“A Magazine of all perfection”: Mathematics in the Early Modern Satire Histrio-Mastix – Suggestions for Classroom Use

In the following, we suggest 3 different topics for student discussions. The first one deals in detail with how geometry and arithmetic are portrayed in Histrio-Mastix and The Nuptialls of Peleus and Thetis. As background, the students will need to familiarise themselves with the points made in our section on Early Modern Mathematics.

The second topic deals with Chrisoganus as a character and how he compares to modern-day stereotypical portrayals of mathematicians: Aloof, all-knowing, recluse, not in touch with the real world, too focused on ideas and oblivious to practicalities, etc. You may want to read some of the sections where Chrisoganus lectures on mathematics (see Chrisoganus as a Mathematician and Chrisoganus as a Stereotype) with your students.

The last topic invites students to compare Chrisoganus (and perhaps the play in its entirety) to Plato’s The Republic. Especially valuable can be discussions on how Chrisoganus measures up to Plato’s concept of the philosopher-king and what roles for mathematics and the new sciences of the Renaissance (as developed by Bacon, Nicolaus Copernicus (1473–1543), etc.) are visible in Chrisoganus’s theories on society. A similar exercise could be worked up for Galileo’s The Assayer.

Topic 1: The muses of mathematics

In the beginning of Histrio-Mastix, geometry and arithmetic have a few lines. Below are the transcribed lines from the play’s opening scene:

Ar[ithmetick]. Her graces in my numbers shall be seene, \\

So full that nothing can be added more, \\

Nor ought subtracted : true Arithmetick \\

Will multiply and make them infinite. \\

. . .

Geo[metrie]. And I will make her powers demonstratiue, \\

In all my angles, circles, cubes, or squares, \\

The very state of Peace shall seeme to shine, \\

In euery figure or dimensiue lyne [Marston 1610, Act I, Scene i].

Question/Task 1. Describe (briefly) how Arithmetick and Geometrie believe that they can help the character of Peace be successful.

In the play The Nuptialls of Peleus and Thetis by James Howell, we also find Geometry and Arithmetic as characters. Read the following transcribed lines.

The first is spoken by Geometry:

I trace the earth all over by account, \\

as farre as Pindus or Parnassus Mount; \\

I Corinth view, where every one \\

Cannot arrive, 'tis I alone \\

Who can by Land-skips, Mapps, and Instruments, \\

Measure all Regions, and their vast extents [Howell 1654, Act III, Scene iii].

And Arithmetic says the following:

My youthfull charms make many hearts \\

With grones, and sighs, and sobs to smart \\

Beyond computing, yet could I \\

To number them my selfe apply, \\

But that thereof I make a smal account, \\

They to so many Cyphers do amount [Howell 1654, Act III, Scene iii].

Question/Task 2. How would you characterise Geometry and Arithmetic in Howell’s version?

Question/Task 3. Compare Marston’s and Howell’s versions of Geometry and Arithmetic. Are they similar or do they differ (and how)?

Question/Task 4. How do these versions of Geometry and Arithmetic fit in with views of the mathematical sciences in the 17th century?

Take a look at the image showing Reisch’s representation of Madame Arithmetica, depicted in Figure 8.

Question/Task 5. Can you find any attributes in the image that relate to the lines from Marston’s and Howell’s descriptions of their arithmetic characters? Which ones?

Question/Task 6. Finally, see if you can find other visual representations of geometry from the Early Modern period and compare one of these to the Geometry characters in Howell and in Marston.

Topic 2: The stereotypical mathematician

The main character of Histrio-Mastix, Chrisoganus, believes that (pure) mathematical knowledge will be the key to keeping the peace in society. We also learn that he does not like that his fellow countrymen indulge in dance and music, because this results in people giving in to vices and failing to uphold peace.

Question/Task 1. Thinking about Chrisoganus as a character, how would you describe him?

Question/Task 2. Do you think that some of these character traits (stereotypes) can be found in modern representations of mathematicians? Which ones?

Question/Task 3. Find examples of mathematicians in popular culture (see this website for inspiration: https://people.math.harvard.edu/~knill/mathmovies/). How does Chrisoganus compare to these modern stereotypes of mathematicians?

Topic 3: Plato and the philosopher-mathematician

Chrisoganus believes that mathematical knowledge and the knowledge of the sciences will be the best way to keep peace. This suggests a comparison with Plato’s The Republic.

Question/Task 1. Read (a summary or the full text) of Plato’s The Republic and prepare your own summary of the main points and arguments. (You can find Plato’s text and a summary here: https://www.sparknotes.com/philosophy/republic/.) How does Chrisoganus compare to Plato’s philosopher-king? Why doesn’t Chrisoganus manage to keep the peace?

Question/Task 2. Could Chrisoganus have succeeded in keeping society peaceful by following Plato’s ideas? What could he have done or said, and what do you think would have resulted from his actions?