In the OOP course, I explained that dimensions could be more complex than axes in R^n for example where points on the x-axis are specified by a real number. For example, in a room that contains several lions and tigers, it can be said that the space of objects is 2 dimensional. Lions and tigers define two distinct axes for this space. The thing is it’s not easy to organise all lions for example in a line (similar to the line of real numbers where all numbers could be placed in a line). The axis defined by lions is more complex. For this purpose, it should be clarified what a lion actually is.
The human brain more or less automatically distinguishes lions from other animals. But if one wants to do the process consciously it becomes a very complicated task. Probably that person should write a list of all the properties of lions. Some properties are not straightforward. For example, behavioural variations cannot easily be notated. Imagine a notation method that identifies all possible such variations. When all properties of lions or tigers are precisely defined (that is all possible variations for all properties could be notated by some notation systems) then it’s possible to construct the dimension defined by lions. However, This “dimension” is a type of space. Every lion then will be a vector in that space.
The same method can be used for memories. There should be some type of tag assignment that organizes memories. Related memories are organized under one tag and so on. Based on the previous discussion, it’s possible to consider memories as entities (similar to lions for example). Then each memory will be a vector in that space. That space is flexible. It means it is reshaped over time. This is true about memories. Not only some details of memories will be lost over time but also they can be reinterpreted once new memories are added.
In R^n axes are always fixed. But in the space of memories, the base vectors can be redefined and so the space will be reshaped over time. As a result, all vectors contained in that space will also be modified. To clarify if lions acquire new traits or some existing traits change over the span of thousands of years, the space that contains lions will also be modified. The same should be true about the space of memories.
The question that arises here is that how consciousness is linked with the formation of this space. I know nothing about consciousness myself, but before working on that topic, the mathematical aspects of the article should be clarified more.