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arlov333
arlov333 • Oct 11, 2007

4D - Discussions

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
mbeychok • Oct 11, 2007
Re: being MATH.

arlov333:

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

Thanks in advance,
Kaustubh Katdare
Kaustubh Katdare • Oct 11, 2007
Re: being MATH.

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
arlov333 • Oct 15, 2007
Re: being MATH.

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
arlov333 • Oct 17, 2007
Re: being MATH.

no replies?!
Kaustubh Katdare
Kaustubh Katdare • Oct 17, 2007
Re: being MATH.

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
xheavenlyx • Oct 17, 2007
Re: being MATH.

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.
Kaustubh Katdare
Kaustubh Katdare • Oct 17, 2007
Re: being MATH.

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
Jerry • Oct 17, 2007
Re: being MATH.

Count me in.
arlov333
arlov333 • Oct 18, 2007
first of all, 4D.

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.
Prasad Ajinkya
Prasad Ajinkya • Oct 18, 2007
arlov, I am trying to visualize this, but to be really really frank. I think its beyond my capabilities to do so, I cant for instance imagine 4 orthogonal axes. The only way to do so would be where the 4D is time, although I am guessing the time-universe thing encapsulates multiple dimensions.


So, an instance of slice in 4D would be a snapshot of the entire world frozen. eh?
crook
crook • Oct 18, 2007
arlov333
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.
agree with everything except the above. Can you explain? I may be too naive to understand the complex stuff, but what happened to the 4th dimension called time 😒 ??
xheavenlyx
xheavenlyx • Oct 18, 2007
we call 4th dimension time because its easy to viz it. Rather than having an abstract 4th dimension...which some mathematicians have a habit of introducing. i saw a video on google about the 10th dimension and how we keeeeep on going about increasing dimensions just as we move from 1st to 2nd to 3rd to blah-th and so on so forth and suddenly they stop on the 10th saying it cant go further or thats where we have worked till. Maybe they like complicated things.

give me one usefulness of the 6th dimension..!?!

Ok, moving on to this topic.

4d can be imagines like this:::

0. 0d is a point.

1. stretch the point and its 1D. (like a line)

2. Parallel the line and connect the ends. 2d with (like a square or rectangle or...)

3. bring in hight. 3D - like a box so : (like a box)

4. bring in time or whatever you can call it.... 4D - The box changes one of its properties in time.... (a box getting shorter by time)

5. 5th dim ?I think is all these properties and dim of an object in a different world altogether. 😀 (like the same box in a parallel universe...😀 😀 )

Well, explaining how you can view each object in a lower dimention by slicing it is kinda difficult to write. Ask someone on college or watch a video on google or youtube 😀

Thanks for all the information though, guys!!

Oh and if you like to see the 10th dimention visually. 😀 here is the link to part one:

https://www.youtube.com/watch?v=JkxieS-6WuA
Kaustubh Katdare
Kaustubh Katdare • Oct 18, 2007
This discussion is to good to be in Chit-Chat Section. Moving the thread to IDEAS|Knowledge Sharing section.
Hey, that youtube link was wicked! I never thought of anything beyond 4D.. and even so, I didnt even understand how we could "draw" 4D in the first place, haha. There was a computer game called 4D Chess.. anyone played it before?
arlov333
arlov333 • Oct 23, 2007
@kidakaka
sorry , i couldnt respond because i was on POOJA holydays..
thanks for trying what i posted, i understand the problem why dont you xheavenlyx-s post. lets take the discussion forward.
@xheavenlyx
i watched the video, that was a pretty good one
@crook
"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."
just imagine a sphere of dia. 'D' imagine it to be passing through a paper.then a set of circles of varying dia. from 0[ie, a point] to a maximum of D will pass through the paper.
is the point clear?
Elisa
Elisa • Oct 24, 2007
arlov333
@kidakaka
sorry , i couldnt respond because i was on POOJA holydays..
thanks for trying what i posted, i understand the problem why dont you xheavenlyx-s post. lets take the discussion forward.
@xheavenlyx
i watched the video, that was a pretty good one
@crook
"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."
just imagine a sphere of dia. 'D' imagine it to be passing through a paper.then a set of circles of varying dia. from 0[ie, a point] to a maximum of D will pass through the paper.
is the point clear?
Its true that the fourth dimension is time. I find it difficult to imagine when people talk about 5th, 6th ... dimension. Can anyone make it very simple to understand?
arlov333
arlov333 • Nov 1, 2007
@elisa
have you seen the video posted above ?
i believe visualising higher dimensions is almost impossible, still we can think about them by folding them down to a 3d space.
u can see a king on th paper,it is tough for him to visualize 3D. now think of a stack of such pictures placed one over the other with a continuous change in the posture of the king,as the king passes through such a pile,he gets older a bit[though such a thing is never told in th comics].he can go back to youth if the process he undergone is reversible.
likewise we pass through the time and so its the 4th D. but there is no path back because of the irriversible processes we undergo..
and for higher dimensions, there is such a thing like folding in or compression of dimensions into smaller one.
better you read it from here
https://aimath.org/E8/e8andphysics.html
arlov333
arlov333 • Nov 2, 2007
do you have anything new?
Krane
Krane • Jan 18, 2008
THE YOU TUBE LINK IS AMAZING..................... it is the secret of time travelling..... @___@......
alexus
alexus • Jan 30, 2008
I really think that it isn't hard to get the idea of viz 4D, but the math? Can somebody explain it 😔
Elisa
Elisa • Feb 2, 2008
alexus
I really think that it isn't hard to get the idea of viz 4D, but the math? Can somebody explain it 😔
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