And that is my point about imaginary and complex numbers. They are neither "imaginary" nor "complex".

 

first of all, it's important to remember that it is not true to say "imaginary numbers don't actually exist". They do exist, and they make many formulas and functions work. For example, let's take the reactance of electronic components. Let's say an inductor in an LC circuit in this example. You wouldn't be able to find the impedance without 'j'. If you take a vector diagram, you need an imaginary axis for the impedance formula to make sense. You have resistance (R) on the x axis and reactance (Xl) on the imaginary axis. The resulting vector is your impedance. Without the imaginary axis, this would never work. Imaginary numbers do, in fact, exist, and they play a very important role in mathematics, and especially in the electronics field.

In case you didn't understand my description, I've included an illustration below:

Regards,
Der Strom

 

One should not hang too much on the idea of existence. Does anything in math actually exist? Ever see a 5 ( not the numeral, not a set that you might associate with 5, but just the number ) ?

In math if "something" fits in a logical context then it exists. In physics we pay the most attention to ideas that are useful.

Complex numbers are both logical and useful.

 

One should not hang too much on the idea of existence. Does anything in math actually exist? Ever see a 5 ( not the numeral, not a set that you might associate with 5, but just the number ) ?

In math if "something" fits in a logical context then it exists. In physics we pay the most attention to ideas that are useful.

Complex numbers are both logical and useful.

Last time I checked, I had 8 fingers and 2 thumbs.

 

Last time I checked, I had 8 fingers and 2 thumbs.

He did say not as a set of objects...

 

One should not hang too much on the idea of existence. Does anything in math actually exist? Ever see a 5 ( not the numeral, not a set that you might associate with 5, but just the number ) ?

In math if "something" fits in a logical context then it exists. In physics we pay the most attention to ideas that are useful.

Complex numbers are both logical and useful.

The whole point is representation. It is not an object, which is why you cannot see it. You can't see your thoughts, yet people still know they exist. You can, however, see what they represent. 8 fingers. 2 thumbs. The value is representative of the objects, and you know that numbers exist. If you think of "existence" as things you can see.... Actually, I'm going to revert to my inner-nerd, and give you this Matrix quote:

What is real? How do you define real? If you're talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain.

 

He did say not as a set of objects...

What is your opinion on the issue then?

If we are relating to "just" the number 5, then how I see it, it is just the adopted convention for notation depending on the language you speak e.g. English on my half.

Would one who does not speak English be able to interpret the figure of 5?

A group of objects need to be identified as a unique representation we can work with that corresponds to that set with easy manipulation.

Ok, how about we don't use notation, and work purely with tally marks in calculations?

The figure of 5 could be a picture of a cheeseburger for all I care, as long as you know what it relates to, then why does it matter?

 

My opinion? Good question...

I'm not sure. Numbers are represented by various cultures in various ways. Yet they all represent these quantities which may exist within physical or quantities, or may be quite abstract.

Perhaps the problems is the dimension of the way we all look at quantities. We start of at primary school being told that numbers fall along a line, that is 1 dimension. Then we find out about numbers less than zero, effectively introducing the concept of infinitely small. Later on, come imaginary and complex numbers along another 'axis' of sorts.

Is there a 3rd or even 4th 'axis' of numbers?

What are numbers? Could we develop an entire new 'number' system which merges these ideas together? Perhaps.

I'm no expert in maths, that's why I'm rambling a bit.

Yet it is this curiosity of the way these clever bits click together that makes me feel happy when I complete a decent equation.

Such is maths.

 

A question of mathematical philosophy.

Are there many imaginary numbers or is there only one?

I already alluded to this in my previous post.

 

My opinion? Good question...

I'm not sure. Numbers are represented by various cultures in various ways. Yet they all represent these quantities which may exist within physical or quantities, or may be quite abstract.

Perhaps the problems is the dimension of the way we all look at quantities. We start of at primary school being told that numbers fall along a line, that is 1 dimension. Then we find out about numbers less than zero, effectively introducing the concept of infinitely small. Later on, come imaginary and complex numbers along another 'axis' of sorts.

Is there a 3rd or even 4th 'axis' of numbers?

What are numbers? Could we develop an entire new 'number' system which merges these ideas together? Perhaps.

I'm no expert in maths, that's why I'm rambling a bit.

Yet it is this curiosity of the way these clever bits click together that makes me feel happy when I complete a decent equation.

Such is maths.

The only time I've heard of dimensions greater than 3 is Linear Algebra.

I'm counting down the days until I've earned the degree where I will be set free.

This is when you will be put in a position to research anything you choose at any amount of depth you choose. This will be stress free from all the mandatory cumbersome paperwork you had to complete along the way for specific deadline hand-in dates that can make your head feel like a washing machine.

This is how I study:

Book X: Page ONE, tap the back-cover a couple of times when you have finished the book.

Book Y: Page ONE, tap the back-cover a couple of times when you have finished the book.

Book Z: Page ONE, tap the back-cover a couple of times when you have finished the book.

And so on.

There is now a consistency of study. No way can I be like that on my course, except for the summer break.

Conclusion - Only one can answer his own problems that lead to so many opinions.

 

Since you bring up dimensions, you guys may get a kick out of this:

Part 1: http://www.youtube.com/watch?v=JkxieS-6WuA
Part 2: http://www.youtube.com/watch?v=ySBaYMESb8o

 

The only time I've heard of dimensions greater than 3 is Linear Algebra.

I'm counting down the days until I've earned the degree where I will be set free.

This is when you will be put in a position to research anything you choose at any amount of depth you choose. This will be stress free from all the mandatory cumbersome paperwork you had to complete along the way for specific deadline hand-in dates that can make your head feel like a washing machine.

This is how I study:

Book X: Page ONE, tap the back-cover a couple of times when you have finished the book.

Book Y: Page ONE, tap the back-cover a couple of times when you have finished the book.

Book Z: Page ONE, tap the back-cover a couple of times when you have finished the book.

And so on.

There is now a consistency of study. No way can I be like that on my course, except for the summer break.

Conclusion - Only one can answer his own problems that lead to so many opinions.

As HG Wells was so kind to point out, we live in a minimum of 4 dimensions. Without duration, nothing can exist, it is an aspect of time.

Math as we know it is a descriptive language.