[dogma1138]

This isn’t about the 3 dimensional structure the neurons occupy, but about their operational degrees of freedom.

Think about how a CNC machine works, you can have CNC with more than 3 axis, for example a 4 axis CNC machine can move left/right up/down backwards/forwards and also have another axis which can rotate in a given plane.

From a more mathematical perspective just think about the number of parameters in a system (excluding reduction) each parameter would be a dimension.

[anu7df]

Appreciate the attempt, but in this example the 4th axis is not independent since the motion along that axis can be achieved, with some complexity, by the motion along the other axes. Granted this is not very useful for a machinist because it will be very tedious to machine a part this way compared to the dedicated 4th rotating axis, but mathematically it is redundant.

I have found it easiest to think of a logical dimensions or configurations when thinking of higher dimensions. Physically it can be a row of bulbs (lighted or not) wherein N bulbs (dimensions) can represent 2^n states in total. The 2 here can be increased by having bulbs that can light up in many colours.

[posterboy]

its not redundant. without rotation it could only ever drill downwards.

Smartphones eg. measure six dimensions of freedome, including rotation about every axis. 3 for location, 3 for orientation.

this has very little to do with synapses.