4d v.03f

The 4th dimension is thickness, There's also the dimension of popularity. 

So you would have 4dA and 4dB... 4dA is when the three dimensional image was connected with another three dimensional image into one object. 4dB is when the main axis (xyz/w) itself were more than just one, due to the relativity or the variability of the variables themselves. 

Since our perception follows the path of natural light trajectories, and thickness are not perceivable to us that way, the axis w in 4dA would be represented separately in a way that it is interchangeable for one of the other 3. 

In terms of 4dB, it is a picture of how many dimensions or axis applicable to the object. The shape is kind of non geometrical even though it is based on geometry. The idea behind it is, if you'd draw an imaginary line between the object in reality, to its copy inside someone's mind, then the object's size would be extended in terms of points of views. The reality is that there are multiple point of views, multiple relativities that governs the behaviors of matters. In this case its relative to perception and memory. 

So if 2 people having perceived the same object met with each other and exchanged their points of views with one another, the shape of the object would change. Even when perceptors never met with each other, we could drew the imaginary lines between them, and it would also be real.

-------------------------------

Hmmm... now I kind of see more why the Intellectual Property Law is important, if an artwork was misused or utilized for things that would defiled its shape, then it could ruin the experience for the author. So the exclusive control over one's artwork really is logical, you'd want your art to be the way its supposed to be, not something else you don't want it to be. 

Not only artworks, other inventions or designs could also be used in ways that are counterproductive to their own sustainability or to humanity as a whole... but too much control over a design especially when it is massively widespread would put a person in an inhumane realm / field voiding him/her off of the relevance of his/herself. Moreover, such limited point of view over something that's so big / influential also would be a counter productive experience for everybody else involved. 

Its not an easy problem... the Intellectual Property Law though is a legacy that often dismissed by even the most distinguished persona. On this I hope that people would build up the legacy and reanimated it, instead of ruining it carelessly

-----------------------------

Now I'm talking about geometric 4d, the easier way to picture it is, when you reached let's say m^4 (meter to the power of four) you'd want to specify what is the object in real life. For example air, water, cotton, etc. By doing this you'd understand that beyond the power of ^3 usually we would time .0 of something instead of a round number. 

The reason being is the purity of the thing per m^4, within water you could have salt or air, within air you could have dust, within cotton you could have air, etc. 

Example:

You wanted to map out the shape of oxygen in space at a point in time

1d:

Was just a straight line

Starting at 2d you defined a pixel

2d:
pixel = gas, others blur; (so define everything that's not gas as others whether it's empty space, water, or solid mass). (x = altitude, y=horizontal distance)

result --> 50 cm^2 

you grasped 1m tall x 1m long space, while blurring everything that's not gas, you got 5cm tall and 10 cm long oxygen.

Mind if you just used no blurs you'd probably got some more oxygen within water or mass, but the scope of measurement in this context would only be gas.

3d:
pixel = gas, others blur; (x = height, y=horizontal distance to the side, z horizontal distance forward)

result --> 100 cm^3 

means you grasped 1m x 1 m x 1 m volume of gas, and found 5cm tall, 10cm and 2cm long of oxygen in it with a particular 3 dimensional shape.

Now you've identified that the 3d picture you've made might still contain some elements of gas that's not oxygen because you weren't taking into consideration the thickness. 

4d:
pixel = gas, others blur. (x=height, y=horizontal to the side, z=horizontal forward/backward, w=thickness)

result ---> 70 cm^4 means you grasped 1m x 1 m x 1 m, x 1 m of air and the 100cm^3 image of oxygen taken was reduced to 70 cm^4 since there were 0.7 concentration of oxygen for the particular cubic m of air. 

Such concentration was rendered as a shape, but due to unlimited complexities of reality some elements might need to be simplified by estimation / a ratio of concentration. 

Or...

4d:

pixel = everything (x=height, y=horizontal to the side, z=horizontal forward/backward, w=thickness)

result ---> 80 cm^4 means you grasped 1m x 1 m x 1 m, x 1 m of space and the 100cm^3 was reduced by 0.8.

The same reason for the result but this time the pixel of "gas, others blur" was not used because the measurer thought that there's no need to specify a type/types of pixel when 4d is already taking into account the thickness of things. The image created would differ from the previous one where there were some oxygen in other spots previously blurred.  

The reason why having a pixel is important is that the 4d plain needs to be attached into a concept otherwise the dimension would be limited into 3d.