Galileo did in fact use a telescope, observe the moons of Jupiter, advocate for the heliocentric model, observe sunspots, investigate buoyancy, and write on physics, and did visit the Vatican twice to defend his work, the second time being made to recant his views, and being confined to house arrest thereafter. One significant liberty that is taken is the treatment of Galileo's daughter Virginia Gamba (Sister Maria Celeste), who, rather than becoming engaged, was considered unmarriageable by her father and confined to a convent from the age of thirteen (the bulk of the play), and, further, died of dysentery shortly after her father's recantation. However, Galileo was close with Virginia, and they corresponded extensively. There are a number of allusions to Galileo's science and to Marxism which are not further elaborated in the play; some of these are glossed below. The discussion of "price" versus "value" was a major point of debate in 19th century economics, under the terms exchange value versus use value. Within Marxian economics this is discussed under the labor theory of value. More subtly, Marx is sometimes interpreted as advocating technological determinism (technological progress determines social change), which is reflected in the telescope (a technological change) being the root of the scientific progress and hence social unrest. The mention of tides refers to Galileo's theory that the motion of the Earth caused the tides, which would give the desired physical proof of the Earth's movement, and which is discussed in his "Dialogue Concerning the Two Chief World Systems," whose working title was "Dialogue on the Tides." In actuality Galileo was wrong. Kepler correctly believed that the Moon's gravity caused the tides. The bent wooden rail in scene 13 and the discussion that the quickest distance between two points need not be a straight line (though a straight line offers the "shortest" path, the fastest descent of a rolling ball in fact follows a curve) alludes to Galileo's investigation of the brachistochrone (in the context of the quickest descent from a point to a wall), which he incorrectly believed to be given by a quarter circle. Instead, the brachistochrone is a half cycloid, which was only proven much later with the development of calculus.