So, then, these coordinates would be moving in an invisible direction...
If you're talking about a theory of physics, yes. However, its possible to discuss systems which a great many dimensions either in the realms of abstract mathematics (which even allows for infinite dimensions) or you can talk about non-physical dimensions.
For instance, suppose you consider an object moving through 3 dimensional space. The space has 3 dimensions, 3 directions. However, the 'phase space' of the object is twice that, because to specify the system you need to give the location
and velocity of the object, position is 3 parameters, velocity is another 3, total of 6. So if you're talking about n objects in d dimensional space then the phase space is of dimension 2*d*n dimensions.
How do we know these are dimensions...what shapes are we describing...
It's possible, if they exist, to measure/detect extra dimensions which are curled up very small by their effect on high energy particle collisions or deviations in the behaviour of gravity. The particular shape of these dimensions (ie what shape they curl up into) is a matter of horrifically complicated mathematics and they have no simple explaination to people who haven't done a fair amount of differential geometry.
No one has ever proven the 4th dimension is time. According to the descriptions AlphaNumeric uses, having infinite vectors, this would be inconsistent with the 4th dimensional time model. These inconsistencies lend credence further to the fact we don't have any solid proof anywhere at all what the 4th dimension is.
I didn't say we use infinite dimensional descriptions of space-time, I was pointing out that mathematicians and physicists are very familiar with the concept of extra dimensions, a great many mathematical systems involve infinite dimensional systems. Even something as simple as polynomials is an example. Think of all the kinds of polynomials you can make by adding together $$1,x,x^{2},x^{3},x^{4}$$, such as $$3x^{4}+2x^{3}-6x^{2}+x-1$$. That's a 5 dimensional vector space because you've got 5 different things you add together.
No one has ever proven the 4th dimension is time. According to the descriptions AlphaNumeric uses, having infinite vectors, this would be inconsistent with the 4th dimensional time model. These inconsistencies lend credence further to the fact we don't have any solid proof anywhere at all what the 4th dimension is.
It was blood pumping in the brain work! Day after day I could fell it pumping. I work very fast when I want to. And, to further clarify, I said convert, which means I took a pre-existing set of plans and modified all of their dimensions to suit German standards. And, because the plans where often incomplete and never included truss systems, I designed them on the spot...which is rather easy. Also, if your familiar with the basic Architectural needs of a home, for example the minimum requirements for a bathroom, and don't need to refer to manuals so often, it is just a matter of exerting your mind.
That's not the same kind of 'dimensions'. You're referring to simply changing from one unit of measurement to another. You aren't doing anything fundamental there, just converting from one choice of length to another. A physicist wouldn't call that anything to do with 'dimensions' or 'altering dimensions'.
I agree, the Scientific Communities do not all give consistent descriptions of what the 4th dimension is. :shrug:
I don't think you have any grasp of what it means when a physicist says 'dimension'. You think that we mean changing imperial units to metric units, things of that kind. Not at all. For instance, I work in research related to how generalised extensions of electromagnetism affect the topology of 6 dimensional compact spaces with SU(3) structure.
That is working with extra dimensions and I say nothing about units of measurement, I work to see how having 6 extremely small extra dimensions of a particular configuration can be made energetically stable so as to explain the particle families we see in nature. The issue of "metric or imperial?" is mute.
If you don't know any vector calculus and you don't understand vector spaces then I don't think you're in a very good position to be whining about how physicists don't pin down what 'the fourth dimension is', you don't even understand basic terminology. Time is a dimension, since you require both the place and time of events to uniquely define them. Newtonian viewpoints had time as a dimension too, it's just it didn't get altered by space or vice versa as it does in relativity. Such things as string theory then extended that, though the notion of Kaluza-Klein reduction is as old as relativity and the mathematical notion of how to describe multi-dimensional systems is hundreds of years old.
I really don't understand how you lot wax lyrical about multi-dimensional things and whine about how physicists/mathematicians are unclear when it's pretty obvious you'd made no attempt to understand what we say. I don't complain I can't speak French to French people. Why?
Because I never learnt it. Or am I missing something? :shrug: