The cigar analogy with rotation symmetry lost me. As each axis measures something different, there is some sense of unit dependency (e.g. measuring height in o

The cigar analogy with rotation symmetry lost me. As each axis measures something different, there is some sense of unit dependency (e.g. measuring height in one axis (cm) and measuring weight in another axis (kg)). It is silly to say one number in one axis with a different unit is comparable to another one in another axis. A different way to say it is that each axis can be (should be) normalized before any kind of factor analysis. The cigar shape is as much a function of per-axis normalization than whatever the underlying pattern is.