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Macavity

Visualising Higher (more than 3) Dimensions!

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Visualising Higher (more than 3) Dimensions! Something of long standing frustration... 
I suspect SOME of you may have constructed a "4-Dimensional Cube"...  Pipe cleaners
and drinking straws?!? Was it completely satifying? But can YOU "think" in 4D plus? ?

I came across this: https://youtu.be/zwAD6dRSVyI (I'll have to think about this! LOL) ?

But I sense lesser-dimensional SLICES of higher dimensions are useful (pretty anyway)!
https://en.wikipedia.org/wiki/Calabi–Yau_manifold (For Supersymmetry Theory etc.) ?

Calabi.jpg.e7bb08006efb32014176144fd3626b99.jpg

Anyone have any other FUN LINKS on e.g. visualising Higher Dimensions, though? ?

Edited by Macavity
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I'm sure you have seen this representation of a 4th dimensional cube. 

8-cell-simple.gif.44cba84cbe20c8569a3177e7ba1510b8.gif

But I suspect that is just what it is, a representation.

We can't see in anything higher than 3 spacial dimensions, so thinking about 4, 5, 6... is literally impossible.

But mathematics can explain it, so that allows us to create 3 dimensional representations of higher dimensional objects.

But in the end the representations are still 3D, since that is only what our brains could perceive.

Maybe in the future we might have ways of upgrading the brain to allow for multi-dimensional thinking. That would be very interesting.

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Yes, living in a 3D universe does constrain visualisation somewhat. Like trying to imagine a new colour. 

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Whilst it is impossible to visualize objects in greater than 3 dimensions it is simple enough to think about them. Objects with a fractional dimension (ie. non-integer) take a bit more effort to get your head round though.

Dimension is a tricky subject. For example, it is possible to specify any point inside a square with two numbers. Two numbers therefore two dimensions, easy. However, if you were to fill a square with a space-filling curve ( eg.  Peano curve, Hilbert curve etc.) then it is possible to specify any point within the square with just one number; the length along the curve until the desired point is reached. Plenty to think about with dimensions.

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Think of an empty space. A tiny sphere appears, grows rapidly at first but slows down, reverses and disappears, speeding up as it goes.

That's a four-dimensional sphere in X,Y,Z and t.

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There's something Faustian about our relationship with higher dimensions. We have the intellectual power to think that they might exist but we are denied the power to conceptualize them. We could re-write the Faustian legend about a mathematician who makes a pact with the Devil to be given the power to enter, visualize and move within them... on the terrible condition that he never return to the dimensions of his birthright...

Olly

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I dont suppose we can ever visualize other dimensions due to us being three dimensional beings of a limited size/scale, if we were very large we would be convinced that there are only two of them and everything is flat, go to the other extreme in size then we would perhaps see lots more dimensions.

Alan

 

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On 22/09/2018 at 18:52, Alien 13 said:

I dont suppose we can ever visualize other dimensions due to us being three dimensional beings of a limited size/scale, if we were very large we would be convinced that there are only two of them and everything is flat, go to the other extreme in size then we would perhaps see lots more dimensions.

Belated thanks for all thoughts here. I still find it hard to visualise. ?
But maybe that's not too much of a surprise / problem. Just found:

https://phys.org/news/2014-12-universe-dimensions.html

(For fans of SUSY) it seems as meaningful as anything I have seen! ?

 

Edited by Macavity
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On 22/09/2018 at 09:26, ollypenrice said:

There's something Faustian about our relationship with higher dimensions. We have the intellectual power to think that they might exist but we are denied the power to conceptualize them. We could re-write the Faustian legend about a mathematician who makes a pact with the Devil to be given the power to enter, visualize and move within them... on the terrible condition that he never return to the dimensions of his birthright...

Olly

Any movie of it would have to be IMAX 3D though.

Regards Andrew 

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