A little off-topic today
Astronomer, lecturer, author, and voice of science, Carl Sagan
introduced many of us oldsters to the tesseract, a four-dimensional analogue of the cube. YouTube provides a video of that segment from ‘Cosmos; A Personal Voyage’, a PBS television series from 1980. Here (see below) Sagan holds the 3D ‘shadow’ of a hypothetical 4D tesseract. Click to play.
Other producers have provided more recent videos
explaining their visions of the fourth dimension and the tesseract using digital animation (see below).
These presentations are barking up the wrong tree.
The fourth dimension is much simpler and very real. We live it every day.
As everyone already knows,
time is the fourth dimension. Space-time provides both the third dimension and the fourth dimension, otherwise known as ‘reality’.
‘Now’ and ‘then’ is all there is to the fourth dimension. Nothing more.
Any 3D shape in the now moment has already moved at right angles from the then moment ever since the Big Bang — when space-time began. How far apart those moments are… or how far apart those shapes are… or in what direction those shapes have moved… are historical givens. Alternatively these parameters up to you, if you are planning something that changes from moment to moment, as any engineer, animator or puppeteer can tell you.
Shadows on 2D walls and tesseracts
are just fanciful illusions in space-time, over-thinking while overlooking the obvious and very real point. When you see a graph or chart that has an X, Y and Z axis and wonder how the next axis lies at right angles to these three, just flip the page and show a new X, Y and Z axis chart that charts another moment in time. You are not stuck with just one page representing just one moment. Later, you can animate those pages by projecting them at 24 or 30 frames per second, when you have enough ‘moments’ to make your point.
There’s nothing more to the fourth dimension
than ‘now‘ and ‘then‘, except to say, it’s a one way street and there’s no leap-frogging in time or space.
The tesseract turns out to be a model
of all the possible futures of a 3D object in space-time. That 3D object can go in any direction and end up anywhere in space for a second measurement for every new ‘now‘ moment. As it always turns out, all possible futures are reduced to one real ‘now‘ moment, ready for the next ‘now‘ moment to come along while looking back on a long line of ‘then‘ moments.
No need to complicate things
any further. Somehow this easy solution has been traditionally overlooked. This may be a novel hypothesis. If not, please provide the citation so I can promote it as a precedent.