Time, or the number of steps in solving the word problem for a finitely presented group, has long been related to the area, or number of 2-cells, of a van Kampen diagram. Space, or memory, is more recently related to the geometric notion of filling length. We show now that filling length can also be read off a van Kampen diagram as the gallery length. This result has group theoretic consequences, including bounds on isoperimetric functions for central extensions (implying a new proof of the "(c+1)-theorem" for nilpotent groups) and examples of class c nilpotent groups with isoperimetric polynomials of degree c for all c at least 2.