Dimensions

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Loard Z

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Re: Dimensions
« Reply #30 on: November 20, 2007, 05:02:06 PM »
me and a  friend used to play 4d noughts & crosses.

I dunno if I could wrap my head around it now
if i remember, austria is an old, dis-used name for what is now Germany.
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ﮎingulaЯiτy

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Re: Dimensions
« Reply #31 on: November 20, 2007, 05:03:58 PM »
I can't say I'm fimiliar with that game.  :)
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Loard Z

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Re: Dimensions
« Reply #32 on: November 20, 2007, 05:07:15 PM »
basically it's like 2-d noughts and crosses, but in 4-d. meaning you have a 4d cube splite into 9 on each side. and you can get 3 in a row across any diagonal.

We started with 3d x's and o's, and built our way up from there.

It was in a Mensa book I was given.
if i remember, austria is an old, dis-used name for what is now Germany.
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ﮎingulaЯiτy

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Re: Dimensions
« Reply #33 on: November 20, 2007, 05:16:51 PM »
Ooo, I get it. But the problem was I never heard it called that. I thought it was called "tic-tac-toe".
If I was asked to imagine a perfect deity, I would never invent one that suffers from a multiple personality disorder. Christians get points for originality there.

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Loard Z

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Re: Dimensions
« Reply #34 on: November 20, 2007, 05:21:03 PM »
oh well. Regional dialects, and the like.
if i remember, austria is an old, dis-used name for what is now Germany.
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Genmotty

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Re: Dimensions
« Reply #35 on: November 21, 2007, 10:41:58 AM »
Hmm dimensions.

Technically all shape dimensions are graphical representations of a surrounding world. Hence time is a dimension so is probability and so is all manner of other observations. However we must also step out of Euclidian geometry to consider high order dimensions.

D0
Non existence, your page is blank, nothing not even concepts.

D1
The point, the point itself signifies existence in its most basic form. A point is both everywhere and nowhere at once it cannot move in space or time or even probability technically D1 is not even an entity it is a concept.

A concept of existence, if you think ‘chair’ that is an example of a D1 object.

D2
The line, called the first spatial dimension it is a concept that is able to evolve, that is you may take a point and change it. Think about it this way, take your D1 point and let it exist in time. Now you have a line.

D3
The axis, called the second spatial dimension. Take your point existing in time and allow it to move left and right only. Now you have the third dimension you can change a concepts physical location.

In more real terms this is the idea of a chair being made in someone’s head. The change from tree, to plank, to chair. Not only does the chair exist as an idea that idea can change.

D4
The cube/The tetrahedron, take the idea of the chair changing through time and make it a ‘2D’ animation on paper.

This is the normal way we humans think because we are a high order dimensional beings. Even those ideas you had before about the concept of the chair, when I wrote that you probably pictured that chair in your head. That was a D4 entity because it existed in knowledge, then it existed in time (hence you could think about it), then you pictured it in a steady state (unchanging) then you ‘flattened’ it, although really you started applying higher order dimensions to it.

D5
The Pyramid, take that animation in your head and make it have depth. This is now a ‘visualised’ entity. We theoretical physicists think that this is the last conceptual dimension because now we taken these ‘ideas’ and start to place them upon higher order dimensions.

D6
The Cubic, this is taking a set of XYZ axis and projecting them as a point in space. That is an entity can exist, there. I repeat an entity can exist there.

On your blank page you have visualise your chair upon it now you begin to put pen to paper and create, “There.” In essence you have taken an entity and applied value.

In algebraic terms you have stated a=1 it is a one-to-many relationship. If you are confused then think of it as you have taken an idea and you have said I want to make it ‘real’.

D7
Appling D6, that is you actually begin to draw your chair (time)

D8
Appling D7 and D6 you draw a line

D9
Appling D8, D7 and D6 you draw a line with width

D10
Appling D9, D8, D7 and D6 you have your chair in front of you

D11
Because you can physically touch your chair and have it exist for any length of time rather than it being there then flicking out of existence. You have a chair. This is the dimension we live in.

Now for any string theorists you already know the mathematical prove that derives us to this position. For the others string theory predicts 11 dimensions minimum.

D11 is actually a probability dimension its like taking that concept of a chair and applying it to everything that makes up the concept of a chair.

Holding all possible flavours of a chair together at one time, not the chair changing but the concept of what a chair is or what it could be under slightly different conditions before we even begin to picture it.

