On 16-11-2009 18:00, Bill Pragnell wrote:
> Invisible <voi### [at] devnull> wrote:
>> 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...
> 
> IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> But, as you say, depends what the local conventions are.
> 
>> Hell, I've seen formulas where pi does *not* refer to the well-known
>> transcendental number!
> 
> Now that's just careless.

Not really, if you have a scheme where s->sigma t->tau then p->pi.

The one I remember (though I forgot the exact formula) is for the energy 
per particle in an electric field. Energy is 'E', per particle it is 'e' 
the expression contained an exponential function that depended on the 
charge of an electron.

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>> 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...
> 
> IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> But, as you say, depends what the local conventions are.

Some people use log to mean base-10. Some use it to mean an unspecified 
base. But (arguably) *most* geniune maths sources use it to mean the 
natural logarithm.

>> Hell, I've seen formulas where pi does *not* refer to the well-known
>> transcendental number!
> 
> Now that's just careless.

It's a standard convention.

http://en.wikipedia.org/wiki/Prime-counting_function

-- 
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>> If you can't add, you're going to have a bit of a problem doing your 
>> weekly shopping, but there's not much need for higher math unless 
>> you're working in some specialist industry somewhere.
> 
> 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. Ditto for an 
> electrical engineer who designed the power supply for your computer.

I'm going to go out on a limb and say that the number of people who 
actually do that kind of things are a tiny minority.

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.

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 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?

Exactly.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Orchid XP v8 <voi### [at] devnull> wrote:
> >> 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...
> >
> > IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> > But, as you say, depends what the local conventions are.
>
> Some people use log to mean base-10. Some use it to mean an unspecified
> base. But (arguably) *most* geniune maths sources use it to mean the
> natural logarithm.

Just looked at wikipedia - it seems you can tell a person's primary field by the
base they expect log x to be in!

http://en.wikipedia.org/wiki/Logarithm#Notations_of_bases_and_implicit_bases

> It's a standard convention.
>
> http://en.wikipedia.org/wiki/Prime-counting_function

I did not know that :-)

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>> Some people use log to mean base-10. Some use it to mean an unspecified
>> base. But (arguably) *most* geniune maths sources use it to mean the
>> natural logarithm.
> 
> Just looked at wikipedia - it seems you can tell a person's primary field by the
> base they expect log x to be in!
> 
> http://en.wikipedia.org/wiki/Logarithm#Notations_of_bases_and_implicit_bases

Crazy stuff, eh?

>> It's a standard convention.
>>
>> http://en.wikipedia.org/wiki/Prime-counting_function
> 
> I did not know that :-)

I'm going to go out on a limb and guess that the people working on 
number theory and investigating the properties of prime numbers didn't 
need to know about the circumference of a circle. ;-)

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.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 16-11-2009 22:22, Orchid XP v8 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.

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On 16-11-2009 21:40, Orchid XP v8 wrote:
>>> If you can't add, you're going to have a bit of a problem doing your 
>>> weekly shopping, but there's not much need for higher math unless 
>>> you're working in some specialist industry somewhere.
>>
>> 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. Ditto for an 
>> electrical engineer who designed the power supply for your computer.
> 
> I'm going to go out on a limb and say that the number of people who 
> actually do that kind of things are a tiny minority.
> 
> 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.

But for those who do there is a window in their development during which 
they are most capable of learning maths. So you try to teach them in 
that period. Besides it is part of our culture. OTOH I know there are 
those cultural barbarians that think that it is cool not to know maths, 
like politicians and most other public figures.

> 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 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.

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Invisible wrote:
> Fredrik Eriksson wrote:
> 
>> Basic high-school level math. I am slightly surprised that you did not 
>> know it,
> 
> What, you mean given that I've never been tought mathematics?

Don't feel bad; my math skills aren't too great either. I just found 
this link: http://math.com/

Evidently you can work your way up from basic skills to more advanced 
topics. I plan to do so, hopefully achieving the ability to decipher 
many of the incomprehensible formulae found at wolfram.com.

Sam

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On 11/16/09 10:12, Darren New wrote:
> Which just goes to show the problem I have with 90% of all matehmatical
> notation. It's so utterly inconsistent that even something like
> (f(f(x))) is ambiguous.

	I'm not a mathematician. But I took enough courses that I almost 
qualified for an MS in Math (which may well be a BSc in some European 
countries, but never mind...).

	I can sympathize with them. There simply aren't enough symbols floating 
around to accommodate all possible uses. Heck, it's painful enough when 
you're typing to be able to type all the standard symbols.

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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. Similarly with
>
> lg^2 X vs lg X^2

	Actually, the 2 means the same thing. In both cases, you're squaring. 
You're just squaring different quantities.


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

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