MADB

[_asbestosman]

...'fractal' dimensions huh?
Here's the reference at the bottom of that wiki:

http://math.bu.edu/DYSYS/chaos-game/node6.html

Also - a bit of a duh moment - a conceptual 'point' has 0 dimensions.

Note - however - that the article talks about the concept in purely mathematical terms. I didn't see a proposed way to map this concept to real world examples - although I'm sure it's possible and I'm just not seeing it yet...

Not only can computers make pictures that look like clouds, mountains, and coastlines--they can also estimate the fractal dimension of real clouds, etc. by various techniques. One that's easy to do is to count the number of squares or cubes that the object or its border intersects. You then count the number of smaller squares it intersects. Eventually it approaches a limit and you can estimate the fractional dimension. This technique can properly give the border of a circle as having a dimension of 1 while the circle itself has a dimension of 2.


I think I should also mention that imaginary time is different than the negative dimension I spoke of. A negative dimension refers more to the size of objects in that dimension. It's is more of a counting number. Imaginary time refers to dicection in time--at least if I understand it properly. It would be more of a vector or position. If I'm right, negative time would merely be going backwards in time. What's the real-world application? Well, you'd have to take it up with Stephen Hawkings, but it apparently gets rid of some singularities for some models of the universe.

How could one have imaginary dimensions? Well, I think first we'd need a coherent idea of an imaginary measurement on a set. I'm not quite sure what real-world sets we can use for that. The only complex measurement of real-world things that comes to my mind is that of waves. One complex number will give amplitude and phase. I'm not quire sure how that could be extended past 1 complex dimension though. I can't see what a 2-d complex signal would be. I know about QAM and the like, but that's still just one complex dimension. Even measuring two or more frequencies simultaneously would appear to be the addition of 1 complex dimension to another but without actually increasing the total number of dimensions. That might change if some other measurement were used, but I'm not sure what would make sense. That's the whole problem. We need a real-world measurement that can be complex and can be multi-dimensional.

The other way to have imaginary dimensions is to extend Hawking's concept of imaginary time to spatial dimensions (or any dimensions in general). This probably has the best scientific application. In fact, I wouldn't be surprised if QM already does it.

[_asbestosman]

Try this experiment, Try to imagine a creature no one has ever heard of and describe it on here. Then break it down. Where does it come from?

How about this...
I'm imagining a 'square circle' right now...

I'm imagining a married bachelor right now.
I'm imagining a generous miser.


jumbo shrimp
military intelligence
;)

[_Imwashingmypirate]

But these things are derived from words you already know.

I am imagining a green elephant monster lamb with purple ears and smokes a pipe of canibis through it's purple wooly trunk It is never going to exist but I put a combination of thing we do know together. It is not possible to make up something completely and entirely new, that does't already exist.

[Guest]

If I'm right, negative time would merely be going backwards in time.

But hang on asb. The only reason that would seem particularly 'outrageous' is because we only ever experience time moving in one direction.

In the 'other' dimensions, we can move 'backward' and 'forward' - no problem. Although backward and forward only make sense with some kind of reference to go by.

To see if I understand what you're proposing:

Let's say I place my 'reference' half-way up a ladder. And let's say that one of the 3 spacial dimensions can be said to lie along the same 'line' as the ladder.

Now I move up the ladder. I'm moving in a 'positive' dimension?
Now I move down the ladder. I'm moving in a 'negative' dimension?

...is that what you mean?

If - somehow - I were to move backwards through time, I wouldn't have thought of it as traveling in a 'different' dimension. I would have thought of it as traveling in the SAME time dimension, just in a different direction along it.

A vector is a value WITHIN a dimension framework right? So 'negative' and 'positive' values of those vectors already handle the notion of traveling in different directions without the notion of a 'negative' dimension - don't they? You can move 'forward' and 'backward' within the one dimension, but suddenly changing direction doesn't suddenly mean you are traveling in a different dimension...!

...does it?

military intelligence

Haha :) That's the best one!

