RHO > what does "scalar" mean then? that something has no dimensions, or no > extension? It means no dimension. One has to have 1 or more dimensions to have extension in that/those dimensions. You can only have 0 or more extension if you have a dimension to have the extension in. Mathematically a scalar is a point or single number, no matter how long like pi etc. One asks how thick is a line? One might be tempted to say, zero thickness, but this is incorrect, as a line doesn't have a thickness dimension in which to have zero thickness. One has to HAVE a dimension before one can have zero extension. A 2x2 2 dimensional piece of gold is not zero thick in the third dimension. If it were, it would be a 2x2x0 3 dimensional piece of gold, which would actually be no gold at all as 2x2x0 = 0. A 2x2 2 dimensional piece of gold however is definitely some gold, albeit 2 dimensional :) Same with a scalar, it is not a 3 dimensional 0x0x0 entity, nor a 2 dimensional 0x0 entity nor even a line of 0 length. It is a zero dimensional entity. In APL, a programming langauge, the AxBxC is called the rho of the object, denoted {a,b,c}. A 3 dimensional object has 3 members in its rho, one for each dimension. Thus a {2,3,4} is a 2 by 3 by 4 object. A 2 dimensional object has 2 members i.e. {2,3} which is a 2 by 3 object. A 1 dimensional object has 1 member, ie {3} which is a 3 unit object. A 0 dimensional object has 0 members in its rho, its rho is the empty set. {zip} Thus a {0,0,0} 3 dimensional object, which is in fact a nothing of no substance, is not the same as a {zip} scalar object of definite substance. People have a hard time picturing a scalar universe, as their consciousness is capable of only picturing 3D spaces. So they mock up a 0x0x0 'point' of 3D space and miss entirely what an infinite scalar universe might be like. Homer Sun Jan 29 15:08:12 EST 2017