Mass vs Weight
"BMI assumes that weight is proportional to volume.
Then weight/height^2 is proportional to the radius of a person, i.e. how fat they are."
But weight is NOT proportional to volume - mass is. Mass /= weight. Weight = mass * gravity; and, consequently, my weight in New Orleans is NOT equal to my weight in Denver... which means that my BMI in New Orleans MUST be different than my BMI in Denver. Therefore, the only conclusion is that BMI, not being an absolute measurement, is extremely flawed.
Density = mass / volume;
mass / volume /= mass * gravity / volume
A 6'4" person with 5% body fat weighing 224 lbs WILL NOT have the same density or volume as a 6'4" person with 30% body fat weighing 224 lbs, but they WILL have the same BMI. How does this make any sense whatsoever?
It's really, really irritating when people believe that mass and weight are the same "measurements" but in different units.