I am imagining a green elephant monster lamb with purple ears and smokes a pipe of canibis through it's purple wooly trunk

Heh - and the green elephant monster lamb with purple ears - smoking a pipe of cannabis through it's purply wooly trunk is imagining a bunch of relatively hairless ape-people bashing on plastic keyboards and sending data to each-other over a world-wide information network and thinking:
"Woah -that's trippy man!"

but I put a combination of thing we do know together. It is not possible to make up something completely and entirely new, that doesn't already exist.

Very possibly true. But I'd still say it is possible to imagine something that doesn't exist. What you've said above doesn't contradict that.

I'm proposing that 'things' can be imagined and described that do not actually exist. The fact that they could be 'analogous to' or 'like' or 'share some part of' real things is besides the point.

It cannot exist in a literal spatial sense, but the idea behind it does exist in mathematics.

Yeah - I am sure it can exist within a mathematical framework. That still doesn't mean it exists in reality.
Mathematics is an internally consistent, logical concept that CAN map to the 'real world' - but that doesn't mean that it is 'a part of' the 'real world'.

Energy cannot be created or destroyed. Therefore as thought it'self is energy, this energy abides by the laws of the spatial dimensions generally as it needs in some ways the spatial dimensions to reside within. And as everything in the spatial dimensions abide by conservation laws so must those things that reside within the spatial dimensions. When looking at Klien Bottle for the first time, My thoughts were, It's just a bottle, until I looked closer. This is a 3-5th dimensional structure, it is hard to comprehend. But is does exist in third dimensions. So here we are introducing fractional dimensions (NOT Fractal), that is dimesions that are in a sense links between dimensions, in that they posses the charactoristics of two or more dimensions. But of course there is no such thing as a fraction (The meaning of a fraction) as a fraction is a whole entity in itself, but that's another story. The proof is amazing, but the words, hard to find.

I'd like to think I kinda get where you're trying to go with this, but I don't see how it's addressing my point. I agree that language can be a problem here...
Maybe asb has a better idea of what you're saying here, and can interpret for me. I find he has a knack of making some things simple to understand :)

[_asbestosman]

When we explain or describe things, we always do so in the context of other things we already know or are familiar with. When we describe dragons, we describe them in terms of animals we are familiar with (like reptiles and bats) and also in terms of experiences we are familiar with such as fire.

Some speculate that the prophet Isaiah saw our day, but described modern inventions like the airplane in term he was familiar with (flying charriots), or lions (because of the jet engine noise).

Now just for fun: I propose a fifth briophud in the universe called the crotificious briophud. It flakutes grazulons which causes them to fritofulate.

Don't worry, I don't have any clue what that means either.

[_asbestosman]

I was conflating dimension last night. complex dimensions imply the ability to move more than just forward or backward. That's where complex time comes in. Complex time allows for certain properties to be explained. Maybe it's just a mathematical convenience, but my guess is that it has implicaitons with actual predictions for interactions.

A complex number of dimensions would imply something else.

A negative number of dimensions implies certain properties of objects being measured--namely that it gets smaller as you magnify it. That's my understanding of the negative dimension thing that wikipedia mentioned.

If I'm right, negative time would merely be going backwards in time.

But hang on asb. The only reason that would seem particularly 'outrageous' is because we only ever experience time moving in one direction.

In the 'other' dimensions, we can move 'backward' and 'forward' - no problem. Although backward and forward only make sense with some kind of reference to go by.

To see if I understand what you're proposing:

Let's say I place my 'reference' half-way up a ladder. And let's say that one of the 3 spacial dimensions can be said to lie along the same 'line' as the ladder.

Now I move up the ladder. I'm moving in a 'positive' dimension?
Now I move down the ladder. I'm moving in a 'negative' dimension?

...is that what you mean?

That was what I meant in regards to complex time and complex spatial dimensions as such. That is obviously not the same as negative number of dimensions. Sorry for conflating.

If - somehow - I were to move backwards through time, I wouldn't have thought of it as traveling in a 'different' dimension. I would have thought of it as traveling in the SAME time dimension, just in a different direction along it.

Me too. However, complex time means something more than that. I'm just not sure one can move in complex time, or only be influenced by it. See Hawkings.

A vector is a value WITHIN a dimension framework right? So 'negative' and 'positive' values of those vectors already handle the notion of traveling in different directions without the notion of a 'negative' dimension - don't they? You can move 'forward' and 'backward' within the one dimension, but suddenly changing direction doesn't suddenly mean you are traveling in a different dimension...!

