dimensionality

[KtownChemist]

Since my last thread was specifically referring to gravity and the 5th dimension I decided to post this new one to explore some more vaguer ideas. It is my understanding that dimensions only come in sets of threes, our X,Y, and Z. But what of the zero dimension? How do you describe an indefinitely small point in a way that makes sense?

 

One way to look at it is that a point represents a system of no change in the next higher dimension. The line y=0 is only one dimensional system with no change in the next higher dimension, so to the second dimension the line is a point; To imagine this picture our line y=0 in x,y coordinates. The line or system takes every value possible for x but only one specific value of y, so now take away the x coordinates and leave only the y axis. the one dimensional line becomes a single point in the second dimension. The same logic can also be applied to the third dimension. An area in three dimensional space only has a single value for Z and so by taking away the first two dimensions our area becomes a point of no change in the third dimension.

 

Altogether we refer to the first three dimensions collectively as Space.

While most people refer to the fourth dimension as time, I believe this is incorrect. Just as space defined as the relationship between three dimensions; Time is also a collection of three dimensions.

 

Therefore a point in the fourth dimension is simply no change of a system (Space) in the fourth dimension. This is easy to visualize since every single still photograph is an example of a point in fourth dimension.

 

Now in order to envision the higher dimensions we simply repeat the same logic but instead of space we are now dealing with time. The fourth dimension can be thought of as a point of no change in the fifth dimension. So unless the fourth dimension is changing we perceive the fifth dimension to not exist. If a line does not change but continues linearly forever; relative to the line the next higher dimension does not appear to exist.

 

The only way we can perceive the Fifth dimension is by inducing a change in the fourth dimension. This change of the fourth dimension is what we commonly think of as gravity. As an object moves into a gravitational field from a constant velocity they begin to speed up in space and simultaneously slow down in the fourth dimension proportional to the rate of acceleration in space. (The slowdown of time is converted to acceleration of space) This also seems to explain why someone approaching an event horizon will in fact be accelerating quite rapidly but appear to stop completely to an outside observer.

 

The sixth dimension is more difficult to relate too but it can be thought of as a change in Time area. Time area just all the possible configurations of a system as it moves along in the fourth dimension. Say you have two pieces of bread, one on top of the other. (each slice is so thin that it has no depth only area) Now each slice represents every possibility of what could happen from 10am to 11am. Since both slices represent every possible configuration of the universe from 10 to 11 they must both be exactly the same right? not necessarily.

In order to understand how the two systems (bread) can differ we must think of time as a whole; The beginning of time till the end of time. The two slices are only identical if every moment of time is identical up till 11am.

Even though at exactly 10am the two systems are in unison, they could have arrived at 10am in two completely different ways. All the different ways a system could arrive at the same exact moment in time with the same exact spatial arrangements is movement in the 6th dimension.

 

In conclusion I believe all dimensions come in sets of three. Just like how you need three separate dimensions to identify something in space you also need 3 separate dimensions to completely identify something in time. Also every dimension can be thought of as the change of the previous dimension.

 

taking this into account, I suppose there could be countless dimensions below us which we perceive as moving in our first dimension

 

 

 

I could write more but ill stop for now

anyone agree?

[Bignose]

Dimensions don't only come in 3's. Where would you get such an idea? Consider a particle described by its location in space, its velocity and its volume. That would be 7 dimensions. Some of the flavors of string theory have 13 dimensions. Any time you need to describe something that is independent of the other variables, you get another dimension. Again, going back to the particle in space example. A particle that is at space location (1,2,5) could have volume of 4 or 5 or 10 or any other non-negative value -- so the particle volume is an independent variable to the space variables. You can have any number of them, you are not just limited by multiples of 3.

 

A zero dimensional object is a point, and it is infinitely small. Because when you specify a point, there are no other values it can take. A line is 1-D, a plane is 2-D and then above they are usually termed hyper-planes.

 

Lastly, you need to be careful of using the word "change" because in mathematical terms, that implies a derivative of some sort. And writing things like "no change" implies that the derivative is zero.

 

E.g. "change in Time area" would imply, to me anyway, so it would be some sort of mathematical form like:

 

[math]\frac{d}{dt_a}[/math]

 

Perhaps if you wrote out specifically what you mean in mathematical terms instead of words -- words have inexact and imprecise meaning whereas the math is very precise -- it would be a lot clearer.