dimensions are nothing but abstract information needed for orientation. dimensions haven`t real, natural correspondence in time and space. there is only an aleatory number of locating parameters, called dimensions. the more specifications (alias dimensions) the more covered phenomena (velocity, acceleration- variations of other degrees than 1and 2, discontinuities, inflations, implosions, ...).

I am sorry Paul , I guess I am looking at too straight forward interpretation of this : Dimensions are variables (independent ) that cannot be further broken down into and we accept as norm (LKM) . So any characteristics of a material if it depends on these fundamental then they are accounted for !!!  

dear Aparna, I agree with you. One can enumerate redundant variables too. the Point is to enumerate exactly those variables which are needed (not more and not less.). for example I would Need 2 variables to determine time! Variation of space, and Variation of Variation of space, so that, for me, time is 2-dimensional.

Ok , we know that space-time are 2 inter-dependent variables , mathematically we can perform "separation of variables" and get the dependency on single variable. The solution (depending on the order of the equation ) can be 2D !!! Again this is based on the formulation of the system's equation (as far as I remember the first order ODE)    

in my opinion it depends on how something is defined. well, my Definition for time is: Motion. we only have got: space (with matter) and Motion. to locate in space one Needs 3 variables (the so called dimensions), and to locate in time one Needs 2 variables (Variation of space and Variation of Variation of space (in other words: velocity and acceleration)). case to locate something more than 5 variables are needed, than one can use more than 5-dimensional spaces. ergo: 5D, or 6D, aso.

Yes , aren't we looking at time as an independent variable and rest depends (or on evolution of time ) . Now , if you say motion changing time !!!!! .

Sorry , I can't think motion is independent ,isn't mass involved !!!!

I guess , if matter and motion are independent then like how you have stated the dimensions increase ...

It dose not mean anything (Squared Second), also it does not represent a principal unit in measuring process! In addition almost events are measured with respect to time as velocity acceleration ...etc. I always told my student to define acceleration as the meter per sec per sec (velocity per time) and not meter per squared second to be more logically understandable, so that means no meaning to squared second as I simply thought!

Regards, Emad

Wait, when we say that m2 is a measure of a two-dimensional space, it is because we are describing two orthogonal length measures. But when we use sec2, as in acceleration m/sec2, are those two orthogonal measures of time? I don't think so, right? They refer to the same time line.

Not to imply that there are no dimensions orthogonal to the time axis, aside from just the first three dimensions. No doubt, there are. Math can easily describe these. Physics, alas, not yet (as far as I know).

dear Emad, when You have to solve a d²t equation by using integrals, then a surface is generated. when one wants to locate, then x,y,z,t should be mentioned. but t(v,a): when 2 persons want to meet one another, then both should mention their Speed and their accelerations (if using a clock, v and a are implicitly included).

dear Albert, to determine time the Variation in space, and the Variation of Variation in space must be specified. (with respect to 2 orthogonal length- space is considered static, whereas time isn`t static, due to its Variation of space)

dear Aparna,

that`s right, but the changings are: Variation and Variation of Variation (in concordance to v->s/t and a->s/t²)

Although I withdrew my previous submission because I took the argument too far, the basis of the first part still holds.

If we accept Einstein's relativity concepts then it is clear that there is no single, universal timeline.

If you and I are walking together at similar speeds then our measure of time are identical and it is reasonable to assume a single, common timeline.

If however, you are walking significantly faster, say close to the speed of light, and I walk at a normal human speed, then our timelines are demonstrably completely different.. Under this logic it is clear that every object in the universe has its own timeline which is dependant on its relative speed to other objects in that frame of relativity (IE frame of measurement) .  

So, if you and I are a two person universe then it is acceptable to define a mathematics that relates our timelines and frames of relativity to each other. This allows us to measure each others time with respect to our own. We can then use this to relate to objects in our wider universe.

Concepts such as multiples of time, time vectors and powers of time become meaningful and the multi-dimensional character of time is separated from the more obvious multi-dimensionality of space

Ian

dear Ian, you are right, when you say . But, I`m thinking at something else: as time depends on 2 variables T(v,a) it is to represent 2-dimensional (for instance like complex numbers- 2-dim plane). that`s why I see time at least 2-dimensional

Even if there is a variation of variation (e.g: acceleration )  it can be represented in multiple Ds it is a vector !!!!

I agree with Ian , it is space that we are looking at , unless you say time is no longer a constant.  I read somewhere , 'c' is not a constant so is time ...

I even have demonstrated that ALL natural constant are NOT constant indeed.

in my opinion is time AT LEAST 2-dimensional.

By Induction Paul , then if continuity in space can have multiple dimensions , why not with time ...

dear Aparna, I don`t understand: I asked the same question as you do...

Wonder , how we can resolve this Paul ???

2 votes for multi-dimensional  time variance, may be it is possible provided the analytical aspects is consistent with already established space norms (is this going in circles) .

dear Aparna, You are right! As it came to aberrations in physics, my motto is NOT: read your… manuals; remake them! That is the name of the game! But it will take time until they do recognize it. much time! 2-dimensional time :))

I don't see why it is so important to relate 2-D with a unit just because it has a 2 in the exponent. Whenever s^2 occurs in a unit, it just means that we are calculating rate of change of something which already has s^-1 in it. Period. Even in a non-uniform motion in a straight line (1-D), I can have a variable acceleration so that I can take a time derivative of it and arrive at something which has a s^-3 in its units. But I don't think that makes it something 3-D. So, I don't really see the point of the question.

dear Satadal, it is an big difference between real sets and complex ones! for instance: the relation of order is not strictly any more