...does it?

Correct. Again, I was conflating the issues last night, and probably haven't been good at distinguishing them yet. Complex dimensions works under the "direction" idea.

A negative count of dimensions works when thinking about measurments on sets such as the thing Mandlebrott did in the wiki link.

military intelligence

Haha :) That's the best one!

I wish I could take credit for that one, but I read it somwehere else long ago.

[_Ren]

asbestosman,

OK - fair enough. I think we're seeing things the same way...

...I'll have to look into this 'complex' time stuff. I'll get back to you when I have a clearer idea on it so I can discuss it more.
...which I think in practical terms is gonna end up being never...!

[_Imwashingmypirate]

If I'm right, negative time would merely be going backwards in time.

But hang on asb. The only reason that would seem particularly 'outrageous' is because we only ever experience time moving in one direction.

In the 'other' dimensions, we can move 'backward' and 'forward' - no problem. Although backward and forward only make sense with some kind of reference to go by.

We don't experience time in any direction. Think of time as a Scaler. Is this comprehendable? We are always in the present. Always so time can go backward and forwards on a different level.
To see if I understand what you're proposing:

Let's say I place my 'reference' half-way up a ladder. And let's say that one of the 3 spacial dimensions can be said to lie along the same 'line' as the ladder.

Now I move up the ladder. I'm moving in a 'positive' dimension?
Now I move down the ladder. I'm moving in a 'negative' dimension?

Think of spatial dimensions as an axis. Because that is exactly what it is. It can be said that finding the function of two domains can produce the z dimension. e.g. [Integral] (x,y) dxy produces z just like [integral] (x) dx produces the y dimension. So an integral of (x,y,z would produce another spacial dimension, but this becomes complex. And so doesn't follow 'mass' laws. Then you can have multiple integrals of 3D structures. I don't really have the apropriate words here.

Try [integral] (x, .... infinity - 0.00001) dx infinity - 1.00001 as well as

[integral] (- infinity +0.00001, ... x) dx infinity + 1.00001 [integral] (x, .... infinity - 0.00001) dy infinity - 1.00001 .... [integral] ( d...+/- infinity +/- 0.00001...d) d(d-1) infinity +/- 1.00001 (+/- ifininate -/+ [integral] with respect to the subsequent previous dimension.
...is that what you mean?

If - somehow - I were to move backwards through time, I wouldn't have thought of it as traveling in a 'different' dimension. I would have thought of it as traveling in the SAME time dimension, just in a different direction along it.

Time IS in a different dimension. We physically abide by the spatial dimension. Higher dimensions are more complex.
A vector is a value WITHIN a dimension framework right? So 'negative' and 'positive' values of those vectors already handle the notion of traveling in different directions without the notion of a 'negative' dimension - don't they? You can move 'forward' and 'backward' within the one dimension, but suddenly changing direction doesn't suddenly mean you are traveling in a different dimension...!

There are different types of vector.

...does it?

military intelligence

Haha :) That's the best one!

I am imagining a green elephant monster lamb with purple ears and smokes a pipe of canibis through it's purple wooly trunk

Heh - and the green elephant monster lamb with purple ears - smoking a pipe of cannabis through it's purply wooly trunk is imagining a bunch of relatively hairless ape-people bashing on plastic keyboards and sending data to each-other over a world-wide information network and thinking:
"Woah -that's trippy man!"

but I put a combination of thing we do know together. It is not possible to make up something completely and entirely new, that does't already exist.

Very possibly true. But I'd still say it is possible to imagine something that doesn't exist. What you've said above doesn't contradict that.

Well when you do tell us. Then in years to come you will probably find that it did really exist. We are so simple in comparison to the complexity out there. We could not possibly come up with something that breaks out of that hugeness.

It cannot exist in a literal spatial sense, but the idea behind it does exist in mathematics.

Yeah - I am sure it can exist within a mathematical framework. That still doesn't mean it exists in reality.
Mathematics is an internally consistent, logical concept that CAN map to the 'real world' - but that doesn't mean that it is 'a part of' the 'real world'.