Thinking carefully to can realise you putting pen to paper is part of the D11 the fact that you choose or made it come to be that it occurred.

You could think about it as the concept of a creation. Even if  (being a determinist) you fate is preset.

Thus we don’t exist in D12 because that would be owning a time machine, going back to change fate paradoxically. However you would die if you killed you own father, but because you can hold multiple probabilities of fate in your hand you would be living all of them at the same time and so would live and die into an infinity of fates.

Any more than that we can only speculate on.

The tesseract is a graphical representation of D2 technically it is the abstract concept of  the donut.



I think Trekky is pre-occupied with looking at graphical/mathematical representations of dimension rather than physical observable dimension.
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Gabe

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Re: Dimensions
« Reply #36 on: November 21, 2007, 01:15:48 PM »
tl;dr
Quote from: Tom Bishop
There is no evidence for an infinite Earth.
Quote from: Tom Bishop
The Earth is infinite.
Warning, you have just lowered your IQ by reading my sig.

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Emporer DAT

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Re: Dimensions
« Reply #37 on: November 21, 2007, 05:54:08 PM »
...Thinking carefully to can realise you putting pen to paper is part of the D11 the fact that you choose or made it come to be that it occurred.

You could think about it as the concept of a creation. Even if  (being a determinist) you fate is preset.

Thus we don’t exist in D12 because that would be owning a time machine, going back to change fate paradoxically. However you would die if you killed you own father, but because you can hold multiple probabilities of fate in your hand you would be living all of them at the same time and so would live and die into an infinity of fates...

Someone set you up the bomb?

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Chris Spaghetti

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Re: Dimensions
« Reply #38 on: November 22, 2007, 01:27:08 AM »


I love the 24-cell or octoplex.

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Pope Zera

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Re: Dimensions
« Reply #39 on: November 22, 2007, 01:55:12 AM »
Holicrap?   :o

Re: Dimensions
« Reply #40 on: November 22, 2007, 03:45:22 PM »
How would you go about making something like that?

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Loard Z

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Re: Dimensions
« Reply #41 on: November 22, 2007, 05:10:45 PM »
basically, you can't.
if i remember, austria is an old, dis-used name for what is now Germany.
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Re: Dimensions
« Reply #42 on: November 22, 2007, 07:01:50 PM »
Well someone did so there must be something you need to know to be able to know what to make.

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Loard Z

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Re: Dimensions
« Reply #43 on: November 22, 2007, 07:10:25 PM »
you can make it on a 3d modeling program. But in real life, no. You'd need a substance able to fold through itself to do it.
if i remember, austria is an old, dis-used name for what is now Germany.
See My Greatness

Re: Dimensions
« Reply #44 on: November 22, 2007, 07:19:49 PM »
I'm talking about how do you know what to make.  How do you know at all what it would look like in 4d?

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Loard Z

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Re: Dimensions
« Reply #45 on: November 22, 2007, 07:21:44 PM »
basically, you take a 3d cube. and draw a line at right angles to all of the points on it, and that's what you'd get. Obviouusly even in a 3d representation, the lines wouldn't actually be at right angles, but theoretically they are.
if i remember, austria is an old, dis-used name for what is now Germany.
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Username

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Re: Dimensions
« Reply #46 on: November 25, 2007, 12:49:58 AM »
This is not accurate at all, but an interesting animation I thought noteworthy of mentioning here:
http://www.tenthdimension.com/medialinks.php
« Last Edit: November 25, 2007, 12:58:59 AM by Username »
So long and thanks for all the fish

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ﮎingulaЯiτy

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Re: Dimensions
« Reply #47 on: December 02, 2007, 05:42:22 PM »
Well someone did so there must be something you need to know to be able to know what to make.

I asked my brother (the creator of those pictures) to stop in and explain it. Hopefully that will be soon seeing as how he has his own agenda and doesn't participate on this site.
If I was asked to imagine a perfect deity, I would never invent one that suffers from a multiple personality disorder. Christians get points for originality there.

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JasonHise

Re: Dimensions
« Reply #48 on: December 02, 2007, 06:28:13 PM »
Alright, some brief notes on the construction of a rotating 4D object.

In 3D, vertices are represented by a 3 component coordinate set (x, y, and z).  A unit cube has 8 such vertices, and centered at the origin and aligned with the coordinate space the vertices would appear at all combinations of x = +/-0.5, y = +/-0.5, and z = +/-0.5.

