Is it pointless attempting to conceive the notion of higher dimensions?

[EastEnder]

If you have a space with a countable infinity of dimensions, is the number of integral-coordinate points in the space countable?

That reminds me - I did a few big lines of K the other night, after some rather strong puff. Lying in bed, I suddenly realised that I understood infinity!

Not in the normal, descriptive sense - I really got it, I could comprehend the true notion of infinity as easily as comprehending a finite plane, or the motion of a cloud or the bounce of toast popping out of the toaster.

It made sense.

For a while, at least............

 

[Azrael23]

You know meditation is free and doesn`t turn your brain to soup.

 

[J77]

Um... what do you put in them?

If you have a space with a countable infinity of dimensions, is the number of integral-coordinate points in the space countable?

Continuous functions.

I work on the space of continuous functions defined over some interval projected onto n-dimensional real space.

 

[s.norbury]

Higher dimensions are fun, that's all. They obviously don't apply to 3D space time and anyone who enjoys the liberating experience higher dimensions will most likely be a crazy fucker, I recommend Salvia Diviorum x20.

 

[rich!]

obviously

i do not think that word means what you think it means

 

[laptop]

I work on the space of continuous functions defined over some interval projected onto n-dimensional real space.

I think I see...

What happens if "real space" is quantised? (Hence my question about integral co-ordinates.)

(Yes, I know, it's maths, you don't have to answer that... but the implications interest me.)

 

[s.norbury]

i do not think that word means what you think it means

Easily perceived

 

[Binkie]

I've done more than enough ket to go exploring hippy, out of mind trips..

Maybe too much.

But that hardly addresses the question of whether the human mind is now, or will ever be, capable of understanding extra dimensions on any kind of tangible level

You postulate 'an extra dimension' in space, which is clearly, and by definition (?) three-dimensional. If the thing that has four dimensions is to have a name, don't call it space. Call it something else.

Is there a spatial phenomenon that can't be explained without this extra spatial dimension? Is there any evidence for it? Or is it, like the God idea, superflous?

You think humans will never understand the fourth spatial dimension. As Stevie Wonder puts it in one of his songs, to believe in things you don't understand would be superstition.

On another point, do you think the human mind is developing significantly? Or is it more that, as Kurt Vonnegut suggests in Galapagos, our minds are actually too developed for the range of problems we currently encounter?

 

[merlin wood]

Is it pointless attempting to conceive the notion of higher dimensions?

No it's not. You can conceive of and represent a further third dimension to a two dimensional flat world and a second and third dimension to a one dimensional linear world. Thus you can think that a fourth spatial dimension is equivalent to a third dimension in a two dimensional world and so on.

 

[merlin wood]

Is it pointless attempting to conceive the notion of higher dimensions?

No it's not. You can conceive of and represent a further third dimension to a two dimensional flat world and a second and third dimension to a one dimensional linear world. Thus you can think that a fourth spatial dimension is equivalent to a third dimension in a two dimensional world and so on.

..and by this means it can be shown that and how an extra dimensional, nonlocally acting cause is needed to produce the natural organisation of matter and radiation.

 

[EastEnder]

Is it pointless attempting to conceive the notion of higher dimensions?

No it's not. You can conceive of and represent a further third dimension to a two dimensional flat world and a second and third dimension to a one dimensional linear world. Thus you can think that a fourth spatial dimension is equivalent to a third dimension in a two dimensional world and so on.

That's not really what I meant - that's just visualising by analogy.

It's not equivalent to intuitive, tangible comprehension.

Personally, I think the answer to my original question is no. At least not the human mind as it exists today.

 

[Masseuse]

I can see fairies.

 

[Crispy]

That's not really what I meant - that's just visualising by analogy.

It's not equivalent to intuitive, tangible comprehension.

Personally, I think the answer to my original question is no. At least not the human mind as it exists today.

I'm with you on this one. I can concieve of the Tesseract, but show me a representation of one and ask me "what does this look like rotated 90 degrees about the V axis?" and I wouldn't have the foggiest.

 

[laptop]

I can concieve of the Tesseract, but show me a representation of one and ask me "what does this look like rotated 90 degrees about the V axis?" and I wouldn't have the foggiest.

* Does some mental algebra *

It looks the same

30 degress - you've got me there.

 

[J77]

http://www.geom.uiuc.edu/docs/outreach/4-cube/mpegs/tesseract2.gv.mpg

 

[Crispy]

* Does some mental algebra *

It looks the same

30 degress - you've got me there.

