linear algebra question...

[soundgarden]

I took Linear Algebra last semester. We were working with vector spaces and one of the students asked if a 4+ dimesion space acutually exits.

Surpringsly my teacher stated that there can be an INFINITE amount of dimensions.

Then she said it is impossible for anyone to fathom a 5+ dimension space, but there are a select few who can imagine a 4 dimension space.

I pondered day and night of a 4-dimensional space until i got really agitated and gave up.

Anyways, I was wondering if anyone has the rare ability to visualize a 4-dimensional space(or know anyone who can).

 

[fitzfan]

i know some one with the rare ability.

 

[fitzfan]

his names google.

 

[bla!!]

lol, some say the 4th dimension is time. So it represents the movement of a 3 dimensional object through time.

After that, It just makes my insides go mushy thinking about it.

 

[zerozero]

The 5th dimension could be spacial displacement. Imagine an object you left on your desk overnight. Tomorrow morning, it is still there so you have your 3 dimensional object moving through time, your 4th dimension. If somebody moved it overnight, then there would have been a spacial displacement over time. It's my theory but it's worth anybody else I guess.

 

[nak-1]

Trying to 'Visualise' anything other than a 3 dimensional space makes no sense. Apart from the fact that a single human eye captures no information regarding spatial information, our concept of a 3 dimensional space is defined purely by the way we experience it. ie. via our eyes and the movement of our bodies in that space. This has been honed by millions of years of evolution, do not expect to be able to expand or modify this ability because it is innate and inherited and totally necessary for our continued survival as individuals.

If you subscribe to any physics model from Newton onwards it is assumed we inhabit a space that has greater than 3 dimensions anyway. In the case of newton the 4th dimension is time, so in this case we all perceive or 'visualise' a four dimensional space. We perceive the 4th dimension as existing through time.

The problem with mathematical n-dimensional spaces is that the properties of each dimension are completely abstract. We can perform operations on these quantities and obtain results. However it is up to the human to interpret those results. Quite naturally we default to interpreting these results with the inbuilt 3-d model we use everyday. This is totally subconcious and probably unavoidable. However it is possible to get a 'feel' for the outcome of these operations and what sort of affect these will have. ie. the human has built a new internal model to represent these abstracts.

This model is not necessarily linked to the 3-d observational model that we all posess. It could be that people who develop a sufficiently sophisticated model at the subconcious level to represent these n-dimensional spaces can 'visualise' a 4-dimensional space. But the use of the word 'visualise' is wrong as it has probably has nothing to do with the way we experience physical spaces

It does not follow that this is necessarily unobtainable for any human in the population but it is very likely that only cetain individuals will dedicate the necessary time and work to develop it though.

Hence only certain people can 'visualise' a 4-dimensional space.

And yes, it twists my head up too in most cases...

 

[Apokalipse]

I think the extra dimension is not possible to 'visualise' but it is possible to think of it
I believe that if the extra dimension is mastered, somebody can jump from one place to another through it
like if a person in a 2D universe 'folded' the universe, they could jump to the other place with the displacement being 0 if they were to travel through the 3rd dimension
displacement = the difference in location between 2 objects

 

[Daf]

Sounds like a case for... Quantum Consciousness!

http://home.infionline.net/~jforberg/id14.html

Daf

 

[quasar]

In my opinion, when talking about the 4 dimensionnal space, your math teacher was refering to the space-time models of the universe, because as nak-1 said, "Trying to 'Visualise' anything other than a 3 dimensional space makes no sense".

When Einstein applied his special theory of relativity to the universe considered as a whole, he came up ultimately with a simple equation whose parameters need to be determined by experience. The equation is...

C = k(M + V) - H²

where k is some constant,
M is the density of matter,
V is the density of emptiness (yeah, I know...),
H is Hubble's constant (a quantity that has to do with the rate of expansion of the universe),

and where C is the GLOBAL CURVE of space-time for the universe. A positive C means the universe is "closed" and the total volume of space is FINITE, a negative C means the universe is "open" and the total volume of space is INFINITE and finaly, a C = 0 means the universe is "flat" and the total volume of space is also INFINITE.

Here's a link of a picture I found through Google: http://map.gsfc.nasa.gov/ContentMedia/990006s.jpg

The sphere represents the CLOSED universe, the saddle represents the OPENED universe, and the sheet represents the FLAT universe.

The principle of these representations is that the SURFACE of the figure (in 2-D) represents the 3 dimensionnal space we know and the 4th dimension, "time", is what gives the 2-D surface its curve. So the trick is simply to imagine our 3 spatial dimension as being simply 2 dimensions (say width and lenght) and let a 4rth dimension give it its curve (or height).

 

[crazybeans]

Have any of you heard of string theory? In string theory there is a possibility of around 10 dimensions mostly relative to subatomic levels. This is not even a proven theory but is believed by many to this day until it is proven false. I believe if any of us are to truly understand any possible dimension beyond our own and utilize that information we need to move past a 2d numeric system. The idea of a 3d+ numerical system is not described as of this time, age or evolutionary position relative to our evolution. Give us a few million or thousand years (depending on who you ask) and we may have it figured out. We believe everything that exists can be figured out by our uninterpretable brains. We are ignorant yet donÂ’t notice the obvious fact of such things. There are greater things than we are out there; we just have to understand that we all are pawns in this life we live. Do you really think we could truly understand it all? We canÂ’t even figure out how, exactly, our brains work! Anyways, we will never knowÂ…