In 4D, all vertices have 4 components (x, y, z, w).  For a unit cube in 4D, there would be 16 such vertices, with x = +/-0.5, y = +/-0.5, z = +/-0.5, and w = +/-0.5.  For other more complex shapes, a fair amount of geometry and trig might be required to figure out what the values of these coordinates are.

To map 3D images to a 2D plane, we project them:  objects with a larger distance from the viewer (greater value for the z component) are drawn smaller because they are farther away.  A very simple projection from 3D to 2D is to make the new 2D point equal to (x/z, y/z).  Granted, for this to work the object needs to be moved in front of the viewer first... using values of z <= zero would cause problems.

To map 4D images to a 3D space we do something similar... points farther away along the w axis are scaled down to appear smaller.  Like 3D to 2D, the most simple way to do this mapping is to choose a new 3D point based on (x/w, y/w, z/w), after the object has been translated far enough away from the camera that all values of w are positive.

Now all that is left is to rotate the object in 4D space over time.  A more interesting rotation is accomplished by making sure that the w component is one of those influenced by the rotation... otherwise it will just look like a static 3D object rotating in 3D space.  The rotation can be accomplished using some simple trigonometry:

current w = cos(angle) * original w + sin(angle) * original z
current z = cos(angle) * original z - sin(angle) * original w

This will result in a simple rotation through the x/y plane (a plane is an axis in 4D, because points that lie on it are not influenced by the rotation).

Now you have all the tools you need to make your own rotating 4D objects (except maybe access to Maya and an understanding of MEL scripting) ;)

Re: Dimensions
« Reply #49 on: December 02, 2007, 07:04:06 PM »
That has to be the best post on these forums.

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Trekky0623

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Re: Dimensions
« Reply #50 on: December 02, 2007, 08:07:11 PM »
It's definitely the most interesting.

Welcome Jason!

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Loard Z

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Re: Dimensions
« Reply #51 on: December 03, 2007, 04:53:11 AM »
meh - I knew all of that anyway. I'm just too lazy to write about it. I'd rather just 1 line.
if i remember, austria is an old, dis-used name for what is now Germany.
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Parsifal

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Re: Dimensions
« Reply #52 on: June 28, 2009, 03:56:13 AM »
Physically speaking, without Einsteinium Dimensions, nor String Theory, there are only 3 dimensions: height, depth, width. Perhaps 4 if you wish to include mass.

How the hell is mass a dimension?
I'm going to side with the white supremacists.

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cmdshft

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Re: Dimensions
« Reply #53 on: June 28, 2009, 09:04:19 PM »
Physically speaking, without Einsteinium Dimensions, nor String Theory, there are only 3 dimensions: height, depth, width. Perhaps 4 if you wish to include mass.

How the hell is mass a dimension?

Because it's quantifiable and not a concept such as time?

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Parsifal

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Re: Dimensions
« Reply #54 on: June 28, 2009, 09:10:13 PM »
Because it's quantifiable and not a concept such as time?

Not a concept? Please, enlighten me as to what exactly gives objects their mass.
I'm going to side with the white supremacists.

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cmdshft

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Re: Dimensions
« Reply #55 on: June 28, 2009, 09:11:50 PM »
Because it's quantifiable and not a concept such as time?

Not a concept? Please, enlighten me as to what exactly gives objects their mass.

No, figure it out on your own.

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Parsifal

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Re: Dimensions
« Reply #56 on: June 28, 2009, 09:22:46 PM »
No, figure it out on your own.

So you can't justify why mass is a dimension. Got it.
I'm going to side with the white supremacists.

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cmdshft

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Re: Dimensions
« Reply #57 on: June 28, 2009, 09:34:11 PM »
No, figure it out on your own.

So you can't justify why mass is a dimension. Got it.

I didn't say that. Don't you love assuming things?

It's called I am a lazy smart person. I don't do work for others. Well, not for pedantics like you, anyway.

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Parsifal

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Re: Dimensions
« Reply #58 on: June 28, 2009, 09:40:16 PM »
I didn't say that. Don't you love assuming things?

It's called I am a lazy smart person. I don't do work for others. Well, not for pedantics like you, anyway.

Not bothering to explain yourself correctly only leads me to the conclusion that you cannot.
I'm going to side with the white supremacists.

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cmdshft

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Re: Dimensions
« Reply #59 on: June 28, 2009, 09:42:11 PM »
Well, you're wrong. Just because I don't want to doesn't mean I can't.