4th dimension

[hrishikeshsukesh]

as x axis is abscissa, y axis is ordinate , z axis is albeit or applicate, what is w axis called as ???

is the 4th dimension time or trength ???

as i j k are considered as unit vectors corresponding to x y z axis, which unit vector corresponds to w or t axis ???

[wendy]

One really can't necessarily suppose that because we can isolate three right axies in three dimensions, then that always applies.

Consider this. We have gravity (height), and motion (forward). This leaves us a single dimension of 'across' space. We divide this into 'left' and 'right'. While few people confuse up from down, or forwards from backwards, there are lots of people who struggle to connect left from right.

In four dimensions, we subtract height and forward from the four dimensions, and we are left with a 2d across space, which means that we no longer can suppose that 'turn left' or even 'turn to 5 oclock' is going to mean anything, because there is no alignment of the circles. In 3d terms, it's like laying out clocks on the floor. There is no reason to point the twelves to the same direction, and when one has the twelves pointing at different places, how is the '5-oclock' going to make sense? All one gets is that 'clockwise' still works, and that's that.

And just as we have intensities of left / right, because our across-space is 1d, in 4d, one has intensities of '5-oclock', because the circle of the clock is as much a perimeter of across-spaces as the left-right points are in 3d.

[gonegahgah]

I like this concise explanation you have provided for this Wendy. Expands it very nicely...