In general a dimension is simply put nothing but a property something can have mapped in relation to other such properties.
You stated the 3 spacial + time dimension, these are just the basic properties of space-time.
However these properties only describe a very tiny sub-set of the actual properties depending on what you’re trying to describe.
Take a glass of water for example. If we mapped some properties in relation to time we might have the 3 spacial dimensions as the position may change, time on top of that as this is our basic relation. But then the temperature could change, the transparency of the water may change (due to collected particles), the volume may change depending on the trmperature or whether someone spills something, the color may change, the state of aggregation may change…
So to put a model together to describe these things one would have to create a 9+ dimensional description of this glass of water.
This would still not describe all properties such a glass could have, but the model would describe the glass in the fashion we stated above.
Also look at your own example, you stated:
>I get the first 4 (height, width, depth and time)
Well with these 4 alone you could describe the 3 dimensional – size – of an object in relation to time.
But that model would for example not be sufficient to also map the position of the object.
So to map the position and size of an object over time you already would have (x, y, z, width, height, depth, time) here x, y and z would be the positional coordinates within some frame of reference.
With regards to the theories however these dimensions can mean different things and even can mean – actual spacial dimensions – of space-time.
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