I was personally interested to see a comment on the statement by Martin S. Rutstein - Doc Rutstein was my mineralogy professor many years ago at SUNY New Paltz where I earned my Bachelor's degree in geology and he's an expert on asbestos having spent a number of decades involved with the science and regulatory aspects of asbestiform minerals (and he led great field trips to Thetford Mines in Quebec).
Those of us with some training in geology will know that "asbestos" is not a scientific term referring to any specific mineral but rather an industrial/regulatory term referring to a group of minerals with specific properties (often not well defined scientifically). In addition, the different minerals which fall into the catagory of "asbestos" do not all pose the same health hazards (how could they, they're all completely different).
Below are three minerals commonly grouped together as asbestos (there are a few others as well). By looking at the formulas, geologists would instantly recognize that blue (riebeckite) and brown (grunerite) asbestos belong to the amphibole group of minerals while white asbestos (chrysotile) is a phyllosilicate from the serpentine group.