>> 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...

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> * 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.

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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.

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>> 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.

Logically, I know such people must exist somewhere. They're just so rare 
it sometimes seems difficult to really *believe* they exist.

>> I mean, doing a job that requires mathematics is like being an olympic 
>> athlete. Hypothetically, anybody can become an olympian. But seriously 
>> guys, how many olympians have you personally met?
> 
> none, but I can name a few who know a lot of them.
> 
> You could also have asked for e.g. opera singers. Most people also know 
> none of those. OTOH I think I have met more than 10.
> 
> So it is all just a matter of who you know and who they know.

Professional singers, actors, athletes, musicians, dancers... I don't 
know any of these people. Admittedly I don't know a huge number of 
people, but my point is just that people who do specialised stuff like 
that are very rare.

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Neeum Zawan wrote:
> 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?
> 

Neither is unambiguous, really. The first one I might read as either
(sin x)^-1 or sin(x^-1). The second I have seen used to represent both
cosecant and arcsin. All depending on which professor was scribbling the
function.

>> 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.
> 

My high school and college professors learned from a different book.
ln(x) was always natural log, while log(x) was either base 10 for the
normal math courses or base 2 for the computer courses. Most of the
time, people were expected to place a subscript noting the base.

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> As far as I can tell, the majority of people in the world have jobs 
> like... Telemarketing. Driving trucks. Working in an office doing filing. 
> Fitting central heating systems. Hotel receptionists.

Yes, the majority of people do a wide variety of jobs :-)

> 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.

I'd say most Chartered Engineers would have used calculus in their job at 
some point or another, there's 180000 of them in the UK.  Call that absurdly 
rare if you want.

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>> As far as I can tell, the majority of people in the world have jobs 
>> like... Telemarketing. Driving trucks. Working in an office doing 
>> filing. Fitting central heating systems. Hotel receptionists.
> 
> Yes, the majority of people do a wide variety of jobs :-)

More precisely: The majority of people are in service jobs. (At least, 
in the UK.) Used to be manufacturing, now it's service.

As far as I can tell, higher math is more relevant to design and 
engineering, which is quite rare.

>> 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.
> 
> I'd say most Chartered Engineers would have used calculus in their job 
> at some point or another, there's 180000 of them in the UK.  Call that 
> absurdly rare if you want.

What's a chartered engineer? And how do you know how many there are?

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> 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.

I guess it depends exactly what you're doing in the real world, but in the 
situations where I've used calculus I've known exactly the function to 
integrate (eg force applied at an exact point during a test).  If I didn't 
know the exact function I wouldn't be able to ask a finite element solver to 
do it either!

> If your colleague can work it out quickly on paper, it shouldn't take long 
> to do it on a computer (Maple, Mathematica, etc).

Sure, but the point is you need to have a good knowledge of calculus to even 
ask Maple of Mathematica to do such things.  If you have never been taught 
calculus at university then good luck trying to solve the problem with a 
computer math tool like Mathematica!

> Just because it's computers doesn't mean it has to be a finite element  or 
> Monte Carlo calculation.

It does for people who don't know calculus.

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On 11/17/09 03:17, Invisible wrote:
>>> 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...

	Yep. What you listed diverges to infinity.

-- 
Be independent! No, not that way! This way!

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On 11/17/09 08:09, scott wrote:
>> If your colleague can work it out quickly on paper, it shouldn't take
>> long to do it on a computer (Maple, Mathematica, etc).
>
> Sure, but the point is you need to have a good knowledge of calculus to
> even ask Maple of Mathematica to do such things. If you have never been
> taught calculus at university then good luck trying to solve the problem
> with a computer math tool like Mathematica!

	Sure, but not that much. I know people who've correctly used computers 
to do this while they thought that the integral of a product is the 
product of the integrals.


-- 
Be independent! No, not that way! This way!

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