Smartypants

 

[GarfieldLeChat]

Specifically, spacial dimensions beyond the three we all know and love.

Theorists are forever telling us there may be anything from 4 to 11, maybe even more! I've heard many different ways of describing them - rolled up too tightly to perceive, adjacent to the obvious ones but so infinitesimally close they're imperceptible, etc, etc.

Now if we assume that there really are more than 3 spacial dimensions, is it even possible for the human brain to conceptualise them in anything more than a vague analogous manner?

Is it even theoretically possible for a being that's evolved to only readily perceive 3 spacial dimensions, to perceive more? In the sense of actually being able to visualise, in any meaningful way, higher dimensions?

Even if it's eventually proven that such things exist, are we forever destined to only be able to understand them in an abstract, metaphorical sense?

Three spacial dimensions are obvious to us, but could a being that evolved in a universe with two spacial dimensions ever conceive of a third - no matter how intuitive it seems to us?

yes we can always concieve .

when cook landed on the island the islanders couldn't 'see' the ship he came from and it took many days for them to be able to perceive the ship which was there and had borne cook.

It was only once the ship had been described to them that could see it at all same goes with any higer dimension. constricted by a language of definable means that you cannot describe the things in front of them even though you can perceive there effects.

so it's not the conception that's the problem it's the decsricption which is at fault.

 

[EastEnder]

so it's not the conception that's the problem it's the decsricption which is at fault.

You're assuming that all things can be described in such as way as to be conceivable to, not just contemplated by, the human mind.

Possibly, but I'd need more convincing.

 

[GarfieldLeChat]

You're assuming that all things can be described in such as way as to be conceivable to, not just contemplated by, the human mind.

Possibly, but I'd need more convincing.

not sure i can old chap these are things which may or may not be there with out being able too 'see' them one is not capable of being able to descerne one way or t'other

 

[merlin wood]

not sure i can old chap these are things which may or may not be there with out being able too 'see' them one is not capable of being able to descerne one way or t'other

Of course you can't directly visuaise anything in extra dimensions of space to the three in world experienced.

But if you think of the problem of non-locality in quantum physics you can indiractly represent an extradimensional cause that would produce non-local effects between quantum objects that are described as being entangled. So you can consider that an equivalent to such a cause could be represented three dimensionally as acting upon two dimsional objects in a two dimensional world.

Such a represention of exta dimensions can be found in Brian Greens book on super-string theory, The Elegant Unioverse (pp 199, 200i in the paperback). Although
in this theory such dimesions are conceived as being curled up on the small scale. I'd say this idea is misconceived because dimesions are treated as if they are things in the world whereas spatial dimensions just as such are just relations in space. So you can ask what is it that separates one set of small scale extra dimensions from another?

 

[GarfieldLeChat]

Of course you can't directly visuaise anything in extra dimensions of space to the three in world experienced.

But if you think of the problem of non-locality in quantum physics you can indiractly represent an extradimensional cause that would produce non-local effects between quantum objects that are described as being entangled. So you can consider that an equivalent to such a cause could be represented three dimensionally as acting upon two dimsional objects in a two dimensional world.

Such a represention of exta dimensions can be found in Brian Greens book on super-string theory, The Elegant Unioverse (pp 199, 200i in the paperback). Although
in this theory such dimesions are conceived as being curled up on the small scale. I'd say this idea is misconceived because dimesions are treated as if they are things in the world whereas spatial dimensions just as such are just relations in space. So you can ask what is it that separates one set of small scale extra dimensions from another?

sorry but how d you know that thye are not in the 'real world' just just 'hidden' from 'sight'?

if quantium mechanics can reproduce the same strawberry in two places at once, not two different strawberries, but the same strawberry in two places it's very possible to concieve that these things are with in the real world merely that we are a the moment with out a decent enough lexicoin.

 

[merlin wood]

sorry but how d you know that thye are not in the 'real world' just just 'hidden' from 'sight'?

if quantium mechanics can reproduce the same strawberry in two places at once, not two different strawberries, but the same strawberry in two places it's very possible to concieve that these things are with in the real world merely that we are a the moment with out a decent enough lexicoin.

If you think of the effects of a force that acts at a distance, like gravity or magnetism, you can say that because they reduce in strength in all directions around objects then they must act in 3D space (although according to general relativity to describe the action of gravity you need to add time as a fourth dimension).

Whereas experiments have been carried out where the effects of quantum entanglement have been measured not to vary between beams of photons at distances of up to 10 kilometres.

