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Imaginary Numbers

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posted on Jun, 14 2013 @ 12:51 PM
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reply to post by kwakakev
 


although your suggestion has come under fire from the OP, it actually makes a bit of sense.

the reason that imaginary units are used in quantum mechanics and electrodynamics is that it superimposes these sign changes over the same quadrants of the plane (aka superposition). the increasing exponent, then, represents a phase change (sign change) as consecutive rotations of the vector. this is similar to the activity you have described.




posted on Jun, 14 2013 @ 12:51 PM
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reply to post by tgidkp
 



so, rather than read and absorb information from someone who has a firm grasp on your proposal

I don't have the time or energy to spend learning something which seems so absurdly complex. I believe the simplest solution is always the best solution. More often than not when a system is so theoretical and abstract it's not the simplest way to understand or solve a problem. It does seem interesting I admit, but even if I had the motivation to learn about it I'd still have trouble understanding it. And when something is so complex that I can't easily learn it in a short amount of time I tend to not waste my time learning it because a simpler answer most likely exists.
edit on 14/6/2013 by ChaoticOrder because: (no reason given)



posted on Jun, 14 2013 @ 01:00 PM
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reply to post by tgidkp
 



the increasing exponent, then, represents a phase change (sign change) as consecutive rotations of the vector. this is similar to the activity you have described.

It's similar because you are talking about 2D vectors on a complex plane and complex numbers are made up of a real part and an imaginary part which both behave very differently. The difference between real and imaginary numbers is very similar in nature to the difference between negative and positive numbers.
edit on 14/6/2013 by ChaoticOrder because: (no reason given)



posted on Jun, 14 2013 @ 01:27 PM
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the neg /pos reals comparison is intended as a justification of ...

it is in no way at all a suggestion of some commonality between the two systems.

if you cannot understand why segregating the real and imaginary components of a complex number is purposeless, then you have not understood the fundamental reason for having an imaginary unit.

squaring (and rooting) a number (even a real) is INHERENTLY geometric and/or dimensional. no if and or but.

if you wish to combine a real and imaginary number, you must solve for the modulus or take the dot-product. this is because both of these numbers retain a geometric interpretation.

unless you have some geometric interpretation for your proposed manipulations, there can be no use for it.



posted on Jun, 14 2013 @ 01:39 PM
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Lets bring this a little deeper....ALL NUMBER were created by mankind, a simple way for humans to try and explain the unexplainable....What is # 1 ??? I mean.....we have fractions, right ??? Or decimals ?? So if one take the concept of decimals and starts counting from 0.00000000000000~ ( To infinity ) Where is it "acceptable" to introduce a # 1 so that the fraction is compilable ???

If the #1 doesn't even exist.....What is all the rest of it about ???



posted on Jun, 14 2013 @ 11:49 PM
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There is a hilarious amount of misunderstanding in this thread. Do they not even try to teach about complex numbers in high school algebra anymore? There is nothing difficult or mysterious about them, and they have plenty of very concrete real-life applications, as well as more abstract ones. (The reasons why we use them in complicated things like Quantum Mechanics doesn't make them mysterious, or poorly understood, or not real--it just demonstrates that they are useful even for complicated things.)

There are two ways to think about complex numbers: algebraically, and geometrically. Geometrically, they are very easy to understand. A complex number
z = x + y i
is just a point in the plane at (x, y)
endowed with an extra relationship that lets us multiply points together:
w = a + b i
z * w = (x + y i)(a + b i) = x*a + x*b i + y*a i - y*b = (x*a - y*b) + (x*b + y*a) i
which is the point
(x,y)*(a,b) = (x*a - y*b, x*b + y*a)

Let's pick a simple example to understand this.
Assume y = 0 and a = 0, and b = 1. So we have:
z = x (a purely real number), which is the point (x, 0)
w = i (a purely imaginary number), which is the point (0, 1)
Then, z*w = x i, which is the point (0, x)
In other words, (x, 0)*(0,1) = (0, x).
If instead we had used the point (0, b) instead of (0, 1) we would have:
(x, 0)*(0, b) = (0, b*x).
Multiplying an imaginary number by a real number rotates its corresponding point by 90 degrees counterclockwise (clockwise if b



posted on Jun, 15 2013 @ 12:39 AM
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reply to post by Moduli
 



Geometrically, they are very easy to understand. A complex number

Well done on being the 5 millionth person in this thread to say exactly what you just said.

