Wolfgang Paul invented an ion trap with this many poles, which is often used in mass spec. According to the zero-component lemma, if a vector with this many components has one of its components equal to zero given certain conditions, all are equal to zero. The metric signature is given as this many minus or plus signs. An example of a vector with this many components is the displacement vector between two events. A vector calculus described by this number is used in (*) 
Wolfgang Paul invented an ion trap with this many poles, which is often used in mass spec. According to the zero-component lemma, if a vector with this many components has one of its components equal to zero given certain conditions, all are equal to zero. The metric signature is given as this many minus or plus signs. An example of a vector with this many components is the displacement vector between two events. A vector calculus described by this number is used in (*) special relativity, as one usually formulates it in terms of the metric space named for Minkowski that has this number of dimensions. For 10 points, name this number of dimensions of spacetime, as it includes time as a dimension.
Wolfgang Paul invented an ion trap with this many poles, which is often used in mass spec.
four