
sin(x) is the value of said function at the number x.

Mindblow anyone? :)

Regards Roman

Post a reply to this message

>> I've also seen pi used more than once as a general variable, rather 
>> than a function name or a mathematical constant. This is why you see 
>> phrases like "e^(i x) where e is the base of natural logarithms and i 
>> is the imaginary unit". Because otherwise it's horrifyingly ambiguous.
> 
> I am working in an environment where the imaginary unit is j (because i 
> is for current). I have trouble adapting.

Hahaha.

Arbitrary conventions FTW!

Post a reply to this message

>> Speaking of which, the base of natural logarithms is "e". And sometimes
>> "e" means 1 + 1/1 + 1/2 + 1/3 + 1/4... And sometimes "e" is just another
>> variable.
> 
>     You're missing some exclamation symbols.

Oh, so it's actually 1/n! then? I didn't actually know that...

Post a reply to this message

> * equivalence, equality, definition, EXNOR, assignment and perhaps one 
> or more that don't have names.

I'm failing to see how equivalence and definition are different. (I know 
some people use the triple-line symbol for this though.)

The main confusion is between assignment and equality, generally. Or, in 
mathematics, between a test for equality and a statement of equality.

> ** See also the concept of '=' in OO languages. Are two objects the same 
> if all fields are the same?

You would first have to define the concept of fields being "the same". ;-)

Fortunately, in a pure functional language, the question becomes a lot 
simpler.

Post a reply to this message

stbenge wrote:

> hopefully achieving the ability to decipher 
> many of the incomprehensible formulae found at wolfram.com.

Yeah, good luck with that. ;-)

Wolfram plays with some pretty advanced stuff. Between the Euler gamma 
function, the Riemann zeta function, spherical harmonics, elliptic 
integrals, Pochammer symbols, Godel numbers, hypergeometric functions, 
the Airy functions and so forth... it could take a lifetime to learn all 
this stuff.

Post a reply to this message