As the name implies, a statement of purpose should be forward-looking as much as possible. The "biographical" element of a statement of purpose should be included only to the extent that it helps to explain what you want to do as a graduate student. You most certainly do not want to start off with recollections of early childhood and the first time you realized you want to be a researcher.
Instead, spend your efforts explaining why you want to be a graduate student in the department to which you're applying. You should make specific reference to how your research will fit into the department's interests. (For instance, don't propose a project in area X if the department doesn't have a specialist in X.)
If you're in a field where the advisor selection is made after matriculation, then you likely want to present a somewhat broader profile. If you show interest in only one professor's work, then you are dependent on the decision of that single advisor (who may or may not be on the admissions committee!).