# Clarification needed on how objects are represented

After watching the latest HTM school video and reading the most recent paper, I tried to write out an example, but I’m not sure its correct so I’ll give it here. Suppose we have a cup with a logo on it. The cup is represented - not as a set of locations with features, but as a displacement vector of the parts it is composed of. For instance, if the handle of the cup is on the left, the displacement vector might indicate that on the left is the handle, 2 inches to the right is a cylinder, and 3 inches down is a disk that is the bottom of the cylinder (or cup). (I realize this is an oversimplification)
Now suppose the logo on the cup has pictures on it. We could say the logo is also a displacement vector. But at some point, you get parts that are not composites. For instance, the handle of the cup is not a composite - its a set of features at locations.
So am I going off track somewhere?
There are also a few sentences in the article that I don’t understand. One is: “learn correct dimensionality of the space of the object”. What is the dimension of the space of a cup? The article continues with “learn how movements update locations in that space” - but isn’t our world a 3-D world where movements always update locations the same way? Another sentence says that path integration has to be learned, but surely in 3D space, you know when you’ve come back to the same point - for instance “up 3 units, then down 3 units” takes you back to where you started from.
I also don’t understand how a grid view representation of an object is orientation independent. Is it also size-independent?
Suppose a person interacts with an object such as a microscope - he puts a slide in the viewing area, and then puts his eye to the eye piece. Is he representing the microscope as a displacement vector, and his own body as another displacement vector, and then going through ‘body space’ to reach ‘object space’?
That’s a lot of questions, but I’m trying to get a hold of the concepts so I can experiment with them. Does nupic allow users to draw 3D objects and observe how they are represented?

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