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

[EastEnder]

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?

 

[rich!]

Somewhere during my degree I realised I could visualise some of the 4 and 5 dimensional surfaces we were studying.

Mind you, there was a lot of acid in my diet that year...

 

[golightly]

Flatland deals with the very topic of how two dimensional beings would perceive our three dimensional world. I reckon it would be very diificult for us to visualise more dimensions without resorting to analogy. As you rightly point out our brains and senses are evolved to just deal with three dimensions. I'd be interested to know how Rich! managed to perceive 4 and 5 dimensional surfaces. Not saying he didn't but I imagine it must really bend the brain.

 

[Binkie]

'Dimensions' are only a mathematical construct. If you want an example of how four dimensions can be used to explain a phenomenon, consider this. A sheet is being blown along in the wind. We need three dimensions (length, breadth and depth) to show where every bit of the sheet is at a given moment. To show how this changes with time, we need a fourth dimension - time. One way to represent this fourth dimension is to film the sheet. Consider any N variables that depend on each other. One way to represent them is a notional N-dimensional 'space'. There are other ways, such as a simple list. Physical space is of course three dimensional.

 

[Shippou-Sensei]

i though flatland was more a political comentary than a dimentional one

 

[Binkie]

Here's an example of a six-dimensional space:

firstname X surname X age X degree X mathknowledge X mediaappearances

Here are a couple of objects in that space:

(Jill, Smith, 30, Arts, 0, 25)
(Pete, Jones, 30, Engineering, 90, 0)

 

[ivebeenhigh]

if you try seeing dimensions as static and physical then seeing 3 is all you can pretty much ever do.

surely its not difficult to concieve a solid object moving in space over a period of time?

C

 

[subversplat]

if you try seeing dimensions as static and physical then seeing 3 is all you can pretty much ever do.

surely its not difficult to concieve a solid object moving in space over a period of time?

C

Now imagine a solid object moving over space and changing volume over a period of time, and you're well into the fifth dimension

 

[Binkie]

... and changing colour as it goes - puts it up to 8 dimensions (colour as red X green X blue).

 

[EastEnder]

Physical space is of course three dimensional.

Is it?

Can you clarify whether you're referring to the innate human perception of physical space, or the absolute nature of space?

 

[Binkie]

Is it?

Can you clarify whether you're referring to the innate human perception of physical space, or the absolute nature of space?

Space as it actually is.

 

[EastEnder]

Here's an example of a six-dimensional space:

firstname X surname X age X degree X mathknowledge X mediaappearances

Here are a couple of objects in that space:

(Jill, Smith, 30, Arts, 0, 25)
(Pete, Jones, 30, Engineering, 90, 0)

But that's just an abstraction.

I could declare an array of N dimensions in most programming languages. Big deal. That's just a way of organising information.

Unless you're suggesting that there is some fundamental difference between the 3 spacial dimensions we are intuitively aware of and any higher ones?

If so, I find that hard to accept. Either a dimension is a physical reality, or it's an abstraction, invented as a means to find solutions to otherwise intractable problems.

For example, one theory I read suggested that there are 5 dimensions, 4 of space and 1 of time. Is this extra spacial dimension on a par with the familiar 3, or is it fundamentally different?

Some theories suggest that extra dimensions are rolled up so tightly that we can't perceive them. Consider a universe of 2 spatial dimensions and 1 of time. Scientists in that universe eventually discover that there is a 3rd spacial dimension, but that it's nature makes it imperceptible to the universe's inhabitants. Is that 3rd dimension any less of a dimension that the other 2? Equally, if there are more than 3 spacial dimensions in our universe, are the 4th, 5th or 6th dimensions any less than the other 3? Either they are spatial dimensions like numbers 1 through 3, or they're not. If they're not, then to my simple mind they're not really dimensions in the intuitive sense at all - they're something completely bizarre. However if they are, but they're not perceptible, then they're worthy of the same recognition as they usual 3. If so, my original query still stands - is it possible that the human mind could ever conceive of these extra dimensions in any intuitive sense, beyond mere abstract analogies?

