Hyper Dimensional Philosophizing

[Oppressed]

I started replying to the thread “Hyper Dimensional Design” because the idea of dimensions beyond what we can normally see is interesting to me. But, I think the thread may be ignored because the original poster was associating it with things like numerology.

For those crazy people who simply enjoy thinking about more dimensions and/or those interested in the science of exploring what might be and the philosophy of what might be, I want to start a thread with the more pure topic of dimensions beyond what we can see and what those dimensions might mean for our existence.

To begin I want to mention some things as I understand them. First, what are the fundamental dimensions that we know of? I believe they are:
1) Length (meter)
2) Mass (kilogram)
3) Time (second)
4) Electrical Current (ampere)
5) Temperature (kelvin)
6) Amount (mole)
7) Luminous Intensity (candela)

There are also a couple angles, but they are considered supplementary dimensions:
8) Plane Angle (radian)
9) Solid Angle (steradian)

Then there are a great number of dimensions derived from these. For example:
10) Area
12) Volume
13) Material Density
14) Force
15) Velocity
16) Momentum
17) Acceleration
18) Power
19) Energy
20) Heat
and so on.

Keep in mind that these dimensions are terms we have created to try and describe how our world works. So far, these terms have served us well in this capacity.

 

[GodMark2]

You seem to be confusing "Units" and "Measures" with "Dimensions".

Units are an ammount of something, like a liter. It's always the same amount, one liter is the same size as any other. Meters, feet, grams, radians and seconds all work the same way.

Measures are a count of the units in something. And you can have multiples of them. Put two separate liters together, and you have... Two Liters! Those liters have a measure of 2, when measured in liters. It would have a measure of 2000 when measured in cubic centimeters.

Dimensions are completely different. The basic concept of a dimension can be thought of as the number of ways you can move, without changing your position in the other dimensions. Say you were confined to a piece of paper. You could move left and right without changing your position up and down any. And you could do the reverse. This shows that, on a piece of paper, Left-Right and Up-Down are two different dimensions. now, on a piece of paper, that's as many different ways to move as there are. You can't move any other direction without leaving the paper, so Paper had two dimensions. On the Earthm you can move North-South, East-West, and Up-Down, each without affecting your position in any of the other directions, and you can't move in any direction other then those, so Earth = 3 dimentional.

You seem to be confusing the ability to take units and combine them (distance / time = velocity, distance / time * mass = momentum) with the ability to move in different directions.

Now, the String Hypothesis posits that there may be many other dimensions, but that most of them are so small that we can't tell if we're moving along them. At this point, this is a mere mathematical curiosity, with no experimental evidence (i.e. it can't be considered real).

 

[Jimbo07]

You might like to start with this thread...

Dimensions

 

[Oppressed]

Actually, what I have stated above is correct. Many people do not understand this and that is why I started out with it, to raise the awareness of what dimension can mean.

What most people think of as dimension is in terms of space as defined by three spatial dimensions length, width and height. Space can be defined with three dimensional variables for most applications but not all. There are three common different ways the basic or simple model of space can be derived:
1) Cartesian coordinates using three dimensions of length.
2) Cylindrical coordinates using two dimensions of length and one dimension of plane angle.
3) Spherical coordinates using one dimension of length and two dimensions of plane angle.

In the consideration for talking about hyper spatial dimensions another thing to keep in mind is that we can’t separate the dimension of time from the discussion. Time is a dimension very unlike that of length.

There are two important points I am trying to make here. One is that what an additional dimension might be like may not be anything like the fundamental dimension of length. Two is that the simple models we have do help us define space are good, but there are points where the models fail. It is because of this failure of the simple model that we seek out a better model that will not fail.

A last thing I want to comment on is to stress that fictional ideas for hyperspace or astral space. This is meant to be a discussion for the fun of it.

 

[Beausoleil]

You seem to be confusing "Units" and "Measures" with "Dimensions".

No, Oppressed is right (mostly). This is the basis of "dimensional analysis".

It's not usually associated with the term "hyperdimensional", however, so in that sense the thread is likely to become confused.

 

[Oppressed]

Beausoleil,

I can easily make mistakes about how our currently accepted science we have for modeling our existence. I can also sometimes have a difference of opinion over some concepts accepted as fact by the majority.