Wow your intelligence is really awe inspiring... you have convinced me.

edit on 15/6/2013 by ChaoticOrder because: (no reason given)



posted on Jun, 15 2013 @ 12:44 AM
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Originally posted by ChaoticOrder
reply to post by Moduli
 



Geometrically, they are very easy to understand. A complex number

Well done on being the 5 millionth person in this thread to say exactly what you just said.

Wow your intelligence is really awe inspiring... you have convinced me.

edit on 15/6/2013 by ChaoticOrder because: (no reason given)


Considering that the most recent several posts you've made show a complete misunderstanding of those five-million-and-one explanations, maybe you should spend more time understanding them and less time criticizing people explaining them to you.



posted on Jun, 15 2013 @ 12:49 AM
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reply to post by tgidkp
 



if you cannot understand why segregating the real and imaginary components of a complex number is purposeless, then you have not understood the fundamental reason for having an imaginary unit.

The reason for having an imaginary unit? In your mind it was invented just so we could have complex numbers right? Actually complex numbers are derived from the invention of imaginary numbers and you can do algebra with imaginary numbers without even knowing what a complex number is.


if you wish to combine a real and imaginary number, you must solve for the modulus or take the dot-product. this is because both of these numbers retain a geometric interpretation.

Oh please can you explain to me how to take the dot product of a real with an imaginary number? The dot-product operation is for math with vectors such as complex numbers... real numbers and imaginary numbers by themselves are not vectors with multiple components and you cannot use the same math on them without combining them into a complex number.
edit on 15/6/2013 by ChaoticOrder because: (no reason given)



posted on Jun, 15 2013 @ 01:04 AM
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Why stop at imaginary numbers? Why not look at quaternions, biquaternions and clifford numbers?
They turn out to be very useful in physics and engineering. Rotations in 3 and 4 space and even Lorenz transformations are readily described by quaternions. Imaginary numbers have deep geometric meaning.

It's not surprising since exp(j * theta) describes a circle of radius 1. Einsteins theory of relativity forces the time component to have a negative "signature", meaning simultaneous events are only defined on hyperbolas of the form x^2 + y^2 + z^2 - t^2 = tau^2 (in the appropriate physical units).

That kind of forces you to look at 4 vectors of the form (x,y, z, it), since it's "norm" will give you the negative signature of time. So actually the imaginary numbers are fundamental in the very equations that describe the universe.



posted on Jun, 15 2013 @ 01:11 AM
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Originally posted by SevenThunders
Why stop at imaginary numbers? Why not look at quaternions, biquaternions and clifford numbers?
They turn out to be very useful in physics and engineering. Rotations in 3 and 4 space and even Lorenz transformations are readily described by quaternions. Imaginary numbers have deep geometric meaning.


Actually, quaternions (and so on) are not so useful in physics. They do not have the correct algebraic (or analytic) structure to be useful, despite many claims on the internet you see to the contrary. Quaternions can be used to describe rigid rotations and, if you're careful to use the right relations, some dynamics (but they cannot generally describe all of Newtonain mechanics correctly).

It turns out the things that do have the correct structure for special relativity, general relativity, quantum field theory, string theory, etc, are various types of tensors and differential forms.



posted on Jun, 15 2013 @ 01:38 AM
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reply to post by SevenThunders
 



Why stop at imaginary numbers? Why not look at quaternions, biquaternions and clifford numbers?

What you mean to say is why stop at complex numbers... there is a difference. Imaginary numbers are different from all those types of numbers and this thread is about imaginary numbers, not highly complex vectors with multiple components (except for complex numbers obviously). In reality you could keep on going forever and create a number with as many dimensions as you want. It's a redundant and useless exercise beyond the first few dimensions.
edit on 15/6/2013 by ChaoticOrder because: (no reason given)



posted on Jun, 15 2013 @ 01:53 AM
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Surprised anyone hasn't mentioned the Mandelbrot set yet or at least I have missed it?




posted on Jun, 15 2013 @ 02:27 AM
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reply to post by ChaoticOrder
 


Mandelbrot Set is connected.

