Interchangeable?

If you don't know where to post something, put it here and an administrator or moderator will move it to the right place.

Interchangeable?

Postby Blue_X » Sat Jun 09, 2007 8:27 pm

I was playing around with the 4D Building Blocks (still trying to totally figure it out) and I was rotating the perspective (I believe thats the right word to describe it) to see the two different lines (red and blue) to line up to see the building blocks different ways. Now I was wondering since x and y are interchangeable since both could be either (yin yang situation, pretty much) so I was wondering could z and w become interchangeable; however, this program contradicts this as where if you line up x on this game you line up y but if you line up z, you don't line up w and vice versa. So I just wondered if anyone had any clarification to this question?

And I'm sorry if I have any improper analogies and/or theories, but please keep in mind that I'm only in 8th grade and all my teachers this year taught me nothing near these fields of science and mathematics.
The Who Rules!
Blue_X
Mononian
 
Posts: 6
Joined: Fri Jun 30, 2006 2:06 am
Location: 3-D U.S.A.

Re: Interchangeable?

Postby papernuke » Sun Jun 10, 2007 2:26 am

Blue_X wrote:And I'm sorry if I have any improper analogies and/or theories, but please keep in mind that I'm only in 8th grade and all my teachers this year taught me nothing near these fields of science and mathematics.


They teach you physics in 8th grade... but general phys. but about the coordinates things, i dont know

oh and also, im in 6th grade, school ends in 5 days :D
"Civilization is a race between education and catastrophe."
-H.G. Wells
papernuke
Tetronian
 
Posts: 612
Joined: Sat Jul 08, 2006 6:33 pm
Location: California, US of A

Re: Interchangeable?

Postby Blue_X » Sun Jun 10, 2007 3:00 pm

papernuke wrote:
Blue_X wrote:And I'm sorry if I have any improper analogies and/or theories, but please keep in mind that I'm only in 8th grade and all my teachers this year taught me nothing near these fields of science and mathematics.


They teach you physics in 8th grade... but general phys. but about the coordinates things, i dont know

oh and also, im in 6th grade, school ends in 5 days :D


Well for some reason I was supposed to learn some physics this year but my school's trying everything new on my grade, so I learned about earth science...for the third time.

But, yeah, I hope you enjoy the end of 6th grade, my school ended two days ago, and believe me, I was happy to get out of middle school.
The Who Rules!
Blue_X
Mononian
 
Posts: 6
Joined: Fri Jun 30, 2006 2:06 am
Location: 3-D U.S.A.

Postby wendy » Mon Jun 11, 2007 7:37 am

A change of axies, in the style of x -> y, y -> -x corresponds to a rotation of 90 degrees in the xy axies. This applies to all pairs of axies.

One should note that there's nothing special about the axis system: we don't live in a coordinate graph. It's just a convenient overlay for understanding the appropriate dimension: kind of like the map grid.

It is just easier to explain things in terms of cartesian coordinates (eg xyz axis) then it is to non-euclidean coordinates, largely because people have wrangled with graph paper in the past, and are thence more familiar with it.

Unlike three dimensions, the fourth dimension leads to a 'false friend' in the coordinate system. This is the notion that because the three axies in 3d are quite easy to set up common to all viewers, it applies in higher dimensions too: this is not so.

One axis is set by gravity: it appears as up/down. The second axis is partially set by time: front/back. Since we are creatures that move against time, this provides an arrow perpendicular to up/down.

There is nothing to set any further axies. In three dimensions, the across space is a line perpendicular to up and forward, and one can set left/right. In four dimensions, the space perpendicular to up/down (eg z), and front/back (eg y), is not simply x, but two axies (wx).

The effect is to imagine a room as a map of a floor of a 4d room, (ie wxy space), and then suppose that our height is y, and the floor is xy. The issue here then is that there is no special way you can place a clock on the floor based on zy axies, that will make individual clocks align. You can still have clockwise/anticlockwise, but this does not correspond to left/right of 3d.
The dream you dream alone is only a dream
the dream we dream together is reality.
User avatar
wendy
Pentonian
 
Posts: 1832
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Re: Interchangeable?

Postby bo198214 » Mon Jun 11, 2007 10:28 pm

Blue_X wrote:Now I was wondering since x and y are interchangeable since both could be either (yin yang situation, pretty much) so I was wondering could z and w become interchangeable; however, this program contradicts this as where if you line up x on this game you line up y but if you line up z, you don't line up w and vice versa. So I just wondered if anyone had any clarification to this question?


I am still not sure what you mean.
You can not swap x and y (if they point in the same direction) with z and w at the same place, because this would change the orientation of the basis.

If you mean to swap x -> y and y -> -x, i.e. the new x points opposite the original x, then you can do it with unchanged z,w. And you can also swap z,w in that way with unchanged x,y and so forth.

Merely lining up one axis does *not* automatically line up other axes. This depends on how you rotate in 4d.
What exactly did you do?
bo198214
Tetronian
 
Posts: 690
Joined: Tue Dec 06, 2005 11:03 pm
Location: Berlin - Germany


Return to Where Should I Post This?

Who is online

Users browsing this forum: No registered users and 2 guests