But, if you can point out a mistake and show me how I made the mistake, I will correct it. If I have a difference of opinion I will change my opinion to shift with what I believe to be most likely true, thus if you present a good enough argument, you can change my mind. Of course, sometimes I might argue the point of view for something I think less likely to be true, because doing so is a good exercise. I do not believe it is wise to hold a single opinion without seriously considering other opinions.

But, I believe the point I am trying to make in the beginning here about dimension is an important one for this discussion.

People tend to think about hyper spatial dimensions as only consisting of something like the 3 spatial dimensions we use to describe space without time. So when they think of adding more dimensions in order to achieve a possible description of hyper space, the come up with extra dimensions that are like the fundamental dimension of length, but somehow different.

The fundamental dimension of time is nothing like the dimension of fundamental dimension length, yet when discussing this subject we should be beginning with 3 dimensions of length and 1 dimension of time.

Does a dimension required to describe hyper space, or some dimensional space beyond what we understand, need to be like the dimension of length? I believe that there is a good change it would not. If such a dimension we so similar to length then there we be a good chance we would already detect it, so something about it has to be different enough as to make it hard for us to detect and understand.

Realizing that dimensions can be very unlike the fundamental dimension length, it is a good exercise to examine what dimensions we know of can be like. How different can the dimensions we already know about be from each other?

It could take only a single fundamental dimension we do not yet understand in order to create a model for hype space. Then, the other dimensions of hyper space might be derived from that newly discovered fundamental dimension and the other existing fundamental dimensions we already know.

It could be that it would take additional dimensions of length and/or time. Perhaps it could be described as 10 dimensions of length and 1 dimension of time. But, especially considering this is an exercise for fun and need not be stuck in what has support in science, suppose you described a space time with 3 dimensions of length and 3 dimensions of time? Suppose you describe space as having a new fundamental dimension, which for the fun of it, we will call astral, and then we use 9 dimensions, 3 of length, 3 of astral and 3 of time?

Some of these models for fun could give rise to explaining some fantasy and science fiction events, such as parallel worlds, time travel, hyper spatial travel and such. They would almost certainly not stand up to scientific testing for being valid, but, the process of thinking about such things might lead us to think of a model that will be better than any we currently have.

 

[PixyMisa]

Length, mass, time and electrical charge (not current) are fundamental.

Temperature, luminous intensity and current are derived. Temperature is a measure of energy; luminous intensity of power; and current of the flow of charge. SI makes these base units, but that's just for convenience, and not a reflection of how things actually work.

Quantity is of course dimensionless; it's just a number. A mole is not a dimension but a constant.

 

[Jimbo07]

No, Oppressed is right (mostly). This is the basis of "dimensional analysis".

I guess it depends on how we're using the word "dimension."

Dimension at Wikipedia

There is a definite confusion here as to how the word is being used. Is it being used to describe units (as in the description of physical parameters)? Is it being used to describe what we might think of as the 4-dimensional spacetime?

It's not usually associated with the term "hyperdimensional", however, so in that sense the thread is likely to become confused.

Uses of the prefix "hyper":

Dimension at Wolfram MathWorld

ETA: PixyMisa, it depends who you ask and what the purpose is:

Dimensional Analysis at Guelph

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...

 

[PixyMisa]

ETA: PixyMisa, it depends who you ask and what the purpose is

Absolutely.

Dimensional Analysis at Guelph

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...

Yep. Oppressed is mixing his contexts, though; dimensional analysis can't be mapped directly to space-time dimensions that way.

Luminous intensity can be described within standard 4-dimensional space-time, for example, but charge and mass are different.

 

[Jimbo07]

Oppressed is mixing his contexts, though; dimensional analysis can't be mapped directly to space-time dimensions that way.

Agreed.

...

So... Oppressed... is this thread supposed to be about fiction or science?

A last thing I want to comment on is to stress that fictional ideas for hyperspace or astral space. This is meant to be a discussion for the fun of it.

I'm a BIG fan of science fiction, both hard-sci-fi and pure fantasy. Are you trying to find the places where some kind of technical definition of dimension (and then, we'd have to define which) can be co-opted for a piece of fiction?

i.e. do we wanna create some Star Trek-esque technobabble?