 

[Binkie]

Mathematics is one of the tools we use to model other aspects of reality. It is also a reality in itself. It exists. To divide the world up into actual and abstract is a mistake. If I make a model of a cat in plasticine aren't both the cat and the model real? It's a good model to the extent it's like the cat. The same goes for your ideas about other parts of the world. The ideas are models and they are useful in proportion to how accurately they reflect the object they're about.

 

[EastEnder]

Mathematics is one of the tools we use to model other aspects of reality. It is also a reality in itself. It exists. To divide the world up into actual and abstract is a mistake. If I make a model of a cat in plasticine aren't both the cat and the model real? It's a good model to the extent it's like the cat. The same goes for your ideas about other parts of the world. The ideas are models and they are useful in proportion to how accurately they reflect the object they're about.

I understand the value of mathematical models to explain aspects of reality. Perhaps it's more an issue of semantics.

Answer me this: What is a dimension?

If dimension 7 is not the same class of entity that dimension 2 is, then why is it called a dimension?

This is what I don't understand. Are higher dimensions, dimensions, or not? If they are not of the same nature as numbers 1 to 3, then why even call them dimensions? Why not make life easier and just invent a different name?

Is a tightly rolled up dimension number 5 just a highly compacted instance of the same type as dimension 2?

If the answer is that higher dimensions are really a notion developed by theorists to explain aspects of the universe, and are not literal extrapolations of the rather more familiar dimensions, then so be it. In that case, I can't help feeling it would have saved a lot of confusion all round if they'd had the imagination to invent a different term....

 

[laptop]

Consider a universe of 2 spatial dimensions and 1 of time. Scientists in that universe eventually discover that there is a 3rd spacial dimension, but that it's nature makes it imperceptible to the universe's inhabitants. Is that 3rd dimension any less of a dimension that the other 2?

Equally, if there are more than 3 spacial dimensions in our universe, are the 4th, 5th or 6th dimensions any less than the other 3? Either they are spatial dimensions like numbers 1 through 3, or they're not. If they're not, then to my simple mind they're not really dimensions in the intuitive sense at all - they're something completely bizarre.

As far as I know, they're purely mathematical objects (and I'm not going near the question "in what sense do mathematical objects 'exist'?" right now). As are the four dimensions we do perceive, in these mathematical structures.

I have wondered whether they imply a universe-within-a-universe in there, from whose point of view our dimensions are rolled up and we're the universe-within-the-universe.

But then I sobered up.

And if these theories are going to work they've got to deal with other questions. Does "rolled up" mean "rolled up smaller than the Planck length" - that is, smaller than the distance below which the word "distance" makes no sense?

If so, in what sense are these extra dimensions "there", when there's no "there" in quantised space, except as defined by counting multiples of the Planck length?

However if they are, but they're not perceptible, then they're worthy of the same recognition as they usual 3. If so, my original query still stands - is it possible that the human mind could ever conceive of these extra dimensions in any intuitive sense, beyond mere abstract analogies?

When I'm working with a multi-dimensional program object, I can move around and sense the geography of its contents quite happily, so long as I don't watch myself doing it.

I have sometimes managed to observe myself visualising four-space-dimensional things

But then I sobered up.

Probably human minds will, eventually.

As a parallel example, I'm fairly sure the basics of quantum mechanics are easier for (younger) people to grasp now than they were 50 years ago.

It feels to me as though in some sense the culture and/or the language gets better at describing these things to itself - which makes it easier for its members/speakers. (Feed me substances to get more armwaving on this.)

