10 Mar '08 18:29>
Originally posted by adam warlockI meant metrics in the "system of measurement" sense. But I'm now almost fully convinced of what I said at 20h14. 🙂
Maybe you are speaking about it in a more mathematical definition?
Originally posted by PalynkaI almost positive then that we talked about different things under the same name.
I meant metrics in the "system of measurement" sense. But I'm now almost fully convinced of what I said at 20h14. 🙂
Originally posted by adam warlockI don't think they're more "refined". In the mathematics we use we just tend to think of a dimension as, say, the values for one variable. Any subspace in a multidimensional space just represents a certain set of combinations of those values across different variables... Restrictions on values for certain variables can be represented by considering only a subspace of the complete hyperplane.
But I'm guessing you guys certainly have more refined defintions of dimensions.
Originally posted by PalynkaI don't think this is that different from the concept of a phase space that Adam mentioned. That generalises the concept of dimension to include momentum as well as position...but phase spaces in general can go even further. They just represent the set of possible values of whatever it is that describes your physical system.
I don't think they're more "refined". In the mathematics we use we just tend to think of a dimension as, say, the values for one variable. Any subspace in a multidimensional space just represents a certain set of combinations of those values across different variables... Restrictions on values for certain variables can be represented by considering only a su ...[text shortened]... of the complete hyperplane.
In that sense, anything can be represented as a dimension...
Originally posted by mtthwIt isn't different at all. All I'm saying is that it wouldn't surprise me if a mathematician found it very intuitive to see time as a 4th dimension.
I don't think this is that different from the concept of a phase space that Adam mentioned. That generalises the concept of dimension to include momentum as well as position...but phase spaces in general can go even further. They just represent the set of possible values of whatever it is that describes your physical system.
Originally posted by Palynkai dont think a mathematician would find time as 4th dimension easy. a dimension that would have different properties that the other three might not be very nice for their equations. time is more intuitive to the average person
It isn't different at all. All I'm saying is that it wouldn't surprise me if a mathematician found it very intuitive to see time as a 4th dimension.
Originally posted by PalynkaWhy couldn't they see time as the 1st dimension? Does dimensioness have to exist in order for time to exist? Can't time exist outside dimensions?
It isn't different at all. All I'm saying is that it wouldn't surprise me if a mathematician found it very intuitive to see time as a 4th dimension.
Originally posted by sonhousetime is a dimension. if we consider the evolution of a 3d object in time, then that object has the 3 dimensions (xyz) and an aditional one: time t.
Why couldn't they see time as the 1st dimension? Does dimensioness have to exist in order for time to exist? Can't time exist outside dimensions?
Originally posted by sonhouseThe ordering is irrelevant. Anything that can be described in units can be represented as a dimension. Dimensions are just part of representations.
Why couldn't they see time as the 1st dimension? Does dimensioness have to exist in order for time to exist? Can't time exist outside dimensions?
Originally posted by serigadoOf course time is a dimension.
I hear/read many times the interpretation that universe is not 3D, that there is one extra dimension -> time.
I personally think that interpretation is WRONG. Time is an additional variable, but it can't be said to form an extra dimension, in analogy to ant living 2D in 3D world.
Why? Because in the jump we make from 2D to 3D we're adding a dimension with ...[text shortened]... o understanding it as another "dimension" in the metric of the universe is really strange.
Originally posted by PalynkaAre you trying to impress someone? Cause I think you are full of BS!
Your previous comments made me think that this maybe comes from the difference between the way a mathematician and a physicist see the concept of dimensions.
For example, I'm used to work with n-dimensional hyperplanes or sometimes even infinite-dimensional ones. For me a dimension is a very flexible concept.
Just a musing about our little disagreement here.
Edit: Hyperplanes, not hyperspaces Mr. Spock.