 

[Oppressed]

PixyMisa,

I’ve tried to explain this but have appeared to have failed. Well, I am not always the best at explaining what I mean, but I will try again.

4 dimensional space-time described in Cartesian coordinates consists of three dimensions of length and one dimension of time. If you are going to talk about some kind of space that has more than these 4 dimensions, then you need to add dimensions. The question is, what kind of dimensions? Do you add more dimensions of length? Would that really work? Do you add more dimensions in time?

Or do you have to add some other type of dimension? But what can a dimension be?

To limit your concept of what a dimension can be hobbles your ability to consider something beyond our current knowledge.

If the extra dimensions were that simple to describe and/or detect, it would not be a question. If such dimensions exist then they are almost certainly something different enough from length that it explains why we can not so easily detect and explain it.

Because we are so familiar with the dimension of length and of using three dimensions of length to define a space, it is an easy natural tendency to try to envision some greater dimensional space in terms of 4, 5 or 6 dimensions of length. However, if something like hyperspace exists, it is likely to require some kind of dimension unlike length.

Perhaps a single extra dimension would suffice and that dimension would function like some type of energy state where it is difficult but not impossible to change such energy states. Nothing in real life supports this, but if you wanted to explain how spaceships in science fiction jump through hyperspace, this might do it. This added dimension would not resemble either length or time.

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.

Just to make sure how I am using “Hyper Dimensional Philosophizing” is clear, I mean te following. With regard to the simple accepted model of space-time that we have, consisting of 3 spatial dimensions and 1 temporal dimension, Hyper Dimensional is referring to these 4 accepted dimensions plus one or more other dimensions.

 

[PixyMisa]

PixyMisa,

I’ve tried to explain this but have appeared to have failed. Well, I am not always the best at explaining what I mean, but I will try again.

No, it's okay. We understand what you mean, and you may well be right - it's just that some of the details in your original post are wrong.

So mass and charge might well be explained by additional dimensions, but all of the others can be explained in terms of what we already have.

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.

That's incorrect. You are, as has been noted, confusing dimensional analysis with space-time.

Let's examine something simple, like motion in a straight line.

We can define position on that line using a single dimension of space - call it s.
We can define speed on that line using one dimension of space and one dimension of time s and t. Speed is the change in s over a period of t, so it's sxt^-1. That doesn't mean we have -1 time dimensions, though.
Acceleration is the rate of change of speed over time: sxt^-2. That doesn't mean we now have two time dimensions (or -2, for that matter). We're just looking at how speed varies over time. We can look at the rate of change in acceleration too, and so on. The dimensions of the value we get change, but it's still the same old one dimension of space and one of time.

Also, angles aren't a different dimension; they're a different co-ordinate system. You can specify a location in 3-dimensional space using two angles and a distance, and indeed that's what astronomers do.

 

[Ziggurat]

4 dimensional space-time described in Cartesian coordinates consists of three dimensions of length and one dimension of time. If you are going to talk about some kind of space that has more than these 4 dimensions, then you need to add dimensions. The question is, what kind of dimensions? Do you add more dimensions of length? Would that really work? Do you add more dimensions in time?

What distinguishes time from space, as a dimension? Well, in one sense, it's only the sign in the metric for spacetime: d² = (ct)² - x² - y² - z². So if you add another dimension, then whether it's time-like or space-like would depend purely one what sign you gave it in the metric. So the metric gives two kinds of intervals: positive and negative, or space-like and time-like (which is which turns out to be arbitrary, but they have to be opposite). It's a lot easier to generalize physical laws when adding more space-like dimensions to our theories than time-like ones, but there's nothing that absolutely precludes doing the latter.

Or do you have to add some other type of dimension? But what can a dimension be?

Well, you could add something else, but you'd need to come up with a new metric which then had three different kinds of separation (space-like, time-like, and something else). But you've got to add it into the metric in such a way that the existing metric is at least some sort of limiting case, which does constrain you. And we know that because the metric I gave above (the Minkowski metric) is at least a good approximation to reality. Just like the Euclidean metric is a good approximation of the Minkowski metric in certain limits.

If the extra dimensions were that simple to describe and/or detect, it would not be a question. If such dimensions exist then they are almost certainly something different enough from length that it explains why we can not so easily detect and explain it.

Extra dimensions can very easily be space-like without being easily detectable. Have you ever heard of compactification?

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.

You are not correct. Your mistake is in assuming that multiple dimensions of time in a unit indicates that it's not describable in terms of 4D spacetime. This is an incorrect assumption. One of the easiest examples to consider to show the problem with this idea is acceleration. What is acceleration? It's the change in velocity per unit time. Velocity is in turn the change in displacement per unit time. So velocity has dimensions of length/time, and acceleration has units of length/time/time. Is acceleration somehow extra-dimensional? No, it isn't. The appearance of two dimensions of time in the definition is the result of acceleration being the second derivative of position with respect to time. Taking further derivatives would increase the number of dimensions of time, but do not require any more time dimensions to exist. d²x/dt² doesn't require there to be more than one t variable.

Let's follow this a little further. What is force? It's acceleration times mass, so force has dimensions of (mass*length)/(time*time). What is work (aka change in energy)? Work is force multiplied over the distance that force is exerted, and so it has dimensions of (mass*length*length)/(time*time). What is power? Power is work per unit time, so power has dimensions of (mass*length*length)/(time*time*time). Two things to notice: 1) we haven't required any extra dimensions in any of this, and 2) we're one dimension away from luminosity, namely we're missing a solid angle. But what is luminosity? It's simply the power radiated per unit solid angle, which is how we get the dimensions you mentioned. Luminosity is NOT fundamental. It, just like velocity, acceleration, force, work, and power, is a derived quantity.

 

[Davo]

It may be shown mathematically there could be other dimensions, but practically is there any physical evidence for there being any other dimensions outside x,y,z and time ? Could anyone clarify/dispute this ?

 

[Ziggurat]

It may be shown mathematically there could be other dimensions, but practically is there any physical evidence for there being any other dimensions outside x,y,z and time ? Could anyone clarify/dispute this ?

Basically in all those theories, the extra dimensions are compactified. Basically this means wrapping that dimension into a loop. It's like the surface of an infinite straw: it's two-dimensional, but if the length scales you're interested in are much larger than the circumference of the straw, then it looks one-dimensional. Finding physical evidence for compactified dimensions may be extremely difficult, even if those ideas are correct.

 

[Oppressed]

I pull many of the references I make from published resources in science. For example, the list of dimensions I give in the beginning are from such a resource. I did not just pick them out of the air and give them my own definition. It could be the resource is wrong, incomplete or how one might wants to view it different.

When dueling in syntax is more important than the underlying point, well, we can have fun with that to I guess.

What we call space-time we describe using terms we created from our observations of space-time. The fact that in our attempt to describe this we typically use 3 dimensions of length and one dimension of time does not mean all dimensions are limited to length and time.

By definition of “dimension” is “to measure out”. It is related to something you can measure. When we measure something we measure it in relation to something else, to place it in some kind of a useful structure to help us understand it. In the process we have developed commonly acceptable ways of measuring something in relation to other things, such as area. Area is a dimension derived from the dimension of length and requires 2 dimensions of length to define it in Cartesian coordinates.

In our measuring of space time we typically use 4 dimensions, but the number and types of dimensions greatly exceed that of the 4 used in the typical definition of space-time. Just as this simple definition of space time requires 4 dimensions to describe it, luminous intensity measured in candela requires multiple dimensional references to describe it. Granted the number of references I made are high, because what is required in some cases is a single dimension squared or cubed.

It well may be that to define some types of hyper dimensional space what will be required is not new dimensions but the inclusion of some dimensions we are already familiar with, such as mass. How well do we really, truly understand mass? What if mass is really directly tied with all real measurements of space, so that in reality space-time consists of 5 dimensions (3 length, 1 time and 1 mass)? What if the phenomena of mass is really from the warping of the 4 commonly considered dimensions of space-time? What is, somehow you could take an area of mass and straighten out this warping and the result was the disappearance of the mass, probably also resulting in a massive release of energy that had been held in the warped space.