Maths is the world. It is fundamental and pure. We do use it to understand things better, but without maths we have very little. Maths is of a higher dimension to us, because maths is less comprehendable and not of mass.

Energy cannot be created or destroyed. Therefore as thought it'self is energy, this energy abides by the laws of the spatial dimensions generally as it needs in some ways the spatial dimensions to reside within. And as everything in the spatial dimensions abide by conservation laws so must those things that reside within the spatial dimensions. When looking at Klien Bottle for the first time, My thoughts were, It's just a bottle, until I looked closer. This is a 3-5th dimensional structure, it is hard to comprehend. But is does exist in third dimensions. So here we are introducing fractional dimensions (NOT Fractal), that is dimesions that are in a sense links between dimensions, in that they posses the charactoristics of two or more dimensions. But of course there is no such thing as a fraction (The meaning of a fraction) as a fraction is a whole entity in itself, but that's another story. The proof is amazing, but the words, hard to find.

I'd like to think I kinda get where you're trying to go with this, but I don't see how it's addressing my point. I agree that language can be a problem here...
Maybe asb has a better idea of what you're saying here, and can interpret for me. I find he has a knack of making some things simple to understand :)

[_Imwashingmypirate]

I have been talking about complex dimensions the whole time. I have been putting across the idea that there are infinate quantised dimensions in evry direction including those we do not understand. it might be in my blog. I will look.

Logically there ought to be negative dimansions, and also "imaginery" dimensions in terms of complex/ imaginery numbers. And even more complex idea's far beynd our understanding

If there are higher dimensions and horizontal dimensions and dimensiond in all complexes ways, then surely there will be lower dimensions. Check my blog.

But also dimensions within dimensions, like a mass web of dimensions of all kinds. Thus horizontal as well as vertical, but also [ argh brain scramble!!!] in every dimension. Am I making sense?

This topic is something I am hoping to develope in, but I for some reason can't get this logically. Maybe I should study more rather than think.

I think I am talking about something totally different to you guys and so I will leave you two to it. I will follow the discussion if you don't mind though.

Pirate.

[Guest]

We don't experience time in any direction. Think of time as a Scaler.

Yeah - ok. That makes sense, and I 'buy' it. I suppose it's just not how I typically hear it described.

Always so time can go backward and forwards on a different level.

Don't know what you mean here though.

Time IS in a different dimension. We physically abide by the spatial dimension. Higher dimensions are more complex.

I agree.

Think of spatial dimensions as an axis. Because that is exactly what it is. It can be said that finding the function of two domains can produce the z dimension. e.g. [Integral] (x,y) dxy produces z just like [integral] (x) dx produces the y dimension. So an integral of (x,y,z would produce another spacial dimension, but this becomes complex. And so doesn't follow 'mass' laws. Then you can have multiple integrals of 3D structures. I don't really have the appropriate words here.

Right. In the sense of you use an integral of a curve to find the area bounded by that curve? (1 dim -> 2 dim).
Or use the double integral of a plane to calculate the volume bounded by that plane? (2 dim -> 3 dim).

Then you can just keep going up...?

So ok - here's a question. According to the method of 'inspecting' or 'constructing' higher dimensions you just mentioned, does the fourth dimension 'act' particularly differently to the first three? In a purely mathematical sense...?

There are different types of vector

Do you mean in terms of true / polar against - say - pseudovectors / axial vectors?
Or do you mean 2D, 3D, 4D vectors?

Or something else?

Well when you do tell us.

Well, since I can't prove a negative, is there much point?

Maths is the world.

Hmmm?

It is fundamental and pure.

Hmmm - yeah. I guess...

We do use it to understand things better, but without maths we have very little.

You mean if we can't understand it? Or if the very concept didn't exist?
I'm guessing you mean in the sense of "Maths existed even while we were still hanging from branches in trees..."

Maths is of a higher dimension to us

...See - it's a nifty idea. Was it Euclid who believed that mathematical concepts literally do exist in some other plane? Can't remember...
...but this is one of the things I'd like you to 'prove' at some point :)

NOTE: I'm not expecting or demanding you to! Please don't see what I'm saying that way.
I'm just describing how I approach things, and what I see as 'minimum proof' of something...
I'm not suggesting you have to do the same, or even that I'm anywhere near right!