 

[Binkie]

A dimension is a set of values. A space is a cartesian product of dimensions - all combinations of those values. A relation is a subset of that cartesian product. I can number (order) the dimensions any way I like. In my example above, you can see the order I've chosen to order the dimensions - I stated the dimensions and their order at the beginning. The dimensions don't have to be numeric, but if you're talking about positions in space they are. Distances in the x, y and z directions are all from the same domain - the set of real numbers. So would the fourth dimension if you chose it to be time. Calling any of these dimensions 'higher' - well the next dimension in your space of interest can be anything you choose. And the dimensions are not 'bound up'.

 

[EastEnder]

As a parallel example, I'm fairly sure the basics of quantum mechanics are easier for (younger) people to grasp now than they were 50 years ago.

It feels to me as though in some sense the culture and/or the language gets better at describing these things to itself - which makes it easier for its members/speakers. (Feed me substances to get more armwaving on this.)

I'm convinced that contemporary lexicon and the associated semantics have an overarching influence on how intuitively such esoteric concepts are understood!

 

[TeeJay]

"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?"

In the future people will be able to see in 10 dimensions

 

[EastEnder]

A dimension is a set of values. A space is a cartesian product of dimensions - all combinations of those values. A relation is a subset of that cartesian product. I can number (order) the dimensions any way I like. In my example above, you can see the order I've chosen to order the dimensions - I stated the dimensions and their order at the beginning. The dimensions don't have to be numeric, but if you're talking about positions in space they are. Distances in the x, y and z directions are all from the same domain - the set of real numbers. So would the fourth dimension if you chose it to be time. Calling any of these dimensions 'higher' - well the next dimension in your space of interest can be anything you choose. And the dimensions are not 'bound up'.

I think that may be missing my original point a little bit. What I'm trying to ascertain is whether there's any point, or if it's even conceivably possible, for the human mind to have any intuitive grasp of more than 3 spacial dimensions.

My knowledge of geometry is more than adequate, and I've studied information theory. If "additional" (to avoid any unwarranted connotations of "higher") dimensions are solely the preserve of mathematical models, then to my mind that implies that they are not on a par with the familiar 3 spacial dimensions.

If that is true, then it would indeed be pointless attempting to visualise them in any physical sense, because they have no physical manifestation.

However, if the mathematical models are tools used to describe physical entities - the erstwhile extra dimensions - then my original query still holds: Is it pointless attempting to use ones mind to visualise extra dimensions?

Obviously they can be described in abstract terms - I can easily explain to anyone bored enough to listen how it's possible to have a 327 dimensional array in a computer program. But that it is most definitely an abstraction, there aren't really 327 dimensions, there's 1 - a linear array that's indexed by 327 indices.

Either extra dimensions are tangible, in which case my original query is warranted, or they're intangible - in which case there's no point wasting any sleep worrying about whether one could ever truly imagine them!

 

[TeeJay]

I think that may be missing my original point a little bit. What I'm trying to ascertain is whether there's any point, or if it's even conceivably possible, for the human mind to have any intuitive grasp of more than 3 spacial dimensions.

What do you mean by an "intuitive grasp"?

Also re. 'tangible' and 'intangible' ... are colours tangible to someone who has been blind from birth - and/or is infra-red tangible to the human eye? Some animals can 'feel' magnetism (eg pidgeons) and other things that humans cannot.

Whether this is important kind of depends on the context surely?

Also, surely everything we think about the world is "abstract" when it is sloshing about our brains? Why should even more abstract ideas be less real than the abstract model we have that lets us put together sensory input from our two optical nerves and construct a 3d image? I accept that models that are more "hardwired" may well feel more automatic than learn mathematical abstractions and they may be more accessable to anyone even without training, but are they really that different?

 

[TeeJay]

Also, maybe some people can "visualise" abstract mathematical ideas better than others. Some people have problems with visualising certain ideas full stop - for other people they may well be easy and feel natural.

 

[Larry O'Hara]

I see

this thread is proceeding largely along rationalist/mathematical lines. I prefer to see reality as far more than that--including time as well as space (hence the conjunction in eternity of past present & future) as well as the realms of sixth sense, intuition, deja vu etc. And also the astral plane (remote viewing aside).

