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Galileo was an Italian philosopher, astronomer, and mathematician. He is most widely known for his development of the scientific method. He is also credited with the formulation of (circular) inertia, the law of falling bodies, and significant changes in the study of motion. The reference that Malcolm makes to Galileo's trial in front of the inquisition stems from claims he made that challenged the widely accepted Aristotlean theories. Galileo dropped weights from the top of the Leaning Tower of Pisa and discovered that speed of fall of a heavy object is not proportional to its weight. This made him unpopular with his colleagues. The reference that Malcolm makes deals with his devotion to the Copernican theory that the sun is the center of the universe and the earth is a planet that revolves around it. Galileo was bought in front of the Inquisition (a powerful papal judicial institution that combated issues such as witchcraft and sorcery) in Rome to defend his good name after it had been defamed due to his perceived asinine belief in the Copernican theory.
Source: Encyclopedia Britannica Online
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