There are no contradictions with theorizing time as a 4th dimension. I will discuss your thinking that you provided in your original post after some initial thoughts of my own.
(By the way, one cannot speak of time being "the fourth dimension," because this depends on the order in which one labels the dimensions, and it is also impossible to distinguish "the" 3 axes of 3 other dimensions because the conceptualization can be constructed differently; and physical bodies would just relate differently in the mathematics)
Of course, the notion of 'dimensions' is highly subjective. One can make formalizations within mathematics, but because there exists a one-to-one correspondence (read up on set theory, countability, and Georg Cantor) between R^n (which can be thought of as n-dimensional [Euclidean] space) and R (the set of real numbers, which can be thought of as a line/continuum/or 1-dimensional space), all we can conclude with reasonable certainty is about our perception and its insight into the nature of relation between objects within reality.
Basically, in a formal mathematical tone, I mean to say that the notion of dimensions is entirely subjective, not objective, because it is possible to theorize and explain away all that we have observed within terms of any number of dimensions.
But, in physics, time may be thought of as a fourth dimension which can explain observed mathematical data about our physical world in a more approachable and intuitive way. This makes it easier to understand what we have observed in physics, which makes it easier to theorize, which means we will be able to set up more original experiments, which means physics as a science will progress faster.
QUOTE
Ok, so.... the 1st dimension is just a line. The 2nd dimension is length and height. They 3rd dimension is length, height and width. So..what is the fourth???
Well, to make it a dimension, you need to have the previous dimensions in it. So, it can't be time. It cant be time because time is constant and is doesnt have any of the other previous dimensions.
I think it is movement. It just makes sense- length, height, width and motion.
I also think we are missing a dimension between 1-2. I think it is angle. Like- degrees and stuff. It makes sense. But, then again, we need 2 lines to make an angle and so it cant be before 2D or after 2D.
I think that the mathematicians and scientists can figure that out...lol
Here is my conclusion:
<<<1d->
A line ( Length)
<<<2d->
Length and Angle
<<<3d->
Length, angle and height
<<<4d->
Length, angle, height and width (depth)
<<<5d->
Length, angle, height, width and motion
The first dimension would be a line. That is correct.
The second dimension is not length AND height. Length is still the first dimension, but the newcomer concept of height is the second dimension.
The third dimension would not be length, height, and width, but rather just the new notion of width.
In more abstract mathematical terms, these dimensions are referred to as the x-axis, the y-axis, and the z-axis. This is a simple and naive approach to structuring space, and is called Euclidean 3-space. (Or, in a set-theoretic tone, you could say R^3, which is a coproduct of spaces...., I won't get into that here.)
The idea of an angle is really just an assignment of a property to 3 points. mABC is the angle of the vertex that is formed by the union of the line segment AB and the line segment BC. This is geometry. But, it can also be traced back to measure theory because angles, in radians, can be described by arc length and the unit circle. All of this can be traced back to what is called the "Foundations of Mathematics." (A highly rigorous formalization of your commonsense ideas.) So really it isn't another dimension, it is a property of points, elements, or subsets within an n-dimensional space, like the idea of distance, area, or volume.
What you mean by a dimension consisting of the dimensions before it is actually that (n+1)dimensional space consists of all of the dimensions of n-dimensional space but extended or continued further along an (n+1)th dimension. Since you misunderstand the difference between an individual dimension and a space composed of many, you think that time cannot be a dimension. It can be.
I have constructed a little portrayal of dimensions which I think you might be able to comprehend. Think of a square along the xy plane. Now imagine a cube in xyz space. You notice that the cube is really just an infinite number of squares aligned next to each other along the z axis. So - we can think of the cube as a continuation of an infinite number of squares along another axis, which may be thought of as an individual object itself. Likewise, you can think of all of physical reality in out '3-dimensional' world at an infinite number of different times, string them into a continuation, and think of it as one large object.
That, my friend, is space-time. Hyperbolic geometry will be a story for another time, though.
(PS - at your apparent level with respect to modern mathematicians, you have no reason to be blabbing about such trivial things

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