amanset
August 16, 2011, 12:47pm
21
Grapefruit:
I did see that, thank you. But it didn’t really capture what I wanted to know specifically about “the” fourth dimension. I did watch the video linked though… still a little confused.
Thanks for this. It doesn’t allow me to visualize a fourth dimension, but does explain why my 3D brain can’t see it.
And Chronos, thanks for trying, but that a little too technical and had a little too much math in it. Kudos to you for actually understanding this stuff, though!
The way I was told to visualise the Klein Bottle when I was at university is a bit of a cheat, but conceptually it works. We are used to seeing projections of 3D images into 2D space. Good examples are our computer screens, televisions and paintings. Due to a variety of things, especially when moving, we can get an idea of depth. A fourth dimension would be perpendicular to that 2D plane (that is showing a projection of a 3D image).
I’m probably awful at explaining it, but with a little bit of contemplating it is reasonably easy to get your head around.
You’re on your own with a fifth dimension.
gallan:
Here’s the way it was explained to me. I don’t know if it’s right or not, but it makes sense.
Think of a cube. That cube has three dimensions: length, width, and height. If we took away it’s height, the cube would cease to exist and it would just be a plane. If we took away it’s width, the plane would cease to exist and it would just be a line.
But what if we took away it’s time? Time ends and what are we left with? Nothing. The line only exists because it has a variable called time.
That’s how it’s explained in HG Wells’ 1895 novel, The Time Machine :
‘I do not mean to ask you to accept anything without reasonable ground for it. You will soon admit as much as I need from you. You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions.’
‘That is all right,’ said the Psychologist.
‘Nor, having only length, breadth, and thickness, can a cube have a real existence.’
‘There I object,’ said Filby. ‘Of course a solid body may exist. All real things—’
‘So most people think. But wait a moment. Can an instantaneous cube exist?’
‘Don’t follow you,’ said Filby.
‘Can a cube that does not last for any time at all, have a real existence?’
Filby became pensive. ‘Clearly,’ the Time Traveller proceeded, ‘any real body must have extension in four directions: it must have Length, Breadth, Thickness, and—Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.’
He goes further but, despite lack of copyright, there’s probably a limit to how much text I should paste.