I know, but you can have two broad classes of theories, those which have time and space affecting one another (relativity for instance) and those where they are completely seperate (Newtonian). In either one time is a dimension.
And there are others still.
The dimension of a system is the number of independent continuous variables.
This makes sense within the mathematical outlook or approach to dimensions.
Each particle requires 3 variables to define it's position in 3 dimensional space and 3 more variables to define it's momentum in 3 dimensional space. Adding more particles means more complexity, means more variables, means more dimensions in your phase space.
This doesn't change what I said earlier, though it explains the mathematical way of working with dimensions as they define them.
Obviously you aren't aware of what the geometry of the objects discussed in string theory are because they are not 'simple attractions' or whatever poorly defined description you want to use. A Calabi-Yaus are not 'spirals of some sort', they do not have simple analogies in terms of everyday shapes, because they are (at least the ones in string theory) 6 dimensional. Yes, the simplest examples are such things as tori but that's just a tiny class of them.
I never said they are simple attraction...did I...please quote me if I did...
I said they are attractions of a sort. I get back to this later...
So you're saying I'm limited in what I can describe using mathematics by how good my calculator is?!
No, you are limited by what you can describe using any system if you can not display visually a perfect representation of that system.
Do you even know what mathematics is about!? It's about abstract logic. Physics is the application of that abstract logic to real world phenomena. There's no muddling, there's only your lack of comprehension. I know the difference between a phase space and a space-time. I know the difference between a moduli space and a vector space. I know the difference between a complete space and a topological space. All are different concepts in mathematics, with 'space' not refering to the space up there in the sky but a concept.
So all those dimensions we spoke of earlier is nothing more then abstract logic at work...
If you know the difference, why don't you specify this earlier as to save time...
I am more curious about what the reality of dimensions are; they could be anything we say they are when they are conceptional...
A vector space is a space with particular properties and again I don't mean a literal 'space' like up in the sky. Look up what 'vector space' actually means.
And...
Not 6'th but 6. String theory has 9 spacial dimensions. There's 3 which are big, the ones we're familiar with and then 6 MORE. So when I say I do work on 6 dimensional spaces I don't mean the 3 we see and 3 more, I mean I talk about 6 dimensional systems which are in addition to the 3+1 we already know about.
OK.
An a picture of the 6 dimensional space would be such things as the Calabi Yaus, so no, I can't draw them. I don't need to, I work out their properties and behaviour from their mathematical definitions. I don't need to draw a sphere to work out the shortest path between 2 points on the Earth's surface, I compute the geodesics of the spherical metric.
OK. How is this being applied...
I really don't see why you're obsessed with this. Do physicists need to include a parameter 't' in their algebra to describe systems in the universe? Yes. Does it matter if you call it a dimension or not? Not really. 'Dimension' is a label we give to things to help discussion. If you don't want to call it a dimension, fine, it just means you're working to a different vocabulary to most other people.
I am not obsessed...I am interested. What you are saying here is a re-cap of what has been said earlier and to this I agree!
It utterly retorts your "But what's the fourth dimension?!" whining because there's no natural ordering to dimensions, nor is there a natural choice of how you label dimensions if time and space affect one another.
There may be a natural order to dimensions in reality, not a conceptional fraction of thought and experience of reality. If there is an order to time then it would seem even more likely.
Also, I am not whining, so please restrain from making such accusations in the future. I am not insulting you directly and personally am I...
Where did I say that? I said I didn't need to, I am able to describe them and their behaviour via their mathematically defined properties. I can describe spheres without having to draw them. All you need to know about spheres can be obtained from the general definition $$S^{n} \equiv \{ x \in \mathbb{R}^{n+1} \, | ||x||=1 \}$$ . Don't need to draw anything, that's the whole reason mathematics is the language of physics, you can do a lot without having to cling to the imprecise nature of visual intuition.
We can see a sphere. You've seen a sphere. Off course when you know that the formula makes a sphere you'll be able to describe it. However, for those things that cannot be drawn and have never been seen, you can never be 100% certain about them, nor can those whom you communicate the ideas to be so, regardless of how well that communication is. It's blind-mans work...
I never said otherwise, I said the converse. You don't need to visualise something to describe it's properties.
To describe a shape in full you do, or at least you need to have seen that shape once in order to fully comprehend the description yourself. Otherwise your partially blind to your shapes...
$$dF=0$$ and $$d \ast F = 0$$. That's the entirety of source-less electromagnetism.
OK.
FFS, it's not 'the 6th dimension' it's 6 extra dimensions. And I know what I'm describing are 6 dimensional object because that's what I construct them to be, I use coordinates $$(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6})$$ and build them up from that.
Are these conceptual or real...
There's no argument amongst mathematicians who do work on systems of varying dimensionality, because mathematics doesn't require 'physical evidence'. For instance, $$S^{7}$$ (using the definition I just gave) is a 7 dimensional sphere. I can work out various properties of it without having to know or care if such things exist in the real world. The number '7' doesn't exist in the real world, but we can apply the concept of '7-ness' to groups of objects. If I have 7 apples I have a group of apples which in some way relate to the concept of '7'. Having 7 apples doesn't give me a physical thing which is '7', I'm attaching an abstract concept to a physical thing. Physicists argue over how to attach physical meaning to particular mathematical systems, that's how you do physics, you look for mathematical systems which, when you attach physical meaning to various thigns in the system, gives the same dynamics as the physical system you've associated it to.
Well said, regardless of whether this is a digression or not I enjoy hearing this angle or description. It does help me to understand where you are coming from better. Thanks!
Mathematicians do not require any physical justification for their work, because they aren't trying to describe nature. Physicists try to describe nature so they can test if the models they think behave like nature actually do but even when a model is shown to be wrong the mathematical concepts behind the model are still perfectly valid because they never needed physical justification.
I am trying to describe the dimensions in nature, not the conceptional dimensions in mathematics that help to describe that nature...even if not fully. This post of yours has cleared up a lot. There is no known way to test for the 4th dimension what it is, it would be nice if there where.
Before pausing I would like to say that I am not saying that time is not a dimension, as I see it time cannot exist without dimensions operating upon each other. Time is a combination of dimensions, like a car is a combination of its parts...a car is not just one of its parts. I will have to get back to this subject on time more later (to play with words...)...
