It came up on another part of boards but i thought i would share my post.
Think of it this way a cube in 4d becomes a tesseract.
Its an abstract concept but one that is central to philosophy maths and physics.
4D adds time to space.
P.D Ouspensky was a russian philosopher he wrote a book called , Tertium organum.
If you are a philosophy student and your memory needs jogging Ouspensky is the guy that negated Aristotle's formula for A is A (Aristotle's law of Non contradiction) ie A is A and also not A Amagnitude can be greater or less than itself.Its the same guy. As in a negative number is itself and the absolute value of a negative number it's opposite. So -11 has a value of - 11 and an absolute value of 11.
Ouspensky put this mathematical formula forth as a negation of Aristotle's law.
Ouspensky understood these things were abstracts but Ouspensky kind of thought things like this were hard to imagine them referring to our world. Yet mathematically they are true.
I think he came up with the idea of a hypercube which was a precursor to the tesseract. But he only described it. But as far as i know he was the first to describe the concept. I mean he was the first to relate the hyper cube to a 4d cube and describe it.
Then this guy Claude Bragdon who was an architect who designed the hypercube. He then made so much money he felt he had to track P.D Ouspensky down to pay him some of the money he got.
Einstein had already come up with spacetime ..fusing time to the 3 dimensions of our dimension. But its not really asking what this might be conceptualized as for normal people. What would a cube seem like to a fourth dimensional being?
There was an article in scientific american in 1939 (many years after) called 'visualizing Hyperspace'. It brought it to the forefront again.
It is just a concept though a concept that is useful in maths and philosophy (logic). But Einsteins theory of relativity and spacetime seemed to point towards it as not just a concept but as a reality.
The hypercube became the tesseract as a model of what a cube would be in a fourth dimension of course only visualized in our third dimension.
It gets all quantum mechanicy now...
Then scientists began to visualize OTHER fourth dimensional phenomena in our third dimension.
It gets REALLY interesting when you start to thing about electrons passing through a fourth dimension conceptually.
Scientists found away to measure the effects of a 4th dimension on materials like 2d electrons. It didn't show a 4th dimension however.
Philosophers (usually logicians) mathematicians etc like to consider it as a concept useful to learn new things.
As far as i know ....Einstein is the only one to have really put his rep on the line and say I predict they will find one. Its clear that einstein could certainly THINK in 4 dimensions and do maths in 4d ... (im just makin this up)
[B]Its Einsteins theory ..the fourth dimension is the baby he was never able to prove.
You kind of have to be careful in saying these things are concepts etc within philosophy and maths ..but like on the other hand **** it because if Einstein predicts there is a fourth dimension that is good enough for me.
Oh just to say ..some people call fourth dimensional space ..hyperspace or elucidean space.