4D - Discussions

[arlov333]

im n engg student[5th sem] nw we r studyn abt complex integrals in math, n me n my ganng here s tryin to make its geometrical interpretation, the riddle is , we hav to think 4D... is ther someone interested to join us n discuss?

[mbeychok]

arlov333:

Would you please be so kind as to rewrite your question in English rather than mobile phone text messaging??

Thanks in advance,

[The_Big_K]

I completely agree. Please refer to our lectures #1-#4. Avoid using slang or sms equivalents of words in posts.

We would like to know more about your discussion on the 4th dimension. Looking forward to your reply,

-The Big K-

[arlov333]

guys.. sorry for the discomfert [ im just a newbie ]
any way , my intension was to get more and more ideas and openions on complex integrals, how it is realated to reality, what its implications are, how can we interpret it physically.. etcetera,
now we are studying about electro magnetics and 4D to realize the truth in complex world. so here im expecting similar thinkers to join the quest.

[arlov333]

no replies?!

[The_Big_K]

This is something that happens when the title of the thread does not give any information about what's being discussed in the thread.

Let's first choose topic - Complex Integrals, Electro Magnetics or 4D.

-The Big K-

[xheavenlyx]

lol, dont scare him off the post biggie

now he even writes etcetera instead of etc, thats torture! Anyway, if anyone knoes what complex integrals are then someone will answer, why dont you time to time give a small description on integrals then complex integrals and slowly we will dive into the problem.

[The_Big_K]

Originally Posted by xheavenlyx

lol, dont scare him off the post biggie

now he even writes etcetera instead of etc, thats torture! Anyway, if anyone knoes what complex integrals are then someone will answer, why dont you time to time give a small description on integrals then complex integrals and slowly we will dive into the problem.

I hope I did not

arlove, mate! I'm not a sadist, believe me! , I personally want to know about 4D. If you can add few points from your discussion with friends, we'll be able to take the discussion further.

-The Big K-

[Jerry]

Count me in.

[arlov333]

Originally Posted by The_Big_K

This is something that happens when the title of the thread does not give any information about what's being discussed in the thread.

Let's first choose topic - Complex Integrals, Electro Magnetics or 4D.

-The Big K-

the big K, thanks for your great concern.
now let me explain a bit about 4D imagination.
4d geometry is a good thinking exercise to try and visualise. Right, imagine a function that takes and returns a real number (ie it exists on the 'normal' number line). You can represent this as a line on a 2d graph, with aeis, say, x and y being at a 90^\circ angle to each other. In this 2 dimensional space, the axes x and y are said to be orthogonal - finding out the x position of a point gives you no information on the y position. You then extend this to three dimensions, we get the x, y and z axes. Again, knowledge of a point in 3D's position on one axis contains no information about the point's position on the other two axes - the three axes are again orthogonal.

Now think of this - you can project a 3D graph onto a 2D graph by taking a slice through at, say, a given Z value. For example, a sphere in 3d with describe either nothing, a circle or a point when projected for a given 'slice' into 2D.

This all works nice and easy because we live in 3D. The conceptual leap comes when you consider 4 orthogonal axes. In a function taking and returning complex values we require 4 values to describe the function's behaviour :

f(z_{1}) = f(a+bi)= z_{2} = c+di

Where z_{1,2} are complex and a, b, c, d are real. These four numbers can represent four orthogonal axis, just as for f(x)=y, x and y represent values on two orthogonal axes.

Try to imagine slices through this 4D space. They will be able to be represented as 3D graphs that you can visualize.