On Logopolis, where the mathematicians perform their block-transfer calculations by chant-like verbal communication, the Doctor gives the lead mathematician, the Monitor, the new dimensions for the TARDIS. Discovering the calculation result to be flawed, the Doctor discovers the Master's handiwork in the death of several mathematicians. Returning to the Monitor, the Doctor finds the Master, who through mind-control of Nyssa (who believes him to be her father) is holding the Monitor hostage