So you can ask where could there be a cause of these non-local effects if this wouldn't surround objects? And you can conclude that such a cause could only produce the effects if it related in space from at least one spatial dimension outside 3D space. So that the nearest 3D equivant to a cause of entanglement effects would be the effects on iron or steel objects on the 2 dimensional flat plane of a card produced by a magnet in a third spatial dimension underneath the card.

 

[Knotted]

Maybe I should rephrase the question:

1) Are the purported extra spacial dimensions of the same fundamental nature as the 3 we're aware of, even if we can't perceive them?

As I understand it, those who purport these extra dimensions would say 'no'.

2) If the answer to 1) is yes, is it conceivable that the human brain could ever achieve the same intuitive grasp of those dimensions that it has of the 3 we're already aware of?

If it helps you can draw 4-dimensional objects on paper using the same trick you use to draw 3-dimensional objects on paper.

To draw a cube:
1) Draw a square
2) Draw an identical (similar) square a bit behind it.
3) Connect up similar corners of the two squares eg. top right to top right.

To draw a 4-dimensional hypercube:
1) Draw a cube (as above)
2) Draw an identical cube a bit behind it.
3) Connect up similar corners of the two cubes eg. front top right to front top right.

 

[Knotted]

I was thinking about trying to explain how metrics and dimensions interact.

basically, in a well-ordered space (like a piece of paper) you can measure the distance between points. There's a matrix you use to do this.

In the spaces we're used to, it looks like
1 0 0
0 1 0
0 0 1

In General Relativity, it looks more like
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 -c2

in other words, a difference in one of the dimensions makes distances shorter rather than longer...

After that, black holes seem quite reasonable.

Not sure if discussing pseudo-metrics of Lorentzian manifolds (which model spacetime) is particularly helpful.

In English a metric is a distance and discussing the 'distance' into the future is a bit odd, especially when the distance is negative.

 

[Knotted]

If you have a space with a countable infinity of dimensions, is the number of integral-coordinate points in the space countable?

No. To take the simplest case of the above where each of your dimensions is a set of two elements {0,1} and the space is

{0,1}X{0,1}X{0,1}X...

Then you have just defined the set of real numbers between 0 and 1 using binary notation, which is a continuum and not countable.

An element of the space could be written:

0.010011010111010010000...

If you prefer to work in decimals take the infinite cartesian product of the set {0,1,2,3,4,5,6,7,8,9}.

 

[Knotted]

If you think of the effects of a force that acts at a distance, like gravity or magnetism, you can say that because they reduce in strength in all directions around objects then they must act in 3D space (although according to general relativity to describe the action of gravity you need to add time as a fourth dimension).

Whereas experiments have been carried out where the effects of quantum entanglement have been measured not to vary between beams of photons at distances of up to 10 kilometres.

Entanglement is just something that happens its not meaningful to talk about it varying it either is or it isn't.

There are lots of effects that do not vary over distance - for example the mass of an object - but it would be odd to say that this necessitates extra dimensions.

The reason that forces reduce over distance is that the field applies across space and the further away from the heavy object/ magnetic pole etc. you get the larger the area that the field applies to. It basically derives from the principle of conservation of energy.

So you can ask where could there be a cause of these non-local effects if this wouldn't surround objects? And you can conclude that such a cause could only produce the effects if it related in space from at least one spatial dimension outside 3D space. So that the nearest 3D equivant to a cause of entanglement effects would be the effects on iron or steel objects on the 2 dimensional flat plane of a card produced by a magnet in a third spatial dimension underneath the card.

I'll eye that with skepticism for the minute.

 

[DogorKat?]

http://www.tenthdimension.com/flash.php

A nice flash presentation which explains how to imagine up to 10 dimentions

 

[merlin wood]

http://www.tenthdimension.com/flash.php

A nice flash presentation which explains how to imagine up to 10 dimentions

Now imagine how, as in superstring theory, there could be a myriad of small scale sets of extra dimensions of space that are separate from one another. And given that spatial dimensions are not made of anything (as in eg. Brian Greene's The Elegant Universe) but are just relationships that you can describe of space.

You can't see height, bredth or depth, only observable things that have these dimensions.

 

[Blagsta]

http://www.tenthdimension.com/flash.php

A nice flash presentation which explains how to imagine up to 10 dimentions

That was a headfuck.

 

[merlin wood]

That was a headfuck.

And if you look at this link you'll find that string theory looks seriously like its on its last legs, at last!