Maths

[Amentep]

I always took imaginary to mean the numbers which could not be represented by objects as opposed to non-existant.

In that event, zero is the original imaginary number.

 

Not really, zero can be quite adequately be represented as the absence of the objects used to represent numbers; if you have 5 apples on a table and remove 5 your lack of apples is 0.

 

samm - Physics? Why'd it have to be physics...give me the abstract world of mathmatics any day.

[Humodour]

If imaginary numbers are required to make mathematics work, then surely they are not imaginary.

 

Your mum is imaginary.

[Walsingham]

If imaginary numbers are required to make mathematics work, then surely they are not imaginary.

 

Your mum is imaginary.

 

For real.

 

I was just interested because we seem to have so many eductaed people on teh board. Maths is something I've come to late in life, but with a convert's enthusiasm.

[Humodour]

If imaginary numbers are required to make mathematics work, then surely they are not imaginary.

 

Your mum is imaginary.

 

For real.

 

I was just interested because we seem to have so many eductaed people on teh board. Maths is something I've come to late in life, but with a convert's enthusiasm.

 

Don't give it a second thought. Imaginary (or rather, complex) numbers are basically an easy notation for a type of vector. If there's anything especially deeper to them then I've spent the past 6 years in the dark!

 

Although note e^(i*@) = -1 when @ = pi+2kpi where k is an integer. Specifically e^(i*pi)+1=0.

 

If you'd like to know some nifty ways of dealing with complex numbers, look up De Moivre's formula. You can do a lot with that, as it relates complex numbers, sin, cos, exponentials, arguments, and powers. We primarily used it for things like roots of unity and finding identities for integration.

[Moose]

I'm a maths graduate, I'll give this a try.

 

Basically it's an unfortunate side effect of how maths has evolved from year dot. People didn't sit down and work out a set of axioms wrought through heavy analysis. They simply went with things like 1+1 = 2, etc - analysis came thousands of years later.

 

Hence we have situations like the square root. The square root of a number usually has two roots and both are real numbers. Often in science and physics we need some way of distinguishing between them, for example wave functions.

 

This is where the term 'imaginary' comes in. They are not literally imaginary numbers. It's just a way of getting past the "poor" way mathematics was designed. Note how I used the word usually above - believe me when dealing with logic it gets frustrating seeing that word crop up.

 

Now I'm sure a maths professor would get angry and what I've said here, but it does hold some merit.

 

If you want to look further into it, pick up a book on Mathematical Analysis.

[Moose]

You know reading back what I wrote makes me laugh, technically it's wrong but the general message is right.

[Nightshape]

See that's the kind of maths I like. That and matrices. There's something... fiendish about matrix calculations. Like a shaggy dog story involving actresses.

 

You'd like alot of Neural Network stuff...

Edited March 23, 2009 by Nightshape

[Humodour]

I'm a maths graduate, I'll give this a try.

 

Basically it's an unfortunate side effect of how maths has evolved from year dot. People didn't sit down and work out a set of axioms wrought through heavy analysis. They simply went with things like 1+1 = 2, etc - analysis came thousands of years later.

 

Hence we have situations like the square root. The square root of a number usually has two roots and both are real numbers. Often in science and physics we need some way of distinguishing between them, for example wave functions.

 

This is where the term 'imaginary' comes in. They are not literally imaginary numbers. It's just a way of getting past the "poor" way mathematics was designed. Note how I used the word usually above - believe me when dealing with logic it gets frustrating seeing that word crop up.

 

Now I'm sure a maths professor would get angry and what I've said here, but it does hold some merit.

 

If you want to look further into it, pick up a book on Mathematical Analysis.

 

Id est: People used to think the square roots of negative numbers didn't exist. And thus, when it turned out you could do some useful things if you supposed they did, there was a dilemma. You see, if you were to propose the square roots of negative numbers did exist, people would look at you funny or possibly execute you for heresy, so instead they pretended they existed, as "imaginary" numbers and all was well!

[Azure79]

I remember learning about imaginary and complex numbers when I was highschool in Korea. The only reason I remember is because my math teacher pronounced the word as, 'Comperex'. I thought he meant complex until he wrote down 'Comperex' on the blackboard. I thought it was a special math term until years later when I picked up math again.

 

Still that teacher was good at maths.

[Walsingham]

See that's the kind of maths I like. That and matrices. There's something... fiendish about matrix calculations. Like a shaggy dog story involving actresses.

 

You'd like alot of Neural Network stuff...

 

Actually i hate neural networks. Fething mental stuff. Great in theory, but I find them impossible to understand at the technical level.

[samm]

There's not much detail to understand anymore once they're running

[Walsingham]

Oh I'll use the bastards, with much satisfaction. I just don't understand them. It's rather like the Welsh.

[samm]

Like this?

[taks]

that's a soapbox? man...

 

taks

[Arkan]

What's the deal with those Madelbrot Sets? Am I right?

[Humodour]

What's the deal with those Madelbrot Sets? Am I right?

 

Interestingly, Mandelbrot Sets are related to both neural nets and imaginary numbers, though each for entirely different reasons (complex systems vs complex arguments).