As far as space-time only being able to be described in 3 dimensions of length and 1 dimension of time, I very strongly disagree. We may prefer this method, but it is very possible to describe space-time in terms of 1 length, 1 time and 2 angles. It might not be as easy, but it is a matter of point of view.

This is a similar issue with what base number system we think in. It is possible to develop a valid view of space-time to used only spherical coordinate measurements in base 3. We might find it much harder to understand and use such a point of view, but that does not make it any less valid. So it is a valid and provable point of view to define our simple view of space-time in the four dimensions of length, angle, angle and time. It may not feel comfortable for you to view it like this, but it is valid.

Sometimes, to look at things through a different point of view results in finding an easy way to solve a very complex problem which might otherwise prove impossible to solve.

PS: I did not say Luminosity is fundamental, I said it is derived and that it can not be decribed only in the 4 dimensions of space-time, but it requires additional dimensions.

 

[Ziggurat]

I pull many of the references I make from published resources in science. For example, the list of dimensions I give in the beginning are from such a resource. I did not just pick them out of the air and give them my own definition. It could be the resource is wrong, incomplete or how one might wants to view it different.

There are mistakes in your initial list. Moles, for example, are a unit, but they are dimensionless. So are radians and steradians. Luminous intensity is not, and has never been, a fundamental dimension - as explained above, it is derived from more fundamental unit. Current can be a fundamental dimension, but this is a choice: you can also use charge as the fundamental dimension instead of current.

It well may be that to define some types of hyper dimensional space what will be required is not new dimensions but the inclusion of some dimensions we are already familiar with, such as mass.

Concievably. But without any idea about how to include mass in such a manner, it's just idle speculation. Nothing wrong with that, but it won't get you very far either.

As far as space-time only being able to be described in 3 dimensions of length and 1 dimension of time, I very strongly disagree. We may prefer this method, but it is very possible to describe space-time in terms of 1 length, 1 time and 2 angles. It might not be as easy, but it is a matter of point of view.

All that actually points to is the fact that the word "dimension" has multiple uses which are not perfectly related to each other. Using polar coordinates rather than Cartesian coordinates doesn't change the dimensionality of the space you're describing.

This is a similar issue with what base number system we think in. It is possible to develop a valid view of space-time to used only spherical coordinate measurements in base 3.

The two issues are completely independent. The coordinate system has no connection to the base numbering system you use. But once again: the coordinate system does not change the dimensionality of a space. And physicists are quite used to using alternative coordinate systems to describe the same spaces - including using coordinate systems which aren't spatial at all (ie, momentum-energy space for quantum mechanics).

PS: I did not say Luminosity is fundamental, I said it is derived and that it can not be decribed only in the 4 dimensions of space-time, but it requires additional dimensions.

In your opening post, you asked what "the fundamental dimensions that we know of" were. You then answered your question with a list that included Luminous Intensity. As for not being able to be described only in the 4 dimensions of space-time, well, that's pretty meaningless, and relies (once again) on essentially mixing different usages of the word "dimension". Again, consider the dimensions for acceleration: length/time². Does that mean there are two dimensions of time? No. It means that the time dimension appears twice in the definition. But it's the same time dimension for both occurances.

 

[Dutch]

Hyper Dimensional Design has nothing to do with numerology, its based on geometry

 

[PixyMisa]

Also, angles aren't a different dimension; they're a different co-ordinate system. You can specify a location in 3-dimensional space using two angles and a distance, and indeed that's what astronomers do.

Just reading Oppressed's posts again, and he notes himself that different co-ordinate systems exist and are equivalent, but still posits angles as additional dimensions. Someone here is very confused.

 

[Beausoleil]

I guess it depends on how we're using the word "dimension."

Dimension at Wikipedia

There is a definite confusion here as to how the word is being used. Is it being used to describe units (as in the description of physical parameters)? Is it being used to describe what we might think of as the 4-dimensional spacetime?



Uses of the prefix "hyper":

Dimension at Wolfram MathWorld

ETA: PixyMisa, it depends who you ask and what the purpose is:

Dimensional Analysis at Guelph

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...

I may apply for Randi's prize, having predicted that this thread would become confused....