“A Magazine of all perfection”: Mathematics in the Early Modern Satire Histrio-Mastix – Chrisoganus as a Mathematician

Now we turn our attention from the muses to the protagonist of the play and consider how Chrisoganus can help us learn more about Early Modern mathematics and how it was viewed at the time. After Chrisoganus is introduced and he chooses to deal with all seven liberal arts and sciences, he in effect becomes the most learned of all the gentlemen. He then opts to withdraw from the rest of society and delve into various books. Early in the play, he expounds his views on science in general and mathematics in particular, expressing an optimistic perspective that the sciences were still in their infancy and much remained to be investigated. This view on science thus partly reflects the contemporaneous transition of the scientist towards new methods and approaches, such as those espoused by the empiricist Francis Bacon (1561–1626) in the early 17th century.

Prior to the Scientific Revolution, observations of the natural world had played only supporting roles in the development of great theories. For instance, Plato (427–347 BCE) and even Aristotle (384–322 BCE) were content with drawing up entire cosmologies (see Plato’s Timaeus) without observable backing, which perhaps did not seem that different from fabled metaphysical accounts of the world. This changed in the Early Modern period, first with a shift towards empirically-grounded models and theories, epitomised by the works of Bacon. Later, the empiricist approach was combined with an entire mathematisation of (the physical) sciences in the hands of Newton and his contemporaries. Thus, whereas Bacon mainly sought to collect facts, Euclid’s geometry and Newton’s and Leibniz’s calculus became the mathematical tools for unifying, exploring, and explaining Earth and the universe with observable data accessed through the senses and theoretical explanations arrived at through pure mathematics.

Figure 9. Engraving by Benjamin Cole (1695–1766), “Monument to Sir Isaac Newton in
Westminster Abbey,” ca 1731. The poet Alexander Pope (1688–1744) wrote an epitaph intended
for the monument: “Nature and Nature's Laws lay hid in Night: God said, ‘Let Newton be!’
and all was light.” The epitaph can be seen as expressing how mathematicians, here personified
by Newton, could see through the temporal and find the perfect truth, much as Chrisoganus
expressed in Histrio-Mastix. National Portrait Gallery D13121. © National Portrait Gallery, London.

In Histrio-Mastix, which predated the careers of Bacon, Galileo Galilei (1564–1642), and Newton, Chrisoganus argues that pure knowledge which does not originate in the senses is truer, as it can refer to causes:

If this be certain, then which comes from sense, \\

The knowledg proper to the soule is truer; \\

For that pure knowledg by which wee know \\

A thing to bee, with true cause how it is, \\

Is more exact then that which knowes it is, \\

And reacheth not to knowledge of the cause [Marston 1610, Act I, Scene i].

Chrisoganus next ranks the different sciences according to exactness; he puts arithmetic and geometry at the top but places music further down the hierarchy because it derives from arithmetic but is mixed with sound.

When Mauortius then challenges Chrisoganus, noting that “all this prooues not wee may know a truth,” Chrisoganus invokes the notion of science (Scientia):

If wee haue this wee call Scientia, \\

We must haue truth of meere necessity, \\

For Acriueia doth not signifie, \\

Onely a certainty in that wee know, \\

But certainty with all perfection [Marston 1610, Act I, Scene i].

The scientific endeavour, as Chrisoganus presents it, can thus prove that knowledge about the world is actually achievable. But further, we may come to reveal exact and necessary truths in all their perfection (this is the meaning of the reference to “Acriueia” in the passage above). As such, his position is much more idealist than the new empiricism that could only provide provisional, inductive knowledge. Instead, Chrisoganus argues for an epistemological position that stresses deduction and considers the mathematical sciences as the epitome of knowledge. In doing so, he did not belong to the strict empiricism of his times but rather was already on the way to the mathematical worldview of Newton and later phases of the Scientific Revolution.

After these introductions, the remainder of the first scene of the play sees Chrisoganus leave to pursue his studies while the other characters contemplate what they should do to pass the time. Soon the merchants and lawyers agree that they will go visit Chrisoganus and attend his mathematical lecture. In that lecture, Chrisoganus further discusses what mathematics is. He starts by confirming that mathematics consists of geometry and arithmetic, but mathematics, he argues, is more than this. Contrary to the natural philosopher, who “considers things as meerely sensible,” the mathematician can deduce from first principles (axioms or natural laws). Thus, mathematics can produce “demonstrations so infallible, the pleasure cannot bee, but ravishing.” In this way, mathematics is the way towards finding truth. Thus, to Chrisoganus, mathematics is not merely a mercantile and practical undertaking, nor an entirely empirical or inductive discipline. Instead, it is the very foundation of the search for knowledge. He attempts to impress his view on his audience by explaining the Sun's movements around the Earth, but soon the audience loses interest and instead decides to go to see a play with “sweet music and delicate songs” next time.^[5]