Being a nerd... imaginary numbers is "real" in our universe.

Read a little about fractal universe.... en.wikipedia.org...



posted on Jun, 15 2013 @ 02:34 AM
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reply to post by ChaoticOrder
 


I am deaf so I can't understand him in the video but I do generally understand.

Maybe or maybe not that the "imaginary numbers" have basis in reality and the universe... and yet they describe them perfectly.




posted on Jun, 15 2013 @ 05:14 AM
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reply to post by ChaoticOrder
 


The existence of negative square roots appears to make logical sense, but for how they are derived has left a hole in the mathematical framework and some complications with how they relate to a real number system. To compensate all the signs are reversed on the directly related operations, we kind of operate in a mirror reflection of the calculation plane so √-1 does exist, but at the cost of making √1 unreachable in this imaginary plane. This method does provide the mathematicians enough of a grasp to work through the calculations, but does overly complicate continued research and development.

As for a more logical explanation of my previous post. Lets start with the basics, what is a square?

x^2 = x * x

In calculating this value we can map one x along the x axis and the other x along the y axis. To put it in context lets measure our square table top surface area. We pull our our ruler and it measures 2 meters by 2 meters, or 2 meters squared = 4 square meters.

What I am proposing is when √-1 pops up, our ruler went into negative numbers when measuring one side of the table. Since the error with the sign did not get pick up here it propagates further down the calculation and requires the imaginary number framework to reestablish proper order.

I am not sure how wide and far imaginary numbers are used in a well tested, proven and real applications, there maybe some similarities between all these cases, but also some differences.
edit on 15-6-2013 by kwakakev because: grammer

edit on 15-6-2013 by kwakakev because: spelling



posted on Jun, 15 2013 @ 05:45 AM
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reply to post by kwakakev
 



To compensate all the signs are reversed on the directly related operations, we kind of operate in a mirror reflection of the calculation plane so √-1 does exist, but at the cost of making √1 unreachable in this imaginary plane.

Well of course, the only place where the real and imaginary number lines intersect is at 0.


What I am proposing is when √-1 pops up, our ruler went into negative numbers when measuring one side of the table.

I can see what you agree trying to say but it still doesn't make sense because if one side is a negative measurement than the other must be in order for it to be a square. You can essentially think of it as a positive being multiplied with a negative because it's the same behavior. However it cannot be described or defined algebraically in that way.



posted on Jun, 15 2013 @ 06:00 AM
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reply to post by tgidkp
 


Quantum spin was one thing I was thinking about when proposing a half charge, but not really sure how it all plugs together. When going down this way I do not expect a few distinct values, but an infinite amount between -1 and 1 that cycle around in a circle. Depending on the application there may even be a need for a more linear charge from -ve infinity to +ve infinity. I am not sure how all the maths will work out as a distinct charge is replaced by a number, but if it helps keep all the calculations on the same plane then this is good.



posted on Jun, 15 2013 @ 06:19 AM
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reply to post by Deaf Alien
 



Mandelbrot Set is connected.

I actually wasn't even aware of that, I've never really looked into how the Mandelbrot Set works. That is pretty fascinating stuff I must admit. I'm reading more into the details of it now, thanks for mentioning it.



posted on Jun, 15 2013 @ 06:53 AM
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reply to post by ChaoticOrder
 


I am just trying to provide some other options to the √-1 dilemma. Without fully understanding the specific function and the role √-1 has I am not in a position to say what is right or wrong. But where we establish the 0 plane can make a difference. What if we are measuring one side of a hole in the ground with the 0 plane set at ground level? Our width of the hole is 2 meters as our height is -2 meters. The surface area of the side of the hole is still 4 meters and can accurately be expressed as 2^2, but the way our components for the square have come together has some problems.

√-1 is the start of all the problems in this thread, this has my attention as for why.



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