 

[EastEnder]

Also, maybe some people can "visualise" abstract mathematical ideas better than others. Some people have problems with visualising certain ideas full stop - for other people they may well be easy and feel natural.

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?

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?

 

[forked brain]

Are we assuming on this thread that 'time' is the fourth dimension, if so, how do people measure time?

 

[TeeJay]

Hmmm. Without some examples of these other dimensions (time has already been mooted as the 4th dimension - not sure what the others are) I don't know if I can really help with specifics, but...

"the same fundamental nature as the 3 we're aware of" - I'm wondering what this "fundemental" nature is - other than you can "see" in 3d. Most animals presumably have some kind of "model" of their environment - at least most complex animals that move around etc and which 'see' or 'feel' their way around it although simple organisms maybe just react to stimuli rather than having any kind of 'map'. Are you saying that something is fundemental if you can "feel" it without having to think about it any further?

Re. "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?" - on one level, no because "seeing" stuff visually (or "feeling" it) is probably hardwired into our brains and no matter how good someone's imagination and mathematical ability is, they won't actually experience other concepts in the same way. On the other hand maybe some people do have the ability to "visualise" other dimensions in their head and their imagination, even if they might find it hard to communicate this to someone without just using mathematical symbols or jargon used only by other people who have got their heads around these concepts.

 

[subversplat]

Are we assuming on this thread that 'time' is the fourth dimension, if so, how do people measure time?

With a watch, usually.

 

[forked brain]

Hmmm. Without some examples of these other dimensions (time has already been mooted as the 4th dimension - not sure what the others are) I don't know if I can really help with specifics, but...

"the same fundamental nature as the 3 we're aware of" - I'm wondering what this "fundemental" nature is - other than you can "see" in 3d. Most animals presumably have some kind of "model" of their environment - at least most complex animals that move around etc and which 'see' or 'feel' their way around it although simple organisms maybe just react to stimuli rather than having any kind of 'map'. Are you saying that something is fundemental if you can "feel" it without having to think about it any further?

Re. "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?" - on one level, no because "seeing" stuff visually (or "feeling" it) is probably hardwired into our brains and no matter how good someone's imagination and mathematical ability is, they won't actually experience other concepts in the same way. On the other hand maybe some people do have the ability to "visualise" other dimensions in their head and their imagination, even if they might find it hard to communicate this to someone without just using mathematical symbols or jargon used only by other people who have got their heads around these concepts.

Some excellent points there:

So, what is definible then?

Is there any thing definite?

The concept of 'time' is what's pulling civilisation apart.

 

[bluestreak]

bosonic string theory suggests there are 26 dimensions. my head is done in trying to cope with the dimension of pomposity that goes on around here in the face of people asking perfectly rational questions.

pomposity. the fifth dimension.

*patents observation*

 

[forked brain]

With a watch, usually.

Some people don't measure time like that, some measure by tides, sunrise, crop duty, fishing season, etc.

 

[laptop]

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?

If I understand the theories correctly, then yes within the theories - but only because they treat the observed dimensions as abstractly as the others.

Which may (I intiut) have some connection with the fact that they're rather abstract theories - I recall reading that no-one has come up with a prediction that could be used to construct an experiment (necessarily taking place within the observed dimensions ) to distinguish one string theory from another.

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?

Clearly not the same, almost by definition of our having evolved in a four-dimensional world.

Evolutionary psychologists (ptui, but they're useful for this sentence ) would say that our intuitive grasp is rooted in the constant need to decide whether that is lunch or whether it's looking at us as its lunch.

Certainly our intuitive grasp leads to, er, intuitions that Newtonian physics says are not what's "actually going on".

It's fuck-all use dealing with either the Planck scale or the whole-universe scale, which is what your 10- and 11- and 26-dimensional theories are doing.